Wikipedia talk:WikiProject Mathematics/Archive Index

From Wikipedia, the free encyclopedia

< Wikipedia talk:WikiProject Mathematics

1 Nov 2002 – Dec 2003
2 Jan 2004 – Aug 2004
3 Sep 2004 – Dec 2004
4 Jan 2005 – Mar 2005
5 Apr 2005 – May 2005
6 Jun 2005 – Jul 2005
7 Aug 2005
8 Sep 2005 – Oct 2005
9 Nov 2005 – Dec 2005
10 Jan 2006 – Feb 2006
11 Mar 2006
12 Apr 2006
13 May 2006
14 Jun 2006
15 Jul 2006
16 Aug 2006

Nov 2002 – Dec 2003

This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

Two suggestions

Two suggestions: add paragraphs for

historical info (different historical views, famous contributors, postulates, scientific debate) and
fields of application

Maybe defer lengthy proofs to the bottom of the page (or a subpage) ? Many readers wil take these for granted, those who want the whole story are willing to scroll forward. Erik Zachte 00:25 Nov 18, 2002 (UTC)

Some ideas

This WikiProject is well thought-out and appears to be consistent with current Wikipedia standards and conventions. In addition to Axel, Pierre, Toby and myself you should also request comment form JakeVortex, tarquin, User:Zundark, User:Gareth Owen, User:Forgottenvector, User:Valhalla, User:Alodyne, User:Steverapaport, User:Jkominek, User:Josh Grosse, User:Archibald Fitzchesterfield, User:Chuck Smith, User:Ram-Man, User:Andre Engels, User:Jheijmans, User:N8chz, and User:Kidburla2002. Also a link to this WikiProject page from the mathematics section of Wikipedia:Wikipedians by fields of interest would be great. --mav 00:46, November 18, 2002 (UTC)

On fine-tuning the appearance

I don't think that it's at all a good idea to try to fine-tune the appearance of HTML constructions on the screen, as with the "double sups to make the limit of integration higher". The reason is that the effect depends heavily on the particular characteristics of the reader's system.

In my case, putting in the double sups made the limit too high, too far from the integral sign (a problem already since HTML doesn't support multiscripts) and way too small. On Chas' system, it was presumably an improvement. Since we can't predict it ahead of time, we should stick with simplicity: one sup. (I take it back if one sup is for some reason illegible on Chas' system. That's a different matter.) — Toby 07:43 Dec 1, 2002 (UTC)

I concur; the double looks better (IE6, Win98/Win2K), but the single sup is still readable (although just at the edge of confusion for me). The Summation notation is much more bothersome:

∑_{i = 2}ⁿ x

reads ambiguously - is that 2ⁿ? or n_x? i = 2 to n? The alternative, although somewhat non standard, is at least unambiguous (although a bit computer-y). Oh when we will we have our LaTex to HTML conversion (he wailed)? Chas zzz brown 21:28 Dec 1, 2002 (UTC)

For sums in HTML, I prefer nowadays ∑_2≤i≤n x. But I guess the topic is mood now. AxelBoldt 00:00 Jan 8, 2003 (UTC)

TeX style

We should probably update our style guide for the new TeX feature. One rule that I would like to see there is this: TeX formulas should not be used inline: "Let $x\in\mathbb{R}$ be a real number". Because of the size issues, it looks bad, uses unnecessary bandwidth and makes it harder for non-graphical browsers. Similarly, don't use fancy fonts like fraktur $\mathfrak{a}$ if it can be avoided, so that HTML can continue to be used for all inline formulas. AxelBoldt 00:00 Jan 8, 2003 (UTC)

I concur with the inline comment; it makes it harder (in my opinion) to follow an argument when the font keeps changing. Chas zzz brown 08:50 Jan 8, 2003 (UTC)

I'll start to edit the main page to this effect a bit; feel free to jump in if anything is controversial. AxelBoldt 18:40 Jan 8, 2003 (UTC)

bold vectors

Note on vectors: my textbooks tend to have \mathbf{v}_1 rather than \mathbf{v_1}. (it seems obvious but it got me wondering). One for the style guide here, maybe? -- Tarquin 10:31 Jan 18, 2003 (UTC)

Differential d

I noticed that we no longer say to leave the differential d unitalicised. I guess that we don't really need an official style, but I'd like to go on the record as saying that I always found texts that didn't italicise it (chiefly from Brits IME) easier to read. -- Toby 09:53 May 3, 2003 (UTC)

Cyclic Groups

The pages for Cyclic group and Klein four-group use the notation C_n to denote the cyclic group on n elements. This seems strange to me; I've never seen this notation elsewhere. The notation I'm familiar with is to use Z_n. Has there been some agreement to use C_n? Dominus 06:29 22 Jun 2003 (UTC)

It's known in Cambridge, perhaps unknown in 99% of the mathematical world. Obviously it is supposed to stop some abuse of notation problems, as in assuming groups are rings, that there is a preferred generator 1, and so on. Charles Matthews 11:44 22 Jun 2003 (UTC)

"Well, Im obviously not getting along with the mathematicians here …"

The following Copied from Village Pump by Theresa knott|Theresa knott 10:59, June 25, 2003 (UTC)

(Start of copied text)

Well, Im obviously not getting along with the mathematicians here; but, I think the "professional" mathematicians are so intent on outdoing each other with their rigorous mathematics that they fail to understand that the non-mathematician is the one who most needs this site, and nearly ALL of the math pages (even on some of the most "simple" and elementary of topics) are nigh-impossible for anyone without the proper training to understand. Kinda a Catch-22 if you see what Im saying.

Its not that I have a problem with rigorous mathematical definitions and proofs, but we also need to have stuff that is "un-professional" "idiotic" "silly", and the like, and of course (most important perhaps), we need "childish" articles on these topics. To be honest, I don't know (and right now I don't care to know) what real, general, and complex functions are. All I know is that every one of my calculus books talks about stuff which either isn't discussed on the wikipedia (or isn't discussed in language which the beginning calculus student is expected to understand).

Now Ill admit, Im not a mathematician. I don't want to be a mathematician. I don't even like math. I don't even understand why math is worth learning. But I do understand that, right now, the wikipedia is about the last place I would go to if I wanted to learn about a mathematical topic. Its not because the wikipedia is inaccurate; but, because the wikipedia seems determidly hostile (in such areas as mathematics) to expressing things "as if a moron had written it"

What Im trying to explain is, a lot of what Im doing in the math section is, to some degree or other, not correct. A lot of it is correct. But some of it definitely isn't. Unfortunately, I have been, more or less, attacked by certain users who remind me of the young John Forbes Nash, with their elitist attitudes, snobbery, and insulting degradation of others. One user actually had the gall to state that he was too busy with his real job, as a real mathematician, to read my crap anymore. He wasn't just referring to my various misconceptions, he was also referring to my inclusion of material which he felt was redundant, redundant to him of course, since he is a "real mathematician".

Let be clear, this wikipedia thing is a lot of work. But the wikipedia isn't going to get better simply by having a bunch of PhDs stroking their phallic egos. What the wiki really needs is a bunch of "ignoramuses" running amuck, trying to learn what the wiki is saying, trying to add to the article with their (frequently incorrect) newfound understandings, and most importantly, BEING CONSTRUCTIVELY CRITIQUED ON THEIR EDITS.

There is a substantial difference between what the wiki claims to be, and what it is. The wiki urges me to "be bold in editing" but the overwhelming response I have gotten, albeit from a handful of more boisterous editors, is a statement of "Get the hell out of here."

Indeed, I have thought about leaving, but I do see some great potential for good here at the wiki, and I do want to improve this site. So I am simply taking a moment to stand up and ask the Wikipedia what it thinks, does it really think that its appropriate to call people stupid because they don't capitalize something (or because they do) or because they forget a comma, or because they get somewhat confused regarding the implicit differentiation of inverse trigonometric functions?

I have made several new friends since I arrived at the wiki this spring; however, I have also met several people who are not friendly. I would like to know what it is that has turned them so sour.

Pizza Puzzle 23:48 24 Jun 2003 (UTC)

Agree, completely agree. The problem is that mathematicians are trained to do things rigorously, and they have to do it that way in order to protect the "correctness" of mathematics. Some may become intolerant to "misconceptions" from non-mathematicians, but I believe most of them are still friendly. Professional mathematicians (not just wikipedian mathematicians) need intakes from non-mathematians (like you, PP) to improve their way of introducing mathematics to general publics. -- Wshun

It should never be acceptable to call anybody "stupid" if they make a mistake; that is attacking the person, not the act. (If I were in charge, all ad hominem remarks would be grounds for banning.) However, we still need to be merciless about bad edits, and if you get constructive criticism, be appreciative, but don't expect it. If you don't know about something, don't put it in. If you're not sure, put it in italics or in the talk page. There are articles that are very good, and unless you understand the content very well, you're more likely to make the article worse rather than better. I have some math background; I can take a look. Stan 04:46 25 Jun 2003 (UTC)

I think I'm the guy that Pizza Puzzle is so annoyed at. And I can assure you I never called him `stupid'. The disputed page was calculus with polynomials and I suggest that anyone following this discussion go check out the history of that page, its associated talk page talk:calculus with polynomials, and pizza puzzles talk page User talk:Pizza Puzzle2 too. From my point of view, I found the page in a very sad state - lots of errors and mistakes - off topic - repetitious - inconsistent notation - strange headings -poorly organised - glaring omissions - all sorts of weird stuff. It looked to me like a page in serious need of a bit of fixing up. So I fixed it up, which is what you are supposed to do yes? Nothing personal in it. I never even paid attention to who had written the thing in the first place, in fact it looked to me like a page that lots of people had dabbled in without paying much attention to what they were doing. It was actually fun to find a maths page that needed something doing to it, since most of them seem to be quite complete.

Anyway I then get a number of notes from pizza puzzle seeming rather put out and asking me to explain what I had done. Which I then did on User talk:Pizza Puzzle2. Subsequently I find that over a period of several days all of the errors and strange stuff that I had weeded out had been reintroduced into the page, plus a bunch of other new errors and oddities so that the page is actually in a much worse state than when I'd first found it. Which was just about enough to make me conclude that wikipedia is a total waste of time™. But I thought I'd give it ONE MORE TRY. So I fix the page back up again (note that I did not simply revert, but considered each part of the article on its merits), and on the associated talk page I explain in detail my reasons for each change (once again) in the hope that this will finally dissuade pizza puzzle from reintroducing them (once again). And yes I was probably a touch short with the guy, mostly because I'd already done all of this - including the explanations - once again. It isn't that I think my prose is so deathless that I can't bear to see anyone tinkering with it. Actually I'm sure the page can still be greatly improved. But to see actual ERRORS reintroduced for no good reason ... well it is more than any sane mathematician should be expected to bear.

user:Hawthorn, please sign your entries with ~~~~

Normally I side with anyone who accuses mathematicians of arrogantly writing stuff which no-one else can understand. However in this case, I find Hawthorn's version makes more sense than Mr. Puzzle's. If PP wants to "add to the article with [his] (frequently incorrect) newfound understandings", he should expect expect to irritate mathematicians. I would advise you both to calm down and deal with the matter rationally. Don't take it as a personal insult when someone reverts your work. You'll have a more constructive debate if you talk for a while before re-reverting. See Wikipedia:Staying cool when the editing gets hot. -- Tim Starling 06:18 25 Jun 2003 (UTC)

(End of copied text)

First let me say where I am coming from. I am reasonably good at maths, though I was taught it by physicists not mathematicians, so I think that I can give some insight. I have to say, PP does have a valid point {though s/he should not get so emotional about it}. I find many of the math's pages somewhat dry, and difficult. I think that on the whole they are too short, have too few examples, and are too formal. I would like to see some verbose text generally talking about the basic principles before a formal definition and proofs. That way the reader can get a feel for the idea before delving in. I am also somewhat worried by notation. I think that some peole are going to be be put off pages if they are unfamiler with notation. Theresa knott 10:59 25 Jun 2003 (UTC)

"I remember the set theory edit wars …"

I remember the set theory edit wars, which ended up with two articles, naive set theory and axiomatic set theory. We could probably do the same thing for other topics, for example having an introduction to XXX article for topic XXX which started with a non-rigorous introduction designed to help beginners to understand the ideas and motivation for the rigorous article on the topic. For example, several of the calculus articles contain non-rigorous treatments which are then followed with rigorous treatments later.

However, there will always be fields of mathematics which are downright baffling for the uninitiated (including, often, other mathematicians who do not specialize in those topics).

Looking forward to reading introduction to topos theory, The Anome 11:14 25 Jun 2003 (UTC) (who has studied some mathematics, but is not a mathematician)

I may just take you up on that ... Charles Matthews 12:23 26 Jun 2003 (UTC)

"I have great sympathy for those who want 'verbose'. …"

I have great sympathy for those who want 'verbose'. I want it, too, in relation with any advanced topic which I'm not familiar with. There is always a problem with dense texts in mathematics. That being said, there is no single answer: correct statements aren't actually improved by being made looser and less accurate. I've not been here long, but I can see that there are various 'modes' I have used: historical/genetic, examples, informal talk. I find excess emphasis on the category theory point of view to be unhelpful; but it is also clarifying in its way.

Put it this way, perhaps. The more 'pure' attitudes can sometimes be criticised for failure of NPOV. I wrote about that at multilinear algebra and Nicolas Bourbaki. So, let's do that criticism in a practical way, by editing in the other stuff. I don't think implications of snobbery help. I do think that the wiki way is about things other than de facto standards of definition, which is always a contentious area (cf. tensor).

By the way, I'm a published mathematician - but not recently.

Charles Matthews 11:22 25 Jun 2003 (UTC)

"Let's put it this way …"

Let's put it this way: I have a tenuous grasp of category theory and am completely lost when it comes to topos theory. Now I think back to myself at age 13, just learning about things like calculus. Just as I needed a way in then, I need a way in for these other topics. It would be useful for many articles to have a header saying (for example, for integral):

Having difficulty understanding this article? Then you might want to learn more about algebra, functions and the theory of limits first.

Do this to enough articles, and we will have a mathematics road map for self-study. The Anome

This is a really cool idea. It would help prevent reiteration of all the prerequisite knowledge in specialized articles, and provide a nice path towards learning difficult stuff. Something like this may even be useful for non-mathematical subjects as well -- certainly the other science articles (physics, chemistry, biology, etc.) would benefit from it, but it could even be applied to articles on history, politics, psychology, or anything else where a foundation of terminology and concepts is necessary in understanding the more complex ideas presented in specialized parts of those subjects. At the very least, some form of "Introduction to terminology" or "Glossary of notations" and the like would be helpful. -- Wapcaplet 12:26 25 Jun 2003 (UTC)

I don't like the idea of putting the "difficulty" notice on articles, though until Wikibooks gets fully on its feet it may be useful. I don't think this idea meshes well with the encyclopedic concept of the Wikipedia. Dysprosia 05:27, 7 Oct 2003 (UTC)

"Oh and one more thing …"

Oh and one more thing.

WRONG: Articles that go "Let there be objects X such that (introduce new notation here without explanation). Then (notation) (notation) (notation) (notation)."

RIGHT: "(Mathematician) invented the concept of X in 18xx to represent (squeezy-pully-twisty things). A simple example, using modern notation is (example). (Explain notation). The idea has now been generalized to (stuff), which has uses in (other fields of math and science). The idea of X can be formalized as follows: let there be objects X such that (notation). Then (notation) (notation) (notation)..."

Not naming any articles in particular. ;-)

The Anome 11:50 25 Jun 2003 (UTC)

Applause! As a maths-untrained person with a yen to learn a little bit about this area from time to time, that is exactly what I would like to see! More strength to your pen, Anome. Tannin

Well, mathematical duckspeak is never going to be awesome teaching. Used between pros it has a high bandwidth; and isn't really so different from other tech-talk. Point is, it's never going to be brilliant prose.Charles Matthews 11:57 25 Jun 2003 (UTC)

That's why it is so important to have an english {as opposed to notation}intor. The Anome 's page layout looks perfect to me. Theresa knott 12:07 25 Jun 2003 (UTC)

I have merged these changes into the suggested structure in the main project. The Anome 12:54 25 Jun 2003 (UTC)

"The point is …"

The point is, the quickest and best way to stop somebody from reinserting material which you think is totally wrong, is not merely to state that its wrong, but to give some sort of explanation why its wrong. Most incorrect material can, in some way, be incorporated; as most of it is not only at least an attempt at expressing some correct concept; but generally the user is trying to express it because the concept is not expressed well enough within the article. In short, everytime a user edits a page and "makes it worse" that is a good clue that the article needs improvement. 209.56.25.241

Just as likely, there is a structural problem with a single article, or group of articles. Some comments are like weeds in flowerbeds: they're just in the wrong place. Why should everyone agree on what is relevant? One person's helpful aside is another person's red herring. Organisation of the material can definitely help. Charles Matthews 15:18 25 Jun 2003 (UTC)

"Can all these people who are agreeing …"

Can all these people who are agreeing with Pizza Puzzle please read his revision? It really wasn't more understandable to non-mathematicians. By all means, make mathematics accessible, but don't make it nonsense. I've campaigned in the past for comprehensible maths (see Talk:Tensor product) but I'm not campaigning now. -- Tim Starling 05:39 26 Jun 2003 (UTC)

As one of the people who agreed with him, I have to say- Yes his version was bad. Yes the new version was better. BUT he still makes a valid point. Maths pages need to be accessible to non mathematicians. Theresa knott 08:37 26 Jun 2003 (UTC)

Just wanted to add some general support for comprehensible maths, though I've not been personally involved with any of Pizza Puzzle's edits. Martin 21:46 26 Jun 2003 (UTC)

Well now, generalities are all very well. But if anyone has a general take on how hypertext (with random access) reconciles with the hierarchical way maths is built up, that would be an interesting separate discussion. I've just looked at the backlinks for calculus with polynomials, to assess who might arrive there. Only three: derivative, tangent, chain rule. All of which seem to need work, too: far from clear that there is a consistent level operating. Why no link from the calculus page? There is a 'first principles' proof on the calculus with polynomials page. Not the way I'd do it, given the product rule and induction. And so on. Charles Matthews 09:43 26 Jun 2003 (UTC)

Issue of readability and pedagogy

I was totally inactive for a year but I am getting back on Wikipedia and I'm glad to see this wikiproject going. On the issue of readability and pedagogy, here's my 2 Euro cents.

Articles shouldn't be "dumbed down", because that assumes that shows disrespect for the reader by assuming they're dumb. Ignorant, maybe; unsophisticated, maybe; but not dumb. I truly believe that nobody is too dumb for mathematics, especially is they have the basic suriosity that leads them to read the wikipedia article. Now, mathematicians struggle with the same stumbling blocks as non-mathematicians, it's just that it was usually long ago, and they always make it past the stumbling block eventually. It would be helpful if, when writing about a topic, we mathematicians tried to remember what stumbling blocks we had to overcome and how we did it, and wrote about it in the article!

I have background both from mathematics and physics. Encountering most mathematical structures in physics first has the advantage that I am aware of more ways to justify to nonmathematicians why a concept is important. I have a keen interest in the history of mathematics, and I try to bring that to bear on my wikipedia contributions. However, both in mathematics and in science, I think things should be made accessible but without making wrong statements. I can't help it, but incorrect statements just make me cringe and I have to reach for the "edit this page" link. On the other hand, I have very strong feelings about the teaching of mathematics, so I genuinely try to make things understandable.

As for the layout of the pages, I tend to favour historical information near the top, not near the bottom. I agree with The Anome's proposed layout: first a short, gentle introduction, then the formal definition, then (in any order) history, examples, and formal development. In this way, the first paragraph of the page appeals to both mathematiciand and non-mathematicians.

By the way, a perfect example of what we are trying to achieve is function. That page does a pretty good job, but it is horrible on many counts. If I could put my finger on exactly what I don't like about it I'd come in and change it, but it's the result of so many people's work that I'd be wary of doing that, too.

I have created a few pages that start with an abstract definition, or contain little else. The reason is that I didn't want to stick the definition in the middle of a long, pedagogical section of another article. I believe none of these "dry" pages are linked from nontechnical pages, so I think they are not harmful. The motivation is in the longer, general pages.

I watch pages that I contribute significantly to, which means I also watch the talk pages. If someone posts a cry for help on one of the talk pages, I'll probably come to the rescue and, at the very least, add one of those having trouble with this page? Look here first! notes. Maybe I'll go in for a full rewrite.

-- Miguel 15:42, August 13, 2003 (UTC)

Styles of Mathematics Articles

I had independently created a page for similiar purposes as this one, because I was not aware of this page. It has some advantages over the format of this page. For the time being, I will informally link it via this talk page: Styles of Mathematics Articles, and leave it open for discussion whether or how it could be integrated or benefited from. - Kevin Baas 19:28, August 4, 2003

(UTC)

History of Mathematics

A public domain e-text of the book "History of Modern Mathematics" has just been completed. The book was published in 1906, edited by David Eugene Smith, Columbia University. It just has 75 pages, but some of the material may still be useful and valuable. Here's a link to the PDF.—Eloquence 23:05, Aug 10, 2003 (UTC)

"The beauty of mathematics …"

The beauty of mathematics is a topic that I would like to see developed on wikipedia. Maybe we can gather a commented list of the most beautiful things in mathematics, from the elementary to the abstract, as a way to communicate to the layman that mathematics is not accounting. -- Miguel 14:38, August 17, 2003 (UTC)

The page has been listed for deletion by jimfbleak. Please see that page for justification and discussion. —The preceding unsigned comment was added by Angela (talk • contribs) 17:09, August 17, 2003 (UTC)

"Template for pages about probability distributions?"

Should we create a template for pages about probability distributions? I know templates exist for various types of content on Wikipedia, but I haven't found any centralised explanation on how to add one to Wikipedia. -- Miguel 15:05, August 17, 2003 (UTC)

"… looking for some help with TeX …"

Howdy folks. I'm working on a personal project (bits of which might make it to Wikipedia eventually), and am looking for some help with TeX. Specifically, how do I get the "model satisfies" symbol (which is like $\vdash$ but with an additional horizontal bar), and how do I get the reverse of both these two?

Thanks in advance,

Onebyone. Template:Unsigned221:37, October 19, 2003

Hi Onebyone. You probably want $\models$ (\dashv is the TeX thing for but it doesn't seem to work here), but I don't know the reverse of the models symbol... Dysprosia 05:51, 21 Oct 2003 (UTC)

Lovely, thanks. I've actually kludged up a reverse models sign using something like {= \! \! | \>} (can't remember exactly what, it's at home), which will do me for the time being. Onebyone 10:03, 21 Oct 2003 (UTC)

About 'iff'

Can I raise the question of whether we want iff in definitions? I don't. I think it's offputting to those not pure-mathematical 'native speakers'. And the idea that it's more rigorous is surely shallow.

Charles Matthews 16:28, 21 Oct 2003 (UTC)

In the absence of an explicitly-stated convention, I think it's marginally more rigorous than "if". I have occasionally used "if" in a definition and meant "if but not only if", although not on Wikipedia as far as I remember. I'd suggest that if "iff" is undesirable, the best replacement for the non-specialist reader is "if (and only if)", since the rigorous alternative is to ensure that "if" is never used other than to mean "iff". Onebyone 16:49, 21 Oct 2003 (UTC)

I don't accept the 'rigour' argument, anyway. Using 'if' there is an implied 'one can assert' in front of mathematical propositions - which no one writes unless in a very careful formal treatment. Those who care about this can imagine it all anyway. Better, I think, just to use normal language: 'an X is a Y with property P'. I haven't checked whether the definitions of legal terms on Wikipedia make a point of this type of care. On the whole I think it's wasted: it's hard to imagine the user who needs it. Charles Matthews 17:58, 21 Oct 2003 (UTC)

Well, I agree that the pedantry is not worthwhile if it is off-putting for readers. On the other hand, I'll take no part in any kind of global edit to deliberately introduce ambiguity, even if that ambiguity can generally be resolved from context. You say "I think this care is wasted", but I suspect that for most mathematician authors it will require extra care to remember not to do this rather than extra care to do it!

"An X is a Y with property P" sounds good to me, especially in the standout definition at the top of the article. Nobody writes articles on topics other than maths saying "a person is a saint if and only if they have been canonised by the Church" or whatever. If there's a more formal section of maths in the article, I do think that "iff" and other jargon words should be used in that section exactly as the author would use them in any mathematical writing.

Onebyone 10:35, 22 Oct 2003 (UTC)

So, my understanding is that the Project isn't trying to prescribe, but is looking for some harmonisation. Charles Matthews 19:02, 22 Oct 2003 (UTC)

mathematical markup

Hi people. I would like to again raise the question of using mathematical markup (namely the <math> tag) versus plain HTML for mathematical content. I have read what pertains to the problem and I am still not convinced of the point of view explained in the guidelines on the main page WikiProject Mathematics. Here's mostly why.

Common ground
- It seems we all agree that mathematical content should come in a different typeface from standard text, e.g. "Let a be a real number" rather than "Let a be a real number". It is my strong belief that it makes understanding math much easier.
- The use of mathematical symbols is sometimes inevitable, and sometimes much shorter than plain text, e.g. $\sum_{i=k}^p u_i$ compared to "the sum of all elements in the sequence with indices ranging between $k$ and $p$ ". (Not to mention that the example above shows that the TeX processing is wrong: it does not treats the formula as inline.)
- However, I fully support the opinion that the Wikipedia should try to reach the "layman" as much as possible, and that implies favoring text to formulas (with the exception of the item above).
Why imho the reasons against using mathematical markup fall short:
- inline PNG looks bad because it is too big and not vertically aligned. True indeed ! it is ugly, but why stick with it ? Though I am not an expert, it seems simpler to configure ghostscript for size and centering. (Not too small for legibility purposes.)
- mathematical markup uses unnecessary bandwidth. That seems overrated, since small png files (the ones that could be replaced by HTML text) are ... small, typically a few hundred bytes (in general much more than the text equivalent except in the example above), so one hundred of them in an entry means maybe 50Kb extra. While not negligible, this remains acceptable even for slow connections. Hence it only marginally slows download speed. However I admit that an increasing number of such files might slow down the Wiki server itself unless solutions are taken (see caching below). I'll be happy to learn more about this. Notice that steps against this overflow can be taken by choosing the HTML if possible or else PNG option, at the possible cost discussed just below. Question: shouldn't that behaviour be the default one ?
- mathematical markup slows down the server because it has to create the png image through the complicated tex->ps->png method, or testing whether it can be converted to HTML first. Now that convinces me much more (and more or less mirrors my experience). Since it is quite true that a lot of inline formulas can be written using HTML, I believe the conversion engine could work much faster (all right ! easier said than done ;-) . If not, see suggestion HTMLmath below.
The argument in favor of mathematical markup is simple but stronger. Though my remarks above plead for conversion to HTML, the main reason for using mathematical markup is to obey the same principle that is behind HTML, XML, CSS, etc: separate meaning from display. By using the <math> tag, you indicate that the content is maths, no matter how you eventually display it (and that may depend who reads it too). You can always change the way it is displayed afterwards, depending on technology (maybe we'll have DSL in ten years :-), on your preferences, and so on. If in two years from now all browsers accept MathML, Wikipedia will obviously render math in MathML. What becomes then of all previously written articles ? If they contain expressions such as 'the real number ''x'' ', then they will have to be changed by hand, while 'the real number <math>x</math>' will be translated into MathML automatically and easily (even for more complicated formulas). And that's only one of the uses of the idea of separating content and display. In short, the main reason for preferring mathematical markup is to preserve the future, i.e. to build something that may last.
Solutions ? I do not know of course all the pros and contras of all this, but if you agree that mathematical markup has to be built in, but yields undesirable side effects (like slowing down the whole thing or displaying badly), here are suggestions.
- Caching: (unless it is already done) if bandwidth remains an issue, why not cache the math pages, i.e. keep copies of rendered pages on another server which will (i) free the main server of outgoing flux (bandwidth problems) and computing time (conversion procedure). I then suggest a move towards the HTML if possible or else PNG choice for better display. If finding willing servers is a problem, why not ask math academic servers throughout the globe ? Many of them host mirrors of much heavier archives such as arXiv.
- One simple thing: make a difference between inline and separate formulas (TeX users will know that). A better solution for all editors would be of course an automatic recognition of whether a math formula is inline or not (not too hard is it ?).
- HTMLmath: a simple suggestion helping the rendering machine: add a tag (say <hmath></hmath> for instance) that caracterizes the content as mathematical but is written in plain HTML, with, whenever possible, some simple conventions: usual letters should be italicized, ^ means , etc. So that <hmath>x^2</hmath> will be displayed as the HTML <var>x</var>2. That idea remains compatible with a future automatic rewriting, while speeding up the procedure for the moment.
- At the very least, if the suggestion above seems too cumbersome, let us provide a tag that describes the content as mathematical (even without anything extra). Or replacing the <it></it> tag. I propose <mi></mi> for math italic.

I hope I have not bored you too much with such a longish article. Please excuse the newcomer's stubbornness (or maybe intransigence ?). : Pascalromon 23:12, 26 Nov 2003 (UTC)

New WikiProject, WikiProject Probability

I'd like to announce a new WikiProject, WikiProject Probability. I started this last week on my user page, and was convinced to move it to a more appropriate home amongst the WikiProjects. It is not quite a list of probability topics, but an effort to catalogue the articles on probability theory and applications, providing a guide (in the form of an annotated table of contents) for those who would like to know more about the topic. I hope such an effort would also expose any defiencies in Wikipedia's coverage of the subject. It is not intended to propose alternate formatting for probability articles. I'd appreciate any and all input from the participants in WikiProject Mathematics. Perhaps WikiProject Probability should even be a sub-project of WikiProject Mathematics?
--Ben Cairns 01:10, 8 Dec 2003 (UTC)

Jan 2004 – Aug 2004

This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

"This article assumes knowledge of" notices

Is it really that necessary to put those "This article assumes knowledge of yada yada yada and blah" notices at the top of pages? If the aim is to help educate the potential reader, it's rather inefficient, unhelpful and redundant in my opinion. Education material should go to Wikibooks. Reference material should stay here. Thanks Dysprosia 09:05, 13 Feb 2004 (UTC)

It's a less-than-ideal solution to a genuine problem. Perhaps we could induce a bit of momentum towards top-down organisation of the whole Project, and get a better overall view, or even consensus.

In my opinion, and based on the fact that mathematical coverage here is getting fleshed out as the weeks and months go by, we could probably also define a more consistent view of the bottom-up 'needs'. There could be a single page telling people things like 'A depends on B' by major topic. One can't really label that exclusively as education; pro mathematicians also are in a constant struggle outside their speciality with questions like "I think this is answered by some bit of algebraic geometry but where does one look for the language and basic statements?" and "I don't understand why they look at X - why is it suddenly fashionable?". These are just upmarket versions of undergrad issues on organisation and motivation, and as soon as one hits the axiomatic approach there is a perceptible requirement to deal with them.

HTH

Charles Matthews 11:31, 13 Feb 2004 (UTC)

Top-down organization is a good idea... perhaps we can instead say "This article is part of the subtopic series/topic/whatever of topic", instead of the "assumes knowledge of"? Dysprosia 22:37, 13 Feb 2004 (UTC)

Hmmm ... that would work if you could be sure that manifold would be in the differential geometry series because serious differential geometry assumes knowledge of manifolds. Now quite a few people might say 'we look at manifolds for other reasons' (eg dynamical systems on them). This is actually fairly typical: the Lebesgue integral would be in both the Fourier analysis and stochastic process series. Taken to its logical conclusion, the map looks tree-like: the 'leaves' are the major research areas, which draw on auxiliary subjects (e.g homological algebra), which are based on more elementary subjects, and so on back to a small number of 'root' topics such as trigonometry, school algebra. Depending on one's philosophy of mathematics, this might give a completely unified map, perhaps with naive set theory as the 'root'. You then find that much of the combinatorics side has been left out in the cold, so in a sense this is too POV. I think it does correspond reasonably well to what a lot of people in the field understand to be the natural organisation. Charles Matthews 08:55, 14 Feb 2004 (UTC)

Ring theory pages

I would like to reorganize some ring-theory-related pages a little bit, specifically these pages:

I would like to redo them as follows:

Move algebra over a field to algebra (linear algebra). Most of the links to this page are currently wrong, so I suspect the current page title is misleading.
Add a page algebra (ring theory), that talks about (associative) algebras over an arbitary base ring, and mention that associative algebras are the special case of algebras over a field.
Add a page for nonassociative algebras, to talk about the general theory of nonassociative algebras. While associative, Lie, and Jordan algebras are special cases, the general theory has a much different flavor. Move the discussion of nonassociative division rings here.
For division algebra, move the discussion about associative division algebras to division rings, which it currently overlaps with. Move the discussion about nonassociative division algebras to nonassociative algebras.
Redirect rig (algebra) to semiring, and mention that the term is sometimes used for semirings with zero and one. This is also not standard terminology. Semiring theorists call semirings with zero and one rigs approximately never. As far as I can tell, the term is primarily used by category theorists. -- Walt Pohl 16:56, 13 Mar 2004 (UTC)

Well, this is mostly OK by me. The non-associative stuff looks a bit as if it was imposed by a Cayley number fan. With due respect to Cayley, it's mostly as Walt says, and once Lie algebras and Jordan algebras are mentioned, the rest of the non-associative stuff is rather specialised. Charles Matthews 16:18, 17 Mar 2004 (UTC)

MediaWiki Side Tables

A week or so back User:Fuelbottle created the MediaWiki pages Template:quantity, Template:change, Template:space and Template:structure, containing side-tables of links, and used the msg: function to display the relevant side-table on each of the pages listed underneath each of these categories on the main mathematics page. More recently User:TakuyaMurata has removed the side-tables from all of the articles in the quantity and space categories. Net result is that some articles have side-tables, but others do not. Can we discuss, and maybe reach a consensus, on whether these side-tables should be (a) removed across the board; or (b) re-instated; or (c) maybe retained in some modified form ? Gandalf61 13:03, Mar 28, 2004 (UTC)

I would vote for (a) removed across the board. I also posted a reference at Wikipedia:Request for comments.-- Taku 00:29, Apr 1, 2004 (UTC)

I agree - these boxes do nothing except take away space that would be better suited for tables and images that add content to the articles. Footers would be better if this type of navigation is needed at all, but frankly a link to the subject article which in turn has such a list would be better. --mav 07:41, 1 Apr 2004 (UTC)

I appreciate the effort Fuelbotgtle put into making the side tables, but I don't think they contribute much to the pages. -- Walt Pohl 08:44, 1 Apr 2004 (UTC)

Really (frankly) WikiProject Mathematics should have addressed navigation needs and issues quite some time ago. It seems that picky discussions always are going to take priority over crude needs for the general reader to find things. Well, such is wiki life: much easier to complain that sheaf theory is hard to understand, than to do something for the calculus student. More fun to lay down the law about the perfect article, too.

From where we are, though. There is a subtopic structure now fairly much in place. Footers are definitely better. They would be worth adding systematically, in areas where (i) the existing article coverage is already fairly complete, and (ii) there are likely to be readers needing hints on where to go, rather than just a typical List of X topics. So, which areas are those?

Charles Matthews 07:51, 7 Apr 2004 (UTC)

I am ambiguous for either (b) or (c). There are advantages and disadvantages to both side bar and footer. Side-bar is more prominent, footer is less intrusive. I appreciate the effort User:Fuelbottle put into making the side tables, and I think they are a great contribution to the pages. I think the mentioned actions of User:TakuyaMurata were uncalled for, rude, subtracted from the overall clarity and navigability of the Mathematics pages, and added nothing. Kevin Baas 16:34, 7 Apr 2004 (UTC)

I have now changed Template:quantity, Template:change, Template:space and Template:structure into footers. They look better now, and I think they are a good way to navigate the main topics. The last few days someone have created Template:Linear_algebra and Template:Calculus, I think these work ok for navigating subtopics, but if they were footers they could include more topics. Fuelbottle 20:25, 7 Apr 2004 (UTC)

I like a sidebar at the top of the page better -- (1) it shows related topics right away (put impt stuff up high where more people will see it) and (2) I think it's easier to read a vertical list than a row of items. FWIW, and thanks for your work on this. Wile E. Heresiarch 02:33, 8 Apr 2004 (UTC)

My 2 cents (I know no one asked...):

I don't just think the sidebars (or footers) are possible to work, I think they're necessary in some form. I think the people who are saying, "well, all these people have to do is go to the main topic page, read it, and find a bunch of list pages" haven't really thought the issue through completely. Pretend for a moment that you are learning calculus or linear algebra for the first time (I know...for many of us, this was a long time ago, but pretend). You have essentially no context in which to place articles, aside from the discussion given at the main page. But the most important point is something that I think Charles already pointed out, and that is that math is a cumulative subject with highly complex logical dependencies among topics. One cannot possibly understand the article on Fourier analysis without first knowing what a vector space or Lebesgue integration is. It's true that links are very helpful within an article (click the link if you don't know the term), but this can be very confusing after a while to the reader. For one thing, the reader has no idea the distance between his or her own knowledge and the knowledge needed to read the article; links can't provide this. For another, even with links, the reader may end up kind of blindly wandering around, not knowing the best order of topics that has proven pedagogically sound in the past. Yes, it's true, wikipedia is not a textbook, but the way I see it, in the "ideal wikipedia", it should be theoretically possible for a reader to understand any article by reading simple articles leading up to more complex, in a logically depending fashion. Providing sidebars/footers or organisation of this type isn't writing a textbook at all -- it's just making a tool available so that the existing information is more usable for everyone. After all, I'm thinking there could be sidebars/footers for category theory, homological algebra, or relatively obscure fields, in time. The longer one stays in math, the more one realises how little one knows, and trying to learn a new field without some kind of guidance to the topics and their logical interdependence is difficult for pros, so it certainly won't be easy for most calc students, say.

By the way, it doesn't seem to me there's any reason that an article can't be in more than one series -- e.g. manifolds was mentioned, why can't this be in differential geometry, differential topology, and so on? This would make it difficult to have sidebars, though, and even with footers it could get cluttered if it's used too often.

Revolver 09:26, 8 Apr 2004 (UTC)

What I think is that (a) wikis do overlapping and parallel systems quite well (redundancy isn't a serious criticism), and (b) centralising, as a point of view, really is POV here (might be my POV). There just needs to be some reasonable agreement on what would be 'clutter' on a page. One footer is OK, surely. More than that ... I'm not sure. So, I get a picture of 'ideal footer' as containing 'stratum before' as well as 'on the same level as these other pages' info. Charles Matthews 09:46, 8 Apr 2004 (UTC)

Reminds me of a quote in Lang's algebra book, I think -- "Unfortunately, it's impossible to present a body of mathematical topics while maintaining a total order", or something equivalent. Really, the whole logical dependence thing seems to me to be something like a directed graph...just throwing out ideas, maybe a single footer, showing (a) the major topics (rarely more than 3 or 4) that are good idea to be familiar with to understand this, (b) similar articles on the same level/topic, and (c) major topics that lead from this. In the hypothetical manifold case, it would seem to me both diff geom and diff top could be part of (c), at least each of these in the modern formulation. If readers want to go "up" or "down" a level, fine, but they only need a handful of places to go. Up close, they may want to be pointed to trees, but at a distance, directions to forest make sense. Revolver 10:02, 8 Apr 2004 (UTC)

Dynamical systems

Not sure if this is the best place to raise this, but our coverage of dynamical systems and chaos theory is pretty inadequate compared to the treatment of subjects like algebra and graph theory. Even the main article at "Chaos theory" suffers from some vagueness - it defines a chaotic orbit, but doesn't really define the terms it uses (dense orbit, sensitive dependence, etc). There are a lot of holes even in relatively basic topics (Poincaré map,box-counting dimension, and James A. Yorke, for example) and there are some other key articles (bifurcation diagram) that have very brief descriptions.

I've filled in a couple holes (the dynamics definition of orbit, for example) and I'll try to fill in some others, but there's a lot of work that needs doing and some of it will definitely require more background than I have.

Isomorphic 00:20, 14 Apr 2004 (UTC)

Agreed that those topics need work. I'll put something on my to-do list. -- Is anyone interested in moving chaos theory to nonlinear dynamics and making chaos theory a redirect? (At present the redirect goes the other way.) "Chaos theory" sounds advertising hype, to my ears. Within the field, people call it "nonlinear dynamics" if I'm not mistaken. Not a content issue, I know, and therefore rather trivial. Happy editing, Wile E. Heresiarch 03:58, 15 Apr 2004 (UTC)

I understand, from reading Strogatz: Nonlinear Dynamics, and a little red book on Chaos Theory which I forget the name of, that Nonlinear Dynamics and Chaos Theory, although related, our distinct fields. Nonlinear Dynamics is theoretically prior, but does not discuss Chaos Theory topics, such as the application of ergodic theory. Perhaps Chaos Theory is heirarchiacly "under" Nonlinear Dynamics, but I believe it is a topic large and distinct enough in itself to deserve it's own page and treatment. Furthermore, as pointed out earlier, Chaos Theory is a (relatively new) part of Nonlinear Dynamics, and Nonlinear Dynamics is not Chaos Theory. Kevin Baas 17:15, 15 Apr 2004 (UTC)

There must be bits of nonlinear dynamics that are not about chaos, though. What about all that 'qualitative theory of differential equations'? Well, big in the 1950s, I guess. The usual thing would be, yes, nonlinear dynamics as top-level (most inclusive) article, section in that talking about chaos theory to set it in its context (cf. singularity theory → catastrophe theory for the big-in-the-1960s analogue); and then 'please see main article chaos theory' from there.

The point about gaps is of course a good one. Sign of the times when WP starts looking less like a Cantor-set encyclopedia, mostly gaps. I don't believe we have the basic Frobenius theorem on matrix powers, which is linear dynamics, yet.

Charles Matthews 14:50, 15 Apr 2004 (UTC)

I understand, from reading Strogatz: Nonlinear Dynamics, and a little red book on Chaos Theory which I forget the name of, that Nonlinear Dynamics and Chaos Theory, although related, are distinct fields. Nonlinear Dynamics is theoretically prior, but does not discuss Chaos Theory topics, such as the application of ergodic theory. Perhaps Chaos Theory is heirarchiacly "under" Nonlinear Dynamics, but I believe it is a topic large and distinct enough in itself to deserve it's own page and treatment. Furthermore, as pointed out by Charles, Chaos Theory is a (relatively new) part of Nonlinear Dynamics, and Nonlinear Dynamics is not Chaos Theory.

If substance is at all restricted to the geometry of the medium, then wikipedia will always be "like a Cantor-set" - fractal (perhaps multifractal) and in a constant state of flux; emergent - like a dissipative system.

Kevin Baas 17:20, 15 Apr 2004 (UTC)

Charles, I think qualitative theory of differential equations would be a great title. It is true that chaos is only one of several possible behaviors, but all the expositions I've seen describe it in the context of other behaviors, and they usually spend quite a bit of time talking about transitions from non-chaotic to chaotic behavior. Also, they typically say something like "here's a quick review of what linear equations can do, and now let's move on to what's peculiar to nonlinear equations"; it seems WP could do likewise. Anyway, there is a lot to do here. Happy editing, Wile E. Heresiarch 15:25, 16 Apr 2004 (UTC)

In putting up the bios for Lefschetz and Pontryagin, I noticed they both moved into that area at about the same time, after the work in topology for which they are also known. I guess at the time the theory started out asking for periodic orbits, which is like a conventional topological question, in that you might be able to prove existence theorems. Then, I guess, you get the Poincaré return map near to a periodic orbit, as a cross-section near a fixed point; and it is the mapping that induces that is typically the source for the discrete-time iterations that also are studied. Also J. E. Littlewood worked on the Van der Pol equation at that time. Smale went into Anosov flows and suchlike shortly after his topological work on the Poincaré conjecture. That's about global structure of flow on manifolds, and builds on Morse theory. When computing became more of commodity, things (it seemed) changed in the direction of being able to look much more closely at given examples; rather than having to be guided by mathematical analysis; there were more things that came up that were clearly true, but not provable. I never went into this field much; so post-1970 I have just heard the jargon that everyone else has. Charles Matthews 15:41, 16 Apr 2004 (UTC)

User:Charles Matthews/WikiProjectMathematics thoughts

I have posted a discussion document at User:Charles Matthews/WikiProjectMathematics thoughts; and invite people to comment (maybe there).

Charles Matthews 15:21, 28 Apr 2004 (UTC)

What to do with references?

Hi, Charles. You seem to be the cult leader for the mathematicians (!) around the Wikiland. So I will post my questions here, and hopefully I can get a feel on the consensus, if any.

1. Wikipedia's recommended style goes against the mainstream tradition in the mathematics community. Which one should we use?

Doe, John; Doe, Jane (1900). Some paper. Some Journal 1, 1–99.

versus

Doe J., J. Doe, Some paper. Some Journal 1 (1900), 1–99.

2. Wikipedia requests references from authors. And I did try to stick with their guidelines. But somewhere along the line I must ask myself: why bother with all the details if they are not going to help the target audience, which are mostly internet surfers who have no interest in digging up the real sources? Why shouldn't we just give them a general reference (some textbook) and be done with it? I fully understand that no one ever forced me or anyone to provide any references. But I still think it would nice if we can agree on a guideline here and get it out of the way.

What are your thoughts?

[bow] Peter Kwok 02:44, 2004 May 27 (UTC)

Well my thoughts are to not confuse the ==References== section with the ==Further reading== section. Use the first for actual references used to create the article and use the second for more general books people can read in order to get more information on the subject. But I leave this to the people actually working on this set of articles. --mav 05:31, 27 May 2004 (UTC)

Ummm ... well, this is just on my own behalf. The use of references to original papers should be fairly limited; it helps to cite the paper with the first proof of a theorem, not least because it makes clear that 'proved in 1935' is saying something about the publication date, rather than when a proof was first found. I don't think we have a standardised citation style. As mav said, other references are probably there to help with background reading — rather than try to give a full bibliography of a subject. There is some general pressure on WP to be ever more academic and scholarly; but footnoting and supporting everything with sources goes against the normal, good survey style. Charles Matthews 08:20, 27 May 2004 (UTC)

1. I assume Peter is refering to Wikipedia:Cite your sources. I use this style in the few articles that I've written (for consistency), but I don't really care.

2. Mav's point is a good one, which I intend to use in the future. Charles is also right that many references destroy the flow of the text. In my opinion, statements that are in "any good textbook" do not need to be referenced just put one or two good books at the end of the article. More obscure statement should ideally be referenced, so that the reader can check them. The underlying reason is that I'm personally rather distrustful towards the Wikipedia articles (no offense to anybody, but it's just too easy for a mistake to slip in and remain unnoticed), so I feel I need to double-check some statements and it helps then if a reference is provided. By the way, I don't agree that the target audience is "mostly internet surfers who have no interest in digging up the real sources," especially not for the more specialized articles in mathematics.

Jitse Niesen 11:22, 27 May 2004 (UTC)

Okay, I think that settles the issue of using general references-- at least for basic results that should be included in most textbooks.

As for the style issue, I don't see any consensus yet. Not that it is an urgent issue now. But the longer it is put off, the harder to convert the references later-- especially when the servers are soo-oo sloo-ooo-oow. For now, I will go with Wikipedia's recommended style, but I will keep an open mind in case things change in the future. Thank you all.

Peter Kwok 18:24, 2004 May 27 (UTC)

Proposal on Chinese surnames

I was updating some information for Chern and encountered a typical problem in writing Chinese suranames. In most regions that use traditional Chinesee people put the last name last, just like the western names. However, in most regions that use simplified Chinese (except Singapore) people put the last name first. When the two styles are mixed, like Dan Sun and Zheng Sining in the Chern article, it becomes confusing. (In this case, Sun and Zheng are surnames. But sometimes Dan Sun is written Sun Dan; and Zheng Sining, Sining Zeng!)

This has been a well-known problem for identifying Chinese on passports. So what people sometimes do is to capitalize or put a red underline under the surname in passports. I propose that we do the same here and

capitalize the first instance of the surname of each Chinese mathemtician in an article-- at least when there is reasonable suspicion for ambiguity.

You can see whether capitalization is useful in the Chern article.

Thanks,
Peter Kwok 20:20, 2004 May 28 (UTC)

P.S. I mistakenly added an entry for "Dan SUN". Later I created another entry for "Dan Sun". So the former should be deleted now.

I took care of this deletion for you - I'm not sure if this followed policy but it seemed alright.

Derrick Coetzee 00:33, 29 May 2004 (UTC)

Thanks, Derrick.
Peter Kwok 22:02, 29 May 2004 (UTC)

I think, speaking only about usage in mathematics, that it is standard to have surname last. (When it comes to weiqi, this would be wrong, in my view! But the point would be to use here the name commonly expected.) Charles Matthews 05:40, 5 Jun 2004 (UTC)

Do we have to begin every article with the word "In"?

I mean, yeah, it is a good style, but not the good style, right? How about a little tolerence for people who sometimes want to put the "in" part at the end of the first sentence (or not using it at all)?
Peter Kwok 19:01, 2004 Jun 29 (UTC)

Yes, it becomes dull. There are a few other ways. But in general: the first sentence is important to define the area; the first paragraph should be able to stand on its own as a summary. Charles Matthews 19:06, 29 Jun 2004 (UTC)

I concur with Charles that we should keep this policy. Although it is banal, it has substantial benefits, not the least of which are consistency and contextualization. Kevin Baas 22:49, 2004 Jun 29 (UTC)

I have no problem with providing a summary in the first paragraph. But I also think that some kind of varieties can't be bad, especially when the first sentence already specifies the context. Right now people just go around and "fix" the first sentences of almost all mathematical articles so that they all begin with the word "In". This kind of practice only creates frustration and doesn't add value to the articles or to the readers. Since there is no ownership in Wikipedia, I think it is more important for all of us to be more tolerant of other people's style and focus more on the content instead.
Peter Kwok 15:12, 2004 Jun 30 (UTC)

Well, although I'm guilty of this myself, one shouldn't get too attached to one's "style"...as articles get edited over a period time, the style seems to morph from the original contributor's (if there was one major initial contributor). And, it's difficult to draw a line between style and content. I understand your concerns about how these little unwritten conventions can get boring or annoying. But, I think they're helpful if they're not applied blindly.

My own opinion is that differences in style or formatting tend to distract from content. It's not that any one choice of style is really bad, but when it's consistent, it's one less thing for the mind to worry about when reading. Keep in mind, one reason it may seem banal is because many of us are looking at many articles every day, editing over and over.

Re: "In mathematics,..." yes, it appears (it IS) banal after a while, but the reason it's there is to give a random reader contextualisation. If an article just launches into cohomology, or functional analysis, or even undergrad ODE's, a random reader may not be able to tell the general subject area, i.e. they may not even recognise that the article is mathematics. Of course, most people who manage to get to these articles will know it's mathematics, but a lot of people wander around exploring, or hit the random page button, or (most importantly) may reach the article because of an incorrect disambiguation.

Myself, I've wandered into some of the physical science, chemistry, engineering articles and actually not known what subject they fell under. It's easier in those areas to give more specific areas (i.e. physical chemistry, electrical engineering, cosmology, etc.) because even the general public is familiar with these terms. Most people have no idea of the subject areas in mathematics, beyond "arithmetic", "algebra", and "geometry" (all high school level). Very few will know that "topology" or "combinatorics" or "knot theory" are areas in mathematics (topology has another meaning in English, and knot theory sounds like something you learn while sailing on a boat), so beginning with these terms might not do much more than saying nothing.

My general opinion is this: the first sentence should be useful and agreeable to both a random wandered and a person dislocated from a bad disambiguation. This usually amounts to a short definition or description, beginning "In mathematics". Not every article has to start that way. There's no need for the article on functional analysis to read, "In mathematics, functional analysis..." when "Functional analysis is a branch of mathematics which..." The first paragraph (or, introductory paragraphs) should be useful and agreeable to anyone who has the remotest chance of really understanding part of the article, and it should lay out the essential facts that you would want someone to read if they never got past the first paragraph. Then, the rest of the article can begin to assume where the typical reader is.

Revolver 00:08, 1 Jul 2004 (UTC)

> Not every article has to start that way

Thank you. That's all that I am saying. No one is going to tell a story about Little Red Riding Hood before he gets to the point. And everybody (including myself) agrees that the first sentence should put everything in context. The only problem is: do we have to all write exactly the same way? For God's sake, this is supposed to be an encylopaedia, not a piece of application form. Yes, there will be random readers who have no prior knowledge of the subject and may not immediately recognize the context. But all they need to do is to read through the first— I am not asking for even the second, just the first— sentence. Is that too much to ask for?

Readers are only one side of the equation. There are users (i.e. editors), too. Wikipedia allows users to freely edit articles. Everybody's work may be overwritten over time unless he wrote something that nobody ever reads. We all know that before we contribute. But isn't it exactly why it is more important to nourish mutual respect among users? Right now I find it hard to work in an environment where style police who have nothing new to add just run around to make other people write like them. (No, Charles, Kevin, and Revolver, I am not talking about you. But I suspect that veterans like you guys are already aware of what's going on.) What IF I do the same to those style police? Wouldn't they be pissed off as much as I am?
Peter Kwok 15:43, 2004 Jul 1 (UTC)

I think there is a house style; and I think there is also a wiki style, based on general tolerance, and not insisting on matters inessential to salvation. One way to look at it, is that style changes alone aren't so much; an edit to change the style is certainly better if it also adds some substance. Charles Matthews 16:12, 1 Jul 2004 (UTC)

So, for instance, a change in style that allows an argument to read more clearly or an example to be better understood is good "style change"; making a notational change that (the editor believes, at least) makes an equation read easier on the eyes or be more transparent, is good; reorganising sections so they follow a more natural order is good; changing tex or math expressions to conform to what's usually used is okay;, but...making cosmetic changes, rewriting a paragraph without making it much different or better, or constantly changing "generalisation/generalization", "neighbourhood/neighborhood" is prob not necc. Revolver 20:27, 1 Jul 2004 (UTC)

Fair enough. I don't deny that some style changes are good, or even necessary, and I don't mind people overwriting articles with richer and better content. It is the ones that added no substance got me. I regard the "In mathematics" changes as cosmetic and think that we should give people more leeway on that issue. If you disagree, fine; but let's draw a line somewhere. Now some people even begin to change journals' standard abbreviations to long names, which is not even recommended by Wikipedia! Not to mention replacing HTML-styled formulae with <math> tags, or adding a line in the article which won't show up in the display, etc. (The intensity has been increased recently. I believe some of the later changes were made just to get me after I expressed my disagreement.) Do those cosmetic changes really do the readers any good? Even though it is not exactly vandalism, however, this kind of style vandalism is just as demoralising.

If this place really believes in the "everything goes" philosophy, then do let things go. However, if this place believes in maintaining a house style, then maybe we need some kind of guidelines or governing body to give users some protection. Right now I feel that I am being targetted up to the point that it is intolerable.

Peter Kwok 22:57, 2004 Jul 1 (UTC)

I see this is a thing with you and User:Michael Hardy, who is more or less a founding Wikipedian. It is unlikely that this is anything personal, actually. As you are both good contributors, I hope you will just leave this for a few days, first. Charles Matthews 07:20, 2 Jul 2004 (UTC)

I understand why you said that. But after waiting a few days, then what? Style vandalism is not going to go away. I am not asking to put a restraint order on a certain individual— I am just asking to regulate a certain behaviour. May that viloator be Michael or me or even you or whoever, I just think that certain conducts are doing more harm than good to this place even though they might be unchallenged in the past.

I read the WP pages and have already learned all about "be bold", "edit and don't just talk about it", and that kind of things. But we all know it is how flame war (or, in Wikipedia's case, edit war) starts. I could have gone into a mud fight and rebutted line by line to see who was a better stylist. I could have even mass reverted articles. But I didn't. It is pointless to committ myself into making the place better if the place is not even what it advertises to be. I want to make things better. And in order to make things better, we need rules. I just come here to share knowledge as a hobby, not to compete with people to see who has more time and higher seniority to have the last say in style. And I can't freely express myself if there is no rule to prevent style vandalists from targetting newcomers and defacing one's work without adding any new and meaningful substance. This kind of behaviour defeats the purpose of Wikipedia and is a big turn-off for serious contributors.

I will take your words for now. But, man, if people don't get serious about this issue, then this place is no fun any more.

Peter Kwok 17:51, 2004 Jul 2 (UTC)

If you actually want me to discuss this with Michael Hardy, at any point, I will. You can send me email. Charles Matthews 18:07, 2 Jul 2004 (UTC)

Comments on Peter Kwok's concerns

I agree with your statement that mutual respect is important. I have always been polite and respectful to you, and moreover, when I noticed your existence I was glad to see another person contributing articles on mathematics, and that remains my evaluation of your work on Wikipedia.

You seem to think that I have targeted you some how. I have not. I do not edit articles without intending some identifiable improvement.

You wrote: "Right now I find it hard to work in an environment where style police who have nothing new to add just run around to make other people write like them."

Would you tell me who those people are? You seem to think I am one such person. I have contributed a far larger number of new articles on mathematics than you and most others, and a far greater amount of substantive mathematical content to article initiated by others.

I also do minor edits such as a small spelling or punctuation correction in a long article. I did several of those in the article you created on the LYM inequality. You stated on the discussion page that those edits contribute nothing. I disagree. But if you don't agree that they contribute anything, that is not a reason to infer that I was personally targeting you. After I created uses of trigonometry, jengod made some small changes for which I saw no need. It is possible that that person knows some reason of which I am unaware why the changes were improvements, and it is also possible that they are not. Even if I disagreed with those edits, I would still conclude only that another person disagrees, and not that I am being targeted or attacked.

As for moving "In mathematics..." to the beginning, there is a reason for that that I tried to explain to you earlier; I did it because I think the article is in several respects better that way, and I would be specific about that if you appeared to be interested.

You wrote: "I don't deny that some style changes are good, or even necessary, and I don't mind people overwriting articles with richer and better content. It is the ones that added no substance got me. I regard the "In mathematics" changes as cosmetic and think that we should give people more leeway on that issue. If you disagree, fine; but let's draw a line somewhere."

Do you regard "cosmetic" as meaning unnecessary or bad? Making an article esthetically better makes it easier to understand and to remember.

You wrote: "Now some people even begin to change journals' standard abbreviations to long names, which is not even recommended by Wikipedia!" ... because some readers may otherwise not understand the abbreviation. If you disagree with that, you could say so, rather than acting as if there is something personal about it.

You wrote: "I believe some of the later changes were made just to get me after I expressed my disagreement." On this point I have good news that will reassure you. You suggested that I may be among those doing this. But I have not done this. When I disagree with the way someone edits or with their opinions about how others should edit, I address the actual content of the disagreement, saying why I think what I think. I do not personally attack them.

You wrote, "Do those cosmetic changes really do the readers any good?". I would say that if they do no good then they are _not_ cosmetic. "Cosmetic" by definition means they make an esthetic improvement in the article, and therefore they do some good.

You wrote "If this place really believes in the "everything goes" philosophy, then do let things go. However, if this place believes in maintaining a house style, then maybe we need some kind of guidelines or governing body to give users some protection."

_Some_ guidelines are in the style manual: usually the title word or title phrase is highlighted at its first appearance, one eschew's superfluously capitalized letters in section headings, etc.

You wrote: "I could have even mass reverted articles." Did the things you object to happen in more than one article? You have mentioned only one to me. What were the others, if any? - Michael Hardy

Michael - I'm sorry that my offer, made above, to deal with Peter's comments above by email was not taken up. This is really not a good discussion. I personally do think you have been stepping over the line recently, in edit summaries, and in other ways (I am not happy with a style change you made recently in something I wrote). Appeals to how many edits you make obviously carry a certain weight; but they don't actually make up for a constant refrain that others lack 'common sense', etc. 'Open sentence' is standard usage in parts of philosophical logic - whatever you may think of it. And so on. I think you should accept that irritation has been caused, and try to work out how to go forward from here. There is nothing to be gained by 'winning' such an argument. There is also a guideline on escalation. We have to accept that there will be friction, from time to time; and not treat such occasions just as a rebuttal-fest. Charles Matthews 19:00, 14 Jul 2004 (UTC)

Clarification: I am not one of the founders of Wikipedia

I fear one of Charles Matthews' comments may be construed by some to mean I am one of the founders of Wikipedia. In fact, Wikipedia was founded early in 2001 by Larry Sanger and Jimmy Wales; the latter has put about $500,000 of his own money into the project. I first edited articles here in October of 2002, if I recall correctly. Axel Boldt was for some time the only person extensively editing mathematics articles here, and I surmise that he is the original creator of the list of mathematical topics. Michael Hardy 01:50, 15 Jul 2004 (UTC)

Typesetting of mathematical formulas

I know it doesn't really matter, but I am always confused by how to write sentences with math in them and saying things like "where m is the mass, b is the buoyancy, and c is the charge") etc. Some people stick commas inside the tex markup and treat the whole thing as a continuous sentence:

If an equation, such as

a + b = c,

is encountered, then c is the sum of a and b.

some people treat the equation like a graphic, with lots of extra words necessary to keep it in complete sentences:

Summing two numbers is represented by the following equation:

a + b = c

In this equation, a and b are the summands, and c is the sum.

Some people put variable descriptions in a bulleted list below the equation, etc. Can we have a little blurb about a nice method of formatting sentences? I just want some advice for a clean style for myself. - Omegatron 16:05, Jul 20, 2004 (UTC)

Links to surnames of mathematicians are often very bad things

Just as the untutored lay person knows who is being referred to when one mentions Shakespeare or Einstein by surname only, so mathematicians know who is being referred to when one mentions Abel by surname in the context of a math article. But a link to Abel is (of course) a link to the son of Adam and Eve who was killed by his brother in the book of Genesis. And how could anyone expect a link to Study to be a link to an article about the mathematician Eduard Study? Sometimes a math article, or substantial parts of one, are intended to be read by people who know little about mathematics, and in such cases linking to "Euler" does not inform the reader as well as if one links to Leonhard Euler. Consequently I think in most cases first and last names should be used. Michael Hardy 02:04, 1 Aug 2004 (UTC)

There appear to be two points about this:

(a) that surname-only links may be ambiguous to the reader or require disambiguation as wikilinks;

(b) that fuller names in links carry more information to the reader anyway, in the absence of the problems noted under (a).

I'm sympathetic to the first point, as I imagine most people are. I find the second point less convincing, really; if there were no link then surname-only does offer much less, but the point is weakened when there is a page to refer to. It is partly a generation and background thing, but I'm happy with Swinnerton-Dyer, just as much as with Peter Swinnerton-Dyer who is really Professor Emeritus Sir Peter Swinnerton-Dyer, Bart. when it comes down to it.

Charles Matthews 16:47, 3 Aug 2004 (UTC)

The main reasons that it became standard to use only surnames for references in published text, have been for considerations of space, and the tediousness of typesetting. That is, they were publisher-centric. However, since, Wikipedia is (essentially) free from such constraints, we can afford to be more reader-centric. Thus, more use of full names is a good thing. The presence of a link lessens but does not eliminate the benefit to the reader of fuller names. Of course, judgment is required to know when more information is too much information. Paul August 15:48, Aug 24, 2004 (UTC)

I don't think it's just a matter of publisher-friendliness. Readers take additional time to read long names too, and there becomes a time when "Leonhard Euler" looks uselessly long to them. So perhaps in introductory articles, the first appearance of Euler could be written "Leonhard Euler", and the next ones can be just "Euler". Otherwise really-big-names like "Euler" could stay as surname only. (Surname-only links like [[Study]] or [[Abel]] are another matter and should always be avoided, indeed, IMO.) --FvdP 19:18, 29 Oct 2004 (UTC)

Note that according to policy, a link is only given when a name is first mentioned or when it is used in a new context. Thus, asking that every link use the full name isn't inappropriate — the ones that aren't links, which is most of them, can go right ahead and use just the surname. Link redundancy and first-name-redundancy coincide.

That said, an advanced article is justified in excluding the first name of well-known mathematicians, even from links, since it can reasonably expect a more experienced reader. Derrick Coetzee 23:18, 29 Oct 2004 (UTC)

The case for LaTeX

In recent days, I have been adding <math>...</math> to every inline math expression I have encountered, starting with articles in Category:Curves and category:Bundles (mathematics). At the time, I thought that the HTML wikitext markup for equations was provisional, and that by TeXifying expressions, I was improving the articles. I didn't know about the existence of the Wikiproject Mathematics page. I'd like to offer my apologies for breaking convention.

That said, I'm perfectly astonished that HTML wikitext markup for inline equations and variables is an official recommendation (not truly "official," but you know what I mean.) I think it's a bad idea, so allow me to flesh out my case here. My proposal is that we should use <math>...</math> markup for any and every expression related to math, including formulae, single-letter variable names, and all inline expressions. Here's why:

Content != presentation. The entire reason that XHTML and CSS were created from the ashes of HTML 3.0 was to separate presentation from content. We can see the effectiveness of that design decision right here in the Wikipedia: I can change the "skin" of the site (which is just a CSS file) and the look of the site changes automatically, in spite of the fact that the content of every page remains the same.
Doing this required tags that were solely devoted to presentation, like ..., ..., and ... to be removed from the standard. They force presentation and content to mix. So why do we require mathematical expressions to be represented in the exact same manner? Why should a variable name be "italic?" What, precisely, does that indicate to the user?
Consistency. TeX is capable of creating beautiful PNG representations of math expressions, but the fonts and styles it uses for PNG do not match the fonts and styles used for the present "wikitext math" style. TeXifying everything will make all variables and equations look consistent. We won't be able to avoid TeX for more complex formulae anyway; we might as well let TeX choose the font for us.
TeX allows the user to decide. If we put all math expressions (including inline expressions and even variable names) in the <math>...</math>, any user will be able to change the look of all math-related pages with a single tweak to their preferences. They can view everything as HTML unless absolutely necessary, or they can view everything as PNG for maximum clarity. That all users' default preferences are not set to the latter is no reason to avoid LaTeX markup.
TeX allows the admins to decide. If, in the future, some brave developer decides to replace our LaTeX engine with MathML or some other more fitting standard, they can write a bot that automatically converts all LaTeX expressions on every page. Alternately, they may decide to change the default fonts for TeX (I don't know if this is possible, but I assume that it is), and again, all math expressions in the Wikipedia will respond to the change. Neither scenario is possible with "wikitext math," which would have to be changed by hand.
PNG images are small. That's the entire point of PNG, and why we use it in the Wikipedias in preference to GIF files. An expression like $\int_0^\infty e^{-x^2}\,dx$ only takes up 680 bytes; this post I am typing is much larger. It would be difficult to achieve better compression without throwing away image quality! In a giant page full of these types of expressions, the bandwidth "wasted" downloading the PNGs is negligible compared to the bandwidth required for (1) the article text, and (2) the Wikipedia logo in the upper left corner.
Now, if you're using a graphical browser, right-click on the previous image and view its file name. Then compare that file name to the one on the WikiProject Mathematics page (where I got it from.) The filenames are exactly the same--5aa3fbdb28e2859859317b8a9d316fa9.png. So server space is not wasted for common expressions like variable names, either, even if they are forced to render as PNGs. There will be only one copy of the PNG file for $\,\!\theta$ , and anyone viewing our math articles will have it cached.
TeX can emulate inline HTML, anyway. One objection to the use of LaTeX markup (and, in my opinion, the most legitimate one) is that some browsers cannot view inline PNG, and the resulting alt-text is incomprehensible. This is true; however, the MediaWiki LaTeX engine creates inline HTML already! Compare:
- HTML style: f(x) = a₀x² + (a₁x)cos θ
- TeX inline HTML: $f (x) = a 0 x 2 + (a 1 x)cosθ$
- TeX with forced PNG rendering (with \left, \right, and \!\,): $\!\,f(x) = a_{0}x^2 + \left( a_{1}x \right) \cos\theta$

But it is true that mixing inline PNGs with ordinary article text can have a somewhat jarring effect; this is unavoidable, and I happen to not mind it at all (I have seen textbooks that have odd line spacing due to inline math expressions; they still sell well.) One possible compromise is to avoid forced PNG rendering unless absolutely necessary (that is, do not use "\!\," or other "artificial" spaces if you can possibly help it), so the user will see the maximum amount of inline HTML. They can still use their preferences to turn PNG rendering on, so we should expect that PNG versions of all of our expressions, equations, and variable names will exist.

I admit that such a proposal will require us to avoid the more traditional style; $x cosφ$ renders as "squashed" inline HTML, and would require parentheses if we did not allow artificial spaces: $x (cosφ)$ or $(x)cosφ$ or $x * cosφ$ , etc. It's easier to simply allow PNG rendering for unsatisfactory expressions, but nevertheless, this proposal does address the inline objection.

I'm not surprised that my sentiments have been expressed before: Wikipedia talk:WikiProject Mathematics/Archive1#Moved_from_Village_Pump (see comments by User:Pascalromon.) I echo his/her sentiments, but I don't think we need changes as drastic as those that he/she proposed. So how about it, everyone?

Ardonik 19:26, 2004 Aug 3 (UTC)

You write I happen to not mind it at all. If most people agreed, we wouldn't be having the discussion, though. Wiki tends to look provisional, and there's a reason (it is). Now, work on format is constructive; but I don't know enough TeX to be happy with it. We have a kind of compromise at present. I expect it to remain until there is a clear technical shift in rendering, making inline TeX the obviously right way to go. Charles Matthews 21:52, 3 Aug 2004 (UTC)

The beauty of TeX is that we can avoid inline PNGs (which I am not opposed to avoiding) and still reap the other benefits of TeX mentioned above by keeping inline expressions in <math> tags. As for not knowing TeX, you don't have to! You add a lot of useful math content to the Wikipedia, Charles, and I figure that the job of less math-literate people like me is to follow in your footsteps, tweaking things here and there. TeXifying equations is one way to do that.
Perhaps it would be to everyone's benefit to mark the "old style" as provisional, so as to encourage intrepid Wikipedians to update it at their convenience to the "new format" without shunning the old style completely? --Ardonik 22:28, 2004 Aug 3 (UTC)

I think inline PNGs are ugly. I don't mind the use of <math> tags if they are properly translated in inline HTML; in fact, I prefer to type <math>f(x)</math>, rendering as

f (x)

, to ''f''(''x''), rendering as f(x) [side remark: I am surprised to see that both expressions render differently; on my display, I prefer the latter]. Unfortunately, not all mathematical expressions are translated into HTML, and I think that these expressions should be either translated by hand to HTML, or put on a separate line. -- Jitse Niesen 20:19, 4 Aug 2004 (UTC)

I will admit that it often takes some degree of coaxing to convince TeX to leave some simple expressions as HTML (for instance, using \(space) seems to invariably cause PNG conversion.) TeX isn't perfect, but I still think the advantages of keeping expressions TeXified more than outweigh the disadvantages.

If the community consensus is to avoid inline PNGs, then the next step is to discuss strategies for keeping TeX from PNG conversion. I am assuming that the conversion program ultimately responsible is latex2html. As seen from this page in the official manual, there are any number of ways to induce image conversion, but there appears to be no option by which one can force HTML output. (Can someone who is more familiar with the world of TeX correct me on this point?) That rules out convincing the developers to change program parameters; I think we'll just have to come up with a list of TeX features to avoid or replace in order to ensure inline HTML generation. But now is the right time to discuss such things, and this is the right place to do it.

Ardonik 07:39, 2004 Aug 5 (UTC)

Use of \mbox

We can use \mbox{ } to force spaces without inducing PNG conversion. Compare:

	Appearance	Markup
HTML	a²b cos x	`''a''<sup>2</sup>''b'' cos ''x''`
TeX (PNG rendered)	${a^2} b \cos x\,\!$	`<math>{a^2} b \cos x\,\!</math>`
TeX (without \mbox)	$a 2 b cos x$	`<math>{a^2} b \cos x</math>`
TeX (with \mbox)	$a 2 b cos x$	`<math>{a^2} b \mbox{ } \cos \mbox{ } x</math>`

Can anyone think of any other HTML syntax that TeX can't handle without PNGs?

Ardonik 11:21, 2004 Aug 5 (UTC)

TeX/HTML currently incompatible

On line bundle, I attempted to view the article using all possible choices of user preferences, and none of them were able to convert things like the "Z/2Z", "RP2", "CP2", etc. (blackboard bold, fractions, etc.) to inline HTML. When strict HTML was selected, of course it returned tex code. The point is that there is no way to use inline math mode while avoiding PNGs. TeX and HTML simply "evolved" from different origins and haven't quite become compatible. I expect this problem will be solved in time. In any case, there's no telling that the solution won't require detailed combing over and editing in the future, anyway. So, I agree completely with you in principle, but think it's too early to work in practice. And I don't think it's that big a deal...it will be a lot of work to make the switch when HTML and TeX become compatible, but with enough people working on it, shouldn't be a problem. Revolver 21:02, 5 Aug 2004 (UTC)

If the \frac notation cannot be used inline, then we should employ a forward slash instead. TeX understands it; see http://turing.une.edu.au/~amth247/Lectures_2003/Lecture_03/lecture/, and in particular the section of fractions and roots. It recommends that the slash notation be used in favor of \frac wherever it would make an equation easier to read; thus "Z/2Z" would become

Z / 2 Z

. In order to prevent the "RP" and "CP" in line bundle from rendering inline as PNGs, it suffices to avoid switching to fonts like \blackbb (and it makes perfect sense that HTML would not be able to handle those.) Again, we can reap the benefits of TeX without generating PNG files. --Ardonik 02:33, 2004 Aug 6 (UTC)

If the community consensus is to avoid inline PNGs, then the next step is to discuss strategies for keeping TeX from PNG conversion....That rules out convincing the developers to change program parameters; I think we'll just have to come up with a list of TeX features to avoid or replace in order to ensure inline HTML generation. But now is the right time to discuss such things, and this is the right place to do it.

Maybe so. I don't know, maybe this comes from seeing articles evolve over months or a couple years, but I don't think this is a urgent problem in any case. Try to avoid the most obvious problems (e.g. I think blackboard bold should be entered as bold for the moment) but it's nothing to get too uncomfortable over. For now, it's probably enough to sit back and wait for the inevitable HTML/TeX compatibility to happen, and then let things sort out. None of these articles are really going to look like they do at present in 2-3 years, anyway. Adding good content and improving some of the weaker "elementary" articles (fundamental thm of calculus, etc.) seems far more important. (BTW, why is FTC listed first in the "calculus" box, before derivatives even?) Revolver 21:15, 5 Aug 2004 (UTC)

It's not urgent (what is urgent in this Wikipedia?) but I feel that we do need to address it. LaTeX is not some relatively new technology waiting for extra features to be added by enterprising programmers. It is mature and fully featured; latex2html itself was around before 1993. There is nothing to wait for. The TeX tools were designed to empower those who love math, and now that they have been enabled in the MediaWiki projects, they are at our disposal. They do everything we want. What reason do we have to avoid them?
Of course I agree with you that adding content is more important than worrying about style, but by formalizing a system now, we ensure that future Wikipedians will know what guidelines to turn to when creating new math and science articles, and that people like me will know how to TeXify articles without ruining them. A thousand times over do I prefer consensus to inaction. --Ardonik 02:33, 2004 Aug 6 (UTC)

P.S. FTC? Calculus box? --Ardonik 02:33, 2004 Aug 6 (UTC)

Fundamental theorem of calculus. Look at the "topics" box on the right. FTC is the first topic. Revolver 19:55, 6 Aug 2004 (UTC)

I agree that <math>f(x)</math> is more logical than ''f''(''x''), and that content is more important than format, but I also agree that the HTML version looks better. Supposedly this will all be resolved when mathml is working. Should we just wait until then? (and how long will that be, anyway?) - Omegatron 02:47, Aug 6, 2004 (UTC)

Well, we have "experimental" MathML support right now, but as for how long we'll have to wait before MathML becomes a widespread standard, the answer is perhaps indefinitely. How could a company that failed to correctly support even CSS 1 be bothered with adding MathML support? Sure, Mozilla might get it eventually (or someone might develop a fork of Mozilla that supports it), but until aforesaid company makes Mozilla or Firefox the default desktop browser, few people will be able to view MathML. Additionally, when MathML support is fully enabled, we won't be able to take advantage of it without putting our expressions in <math> tags first, so we will be better off TeXifying our expressions now than continuing to use raw HTML and piling up the amount of conversion that will need to be done later.
Honestly, what do we stand to gain by waiting? --Ardonik 03:37, 2004 Aug 6 (UTC)

A few points. (1) Actually there is a free plug-in for Explorer available and Mozilla et al. have already a reasonable support for MathML (but you need to download some fonts). (2) What happens to <math> is determined by a home-grown transformation that might be changed if desired. (3) MathML is not really functional right now. I think the last point is important. There should be at least one way to see the ideal end-result. -- Jan Hidders 11:22, 6 Aug 2004 (UTC)

Yeah, I used the MathML player when I was still in IE. It seemed to work fine, and is free. MathML is probably the ideal future solution, but ideals are commonly nonviable.

Maybe we can make some sort of compromise? add an attribute "inline" to the math tags ( <math style="inline">, etc. )to make it format as HTML if at all possible, or in small-lettered, center-aligned TeX if not? And when converting to HTML, change the span.texhtml { font-family: serif; } to something that renders prettier? Perhaps just leave it in the default font? - Omegatron 13:36, Aug 6, 2004 (UTC)

From what I can gather, TeX's chief weakness is its inability to guarantee the generation of inline HTML (by default, of course; user preferences would always be able to force PNG generation.) I am convinced that this can be worked around, but I openly admit that the solutions (like using \mbox{ } instead of a space) are cumbersome. Another weakness is that the inline HTML is rendered in a different font than the HTML that surrounds it. Only the developers can fix this problem, as they control the MediaWiki CSS.

At the same time, responders seem to generally agree that there are tangible benefits to preferring the <math> markup to ordinary HTML.

I see the workings here of a possible compromise:

Content and accuracy are more important than anything else. Compared to these, the beauty of a page's math should be an afterthought.

(I'm afraid I can't agree that considerations of beauty "should be an afterthought". Of course content and accuracy are of paramount importance, but if an article is so off-putting, that it isn't read, well … Paul August 16:34, Aug 24, 2004 (UTC))

Allow people to continue creating and formatting equations in the "wikitext math style" currently described on the WikiProject Mathematics page, but recommend use of the <math> tag for future entries.
When using LaTeX, the "house style" will be to avoid generating PNG images for inline equations and variables. Anyone TeXifying wikitext math must be careful to preserve the HTML format for all inline expressions and variables; when this cannot be done, they should leave the expressions and variables as they are. Conversely, if the TeXification of a page's math expressions is done correctly, there should be no reason to remove it.
The WikiProject Mathematics page will feature a tutorial on how to keep LaTeX from generating images so that Wikipedians can share tricks like \mbox{ } with others. I can help to write this.
Expressions on their own line may freely be converted to PNG, so house style will be to prefer that complex expressions remain on their own line whenever possible.
Convince the developers to use a prettier font-family, font-weight, font-style and font-size for inline HTML conversion (what specific settings would be ideal I do not know.)

Does this sound like a reasonable set of guidelines? Would anyone be opposed to them, and if so, what can I do to improve them? --Ardonik 19:10, 2004 Aug 6 (UTC)

"Well, the ideal solution would be …"

Well, the ideal solution would be to just have any and all articles that use mathematical expression to jettison HTML entirely and have the whole thing be a LaTeX file. This would eliminate all the problems. (I'm being facetious, of course...but also trying to indirectly point out what the problems are short of doing this.)

From what I can gather, TeX's chief weakness is its inability to guarantee the generation of inline HTML.

It's a bit more than that. For people who dislike the ugly "discontinuity" of alignment between HTML and PNG, and find it personally disruptive, solving this problem would still these people to choose "always HTML" and so give up inline PNG images altogether. But why should they have to do that?

The guidelines sound alright. I still believe that for relatively simple things, it's best to leave in HTML as we've always done. I'm talking about the greek letter "π", for instance. Or, single variables, like "x" or "y". Nothing gets me more than seeing a variables that stands out nearly TWICE AS TALL as the text size I'm reading. For more complicated inline expressions, I have a lot more tolerance and understanding. But, even something like Z/2Z, doesn't seem to need texifying. Of course, I'm sure I draw the line much farther than most other people.

Revolver 19:50, 6 Aug 2004 (UTC)

Here is where you and I disagree--I think anything related to math should be TeXified, so as to indicate that the information being marked up is math and not prose. I've already outlined my reasons for preferring this, so I'll have to accept that we will differ on this point. But remember that with inline HTML generation, the user should not see any drastic difference between π (π) and <math>\pi</math> (

π

). The only real difference to the user will be that they can change the look of the second one on the fly with a single change to their preferences. --Ardonik 20:48, 2004 Aug 6 (UTC)

Your assertion is just not true. Obviously, you have never attempted to do this on IE personally, or you wouldn't claim this. Here's the problem: too many math expressions are not changeable (or won't change) to HTML. So, even after changing preferences, the user is STILL bombarded with a ton of inline math expressions, esp. at articles like curve and a lot of the category and algebraic topology articles. These things can't be changed to HTML, and given that there will always be a wide variability in the size people choose for their fonts, someone will be left looking at disruptive text. Revolver 17:45, 24 Aug 2004 (UTC)

Crazy idea

This may seem like a crazy idea, but it would be something I would be willing to contribute time toward. There is a company which makes a semantic interface onto LaTeX (Scientific Works), which you can enter into directly (not WYSIWYG, but logical interface). It takes very little time to enter stuff, about as fast as using a word processor. Then, there is a viewer that comes with it which is free for anyone to download on the internet. So, once you make a file, you just direct someone to download the viewer and view the file with the viewer. There is absolutely no TeX code involved at all.

While this is clearly not workable for the wiki pages that people work on, it might be possible to do periodically for some of the more important math and technical pages, I'm thinking of Wikipedia 1.0 in particular and its updates. The number of articles here wouldn't be too much, it would be much better visually, and both the wiki-HTML-PNG version as well as the Works version could be available for people to choose.

Otherwise, I'm just starting to think, while the CD-ROM viewers of 1.0 will have the option of which way to see it, the people reading the paper version will not.

Revolver 20:10, 6 Aug 2004 (UTC)

The best way to integrate any document-viewing plugin is with XHTML's <object> tag; say, something like

 <object data="proof.tex" type="text/plain" width="400" height="200">
   alternative text (i.e. inline HTML for the proof)
 </object>

sort of like an "applet" for math pages.

Yet I would still prefer the current system of integrated LaTeX to this--the user doesn't have to know that we're using a LaTeX back-end, and we can swap it out with something more effective (read: MathML) at any time. It's definitely not as easy to use as a WYSIWYG editor, though.

Ardonik 20:57, 2004 Aug 6 (UTC)

My own two cents: In principal, I completely agree with the idea of writing all math code in TeX. That being said, I must object to actually doing this at present. I personally think that all inline TeX—whether rendered as HTML or PNG's—looks terrible. More than once I've avoiding reading a math article (let alone bothering to edit it) simply because I don't want to get a headache trying to wade through the changes in font sizes. In principal, the TeX->HTML shouldn't look bad, but it does. Yes, I know this can be fixed by a simple change to the wiki CSS file, but no one seems to be doing this. In the meantime, I'd much rather have a article that I can read rather than one which is semantically "correct".

Point 2: I think the real push should not be towards getting everyone to TeXify everything, but rather towards getting the wiki developers to implement MathML output. I believe that MathML is a viable solution now! Not some distant future. MathML looks reasonable in Mozilla browsers and plugins are available for other 'less competent browsers'. If you ask yourself why there isn't better browser support for MathML, the answer is pretty obvious: there just isn't much demand for it. What's needed is a site like Wikipedia, with its large quantity and quality of math content, to start outputing things in MathML to increase demand. Who should we be talking to, to push this matter?

In the meantime, I will continue to use pure HTML for everything inline simply so I can read it. I will starting inputing TeX as soon as wiki starts outputing MathML. As to having to rewrite all the articles when this happens, I don't think it's such a big deal. It's not like it has to be done all at once. Articles are getting edited all the time, they can be converted piece by piece. And until they are, it's not like they're going to be unreadable.

Fropuff 04:08, 2004 Aug 8 (UTC)

For changes to the CSS file you could do a request at the wikitech-l mailing list [1]. I suspect that if you make clear that this is a common complaint in the math community there will be a quick response. I'm not really an expert on CSS matters, so I cannot do this myself. As far as real support of MathML goes, see the discussion on this in this newsgroup last week (in August 2004) with subject "Status of MathML support". -- Jan Hidders 09:51, 8 Aug 2004 (UTC)

Fropuff, you think that neither TeX's PNG rendering NOR its inline HTML look good? Honestly, is the serif font on your browser that ugly?

I've performed an experiment in the interest of furthering this conversation. I have just TeXified the entirety of the determinant article, trying as much as I could to keep inline statements from rendering as PNGs. I will disclose now that in four areas, I failed to accomplish this task, though not for lack of trying:

The \approx symbol in TeX apparently forces PNG output, in spite of the existence of the ≈ entity in HTML. I could not find a suitable replacement for this.
I was unable to specify a bold font for the "R" characters in $\textbf{R}^n$ without generating PNGs. From the documentation I read today, it seems that the command to do this is \textbf, but it apparently has the same effect as \mathbf in the MediaWiki.
The correct way to prevent $| A |$ from looking spaced out is to use the \left and \right commands, but for reasons unknown to me, <math>\left| A \right|</math> displays as a PNG: $\left| A \right|$ .
I couldn't find an inline sqrt or a square root symbol. Using \sqrt{} guarantees PNG output.

Anyway, here are links to the old version and the current version. Compare the way they look. Except for the places I mentioned above, how similar are the two articles? Do those of you who dislike TeX's HTML output still dislike the text that you see?

It took me several hours of browsing through manuals and latex files to fully TeXify the article (I'm still learning TeX, too), but if any of you feel that I've mangled it or inserted something contrary to fact, please revert my changes.

Ardonik 11:33, Aug 8, 2004 (UTC)

Determinant#Derivative is somewhat messed up. The first two expression render differently of the last two... IMO major, i.e. long, expressions should (be allowed to) render as PNG and be placed in a new line, for clarity; there should be no "tricks" when writing <math> so that it is easy to edit and convert to some later format; expressions and/or single letters/symbols inline with text should be <math> also, although uglyer it is more clear.--Nabla 12:40, 2004 Aug 8 (UTC)

I honestly think the old version of the determinant article looks far better. If there isn't a whole lot of inline TeX, the effect isn't too bad, but take a different example with a higher density: compare the current version of Representable functor to the last unTeXified version [2]. Again, I think the old version is far more readable.

"Honestly, is it the serif font on your browser that's ugly?" No, I actually approve of the serif font. It's the size that bothers me. PNG's are too large, the text of the TeX/HTML is too small (hard to read in fact). When the two are used side by side its just a mess. I know this may sound nitpicky, but I honestly get a headache trying to read that stuff.

Fropuff 14:26, 2004 Aug 8 (UTC)

I agree with Fropuff that the inline PNGs are very ugly and with Ardonik that it would be preferable to use <math> tags to deliminate maths expressions. The discussion that Jan pointed to shows that we will probably not have MathML output in the near future. The only satisfactory resolution, as far as I can see. is to improve the translation of <math> environments to HTML, so that for instance <math>|A|</math> automatically renders as |A|. -- Jitse Niesen 18:19, 8 Aug 2004 (UTC)

Is it just me, or do the HTML sup constructs show up really low? Compare x² to $x 2$ . This makes articles that contain many superscripts very hard to read because the superscripts are hard to distinguish from regular text. TeX/HTML renders the superscripts much better in my opinion. Gadykozma 14:14, 27 Aug 2004 (UTC)

The both 2's look to be at the same height for me - the bottem of each "2" just below the top of the "x". Paul August 16:33, Aug 27, 2004 (UTC)

The TeX version looks awful -- the x of x^2 protrudes far below the "baseline" of text. The HTML version is balanced in height and more readable. Revolver 09:00, 31 Aug 2004 (UTC)

Maybe it was a linux problem, or the specific version of Mozilla/Galeon I usually use. Now I'm on windows and both look fine. Gadykozma 18:59, 1 Sep 2004 (UTC)

A clarification

A Clarification -- one more reason I prefer HTML. Besides lots of things not being able to render in HTML, there is another big problem. Many people urge me to change my preferences. But then a lot of expressions I wish were KEPT in TeX get changed to HTML when I don't want them to!! This happens for example at the article pi. Long, single-line expressions get chopped up and rendered often in a silly manner. Besides, for single-line, I WANT TeX. Why should I be force to give it up?? Revolver 09:04, 31 Aug 2004 (UTC)

Good point. The preference "HTML if possible or else PNG" renders fractions as HTML, which looks terrible (at least in my browser). A possible solution is to change the software so that all single-line expressions are rendered as PNG, even if they could be rendered as HTML. With single-line expressions, I mean lines that contain only a <math>...</math> construct, and possibly white space. I do not know how feasible this is technically. What do people think of this idea? -- Jitse Niesen 10:22, 31 Aug 2004 (UTC)

Its strange nobody seems to have mentioned the project for a paper version of wikipedia, meta:Paper Wikipedia. This seems very relevant to the question whether LaTeX or html markup is to be preferred. Gadykozma 18:23, 5 Sep 2004 (UTC)

Editing the articles on set theory.

Although I've been editing for about a month, I've just discovered this page.

I've been doing more and more edits to the articles on set theory, and I'm contemplating rewriting the article Set. I posted some discussion concerning my proposed changes at Talk:set and Talk:naive set theory but so far no one has responded. Perhaps no one is watching these pages, or has nothing to say regarding my posts ;-) However, at the risk of being accused of not being bold, I'm reposting them here, just in case anyone cares. If not I will go on blissfully editing to my hearts content - until someone objects.

(The following comments and proposal is now pretty much moot, as I've made the changes I proposed below. Paul August 21:00, Aug 27, 2004 (UTC))

I think there is too much overlap between the articles Set and Naive set theory.

In reviewing the change history for Set, I find that the earliest versions of this article (can anyone tell me how to find the original version, the earliest I can find is as of 08:46, Sep 30, 2001) contained the following language prominently placed in the opening paragraph:

"For a discussion of the properties and axioms concerning the construction of sets, see Basic Set Theory and Set theory. Here we give only a brief overview of the concept." (The articles referred to have since been renamed as Naive set theory and Axiomatic set theory resp.)

As subsequent editors, added new information to the beginning of the article, the placement of this "brief overview" language, gradually moved further into the article, until now it is "buried" as the last sentence of the "Definitions of sets" section. Consequently I suspect that some new editors are unaware that some of the material being added to this article is already in, or should be added to Naive set theory or even Axiomatic set theory (e.g. Well foundedness? Hypersets?).

If it is agreed that, Set is supposed to be a "brief overview" of the idea of a set, while Naive set theory and Axiomatic set theory give more detail, I propose two things:

Add something like: "This article gives only a brief overview of sets, for a more detailed discussion see Naive set theory and Axiomatic set theory." to the opening section of the article Set.
Move much of what is in the article Set to Naive set theory or Axiomatic set theory.

Comments?

Paul August 20:23, Aug 16, 2004 (UTC)

I have moved the sections on "Well-foundedness" and "Hypersets" to Axiomatic set theory, which I think is a more appropriate place for them - based on the idea expressed above that the Set article shold be a "brief overview". Paul August 07:34, Aug 18, 2004 (UTC)

I should have added a third item to my proposal:

3. Rewrite the remaining parts of Set in a more elementary style. (The idea being that Set would be at the elementary/high school level, Naive set theory would be at a high school/college level and Axiomatic set theory at a college/graduate school level)

~~If you want to look at a first draft of a rewrite of Set, see: Paul August/Set.~~

I've now completed my rewrite of set Paul August 21:00, Aug 27, 2004 (UTC)

lastly, a couple of questions about notation. Why is "{}" preferred over ∅ for the empty set? "{}" looks kinda ugly to my jaundiced eye. Also is A\B preferred over A - B for set theoretic difference?

Actually I've got lots more questions, (especially about markup - are there any standards?) but that's enough for now. If this is not really the right place for all this, then my apologies. Paul August 03:47, Aug 19, 2004 (UTC)

Have at it. Your changes sound good to me. I think ∅ is far more common than {}. I've always preferred A - B to A \ B, but the latter seems more common and is used (presently) in the article Complement (set theory) — Fropuff 05:03, 2004 Aug 19 (UTC)

(Note: I've taken the liberty of moving the disccussion on "{}" versus ∅ which used follow here to the following new section below. Hope that's koser ;-) Paul August 18:14, Aug 24, 2004 (UTC))

A friend of mine recently pointed out to me another article that should be considered in a revision of our set theory coverage: Language of set theory. It's a poor article currently, but you might be able to take it somewhere. I was thinking perhaps that it should highlight how other mathematics can be built using set theoretic language (for example, how relations, functions, and ordered pairs are expressed as sets.) Isomorphic 18:05, 19 Aug 2004 (UTC)

Yes this article needs some help. I'll see what I can do. Paul August 21:00, Aug 27, 2004 (UTC)

Notation for the empty set: "{}" vs. ∅

(Note: I've taken the liberty of moving the disccussion on "{}" versus ∅ from the previous section to here. Paul August 18:14, Aug 24, 2004 (UTC))

Why is "{}" preferred over ∅ for the empty set? "{}" looks kinda ugly to my jaundiced eye. Paul August 03:47, Aug 19, 2004 (UTC)

… I think ∅ is far more common than {}. Fropuff 05:03, 2004 Aug 19 (UTC)

The reason that some prefer {} over ∅ is that many popular browsers such as explorer and konqueror cannot display ∅. -- Jan Hidders 08:46, 19 Aug 2004 (UTC)

hmmm all my browsers Safari, OmniWeb, IE (all on Mac OSX) display it fine. Paul August 12:29, Aug 19, 2004 (UTC)

My IE under Windows XP doesn't and neither does Konqueror (on Mandrake Linux). For the record: IMO we should use ∅ anway. In fact, I think that if looks are important there is no problem as long as there is a free, open source browser that can be easily installed on several platforms, is standards-compliant and displays the article as it is suppposed to look. But that's just me. :-) -- Jan Hidders 13:06, 19 Aug 2004 (UTC)

Based on the above It looks like there might be an emerging consensus that &empty is better than {}. any objections? I wouldn't mind going around and changing {} to &empty. But it's a little work, and I don't want to do it if anyone is just going to change them all back. Paul August 20:17, Aug 22, 2004 (UTC)

You have my vote. But we/you should probably first try to formulate a policy on the project page. That gives you something to point to when watchers of articles who didn't follow this discussion start complaining. Formulating such a policy and trying to make it sound sensible is IMHO a good sanity check to see if this change is ad-hoc or can be fitted in the broader picture. -- Jan Hidders 21:46, 23 Aug 2004 (UTC)

Jan makes a good point. I've frequently included HTML entities for various symbols in my posts, and sooner or later someone will come along and change them because they don't display in browser X (almost always IE). A few of the named entities that won't display in IE (with default fonts on my Windows 2000 system) include

∅ (∅), ∉ (∉), &lowast; (∗), &otimes; (⊗), &lang; (〈), &rang; (〉), and &alefsym; (ℵ)

The unnamed symbols that I most frequent want are U+210F (ℏ) and U+21A6 (↦). These I've avoided using altogether as I think support for them is probably worse (although they both dispaly fine in my default browser). My personal vote is to say anything in Unicode is fair game (it's valid HTML after all), but I may be in a small camp on this one. -- Fropuff 23:04, 2004 Aug 23 (UTC)

It's very annoying that on some browers I use (I use multiple computers and multiple browsers) many of the set theory articles or just articles with lots of HTML set theory notation are completely unintelligible, because they read as "A (BOX) (B (BOX) C) = (A (BOX) B) (BOX) (A (BOX C)), unless A = (BOX) or B = (BOX).", or worse "(BOX) (BOX) A = A if and only if A = (BOX)". With many of these, I don't even bother to read them, I just leave. I suspect lots of other readers do as well. Revolver 17:29, 24 Aug 2004 (UTC)

Having said this, there are some symbols that are impossible to render HTML (intersection?) and so I often end up using it anyway. Revolver

So Revolver, does this mean you prefer we stick to using "{}"? Paul August 18:14, Aug 24, 2004 (UTC)

For now, yes. It's not as good as << empty set >>, but it's better than << (BOX) >>. Revolver 07:32, 26 Aug 2004 (UTC)

I'd say it is better to use the TeX version ( $\varnothing$ ) than {}. This is, at least, both standard notation and universally visible, if somewhat ugly when set inline with normal text. -- Fropuff 21:48, 2004 Aug 27 (UTC)

Well I also like $\varnothing$ better than {}, just about anything would be. Should this be the preferred way? Paul August 23:56, Aug 27, 2004 (UTC)

I make a very strong vote against ∅. Why? Almost all our readers use IE, which doesn't support it! I like <math>\varnothing</math>, because the software can render it according to user preferences and HTTP browser information, which is the best solution for everyone (if it doesn't do this now, at least the potential is there). Derrick Coetzee 01:39, 28 Aug 2004 (UTC)

Agreed. I'm only wondering if there is a difference for you between $\varnothing$ (<math>\varnothing</math>) and $\emptyset$ (<math>\emptyset</math>). On my Mozilla (under the pref. "HTML when possible" for math) the latter renders better. -- Jan Hidders 01:56, 28 Aug 2004 (UTC)

The same difference there is between $\epsilon\!\,$ and $\varepsilon$ , between

φ

and $\varphi$ and between

σ

and $\varsigma$ . — Miguel 23:21, 2004 Dec 3 (UTC)

Oh, yikes, Firefox's math HTML rendering is inconsistent with TeX! — Miguel

Depend's on what you're preferences are. When they both render as PNG's I like the \varnothing one better. But certain preferences will convert \emptyset to the HTML ∅. So maybe that's the better one to use. -- Fropuff 02:17, 2004 Aug 28 (UTC)

For me, under Safari for any math rendering preference setting:

∅ (&empty) looks like a circle with slash - my preference
$\varnothing$ (<math>\varnothing</math>) looks like a circle with a slash- a little bigger circle, slightly more horizontal slash - my second preference.

With either "recommended for modern browser" (not sure what this pref means exactly) or "Always render PNG", then

$\emptyset$ (<math>\emptyset</math>) looks like a rather ugly oval taller than wide with slash. - don't like this one much, but better than "{}"

While with "HTML if possible or else PNG"

$\emptyset$ (<math>\emptyset</math>) looks the same as &empty.

How does IE render <math>\emptyset</math> ? Paul August 04:18, Aug 28, 2004 (UTC)

IE, with default preferences renders both <math>\emptyset</math> and <math>\varnothing</math> as PNG's. The former looks like a tall, skinny oval with a slash through it, and the latter as a circle with a slash through it. -- Fropuff 04:33, 2004 Aug 28 (UTC)

Given all this, I vote for $\emptyset$ , because it yields HTML where settings allow it and works in IE. It's also very common in LaTeX documents. Do we have consent? Derrick Coetzee 04:38, 28 Aug 2004 (UTC)

I support a <math>...</math> based solution. Personally, I would prefer \varnothing over \emptyset, but if the majority style here is \emptyset, I can stick with that, too. FWIW, in my LaTeX documents I usually have a global redef in the global preamble, as in \def\emptyset{\varnothing}, and then use \emptyset later on. BACbKA 23:25, 3 Dec 2004 (UTC)

I think the notation {} is too confusing. We should use some variation on the slashed O sign, even if it doesn't render properly everywhere. Gadykozma 05:03, 28 Aug 2004 (UTC)

In my opinion {} or { } is better because it still has a connection to the set notation due to the braces. whereas $\emptyset$ is a completely new symbol and the connection with emtpy set has to learned and cannot be inferred. MathMartin 22:28, 3 Sep 2004 (UTC)

If by "completely new" you mean "widely used in papers for decades"... keep in mind this is the default LaTeX empty set symbol. Derrick Coetzee 23:12, 29 Oct 2004 (UTC)

This was my personal opinion (I should have said so). Of course we should use the symbol which is most common, if this is $\emptyset$ so be it. MathMartin 21:41, 22 Nov 2004 (UTC)

I would say that {} is the empty set, while $\emptyset$ is a symbol for it. Which notation to use should depend on the context. — Miguel 18:01, 2004 Nov 26 (UTC)

Out of curiousity could you provide an example where it is better to use $\emptyset$ than {} ? MathMartin 22:00, 3 Dec 2004 (UTC)

Sure: $\{\emptyset\}$ is more readable than

{{}}

. — Miguel 23:06, 2004 Dec 3 (UTC)

Avoid notational conventions! Sometimes "{}" works better, sometimes "∅" works better; sometimes TeXvc works better, sometimes it doesn't. There are special circumstances; if a common browser cannot render a version, then it's justified to warn writers against that version. Still, the only basis for debate in that case is to determine whether the special circumstance obtains, and the only conclusion to draw is that the number of options is lowered by one. Of course, people that are interested in æsthetics are free to discuss their personal preferences as much as they like; I have my own opinion on this matter, which I'd be happy to chat about on my talk page or even by email. But Wikipedia does not need a standard for every notational debate. -- Toby Bartels 23:55, 3 Dec 2004 (UTC)

∪ symbol displays as box?

Someone edited the set article, changing each set union symbol "∪" (i.e &cup) to an uppercase U, because they were displaying as boxes. Is there a problem with rendering ∪? It looks ok for me (Safari, IE, OmniWeb on MAC OSX). Does anybody else have problems with this? Paul August 19:48, Aug 31, 2004 (UTC)

The right thing to do if your browser does not display "& cup ;" is to use <math>\cup</math>, never to replace it with "U". — Miguel 23:41, 2004 Dec 3 (UTC)

Schaun MacPherson

At User_talk:ShaunMacPherson, I have invited that person to discuss on this page his implicit decision to move hundreds of articles titled ABCD's theorem to ABCD's Theorem with a capital T, and similarly for conjectures, lemmas, axioms, etc. In case anyone can be more effective in persuading him that I can, I mention that here. (If you are Schaun MacPherson and do not wish to pursue the matter, please feel free to delete this section.) Michael Hardy 20:40, 31 Aug 2004 (UTC)

Personally, I don't think the word theorem, lemma etc. should be capitalized in this context. But it's a minority view. A number of editors threw out my preferences and capitalized them. Gadykozma 23:51, 3 Sep 2004 (UTC)

Sep 2004 – Dec 2004

This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

New Article: The algebra of sets - request for comment.

I've just created a new "set theory" article: The algebra of sets I'd be interested if anyone has any comments. In a sense it's an expanded version of Simple theorems in the algebra of sets the latter being primarily just a list. One could argue that consequently the latter article is no longer necessary. But I can see the possible use of an article which simply lists results. Comments? Paul August 03:53, Sep 6, 2004 (UTC)

Hmmm - a few questions relative to the integration with the rest of WP. What you mean mostly is 'here is some explicit information about the Boolean algebra of sets'. Which might be useful to some people, indeed. Since the 'set of all sets' is chimerical, your 'algebra' is not precisely a Boolean algebra; the subsets of a given set X would give a Boolean algebra. I think this kind of placing would be helpful; and probably renaming the page. Charles Matthews 08:07, 6 Sep 2004 (UTC)

Charles, thank you for your comments. As to the title, I took my lead from Simple theorems in the algebra of sets. The word "algebra" here is not being used as a technical term, as say in "Boolean algebra" or "linear algebra" but rather as a descriptive term, for this collection of facts concerning "the basic properties and laws of sets, the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion." The motivation for using the word "algebra" beyond it's descriptiveness, is to help the reader make the connection to the perhaps more familiar notion of algebra of numbers. It is a relatively common way of describing this material. For example Robert R. Stoll in Set Theory and Logic has a section titled "The Algebra of Sets", as does Seymore Lipschutz in his Set Theory and Related Topics (Schaum's Outline Series). Having said that I'm not opposed to finding a better name for the article. I had also considered simply "Set algebra" as an alternative name. What name are you proposing? As you say, and as is pointed out in the article, the power set of a given set is a Boolean algebra. As to your other suggestion of "this kind of placing would be helpful" I'm not sure what this means, could you please be more specific? Thank you again. Paul August 16:41, Sep 6, 2004 (UTC)

I would like to see even more analogies with usual algebra. A) You never say explicitly which operation is the analog of addition and which of multiplication (does this make sense? If not, the article should explain that too). B) Analogs of (a <= b) => (a+c <= b+c) should be highlighted. C) perhaps to put to the right of every inequality the anaolg (if it exists) in usual algebra? Arrange everything in comparison tables? I feel I'm starting to float. Think about these. Gadykozma 12:13, 6 Sep 2004 (UTC)

Gadykozma, thanks for your comments. As far as the analogy holds, union is the analog of addition (in fact the union of two sets has been sometimes called their "sum") and Intersection is the analog of multiplication. The article used the order of their mention to try to make this clear (perhaps a well placed "respectively" is needed.) As I partially said above, the use of this analogy is to help motivate these ideas for the reader, and to help place these facts concerning set theory in an appropriate setting. Including the fact that A ⊆ B ⇒ (A ∪ C) ⊆ (B ∪ C) is probably good in it's own right, that it continues the analogy is also nice. But I think we should be careful about relying too heavily on the analogy. It is not meant (by me at least ;-)) to be an article about the analogy. Paul August 16:41, Sep 6, 2004 (UTC)

cdot and times

In LaTeX markup, does \cdot equal \times?, that is do they represent the same mathmetical function or is it just a center-aligned dot? -- Ævar Arnfjörð Bjarmason 13:08, 2004 Sep 12 (UTC)

\times: $5 \times 5 = 25$ ; \cdot: $5 \cdot 5 = 25$ -- Ævar Arnfjörð Bjarmason 13:08, 2004 Sep 12 (UTC)

Yes, they are both multiplication. \cdot is more appropriate for advanced texts and \times for beginner level texts. Also \times is used in advanced text to denote "special" kinds of multiplication like vector product or Cartesian product. Gadykozma 14:49, 12 Sep 2004 (UTC)

variable letters

Probably doesn't matter, but is there any standard for variable letters? For instance, most people use i for the imaginary number and f(t) for a function vs time, but I am used to engineering convention, which uses j for the imaginary number (because i is current), and x(t), since f is frequency in fourier transforms, etc. should we just use whatever variables are conventional in each specific topic? and what about a topic like fourier transforms which are used in contexts with i for current but also used in unrelated contexts where the majority of people would be used to i for imaginary number? - Omegatron 01:34, Sep 19, 2004 (UTC)

Don't use j for the square root of -1, unless the article has a strong engineering flavor, and in this case warn in the beginning.
Other issues you raised are pretty free. Not that I like x(t), but I don't see it as very distracting to understanding. Gadykozma 02:11, 19 Sep 2004 (UTC)

ok. should you mention this on the wikiproject page? yeah, and x(t) is confusing because of f(x). but then it would be confusing when you transform to X(f), etc. etc. - Omegatron 02:21, Sep 19, 2004 (UTC)

In some cases, x(t) is the most appropriate, e.g. the vector-valued function of time x(t) = (x(t), y(t), z(t)). Revolver 05:48, 24 Sep 2004 (UTC)

Simple formulas

Some of what you say just isn't true: "If you enter a very simple formula...this will not be displayed using pgn but html, like this:", but this does display as a PGN for me. If you ask me to change my preferences, then many legitimate LaTeX formulas will becomes emasculated (see pi.) To see what I mean, you say the L^infin is "horrid", but it looks exactly the same as the L^p above to me! Why is one horrid and the other not?? Revolver 20:43, 22 Sep 2004 (UTC) (Moved from project page 23:15, September 22, 2004 by Gadykozma)

It depends on your preferences, browser rendering of HTML, etc. I have tentatively converted to the "everything in math tags no regular text in italics" camp, and even switched my preferences to "render everything in PNG". It takes a couple articles to get used to but then I liked it. Most math websites look like that anyway. - Omegatron 20:46, Sep 22, 2004 (UTC) (Moved from project page 23:15, September 22, 2004 by Gadykozma)

That's what I have now!! I've had it for weeks or months that way and still hate it. Perhaps it's my HTML text size relative to PNG. The PNG's are just TWICE as tall and FOUR times as big as HTML. This is what he meant above by "horrid". Revolver 21:16, 22 Sep 2004 (UTC) (Moved from project page 23:15, September 22, 2004 by Gadykozma)

Actually, I think they were showing that the HTML rendering of TeX (not the PNGs) and the plain old HTML letters look different. The TeX rendered into HTML is in a serif font and kind of weird sizes, so it doesn't match with the rest of the text. I guess some people like it like that. You can change it in your user css if you really want, although you, Revolver, have always PNG, so it doesn't matter. - Omegatron 23:56, Sep 22, 2004 (UTC)

Also, does it do this for you?: do the PNG's go below the bottom justification of the HTML text? It does for me. It's just the size of them, it's that they protrude below the line of text, so that e.g. the "p" in L^p is no longer a superscript, it reads horizontally on the same level as an HTML "p" (or very close). Revolver 21:19, 22 Sep 2004 (UTC) (Moved from project page 23:15, September 22, 2004 by Gadykozma)

They look centered in the middle of the line to me. I used Firefox. Bigger than the rest of the text, but I am used to it, and it looks better than the TeX rendered as HTML. You see it like that on webpages all the time. - Omegatron 23:56, Sep 22, 2004 (UTC)

OK, I guess I didn't write it quite as well as I intended. What I had in mind was to convey two points:

How Wikipedia displays simple formulas with the default parameters, which is what most users use (this need to be said!)
That people don't like when you change their text from one to the other (the only thing that everyone agreed on in the very very very very very very very long discussion).

Anyone has a better idea how to convey this information? Gadykozma 23:31, 22 Sep 2004 (UTC)

Upright differential operators

I was extraordinary happy when I saw that subscripts that are not variables should be upright Far from everyone has understood that. Another thing people, even here at Wikipedia, don't put uphright is the differential operator, and I dislike it from the bottom of my heart! ;-) Wouldn't it be a good idea to advocate such "d":s, in integrals and derivatives, too be put upright rather than in italics? - Jolson 17:40, 2 Oct 2004 (UTC)

In my experience, the "d" is upright in England but italicised in the United States. Being a United Stateser myself (my own personal conventions notwithstanding), I've seen quite a few examples of italics in the US and no exceptions. (More precisely, every time that I've ever noticed an upright "d" in published material, it turned out that the material was published in a foreign country.) Speaking more broadly, I'm against instituting unnecessary conventions on Wikipedia, and caution you (to avoid upsetting some people) against editing articles to fit your conventions. But by all means make your own "d"s upright when you write a new article (or rewrite an old one), if you wish. -- Toby Bartels 01:10, 4 Dec 2004 (UTC)

Pages for review

Hi guys. Could you review my page Marcinkiewitz theorem for correctness, fullness and especially readability? I tried to write it so that it will be readable (enjoyable?) by any graduate student or equivalent. Thanks Gadykozma 15:09, 8 Oct 2004 (UTC)

I'm pretty sure the name is usually Anglicized as Józef Marcinkiewicz. I've changed the links accordingly. Terry 06:01, 2 Nov 2004 (UTC)

Yes, sorry. Gadykozma 14:01, 2 Nov 2004 (UTC)

Here is another one I'd love input on, especially since I have no clue about the topic: Hearing the shape of a drum Gadykozma 14:24, 16 Oct 2004 (UTC)

OK, you want research pages here is one loop erased random walk. Tell me what you think. Gady 19:00, 7 Nov 2004 (UTC)

Another to review, if you please, for completeness and especially accuracy: Small set.—msh210 22 Nov 2004

And another: Modulo. —msh210 21:32, 7 Dec 2004 (UTC)

Wikipedia:Math 1.0

I found Wikipedia:Math 1.0 in a dusty corner. I think the goals and information needs to be merged with this WikiProject. Please take a look and salvage what you can. -- Netoholic @ 19:45, 2004 Oct 26 (UTC)

Well, it's kind of optimistic. It would be great to have the mathematics of the 1990s, and the twenty-noughties even, properly covered here. In many cases that would involve just writing articles with 'long words' in them: red links to concepts that we don't have. So, sometimes it looks like we should just expand coverage of 'core areas', with the long-term goals of getting to the frontier of research. Sometimes I add surveys of topics, to move things ahead; or add isolated (at present) theorems or conjectures. What really does need to happen is that the coverage as a whole stays balanced, even if it's a bit humiliating that the Atiyah-Singer index theorem is 40 years old, and we really still can't state it exactly, yet. Charles Matthews 19:57, 26 Oct 2004 (UTC)

Thue-Siegel-Roth theorem

Looks like the math formula need some work in this article - Thue-Siegel-Roth theorem, figured someone here could fix them. -- Netoholic @ 04:41, 2004 Nov 2 (UTC)

Yes, the second had an inequality reversed, thanks. Charles Matthews 07:51, 2 Nov 2004 (UTC)

Computability logic

As I have been editing a lot of articles in theoretical computer science lately, I noticed many references to computability logic on the pages. The ones I checked were inserted by User:Kntg. He is also the main editor of the computability logic article. My guess is the real name of the user is Giorgi Japaridze and he is hyping his own stuff [3]. I am unable to decide whether his ideas should be included in wikipedia or not, they seem to be relatively new. What do you think ? MathMartin 18:06, 14 Nov 2004 (UTC)

Since nobody responded, I looked into the matter though I do not know that much of either theoretical computer science or Wikipedia policies. As the article on computability logic explains, it is a new theory proposed by Japaridze in 2003 (MathSciNet lists only two papers on computability logic, both by Japaridze and published in 2003 and 2004; I've found no other references). User:Kntg has inserted a lot of references to Japaridze's work: they may be the same person or related (academically). I think there is no harm in having the computability logic article, though the status of the theory should probably be explained better. In my opinion, some links to the computability logic article are over the top (for instance, those at algorithm and computer science). Can somebody please give some further guidance to MathMartin? -- Jitse Niesen 13:22, 16 Nov 2004 (UTC)

I've had my eye on this for a while. The papers (or at least the one(s) in Annals of Mathematical Logic) are respectable. The links are not worth the prominence they are sometimes given; but I haven't done much about it except to tone down the coverage a little. At the moment it falls into the category of being a little bit annoying. We do have at least one active logician (User:Chalst) who could be consulted. Charles Matthews 13:38, 16 Nov 2004 (UTC)

My main objection are the links he inserted in many computer science articles not directly related to the computability logic article. I will remove them where necessary. I will leave the computability logic article as is, althought I do not think recent research material (2003, 2004) is appropiate for wikipedia inclusion. MathMartin 14:03, 16 Nov 2004 (UTC)

Japaridze and Computability Logic

I only just noticed this discussion. I had seen the disproportionately high profile the topic has taken, and wondered if maybe Japaridze was promoting his own material. A few points:

While I'm sure that whoever did these edits has some investment, careerwise and/or emotional, in the topic, there are reasons to doubt it is Japaridze, namely whoever it is hasn't done a terribly good job of summarising the topic; I would normally expect a researcher to do a better job than this;
I don't follow the detail of Japaridze's work myself, but a close colleague of mine does, and it is the real thing: solid research work that is well-motivated and perhaps has the potential to make a real impact;
The edits are gung-ho and lack perspective but they were not abusive and they have stopped. Take care when reintroducing appropriate perspective not to throw away perfectly good content: that cure would be worse than the disease. ---- Charles Stewart 21:55, 9 Dec 2004 (UTC)

PS. A point about the "no research" rule: the interpretation given at the authoritative Wikipedia:What Wikipedia is not says:

Primary research such as proposing theories and solutions, original ideas, defining terms, coining words, etc. If you have done primary research on a topic, publish your results in normal peer-reviewed journals. Wikipedia will report about your work once it becomes part of accepted human knowledge. But of course you don't have to get all of your information on entries from peer-reviewed journals. See Wikipedia:No original research.

which I understand as saying that once ideas have passed the test of peer review, they are fair game for summarisation on Wikipedia. So Japaridze's work passes that test. ---- Charles Stewart 22:01, 9 Dec 2004 (UTC)

Thanks for your input. I think the business has been handled adequately, so far; the edits have been 'POV', obviously, but the WP response has been 'professional', i.e. proportionate, patient, and not too reactive. Charles Matthews 08:32, 10 Dec 2004 (UTC)

Trace

I'm wondering if we have an article on trace as it pertains to my understanding of it in crypto. That is, if $\beta \in GF(2^m)$ then $\operatorname{Tr}(\beta ) = \sum_{i=0}^{m-1} \beta^{p^i}$ (forgive the crappy LaTeX, this isn't an article, just trying to get my point across ;)). I see trace (matrix) and field trace, but neither seem to be a good fit. If someone who understands these trace articles better can confirm that neither is what I'm speaking of, let me know and I can write up an article about the trace and its properties. Thanks. CryptoDerk 00:09, Nov 17, 2004 (UTC)

It's the special case of the field trace appropriate in a finite field of characteristic two (notation here: I think you mean that with p = 2, or GF(p^m). That's because any trace map is the sum of images of an element when you apply all elements of the Galois group to it; and here the Galois group is cyclic, generated by the p-th power map. Charles Matthews 08:45, 17 Nov 2004 (UTC)

Thanks. CryptoDerk 15:46, Nov 17, 2004 (UTC)

Zech?

Does anyone know who Zech's logarithms are named after? I tried various google searches and the only thing I can find is that there's some guy Boris Zech who published something in 2004 (although since the title is in German, I don't know what it's about), but MacTutor doesn't seem to have any info on anyone named Zech. Mainly, I'm just curious but it'd also be nice to have that info in the article. CryptoDerk 20:26, Nov 17, 2004 (UTC)

Category:Topological spaces and List of manifolds

It seems to me that Category:Topological spaces and List of manifolds largely duplicate one anoher. (More accurately: they would duplicate one another if they were full.) Seems like an unnecessary redundancy. Perhaps we can do as follows: Add Category:Manifolds as a subcategory of Category:Topological spaces; list manifolds only there (not in the parent category, per WP:CG), and get rid of List of manifolds. What say you all? —msh210 15:00, 26 Nov 2004 (UTC)

No. We have had a similar discussion. Lists are in general more useful and flexible than categories. I don't understand the argument, actually. Redundancy is not a criticism on a wiki. Charles Matthews 17:02, 26 Nov 2004 (UTC)

SKI combinator calculus

I just created the beginning of this article and would like to invite my fellow mathematicians to contribute and edit. I've just started to learn Wiki LaTeX, but I think I did a pretty good job with things. --L33tminion | (talk) 04:01, Dec 2, 2004 (UTC)

I'm sorry to break the news, but it doesn't seem that there's anything in SKI combinator calculus that wasn't already in the article on combinatory logic. Perhaps SKI combinator calculus (and SKI calculus) should redirect to combinatory logic, and anything in SKI combinator calculus not already in combinatory logic should be merged there. -- Dominus 18:03, 2 Dec 2004 (UTC)

Looking at the two articles, I'm not sure that they are redundant, even though they do cover some of the same information. If a merger is necessary, I don't know where to begin. However, I think that an article on the SKI system could exist independently from the article on combinatory logic in general. --L33tminion | (talk) 15:41, Dec 3, 2004 (UTC)

Spoof edits alert

User:Jim Slim vandal attack

User:Jim Slim, clearly mathematically literate, has been adding plausible nonsense to general topology and functional analysis page. Please will all look out for 'tweaks' of mathematical articles that are jargon-filled rubbish. There was a whole hoax page. This is an exploratory vandal attack, testing us. Charles Matthews 14:23, 16 Dec 2004 (UTC)

Since the user page claims that none of his edits are good faith, I suggest that we don't seek any good addition he has made amidst the rubbish, but rather have an admin block the account and do a blanket automatic revert. BACbKA 14:49, 16 Dec 2004 (UTC)

I blocked him right after Charles put the note on the page. CryptoDerk 15:27, Dec 16, 2004 (UTC)

There was another hoax page created recently, which I deleted. Can anyone verify that Cayley-Newbirth operation matrix is genuine? I now think it is suspect. Charles Matthews 22:00, 16 Dec 2004 (UTC)

I checked it on google (and also "Bayleigh equivalence") and only references I found were copied from wikipedia. I think it's a hoax. Samohyl Jan 00:43, 22 Dec 2004 (UTC)

It is now at VfD: Wikipedia:Votes for deletion/Cayley-Newbirth operation matrix. Please come and vote - there are good reasons. Charles Matthews 22:47, 22 Dec 2004 (UTC)

We now have an 'admission' of the hoax nature of the page. I am taking this forward at User talk:ExplorerCDT. Charles Matthews 12:55, 24 Dec 2004 (UTC)

It appears this isn't the first issue with this user, see Wikipedia:Requests_for_comment/ExplorerCDT. Terry 13:44, 24 Dec 2004 (UTC)

Current position re User:ExplorerCDT

See User:Charles Matthews/Hoax investigation for deleted user talk

User talk:ExplorerCDT is now being purged of what I write there, allegedly unread (fingers-in-ears and adolescent abuse). The current and unsatisfactory position with this user and hoax material is this:

claims has edited here only since September, and as an anon only as the presumed User:66.171.124.70;
claims no sockpuppets;
claims mathematics background not much more than some calculus;
claims has not edited mathematics pages;
claims not the author of the hoax CNOM page;
claims no knowledge of that page;
claims no associates or easy access to mathematically-educated persons;
claims no knowledge of other recent hoaxes here;
no explanation of behaviour at Vfd;
no explanation of allusion to 'clues' at Vfd.

Certainly no apology at all. Standing against this user are a number of things. User page has a number of loudmouth points, in particular against civility and 'hatred' of conventions on lower-case (a possible gripe?). In effect it admits user has tested the system with pages to see how quickly they are deleted.

The 66.171.124.70 edits include vandalism and cutting mentions at Vandalism in progress. Starts with edits to a secret society page, a recurring interest (which is one reason why thinking a 'conspiracy' to hoax is not really far-fetched, at least to me). Abuse in edit summaries, edit wars, tasteless edits, generally obnoxious behaviour. There is no real reason to doubt this is the same user (cf. continuity of the Rutgers University edits) given that the first half of the IP number has been admitted.

The whole pattern is suspect, to me. There are some scholarly edits. If you asked me 'is this a potential malicious and disinformative editor?' I would say yes. No smoking gun as far as hoax mathematics, though.

Oh yes, and claims inside knowledge of the Mafia.

Well, happy holidays everyone.

Charles Matthews 19:12, 24 Dec 2004 (UTC)

I don't need to answer to you, with your Torquemada-esque Inquisition, sneakily worded insinuations, and boldfaced accusations (without merit). I've given you the answers your required. No matter what I say, you will still think I'm responsible for the CNOM hoax. I didn't even know Wikipedia existed when it was created. Sure, this is going to be rude and hostile behavior but take it on its face value. Go fuck off you pompous windbag! —ExplorerCDT 20:34, 24 Dec 2004 (UTC)

It is being mooted that the ArbCom should be brought into this. Now, that really would be inquisitorial, and an adversarial process where just about anything you ever wrote here could be brought up. Think about it. Charles Matthews 20:56, 24 Dec 2004 (UTC)

I have, and everything points to you on a crusade, and being an ass about it. —ExplorerCDT 21:10, 24 Dec 2004 (UTC)

I think that disinformation added to WP by bad faith editors is a potential problem to which there is no single, simple solution. I think hoaxes are no joke at all. What do you think, sir? Charles Matthews 21:13, 24 Dec 2004 (UTC)

I would agree, except I take your question as a loaded allegation that I'm responsible for the hoax (which I am not). —ExplorerCDT 21:46, 24 Dec 2004 (UTC)

Hard to explain your behaviour at VfD, then. You don't have a particular interest in mathematics here. You don't have that much background in it. You decide to make circumstantial claims that the page is genuine, citing a classic text which just happens to be one of the longer works you could have mentioned. Given your remarkably arrogant approach generally, and your specific evasiveness about the 'clues' ... Ah yes - reminds me to ask, what were the 'clues'? The thing does fit together like a crossword; while

matrix = womb

is general knowledge, the

John von Neumann -> John Newman -> James Newbirth

and

Bayleigh -> Cayley, Caesar cipher/caesarian

things (assuming I'm not imagining it all) requires a certain kind of puzzle-oriented thinking.

Charles Matthews 22:13, 24 Dec 2004 (UTC)

The user page itself didn't sound that aggressive to me, but ExplorerCDT certainly seemed like he tacitly admitted he knew about the hoax. His behavior since then has been very odd. -- Walt Pohl 22:24, 24 Dec 2004 (UTC)
I agree with User:Waltpohl. I left a comment at ExplorerCDT's talk page, which was quickly deleted [4]. Dbenbenn 22:27, 24 Dec 2004 (UTC)
Yes, ExplorerCDT's actions seem very odd. I, like many other editors I suspect, would like some explanation of them from him. Paul August ☎ 22:40, Dec 24, 2004 (UTC)
At this point in time, I don't trust ExplorerCDT enough for an explanation by him to be sufficient. I feel that a third-party investigation should be undertaken. --Carnildo 08:39, 25 Dec 2004 (UTC)
He has claimed that his initial support of the hoax was based on a misreading of Ablowitz & Stegun, and has almost promised to back this up with a page reference, see User_talk:Paul August and User_talk:ExplorerCDT, although he claims currently that his copy of A&S is packed away due to a move. If that page reference is provided and checks out then I think that would be a satisfactory explanation of events and no further action or investigation would be necessary. Benefit of the doubt, etc. Terry 23:58, 25 Dec 2004 (UTC)
- In my opinion, he's obviously lying. Here's why I think so: Anyone with even a moderate amount of mathematic sophistication would have immediately recognized that article as being pseudomathematical nonsense, and a number of the other participants in the VfD discussion did point this out. ExplorerCDT not only claims to own a copy of A&S, but also implies that he spends enough time actually reading it that he can not only recognize that the topic is covered there, but also that he can recolect that it is referred to in "several mentions and footnotes", without even having to check. But someone who owns and browses A&S with that degree of seriousness has far more than enough mathematical maturity to immediately recognize that the CNOM article was nonsense, and that even if it weren't nonsense, it is not the sort of thing that is covered in A&S. What we have here is someone who has heard of A&S but who is not sufficiently familiar with its contents to realize that his claim was an obvious lie. -- Dominus 01:32, 26 Dec 2004 (UTC)
  - In my opinion, Dominus, you're a jackass who hasn't seen straight for years...that's the problem with your head so far up your ass. —ExplorerCDT 02:09, 26 Dec 2004 (UTC)
    - Your comment would be more convincing if you actually refuted his argument. I suggest you try this before resorting to insults. Isomorphic 07:08, 26 Dec 2004 (UTC)
      - Sorry, but there's no sense refuting the deluded close-minded rantings of someone (Dominus) who should have been institutionalized long ago. Only the insane engage in exercises of futility, and I'm not close to being driven insane (yet). Just rage. —ExplorerCDT 07:11, 26 Dec 2004 (UTC)

Further point, though. 66.171.124.70 comes up as Herndon VA when I do a whois search. Given the data below, do you really expect us to regard that as a coincidence? Charles Matthews 11:28, 27 Dec 2004 (UTC)

Yeah, I wonder if in your investigative work, Detective Matthews, you came to realize that IP address is one of a block of IP addresses owned by Verizon. The Virginia legislature gave benefits an tax write-offs to computer companies, and most large internet providers have located their headquarters there (including AOL, fyi). For someone who appears to be somewhat intelligent, you really are clueless. I live in NYC and haven't been to Virginia in 4 years. —ExplorerCDT 18:09, 27 Dec 2004 (UTC)

Yes, I realized that my limited technical knowledge might be exposed. This was, however, one way in which your lack of complicity might have been supported. I am still interested in the Virginia connection. Charles Matthews 17:37, 28 Dec 2004 (UTC)

Traceroute indicates a location for 66.171.124.70 near Newark, which would be consistent with the interest in Rutgers. Geobytes confirms this with a Jersey City result (right near NYC). Michael Ward 17:57, 28 Dec 2004 (UTC)

I've opened an RfC on this: Wikipedia:Requests for comment/ExplorerCDT 2 --Carnildo 23:01, 27 Dec 2004 (UTC)

User:199.248.201.253

This IP number clearly had a close interest in the CNOM page, wikifying it and linking from Arthur Cayley. Later this IP number created the hoax Bryleigh's Theorem page. Other vandal edits (I'm going to ban anyway on the strength of a long track record), including impersonations. Geography: Maryland/North Carolina? I'll do a whois on some of these IPs. Charles Matthews 10:29, 27 Dec 2004 (UTC)

That's Frederick MD for 199.248.201.253. 65.177.73.18, original creator, comes up as Reston VA. Charles Matthews 10:41, 27 Dec 2004 (UTC)

Text of the Bryleigh's Theorem page:

In differential equations, Bryleigh's Theorem is associated with the existence of and validity of solutions to these equations. In general, Bryleigh's Theorem states that if we have a solution to a differential equation, and this solution satisfies the differential equation, then the solution is a "valid and true" solution, no matter how we may have obtained this solution. Among other important guarantees, Bryleigh's Theorem guarantees the validity of the guess-and-check method of solving differential equations, in which we try to guess elementary antiderivative solutions. Bryleigh's Theorem is first noted in a 1785 work of English mathematician Jayne Bryleigh (1720-1801). It is an important generalization of Kimber's Third Theorem and Bonnie's Slope Field Lemma. Bryleigh's Theorem is often also applicable in other realms of mathematics, such as linear algebra and group theory.

Charles Matthews 11:10, 27 Dec 2004 (UTC)

Also a possible link to University of North Carolina at Chapel Hill. Charles Matthews 11:16, 27 Dec 2004 (UTC)

Qualculus

"Qualculus is a branch of mathematics involving the modeling of changes in state...." Google turns up only 5 hits, none to academic sites. search. This smacks of hoax to me. See also Roidiphidol by same anon author, with no Google hits. If none of the math experts around here have heard of Qualculus, I will vfd. Michael Ward 18:36, 27 Dec 2004 (UTC)

This has actually been used to design computer systems but is not well known. Some companies where it has been used are Lucent, IBM and OCLC.

The update to this shows some significant material which demonostrates factual computer knowledge. It also has examples of how it would be used to design a database. This is not out of line with computation.

The past projects this has been used on include IBM's Corepoint SA, Lucent Technologies 7RE PTS switching system, and OCLC RMS intergration project.

It has been mostly used by computer consultants. There have been some white papers on this but not widely distributed. Since it was originally developed by University of Wisconsin students, it is regarded as public domain.

—The preceding unsigned comment was added by 24.145.133.16 (talk • contribs) 19:14, December 27, 2004 (UTC)

Note, above comment is by 24.145.133.16, one of the two anon ip's to Qualculus. Both ip's resolve to Columbus OH, suggesting the possibility that this anon is actually the orginal author of Qualculus. Michael Ward 19:21, 27 Dec 2004 (UTC)

Both articles look bogus to me. A couple of "white papers", do not, a branch of mathematics make. Either a hoax or "original research". Unless better references are provided both should be deleted. Paul August ☎ 19:38, Dec 27, 2004 (UTC)

Looks very bogus. I'll ask a friend who's at Wharton later today, since this isn't my area, but "baka" (the Baka matrix) means stupid in Japanese, I believe. CryptoDerk 19:45, Dec 27, 2004 (UTC)

In this case, Baka is a person: [5] 24.145.133.16 —The preceding unsigned comment was added by 24.145.133.16 (talk • contribs) 06:42, December 28, 2004 (UTC)

I agree that it is very suspect. Note that Qualculus says that the project was listed in Apple Computer's "Wheels for the Mind" in the winter 1986 edition, while [6] (follow the link, then click on "Wheels for the Mind" in the sidebar) suggests that the first issue of this magazine was in Nov 1998. However, I would recommend waiting a few days and making absolutely sure that the article is bogus before listing it. Note that we also had to argue a bit before the article on Cayley-Newbirth matrix was accepted as a hoax.

Wheels for the Mind came out about the time the Macintosh came out, which was around 1984. 24.145.133.16 —The preceding unsigned comment was added by 24.145.133.16 (talk • contribs) 06:42, December 28, 2004 (UTC)

To the anonymous contributor 24.145.133.16 (cross-posted to User talk:24.145.133.16): This should be rather easy to resolve, since you are apparently familiar with Qualculus. Could you please give some verifiable information, like precise references to the white papers or the participants of the Wisconsin project and any reports they wrote? Thank you.

Jitse Niesen 20:26, 27 Dec 2004 (UTC)

24.145.133.16's answered as follows:

"A draft of the white paper can be be found at: http://www.angelfire.com/movies/heme/Math/Nadair.htm

David Baka was the lead of the project.

The discussion on "Wheels for the Mind" is incorrect, It was started well before 1986. I have hard copies of it. Of course that was before the internet."

I verified that the magazine was indeed around in 1986. However, I'm still looking for more verifiable information, like answers to any of these questions. Do you know the title and/or author of the article in "Wheels for the Mind" in which the Wisconsin project was described, or perhaps the page number? Where did you get the magazine (separate editions are published in different countries). Is this design methology described in other professional or scholarly journals? In which department and context did the Wisconsin project take place? What is the current occupation of David Baka, and what was his position in Wisconsin? Thanks again, and sorry about giving you such a hard time. -- Jitse Niesen 15:27, 28 Dec 2004 (UTC)

OK, I asked my friend who is getting a Ph.D. at Wharton. He states "This is bullshit. I've never heard of any of this and... my area IS matching supply with demand". CryptoDerk 20:49, Dec 27, 2004 (UTC)

This has got to be a hoax. It looks like they took SQL as the model, and then added a bunch of vague verbiage. -- Walt Pohl 05:52, 28 Dec 2004 (UTC)

SQL is a common database language so any subject about databases would probably fit SQL. The purpose of the example is to use something that is familar and build on it. I have used this method to design databases. I have also used it to design Java programs.

I have found it much more useful then flow charts or UML because it lends easily to asking questions, where as other methods tend to pigion hole you into a particular design.

If no one here uses it, that's fine with me. I don't need a PHD from Wharton to figure out how to design something.24.145.133.16

—The preceding unsigned comment was added by 24.145.133.16 (talk • contribs) 06:42, December 28, 2004 (UTC)

White paper

The "white paper" written by David Baka and posted at [7] seems to be somebody's (bad) attempt to model a query access and processing language. Whatever it is, that white paper is very badly written. David Baka appears to be a real person, however. According to his summary at Amazon [8]

Dave Baka has written code for almost every major telephone company in the US. He has been a consultant to several Fortune 500 corporations including IBM and Lucent Technologies.

However, whatever Qualculus is, if it is anything at all, it is not "a branch of mathematics involving the modeling of changes in state. It is related to computation and discrete mathematics". The way it is described in the article, it is at best a graphical database query access language for commercial use. Also the following post at free republic makes the whole thing look very suspicious.CSTAR 18:05, 28 Dec 2004 (UTC)

A search for "Baka matrix" finds only the Angelfire pages. A search for "Baka matrices" finds nothing. This is either an idiosyncratic concept with no references elsewhere, or a hoax. And this [9] suggest pseudomathematics at best. -- Anon. —The preceding unsigned comment was added by 80.168.225.12 (talk • contribs) 18:09, December 28, 2004 (UTC)

Yep, basically agree. Although I was more inclined to regard it as an idiosyncratic concept, the URL path is certainly strange...movies? www.angelfire.com/movies/heme/Math/Qualculus.htm. There is no reason to be sure it is even Baka's "white paper" at all. CSTAR 18:54, 28 Dec 2004 (UTC)

BTW, baka in Japanese means crazy. Charles Matthews 13:47, 29 Dec 2004 (UTC)

"I am taking this to vfd"

I am taking this to vfd. None of the math-savvy editors here have heard of it. Possibly some computational experts over in vfd will recognize it, but I doubt it. No verifiable info given. No references given. No google evidence found. Article is not intelligible. Sole anon defender is likely orginal author (based on ip location). Original research at best. Probable hoax. Michael Ward 18:51, 28 Dec 2004 (UTC)

Using images from the St.Andrews Uni. they believe are public domain?

There are a lot of mathematicians' biographies at the Uni. of St. Andrews, featuring photos that they believe are in the public domain, yet haven't kept appropriate records about every image history. Is it OK to upload such images to Wikipedia? How should I tag them? BACbKA 21:25, 7 Dec 2004 (UTC)

I can't provide a reference page on this, although maybe someone else can, but I recall a user contacting them about using materials from their website and they said no. That being said, I'm not sure if that applies to materials that even they may not have permission for, or if they were referring to text only. I believe that the user that contacted them did post their reply on their user page or a subpage of their user page. CryptoDerk 13:20, Dec 9, 2004 (UTC)

Look at User:Wile E. Heresiarch, bottom of the page, for this. Charles Matthews

Thanks for your reply. I would presume this is about the biographies proper though, and not the images they themselves describe as public domain to the best of their knowledge. Have you followed through the above link on copyright and read what they say themselves about their images? BACbKA 14:20, 9 Dec 2004 (UTC)

My opinion, FWIW, it that a fairuse tag would be appriariate, since its wording mentions the public domain; and I would take the trouble to point back at (and copy the text of) the St. Andrews webpage in the Image page. In the event that an issue is ever raised, at least we will have an audit trail which supports our contention of fairuse. Just my opinion, though. --Tagishsimon (talk)

Why fairuse and not pd, if the wording mentions the public domain? I've tagged commons:Image:Aleksandrov_Aleksandr_1950s.jpeg as PD meanwhile and did like you suggested wrt pointing back and copying the text. Everybody is welcome to re-tag/re-annotate there if I did smth wrong. Thanks a lot to everyone for the guideance! BACbKA 22:28, 10 Dec 2004 (UTC)

Considering that they seem conscious of image copyright issues, I'd wager that these images are quite likely to all be public domain. We have enough images falsely marked public domain that if we did use them in print, some careful filtering would be necessary in any case. Independent verification for each wouldn't hurt, though. Deco 20:33, 10 Dec 2004 (UTC)

Thanks. OK, I've asked around various people about the only specific image I have uploaded from there so far for the Aleksandr Danilovich Aleksandrov article, and they also think the image is in the public domain since they believe they've seen it in the Soviet media back in the 50s. Independently, I am working to get a solid specific permission to use a much better image from [1] depicting A.D. in 1952, so it's temporary in any case. BACbKA 22:21, 10 Dec 2004 (UTC)

I came across the University of St Andrews site independently (googling Paul Halmos), then remembered this discussion. I agree that what they say about PD is probably fine. While at st-and.ac.uk, I looked up Eugene Dynkin, an old advisor of mine. The picture they have of him is just a lower-quality version of the picture he has on his personal web site. Just another data point to keep in mind. Dbenbenn 02:15, 24 Dec 2004 (UTC)

Jan 2005 – Mar 2005

This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

Graph (mathematics) vs Graph theory

I am currently working on graph (mathematics) and graph theory. It is not clear to me what sort of distinction to draw between those two articles. User:Oleg Alexandrov has similar problems on matrix (mathematics) and matrix theory. Other articles having the same problem are

My opinion is the basic article (e.g graph) should contain

brief motivation
definitions
examples
generalizations of definition

whereas the theory article should contain

history
detailed motivation
relation to other areas
important problems

Any comments ? MathMartin 12:35, 7 Jan 2005 (UTC)

I don't think there should be two pages at all. One of them should be a redirect to the other and all the material should be on the same page unless some subtopic (maybe "History of X theory") grows large enough to be its own article. --Zero 13:18, 7 Jan 2005 (UTC)

I think for all of these topics, there should be the two pages mentioned (and more, each should eventually have a "history of" article also, giving a detailed and comprehensive history), and I think that MathMartin's description of how they should differ seems reasonable to me. See also Set theory, Set, Naive set theory and Axiomatic set theory. Paul August ☎ 14:19, Jan 7, 2005 (UTC)

I think Zero has a point. Ideally, one article should be enough. However, the longer articles get, the harder is to keep a "global picture" of the article. This has many consequences, among them being that mistakes are easier to slip through, consitency is harder to keep, etc. This is especially true on such an anarchic place like Wikipedia, where ultimately nobody is in charge of anything. So I would suggest splitting articles, which clear motivation, like MathMartin suggests. To to a good job at that, is not so easy though. Oleg Alexandrov 19:18, 7 Jan 2005 (UTC)

Here is my current (changed) opinion on this topic. In general there should be only one article called X theory. If this article grows too large certain parts of the article should be put into separate articles (like history of X theory) so that we get a hierarchical structure of articles. The subarticles (like history of X theory) should have a name making it obvious what sort of content belongs to the article. The subarticles should have a link to the main article at the top.

I think this hierarchy of articles is preferable to my earlier suggestion of parallel articles because it provides a

clearer and more intuitive structure for the reader
allows for better editing as the article can grow gradually from one article to a tree of articles without the need for restructering several articles at once

Several articles like french language, france or category theory already use this structure. I will merge graph (mathematics) into graph theory to provide a concrete example. MathMartin 15:15, 9 Jan 2005 (UTC)

Please don't. There is a specific need for short articles that give a definition and some examples, versus longer articles that talk about the theory in general. -- Walt Pohl 08:19, 10 Jan 2005 (UTC)

I already merged them. Can you point to any discussion on this subject or give a more detailed explaination ? MathMartin 10:12, 10 Jan 2005 (UTC)

MathMartin: As I said above, I think it would be better if these articles were kept separate. I agree with Walt Pohl, that there is a need for a short article that, for example, defines "graph",and gives some examples, so that a user doesn't have to wade through a longer article for that information. I think your original idea was correct, and so did Oleg Alexandrov, who gave some excellent reasons for supporting your idea. I don't understand why you changed your mind? I think you should consider changing it again ;-) Paul August ☎ 22:10, Jan 10, 2005 (UTC)

I also agree. It's nice to be able to say "In graph theory, the 'Petersen graph is a graph that ...". The first link gives the broad theory, the second gives a particular definition. Dbenbenn 22:26, 10 Jan 2005 (UTC)

I've always assumed that was the rationale for the division between X and X theory, though I'm not sure I've ever seen it spelled out. The rationale, as I have perceived it, is: most of the time, an article that mentions X just needs the definition, and not the whole theory. For example, the integers form a ring; it's sufficient to be able to jump to the definition, rather than a topic on ring theory, which will talk about noncommutative rings, ideals, etc. It makes using convenient math terminology somewhat more intimidating to use.

It could be that the way you're suggesting really is better, but since it's something of a de facto standard on math pages, I think it's something we should hash out here. -- Walt Pohl 23:10, 10 Jan 2005 (UTC)

I think MathMartin's action was a little premature given the active discussion on the issue, but on the other hand I think the structure is better now than it was before. I have no problem with an article containing mostly definitions, but the problem with the 2-part structure is that the theory page either has to repeat the definitions or to leave them out. The first is clearly undesirable. The second is also undesirable since someone reading the theory page should not need to flick back and forth to another page in order to understand it. I think the structure MathMartin has established is actually pretty good; of course there is always room for tweaking. --Zero 00:22, 11 Jan 2005 (UTC)

There is no harm in repeating the definition — as long as they are the same! ;-) Paul August ☎ 02:51, Jan 11, 2005 (UTC)

Even if they start off the same, sooner or later they will diverge. It always happens that way. --Zero 06:43, 11 Jan 2005 (UTC)

Well they don't have to be identically worded, as long as they are mathematically equivalent. Different ways of presenting the same definition can be a good thing. Of course, a definition may be edited, so as to become incorrect. And, of course, this can happen, whether there is one version of the definition or not. However, such an error is less likely to occur, and is easier to fix, if there is another "repeated" definition to which to refer;-) Paul August ☎ 15:21, Jan 11, 2005 (UTC)

Please, keep them separate. From a purely mathematical point of view, graph theory is a different entity than graph, it is like set of all theorems about graphs. Also, graph theory evolved (among other things) from study of minimal weighted spanning trees - where the spanning tree was defined as a rigid body of rods connecting set of points in Euclidean space, and the weight was given by the length of rods (that's definition Jarnik and Boruvka used, I think). See Boruvka's algorithm,Prim's algorithm (now I am looking at it, and don't quite understand the difference among these algorithms - it seems that they only differ in clever use of data structures, but the greedy method is always used; they should be merged in one article probably). Anyway, such historical connections are inapropriate in article about graph. Samohyl Jan 16:48, 11 Jan 2005 (UTC)

I will try to separate the pages again while trying to keep the hierarchical structure. My main point is, if we have separate pages on topics which are very similar, the ordering/relationship between the pages should be sufficiently clear even to a novice reader/editor. MathMartin 17:01, 11 Jan 2005 (UTC)

There is no need, necessarily, to remove any current content from Graph theory. As long as what is there now is relevant to it, which presumably it is. All that needs to be done, really, is recreate the Graph (mathematics) article, more or less as it was before the merge. There can be considerable content overlap between the "theory" article and the "graph" article. In my view, the main difference between them should be functional. The "graph" article should be narrow and concise, just explaining what a graph is. The "graph theory" article should be broad and comprehensive, saying what a "graph" is, in detail, as well as what "graph theory" is, in as complete a way as possible.

The problem of article "structure" is an important one. Martin is right to be considering it. I am glad he has brought it up here for discussion, and I would like to thank him for doing so. (Martin: Thanks ;-) As he says, having separate but related articles, for which the relationships are unclear is problematic. For example there is a real danger (and this may have already happened, to some extent) of our "graph" article becoming, more and more, like an article about "graph theory", without its editors being aware of, or taking sufficient notice of, the fact that there was already an article on "graph theory". We need to be vigilant against this. Adding some italicized disambiguation text at the beginning of each article explaining what the article is about and the existence of the other article, might help, in this regard.

Figuring out the best way to organize our mathematical content is a difficult problem with no easy solution. It will behoove us to give lots of serious thought to this and devote more time discussing it. I will say though, that I don't think that the ideal structure for these articles in Wikipedia is a "hierarchical" top-down one. Wikipedia just isn't like that. Nor in reality are most of the topics it covers. Even in mathematics where one might in principle organize all of the subject in one great hierarchy — and mighty and heroic attempts have been made to do just that — this is not, in my opinion, the best way, really, to think about mathematics, nor to learn it, nor to present it in an encyclopedia. The "true" structure of mathematics, in my view, while involving many hierarchies, is much more complicated. And, as it happens, Wikipedia is well suited to reflect this ;-)

Paul August ☎ 19:10, Jan 11, 2005 (UTC)

I have separated the pages and fixed the links. I did not duplicate the definitions because I think duplicating basic definitions is confusing for the reader. I think graph theory is understandable even without a definition of what a graph really is, because of the informal discussion in the introduction. MathMartin 18:39, 11 Jan 2005 (UTC)

I'm new here, so I can give an outsider's view on the split structure -- it's terrible. Not least because graph leads to a disambiguation page which confusing in itself -- until you finally realise you want graph (mathematics)... and then that all the information is under graph theory. A hierarchical structure under graph theory would lead to much less confusion. It does not necessarily mean graph theory has to grow out of hand as it can lead to more subtopics. Also on subtopics, I'd like to start a discussion on better linking to graph theory applications (as I said, I'm new, I'll take a look round first). Particularly I notice that network analysis and social networks could be better brought together. --stochata 20:33, 30 Jan 2005 (UTC)

I just flagged all three articles (Graph theory, Graph (mathematics), Glossary of graph theory) for a merge, ignorant of this discussion. I do agree that more than one page is a Good Idea, but I don't think the way the material is now sorted out is any good at all. I'm a fairly smart guy, with plenty of background. (Not to put on airs, but my mother was a prominent graph theorist and I grew up with the material the way other kids grew up with Curious George.) And still, when I read the "introductory" material at Graph (mathematics), I about drowned -- I am a little out of practice.

I just finished reworking and expanding Seven Bridges of Königsberg; this was one of my bedtime stories and I know it by heart, but I wanted to be sure to use all the correct terms. I ended up researching the jargon on the net external to WP and building my own glossary, which I slipped into Graph theory -- the only place I expected to see any general article on the subject. I'm not sorry I did, either; I sure didn't duplicate the advanced article at Glossary of graph theory, which reads more like a syllabus or perhaps a sheaf of classnotes.

I am going to go way out on a limb here and say I may be the most qualified individual to work over this stuff. Most folks know nothing at all about the subject and could care less. Experts know the material so well that they have difficulty explaining it to the unwashed horde. This is not the place for a textbook. Yes, there's no harm in presenting some advanced material (what experts consider to be the absolute minimum basics) for the few who are willing to work through it. But the bulk of people who visit just need to get a quick handle on the topic. I am a long way from being an expert on graph theory, but I believe I at least know enough to know when I don't know what I'm doing, and I won't monkey with anything like that without discussing it. I would like an expert to work with me on this, to check my work as I go along, to make suggestions.

If you want to see how I go about things, then besides looking at the seven bridges, you can check out my one-day glossary at Graph theory#Glossary. I think that is the kind of introductory material that needs to be most accessible to the casual reader. I shouldn't throw out the advanced stuff, but it should be clearly so labeled and better organized.

I see that this area has already been the subject of one hasty restructuring. I plan to replicate the existing material on a few dummy pages and edit them there. When this group reaches some sort of concensus on the dummies, we can change the "real" pages to follow.

Again, if it's not clear, I'm here recruiting an expert buddy for this effort. — Xiong (talk) 02:41, 2005 Mar 21 (UTC)

I have also been struggling with these unstructuredly interrelated pages. I have to say that I think what happened to the set theories is extremely horrible in ways of structure and duplication and ease of finding what you're looking for. Also in this way it is extremely hard to add information, since it is quite unclear what the best place for it is. Thus I would also ague for a hierarchic approach. The fact that mathematics may not be hierarchical itself doesn't present a problem, because of all the wikilinks. Graph theory may be an ideal area to work on, since there are so many excellent examples (wikipedia itself!) and could thus have a great motivational sections. As an aside I really dislike the glossaries. Perhaps we should incorporate them into the main storyline. And while we're at it add some lemma's, which are the reason d'etre for all those defs after all. -MarSch 13:37, 7 Apr 2005 (UTC)

joy of tex

I am trying to put a few equations in Hull-White model, but, at least on my browser the equations seem to come out in different sizes. Any tips on how to make the page look a little neater? Thanks. Pcb21| Pete 23:03, 13 Jan 2005 (UTC)

The size problem is because some of the equations are images generated by Wikipedia, which doesn't know the browser's font size. You could fix the problem by forcing all the displayed equations to be images, but I think that solution would be worse than the problem. Dbenbenn 23:33, 13 Jan 2005 (UTC)

Not necessarily - at least the page looks consistent. I've done so. Try to also avoid inline <math> (use HTML), since that usually comes out as a PNG inline and doesn't look very nice. Dysprosia 23:51, 13 Jan 2005 (UTC)

Bug in new version

Has anyone noticed that putting math tags inside a link (like this: [[Lp space|<math>L^p</math> space]]) no longer works? (See Sobolev space for an example). When did that happen? Should we file a bug report? Where do you file bug reports so that they are actually noticed? Uffish 02:56, 14 Jan 2005 (UTC)

Bugzilla

A little note on using purple dotted boxes

Don't. JRM 19:02, 2005 Jan 16 (UTC)

Or less facetiously: at least use "class='theorem'" or similar in addition to the style comment. This will allow updated style sheets to render theorems in whatever fashion the user wants, and to override any style you put in.

Wikipedia:WikiProject Mathematics has this article lost focus?

Greetings from a fellow mathematician. I am happy there are so many of us hanging around on Wikipedia. And I like the Wikipedia:WikiProject Mathematics thing. However, it seems to me there is just too much stuff in there, which could be better organized.

For instance, the second half of it could be condensed in a usage and style manual for writing Wikipedia articles on Mathematics, and put on a separate page. It could also be merged with Wikipedia:Styles of Mathematics Articles which seems to have never got off the ground.

The list of participants is getting large. Maybe it could go in a separate article too.

Also, some of the stuff in the article could be safely moved to the talk page, after incorporating all the insights written there in the usage and style manual above.

These are just some thoughts. It just looks to me this page lost some focus. What do you think?

Oleg Alexandrov 05:15, 18 Jan 2005 (UTC)

Yes, we could use some subpages now. Charles Matthews 13:58, 18 Jan 2005 (UTC)

I wasn't ever aware of it having any focus. If the question is whether it lacks focus, I will agree. But it has never been clear to me what this page is for. -- Dominus 14:21, 18 Jan 2005 (UTC)

I agree with Dominus that this page never really had focus. We've just used it as a place to thrash out issues on math pages. -- Walt Pohl 20:18, 18 Jan 2005 (UTC)

I agree with all of the above. Oleg: If you want to try to improve the focus and organization of the page in some of the ways (or others) you mention, I think that would be fine with me. You could just go ahead and give it a go ;-) ( See: Wikipedia:Be bold). But be prepared for possible objections to any changes you make ;-) Or you could try to discuss changes here first, especially if they are significant. Paul August ☎ 20:59, Jan 18, 2005 (UTC)

To be specific, I want to make some of this stuff into a true usage guide for math articles, that is a Wikipedia: Manual of style for math articles. How's that? Oleg Alexandrov 21:31, 18 Jan 2005 (UTC)

And I do mean on a separate page.... Oleg Alexandrov 21:42, 18 Jan 2005 (UTC)

Wikipedia:How to write a Wikipedia article on Mathematics

Well, having heard several why`s, one be bold, and no no`s, I forked out an article with the title above. Such an article is obviously necessary, and while what is here at WikiProject Mathematics has good stuff, it looks too much like a talk page. This new article still needs lots of work. For now I did not do much, as I don't want to wake up tomorrow morning seeing in my watchlist things like "reverted", "redirected", or even "submitted for speedy deletion". :)

If nobody objects (if you do, say it now :), then in several days I will continue polishing the new thing. Of course, if you contribute things to it, or if you simply add it to your watchlist, it will help.

Oleg Alexandrov 02:55, 20 Jan 2005 (UTC)

Thanks Oleg. I have reorganised and updated the project page; now there is much common material, and you may want to cut out from the project page most of the issues covered in your 'manual'. Charles Matthews 10:19, 20 Jan 2005 (UTC)

\pi image in Template:Math-stub

There is some debate over the use of a \pi image in Template:Math-stub; there's small edit war going on. Please see Template talk:Math-stub#Pi_image if you care to voice an opinion. (Please do not discuss this here; discuss it there; thanks.) —msh210 04:47, 27 Jan 2005 (UTC)

PlanetMath

I've been talking with the guy that runs planetmath.org (we go back 6 years). I'm in the preliminary stages of setting up a project to move over the content from PM to WP. Uncreated articles can pretty much be copied directly over, but others can be merged in or if the WP article is better then nothing needs to be done. PM's under the GFDL. The major difference between WP and PM is that PM allows users to own articles. Anyway, I'm wondering what you all think of this, and whether it could be a subproject of this project or if it should go somewhere else. I haven't been able to find precedent on this sort of thing. If anyone wants more details/has questions, please let me know! CryptoDerk 05:06, Jan 27, 2005 (UTC)

Hi everybody, I run PlanetMath. I'm here to help out with this process as best I can. I also would like to go the other direction, porting some Wikipedia content to PM, but that is of course mostly my problem. I just need to figure out how to best get the math subset of articles from here. Though, I do have the same history preservation problem you've been discussing for the PM->WP port, so I am especially interested in that discussion. Please know that you have me as a resource to provide advice and possibly system enhancements that would make the porting job easier. --Aaron Krowne 05:40, 28 Jan 2005 (UTC)

That is a great idea. Just yesterday I copied the very nice Potential theory article from there, as here there was nothing. Their articles are more formal than what we have in here. So when copied over those articles (a) need some more introduction and motivation, (b) some sentences need to formulated to use less symbols and some formulas HTML-ized (e.g., make $x\in\mathbb{C}$ into x in C) (c) Links to other Wikipedia subjects need to be made, and this can be time-consuming. But doing all these is well-worth it.

Those people use an idea which I find extremely nice. Each article has an official maintainer who actually has a big picture of the article, and screens all the incoming changes.

Oleg Alexandrov | talk 05:37, 27 Jan 2005 (UTC)

Yes, formality is one reason why he doesn't just want to merge the two together -- he intends to keep running PM primarily for researchers and research-related interests. So... should an organizational page for this be a subpage of this WikiProject in mathematics, or should it go somewhere else? CryptoDerk 05:48, Jan 27, 2005 (UTC)

While that is the way the site has developed, we would actually like more introductory and, shall we say, more "pedagogically complete" articles. I think in terms of coverage it is probably more natural for PM to subsume Wikipedia's math section. However this is all academic... for now we should each just focus on how to copy over whatever portions of the other's content we want. --Aaron Krowne 05:40, 28 Jan 2005 (UTC)

There is of course room on Wikipedia for such a page. The big question is, what should be there and what is a good way of going about it. Oleg Alexandrov | talk 02:35, 28 Jan 2005 (UTC)

I can easily generate lists of pages of articles on PM as well as relevant redirects (PM entries a list of synonymous names at the end of the articles). The most important thing is coming up with a protocol for converting them (differences in style, including LaTeX, etc.) -- I'll come up with a draft page in my user space and post a link here within the next day or so. I think the most important decision that needs to be made is how to refer back to PM. It's my understanding that we need to provide a link to the history on PM, but do we do it like the EB 1911 notice "This article based in part on information from Encylopedia Britannica 1911" or do we put it in an "External link" section? CryptoDerk 03:12, Jan 28, 2005 (UTC)

I don't know that wholesale copying of PM articles to WP is appropriate, given the significant differences in purpose, organisation, presentation and form of PM -- but then I'm not sure that this is what you are proposing. The problem lies not only in identifying articles that don't yet exist on WP, but also in making sure that the topic isn't covered elsewhere (as is very common on WP). In a lot of cases, inclusion of a theorem or concept in a wider article is preferable in the context of WP, while it might reasonably be expected to have it's own entry on PM.

On other notes...

References back to PM might best be done (when content has been copied) using a new template for that purpose, if this becomes a common thing. That would make is trivial to append such a notice to the end of the relevant articles. Text to link back to the appropriate canonical name of the PM article can be included as an input into the template (IIRC).
A subproject of this one would probably be appropriate, I think. An excellent start (and this would go some way to addressing my reservations above) would be to compile a list of PM articles that don't appear to have WP equivalents, so that people can go there, take up the cause of a particular topic and work out what needs to be done with it. That would be a great place to track the status of such articles, too, as they will often need significant editing. This may be exactly what you are imaginging, in which case I'm all for it.

All in all: great idea, good luck with it, and I look forward to hearing more! Oh, and my kingdom for PM's TeX to HTML system, but I guess it wouldn't quite work on WP.

Ben Cairns 04:12, 28 Jan 2005 (UTC)

I agree with you that this shouldn't be a wholesale copying over of articles. In the draft page I'll be sure to set up some guidelines (that will undoubtedly be changed), but I'd say the majority of the encylopedia entries are probably useful. Some will need to be combined in some cases (they frequently have separate articles for proofs, for example).

A template is indeed what I had in mind, and yes it's possible to include a variable to link back to the appropriate PM article, even if it's named differently over here.

I imagine when all this is set up with just a raw listing of articles, some people can work on creating articles over here while others can work on categorization, perhaps with the following categories:

Article already exists on WP and PM content is already similar or less than what WP has, so no need to copy.
Article already exists on WP but PM content is different or better (stubs).
Article doesn't exist and should be converted.
Article has already been converted.
Unknown status, or unchecked (no category).

Once again, this is still preliminary, so don't yell at me if I'm leaving something obvious out :) CryptoDerk 04:34, Jan 28, 2005 (UTC)

Is there a list of PM article titles? One way to do all this would be to create a page like the mathematics Requested Articles page, but dedicated to PM articles. Since different articles will need to be treated different ways, we could see how much is accomplished by redirecting and sorting on such a page, and compiling a list of non-transfers, with reasons. In any case, it needs to be a case of involving the broad community, rather than having a rigid plan. Charles Matthews 10:45, 28 Jan 2005 (UTC)

I agree, with both the most recent posts above. Sounds almost like a (broad, community-based and certainly not rigid) plan... Ben Cairns 12:59, 28 Jan 2005 (UTC).

Now, I think what I understand from what Charles said is the following (I could be wrong, but this makes sense to me): We should make a list of PlanetMath articles, or maybe several lists, grouped by subject area, as there are many articles there. Each element in the list should have several things. First, very importantly, the title of the PlanetMath article, second, the title of the corresponding Wikipedia article(s) if any, third the status of the Wikipedia article as compared to the Planet math one (say, "WP article is just a copy of the PM article", "WP article is better than the PM one", "Some merger recommended (which way)", etc). This comment thing is very important, because people seeing this can decide what to do, and update the status line after they took action. This also implies that the status comment must be signed (four tildas) by the user who did the comparision, so that after a long enough time another comparison is made.

What do you think? Now, the first element on each list entry, the PM article title, can be easily auto-generated, and new elements in the list can be easily added automatically later as new articles show up on PM. The second and third elements for each entry will need to be community based, as will take a huge effort to comment on thousands of articles. Oleg Alexandrov | talk 16:06, 28 Jan 2005 (UTC)

This is what I was planning on doing. There will be a lot of grunt work by users that needs to be done. CryptoDerk 16:51, Jan 28, 2005 (UTC)

Something like this seems reasonable. Paul August ☎ 17:46, Jan 28, 2005 (UTC)

I'm not sure this is a good idea. Don't get me wrong, I love PlanetMath. But a world in which there is only one comprehensive open-content math reference is not as good as one in which there are two. -- Walt Pohl 16:37, 28 Jan 2005 (UTC)

User:akrowne (the PM creator) was receptive of the idea, and I think he may have even been the one to approach ME about it a few months age, although I'd have to dig through my IRC logs. Similarly, he plans on grabbing some WP content and using it in PM. I do think that even with content exchange the two will serve different audiences. You've got people who might prefer the author control, setup, and community of PM, and PM has growing sections on things that WP doesn't offer — such as papers, books, and expositions. CryptoDerk 16:51, Jan 28, 2005 (UTC)

I think PM and WP can share content and remain independent. Paul August ☎ 17:46, Jan 28, 2005 (UTC)

But what's the point? It's not like either Wikipedia or PlanetMath are hard to find. They both score high in Google searches. So it doesn't help readers any. Maybe someone would have come along and written a great new potential theory article. Now we just have the same text in two different places. What good did it do?

I think a better idea for a project would be one to make sure that Wikipedia has an article for each PlanetMath article, and that each Wikipedia article links to the appropriate PlanetMath article. Actually duplicating the content seems pointless to me. -- Walt Pohl 20:33, 28 Jan 2005 (UTC)

Well, I think for one it can help fill in some red links. Plus, getting content from other places is, at the very least, a good starting point for building our own. Also, in the case of articles we already do have, we can make them better. WP integrates other free content (PD images, 1911 EB), so why not this? CryptoDerk 20:53, Jan 28, 2005 (UTC)

PD images are obviously a good idea, but I think Wikipedia has been ill-served by including material from things like the 1911 EB. Most pages based on 1911 EB entries are either terrible, or have been so completely rewritten that you couldn't tell they ever used EB. A couple of the math pages has history copied from an old public domain source, and they just sit there, undigestible lumps of text that no one really understands and everyone is afraid to edit. I don't think that will be a problem with PlanetMath, but inclusion of 1911 EB material is not an inspiring example. -- Walt Pohl 01:59, 29 Jan 2005 (UTC)

OK. Draft up at User:CryptoDerk/planetmathproject. Feel free to comment and change it. CryptoDerk 18:03, Jan 28, 2005 (UTC)

See User talk:CryptoDerk/planetmathproject how an automatically generated list of articles from Planet Math looks. Does not look optimistic. Oleg Alexandrov | talk 02:59, 29 Jan 2005 (UTC)

Notice: Wikipedia:WikiProject Mathematics/PlanetMath Exchange is now the location for this project. Active discussion is also going on here: Wikipedia talk:WikiProject Mathematics/PlanetMath Exchange. Additionally, when it goes live we should include a link to it from the main WikiProject Mathematics page. CryptoDerk 16:51, Jan 30, 2005 (UTC)

(I took the liberty editing the above notice to add a link to the talk page. Paul August ☎ 17:27, Jan 30, 2005 (UTC))

Where to contribute math articles? Wikipedia or Planet Math?

Hi,

I'm a newcomer here.

User:Oleg Alexandrov has insinuated on multiple occasions that the math articles that I write are far too complex and complicated for Wikipedia, and most recently suggested that I contribute to PlanetMath instead. I would like to get a clear statement from the Wikipedia math community whether this is indeed the key difference between Wikipedia and PlanetMath, and whether it really is the Wikipedia policy that practicing scientists/academics are encouraged to work on PlanetMath, leaving lay topics for lay authors on Wikipedia.

I am rather discouraged and disappointed; I wish I'd been told this *before* I got involved in wikipedia, and not after, as I have already invested a good bit of time in the enterprise, and its seems that it may all have been for naught.

I am also confused by Oleg's stance on this issue, as almost every math article in wikipedia seems (to me) far more complex and advanced than those which I write. For example: the list of articles that I've started or made major revisions to is here: User:Linas#Misunderstanding things; essentially all of these deal with undergraduate mathematics topics that some typical undergrad math major might encounter in school. By contrast, wikipedia has massive and massively complex articles such as Artin conjecture and Jet bundle and Banach space and Lattice (order) and Sheaf and Scheme (mathematics) which are not only advanced graduate-level topics, but are areas of active academic research. So this simple math /complicated math division leaves me perplexed.

My goal in writing for wikipedia was to have something to replace my paper copy of Abramowitz & Stegun: simple, concise, informative, filled with facts that you never knew or had forgotten, the universe of math at your fingertips. Just plain-old straight-ahead stuff, nothing fancy.

I think a clear editorial policy for acceptable content for math articles for wikipedia should be spelled out up front; if complexity is really an issue, then I strongly encourage a mass migration of the advanced math articles out of wikipedia and into planetmath, where they can serve some actual, useful purpose, instead of splitting the community between two wikis.

linas 06:04, 29 Jan 2005 (UTC)

Now I am in hot water. What I had mentioned to Linas was about style, not content, see character group for style which I don't quite like. But oh, well, it is good this topic is raised. What is a good Wikipedia aricle? I would also need that for the Wikipedia:How to write a Wikipedia article on Mathematics with which I am struggling. Oleg Alexandrov | talk 06:13, 29 Jan 2005 (UTC)

Hi Linas, I agree with you; Wikipedia should have as much "notable" math as possible. Please don't move to PlanetMath. "The universe of math at your fingertips": exactly! Wikipedia is not paper. We can always organize a subject so it has an easier overview with more detail later or in a subarticle. dbenbenn | talk 07:34, 29 Jan 2005 (UTC)

On further thought, I realize that I am (perhaps like everyone) using Wikipedia (and the web in general) in two very different ways, and that this is the source of the problem. When I am reading about a topic about which I know very little e.g. Banach space, I find the "lots of words; few formulas" approach to be excellent, as it lets me learn the subject quickly and painlessly. However, once I know the topic very well, I find that the words get in the way of the formulas: they start hampering understanding, not helping. They mislead, they are inexact intellectually, they clutter the page visually. The articles that I am contributing to wikipedia are mostly on topics I feel comfortable with; ergo, I like them better when they are mostly formulas with few words ... that is, reference articles in the style of Abramowitz & Stegun ... or my recent Christoffel symbols. I see the need in the world for both styles: the introductory article, and the compendium/reference. Now, how to resolve that tension in an editorially pleasing way? linas 07:48, 29 Jan 2005 (UTC)

Thus, perhaps, I nominate a new article style (and article naming convention), the style being called "reference" and the naming convention being that if "XYZ model" is the article that provides intro and examples and generalities, then "XYZ model (reference)" would be the long, exhaust(-ive/-ing) list of theorems and formulas. That would resolve several ugly pages I've been struggling with. For example, Upper half-plane is a prime candidate for this kind of split.linas 08:00, 29 Jan 2005 (UTC)

Linas - I don't think there is any problem with the level of the articles that you have started - the ones I have seen are, as you say, at the level of standard undergraduate mathematics. As for style, this will always be a largely subjective matter. A mathematical article that starts out as a concise summary of defintions and main results may be seen as a skeleton by other contributors, who will add introductory material, history, motivation, examples, applications etc. Eventually the article may become so large that the original neat skeleton is lost to sight, and the article needs to be re-arranged or maybe even re-factored. This is all part of the dynamic, open and collaborative nature of Wikipedia.

As an aside, I notice that the "ownership models" in Wikipedia and PlanetMath seem to be rather different. In the Wikipedia ownership model, an article does not have a single owner, and all users have free access to all articles. I understand (from reading [10]) that the default ownership model at PlanetMath is that an article has a specific owner (usually the person who started the article), and the owner must review each proposed change to that article, and may reject changes that they disagree with. It would be interesting to see if this leads to differences in the style, level and coverage of articles at the two sites. Gandalf61 10:33, Jan 29, 2005 (UTC)

I don't see that there is any overall feeling about level of WP articles, on mathematics. There was once a consensus that we were speaking to undergraduates with a year or so of university work behind them. That was just an indication; textbook material, as such, should be in Wikibooks. All one can really say, is that additions to a given article should in some sense match the approach there: any sudden changes of level can be unnecessarily confusing to readers, and should be flagged in some way, such as 'from the point of view of complex analysis' if one is switching away from a real-variable calculus topic.

Linas, I think you shouldn't generalise too much about this. There is certainly room here for any contributions of almost any level, if they integrate properly.

Charles Matthews 16:44, 29 Jan 2005 (UTC)

Linas: Please don't leave. From what I see, your contributions have been valuable and appropriate. Wikipedia is meant to be comprehensive. It should contain all of "notable" mathematics, from the general and introductory to the technical and advanced. "The best way to organize and present all this is not as clear. As Gandalf61 says, Wikipedia should provide "introductory material, history, motivation, examples, applications etc", Wikipedia can accommodate several overlapping and interrelated articles dealing similar subjects, see for example, this constellation of set theory articles:, set, subset, set theory, Naive set theory, Axiomatic set theory, Algebra of sets and the as yet unwritten History of set theory, Motivations of set theory, Applications of set theory, Frontiers of set theory, etc. See also the above discussion "Graph (mathematics) vs Graph theory". So something like what you suggest might be appropriate, but should probably be discussed some more, with some examples. Paul August ☎ 17:03, Jan 29, 2005 (UTC)

MathWorld references

So many mathematical articles reference MathWorld that I decided there should be a reference template, similar to Template:Book reference or Template:imdb title.

produces

Eric W. Weisstein, Happy Number at MathWorld.

Feel free to edit the template if you feel strongly about the form of the citation. (I purposely decided not to follow Weisstein's referencing instructions. I think "A Wolfram Web Resource" is a bit much.) What do people think? Start using it in math articles? dbenbenn | talk 04:31, 29 Jan 2005 (UTC)

I like it. I'm actually surprised we didn't already have one :o CryptoDerk 04:52, Jan 29, 2005 (UTC)

Main problem is that not all the MathWorld articles are written by Weisstein. Tompw 15:48, 29 Jan 2005 (UTC)

Yeah, I've noticed that too. They still say that Weisstein should be credited as the author, though. It isn't clear to me what kind of license they use at MathWorld for submissions; I suspect it's something like you transfer your copyright to them.

Do you think, for example, that a reference to Petersen Graph should credit "Pegg" as the author? I'm inclined to not bother; but if it's an issue, feel free to make another template, say Template:MathWorld author that would take a third parameter. dbenbenn | talk 20:48, 29 Jan 2005 (UTC)

Wikipedia:WikiProject Mathematics/PlanetMath Exchange -- version 0.1 -- comments requested (on this page)

Introducing the new subproject of WikiProject Mathematics:Wikipedia:WikiProject Mathematics/PlanetMath Exchange. Before you jump there, let me describe what to expect.

We have a purpose section, an instructions section, and the list of subjects in mathematics (according to AMS Subjects classification). Each subject list will contain the titles of all PlanetMath articles on that subject (automatically generated). For now, all lists are red links, except for Functional analysis, scroll down the page for that.

This is done on purpose. There is enough stuff to give people an idea of what to expect, and we are in preliminary enough stage that everything can still be modified.

I would like to invite people to share their thoughts here. Some of us believe that this project, rather than making Wikipedia a clone of PlanetMath, or the other way around, will instead benefit both of them. Oleg Alexandrov | talk 06:11, 31 Jan 2005 (UTC)

By way of summary, some of the things which have been discussed on Wikipedia talk:WikiProject Mathematics/PlanetMath Exchange) and tentatively agreed upon there and/or accomplished are:

We should go forward with this project.
The project name should be: "PlanetMath Exchange".
It should be a subproject of this project with the project page at: Wikipedia:WikiProject Mathematics/PlanetMath Exchange. A first draft of that page now exists there,
There should be an auto-generated list of all PlanetMath articles. The first auto-generated list of PlanetMath articles has been created here: Wikipedia:WikiProject Mathematics/PlanetMath Exchange/46-XX Functional analysis.
There should be a template created to facilitate the creation of a link to the appropriate PlanetMath article in any newly created WP article based on a PM one. Such a template has been created: Template:planetmath. Additionally Template:planetmath reference has been created for a general reference.

Comments? Paul August ☎ 06:20, Jan 31, 2005 (UTC)

Note: I modified #5 to include the other template as well. CryptoDerk 06:29, Jan 31, 2005 (UTC)

Begging the question

I'd like to point people to the mathematical remark in the article Begging the question. See also my comment on the talk page which has thus far generated no responses. There's gotta be a better example than either of these two. - dcljr 06:01, 9 Feb 2005 (UTC)

New Mathematics Wikiportal

I know I've posted this on most of your user talkpages, but I felt it was important to add to the project page as well.

I wanted to point out to you the new Mathematics Wikiportal- more specifically, to the Mathematics Collaboration of the Week page. I'm looking for any math-related stubs or non-existant articles that you would like to see on Wikipedia. Additionally, I wondered if you'd be willing to help out on some of the Collaboration of the Week pages.

I encourage you to vote on the current Collaboration of the Week, because I'm very interested in which articles you think need to be written or added to, and because I understand that I cannot do the enormous amount of work required on some of the Math stubs alone. I'm asking for your help, and also your critiques on the way the portal is set up.

Please direct all comments to my user-talk page, the Math Wikiportal talk page, or the Math Collaboration of the Week talk page. Thanks a lot for your support! ral315 02:54, Feb 11, 2005 (UTC)

ral315: This is a better way to communicate to the Wikipedian mathematics community, rather than posting on everybody's talk pages — some people consider that to be spamming. Your portal looks interesting. I'll put in on my watchlist and lend a hand as time and interest permits. As for mathematics articles needing attention check out Wikipedia:Pages needing attention/Mathematics. Paul August ☎ 06:27, Feb 11, 2005 (UTC)

As I said on User talk:Ral315#Wikiportal, personally, I really appreciated the note you left on my talk page. It might have been months before I'd have found the portal without it, as I'm much more active in other areas right now. And over the years, whenever I've taken the trouble to identify the people I thought would be interested in something and give them each a personal heads-up on it, I've only ever had thanks. But within Wikipedia there are many sub-communities, and this one seems not to like it. I've noted that now, and I'm sure you have too. I'm not convinced it's representative of the whole of Wikipedia, or even the Maths community, but certainly take it as applying to the more active members of this Wikiproject. Andrewa 13:05, 11 Feb 2005 (UTC)

Tex rendering -- help!

Can someone sort out my TeX rendering at effective population size please? I have most of it, but I'm not sure how to group subscripts/superscripts together e.g. p [sub] 1 + q [/sub] sort of idea. Dunc|☺ 15:03, 25 Feb 2005 (UTC)

Oh, I sorted that one myself. But I'm still stuck on having a fhat [sub]foo[/sub] because they won't go together, which leaves a gap and {} don't seem to work ?!? Dunc|☺ 15:26, 25 Feb 2005 (UTC)

Fixed. dbenbenn | talk 20:38, 25 Feb 2005 (UTC)

binomial expansion of (p_1 + ... + p_n)^c

I've asked this on Wikipedia:Reference_desk#.5B.5Bbinomial_expansion.5D.5D too, but, what is the binomial expansion of $(p 1 + ... + p n) c$ ? I don't think this is covered in the articles that are there at the moment. (I want to derive the fully general Hardy-Weinberg law). Dunc|☺ 19:22, 2 Mar 2005 (UTC)

Assuming c is an integer > 2, refer to the multinomial theorem. Charles Matthews 20:52, 2 Mar 2005 (UTC)

\phi or \varphi

It seems to be the norm on wikipedia to use $φ$ for writing one of the angle coordinates in spherical coordinates. I think that it is usually the norm to use $\varphi$ in mathematics and physics. I'd be willing to go through and change a bunch of the pages that use \phi to use \varphi instead. But I don't want to go against established policy. It just seems to me that the 'pedia should use the conventions that are common in mathematics. Has there been discussion about this issue before?

--Jacobolus 06:01, 6 Mar 2005 (UTC)

I believe the Wikipedia norm is the correct one. Dysprosia 06:19, 6 Mar 2005 (UTC)

As do I. Surely, it's a case of using one letter followed by another: theta (

θ

) then phi (

φ

). If varphi ( $\varphi$ ) were correct, surely we'd use vartheta ( $\vartheta$ ) for the first angle we designate? --stochata 13:32, 6 Mar 2005 (UTC)

I think that the "var" in "\varphi" just means "variant phi symbol", and doensn't necessarily imply that "\vartheta" should be used for theta. In all of the math books I just looked at (many of which are layed out in TeX), spherical and cylindrical coordinates were laid out using varphi. In the two physics books I looked at, the phi symbol was used. So I'll stick with phi I guess, as it appears (see discussion below this one) that the physicists' notation is winning out for other coordinate systems. --Jacobolus 18:19, 6 Mar 2005 (UTC)

I use \varphi when I write mathematics in TeX (In fact, I \let\phi\varphi), but I prefer \phi here. The wiki software is able to display \phi as an actual character, whereas it generates an image for \varphi. dbenbenn | talk 17:59, 6 Mar 2005 (UTC)

One pesky problem is that in many html fonts, phi displays inline as the varphi symbol, which means that there is visual inconsistency between rendered formulae and inline variable names. --Jacobolus 18:19, 6 Mar 2005 (UTC)

Note that in my comment below on the notation used by mathematics tutors for my undergrad -- I link to their book. They use phi rather than varphi. (Indeed, Jacobolus, the inline phi appears as varphi on my browser) --stochata 11:58, 8 Mar 2005 (UTC)

use of phi and theta in spherical coordinates

Hi all. I noticed recently that the articles on Vector fields in cylindrical and spherical coordinates and on Nabla in cylindrical and spherical coordinates have theta as the polar angle, phi as the longitude angle, r as the length of the vector, and rho as the length of the vector projected into the plane. In the article about Coordinates however, these uses of phi and theta, and respectively rho and r, are switched. This seems unnecessary conflict. I realize that physicists don't agree with mathematicians on the correct order of these terms, but at least some explanation should be given for the unwitting visitor, who might otherwise be very confused to see rho's and r's swapped so casually.

And then, some consistent drawings of coordinate systems and vector operations, etc. in these coordinate systems should be made. Here's my drawing of spherical coordinates: Image:Spherical_Coordinates.png. I'd be willing to make more drawings. But first some decision should be made about which convention to follow. That used in math or that used in physics.

Tied to this issue is my previous question about varphi and phi. Is one preferred as a coordinate name?

--Jacobolus 08:16, 6 Mar 2005 (UTC)

It should be only a matter of picking one standard and sticking to it. Dysprosia 09:49, 6 Mar 2005 (UTC)

I have never noticed a difference! I was taught to use theta, phi, r in my mathematics lessons at school, and later simply continued to use it through a physics degree. Which do we suppose is used by which category of people? (And maybe country of origin also affects the system used!) --stochata 13:38, 6 Mar 2005 (UTC)

I would agree with stochata that r is the prefered notation for the length of the vector, and so then ρ is the projection. And I agree with Dysprosia that consistency is what matters above all. So since you raised this issue, could you go through the pages using spherical coordinates, (like start at spherical coordinates, see what links there, etc), and change the notation in those places to keep things consistent? That would be much appreciated.

About the picture, I like it. Just one small remark. You will need to of course use a scaled version of it. In the scaled version you will need to make sure the fonts are the right size, and that aliasing is not too bad (pictures which have thin lines and thin curves tend to look ugly unless antialiasing is employed in some way). Oleg Alexandrov 16:24, 6 Mar 2005 (UTC)

I would argue in favor of the usage in Vector fields in cylindrical and spherical coordinates. Where

(r, θ, φ) are spherical coordinates with θ being the colatitude (angle with the positive z-axis) and φ the azimuthal angle.
(ρ, φ, z) are cylindrical coordinates with φ the azimuthal angle

The reason is that this usage is almost universally used by physicists. I think the reason stems from the fact that this is the notation used in Jackson's Classical Electrodynamics — the de facto textbook on electodynamics, where these coordinate systems are heavily utilized. Mathematicians may differ in their usage, but at least this way we include many mathematicians and nearly all physicists. -- Fropuff 17:34, 2005 Mar 6 (UTC)

Ok. So the notation used in Jackson and Griffiths and elsewhere in physics will be the norm. I'll make a prominent note at the top of the Coordinates (elementary mathematics) page (Aside: why is this called "elementary" mathematics... maybe just Coordinates (mathematics) would be better??), and then go with the physics notation. One last question. For inline text, is using the <math> and </math> tags frownned on? I've seen conflicting reports, and the usage seems to vary greatly between articles. I would generally be inclined to use them, but I'll try to stick to whatever the accepted standard is. --Jacobolus 18:12, 6 Mar 2005 (UTC)

One could argue that coordinates (mathematics) should discuss coordinates on arbitrary manifolds (or even more general spaces, i.e. with singularities). As far as inline TeX goes: the reason we try to avoid it is that the inline PNG's are too large and look bad with the surronding text. There has been lengthy arguments about this (see /Archive4(TeX)) and not everyone agrees. -- Fropuff 19:04, 2005 Mar 6 (UTC)

I've just checked the book by my undergrad tutors [11], and they certainly use theta, phi, r for spherical polars (and phi, rho, z for cylindricals as Fropuff suggests). Note that Riley was originally from a mathematics background. --stochata 11:55, 8 Mar 2005 (UTC)

My 2 cents: I am a mathematician, and I prefer the physics/engineering convention for several reasons.

Foremost is that, despite the beliefs of many ignorant American mathematicians and the usage of almost every American calculus textbook, the physics/engineering convention is simply by far the most widely-used convention of the two, throughout the world. It is the convention for virtually all (American and non-American) scientists, and for many, if not most, non-American mathematicians. American mathematicians are really the only group of users who enjoy a majority POV on this issue; it is only because of calculus textbooks that the whole world does not agree.

My second reason for favoring the physics/math convention is that it has far deeper historical origins in physics and science than the American usage does in math. The effort required for Americans to change would be far less than the effort required to re-write classical physics texts.

But, my most important reason is that the American convention is fundamentally flawed from a mathematical viewpoint. If this were simply a matter of two symbols getting interchanged, that would be one matter. But the American convention produces a left-handed coordinate system, and I don't think I need to explain why that poses a tremendous problem.

I taught a vector calculus class a couple years ago, doing something perhaps against better judgment -- teaching the non-American convention while the text used the American one. Of course, I also freely used differentials and the type of informal arguments physicists use for deriving tangent vectors, and so forth. I just made sure that I never assigned any problem using the textbook convention, and I told them not to read that part of the text. There wasn't too much confusion resulting, I mean, at least among those who weren't already confused by the time we reached general coordinate systems. Revolver 07:17, 12 Apr 2005 (UTC)

Relevant proposed naming convention: ambiguous adjectives

There is a proposal at Wikipedia talk:Naming conventions (ambiguous adjectives) that could affect several mathematics articles. -- Toby Bartels 08:40, 2005 Mar 7 (UTC)

Soliciting input on Estimation theory

Just seeking input on a new article: estimation theory. (Estimation didn't take a purely statistical explanation and I better know it as estimation theory.) Please leave article specific commentary on it's talk page instead of here. Thanks. Cburnett 06:56, 8 Mar 2005 (UTC)

straight or italic d?

What are your opinions about the use of upright d versus italic d in integration and for the exterior derivative? Currently, probably because it is less LaTeX, italic d seems predominant. Personally I prefer upright d as this more clearly contrasts with possible use of d as a function or number(distance). Examples

$\int f\,d\mu$	$\int f\,\mathrm{d}\mu$
$\frac{dy}{dx}$	$\frac{\mathrm{d}y}{\mathrm{d}x}$
$\int d(vx, z/x^2) \ln(x+1) \,d (x \mapsto \cos(x)d(x, w))$	$\int d(vx, z/x^2) \ln(x+1) \,\mathrm{d} (x \mapsto \cos(x)d(x, w))$
$\int fdt\wedge dx\wedge dy\wedge dz = \int f\,dt\,dx\,dy\,dz$	$\int f\mathrm{d}t\wedge \mathrm{d}x\wedge \mathrm{d}y\wedge \mathrm{d}z = \int f\,\mathrm{d}t\,\mathrm{d}x\,\mathrm{d}y\,\mathrm{d}z$
$d\det\left({}^a_c {}^b_d\right) = d(ad-bc) = add + dda - bdc - cdb$	$\mathrm{d}\det\left({}^a_c {}^b_d\right) = \mathrm{d}(ad-bc) = a\mathrm{d}d + d\mathrm{d}a - b\mathrm{d}c - c\mathrm{d}b$
$d\det\left({}^a_c {}^b_d\right) = d(ad-bc) = a\,dd + d\,da - b\,dc - c\,db$	$\mathrm{d}\det\left({}^a_c {}^b_d\right) = \mathrm{d}(ad-bc) = a\,\mathrm{d}d + d\,\mathrm{d}a - b\,\mathrm{d}c - c\,\mathrm{d}b$
$\int f(x_1, \ldots, x_d) \,d_dx$	$\int f(x_1, \ldots, x_d) \,\mathrm{d}_dx$
$df(V) = V(f) = \left.\frac{d}{dt}\right\|_{t=0}f(\gamma_t)$	$\mathrm{d}f(V) = V(f) = \left.\frac{\mathrm{d}}{\mathrm{d}t}\right\|_{t=0}f(\gamma_t)$
$Δ: = (d + d ) 2 = d d + d * d$	$Δ: = (d + d ) 2 = dd + d * d$
$\Delta := (d+d^)^2 = dd^+d^*d\,$	$\Delta := (\mathrm{d}+\mathrm{d}^)^2 = \mathrm{d}\mathrm{d}^+\mathrm{d}^*\mathrm{d}\,$

Also, when defining something, do you use := instead of = and why? MarSch 17:30, 11 Mar 2005 (UTC)

It is standard to use italics for differentials such as dx (e.g., see Wolfram: [12]). The spacing ought to give you a clue to the nature of the symbol, note that you should add a little space to distinguish the variable (see Lamport p.50). e.g., $\int d\, x \, dx$ . --stochata 23:35, 11 Mar 2005 (UTC)

I like the idea of using a vertical "d", but it is not common. I think that in Wikipedia we are not supposed to be trend-setters but should follow common practice, so we have to use the italic ''d". --Zero 02:22, 12 Mar 2005 (UTC)

It's my estimate that this is largely a US/UK thing (with Americans using italics and the Brits using an upright shape). Personally, I prefer to use both a thin space and an upright shape -- why be coy? (I've added a row to the determinant example, so that we can all see what all four possibilities amount to there.) As usual, I oppose any sort of policy decision for all articles; we should follow the usual rule of tolerance for variation that applies to US/UK spelling differences. -- Toby Bartels 23:56, 2005 Mar 12 (UTC)

Toby, I am British (and currently in Britain) and I prefer the italic version (although I have seen the upright 'd', it doesn't strike me as that common -- although my area doesn't tend to use derivatives that much). I look forward to articles with phrases such as "dx, or dx in American mathematics" :-) --stochata 12:18, 13 Mar 2005 (UTC)

The Brits have spoken. :) I would say we need to restrict transatlantic differences to spelling (and politics) only. Italic dx has been the style on Wikipedia, and I think it should stay this way. Oleg Alexandrov 19:45, 14 Mar 2005 (UTC)

Shades of varphi! I think its a terrible idea to go out and try to retroactively edit hundreds of pages to use a different font in the math typsettings. Authors of new pages get to pick thier symbols, but they should make at least token attempts to be consistent with nearby articles. For the record, I have no love for := I sometimes use $\equiv$ in the privacy of my own room, but I would not subject the public to such degradations. One man's definition is another man's theorem. linas 16:21, 14 May 2005 (UTC)

My vote goes to "thin space (/,) and upright d", for better semantics and for all the other reasons mentioned here PizzaMargherita 07:06, 1 December 2005 (UTC)

Reformat of Participants list

I'm thinking about changing the format of Wikipedia:WikiProject Mathematics/Participants, making it into a table like so:

User (T¹ C²)	Areas of interest	Comments
Andrewa (T C)
AxelBoldt (T C)
Charles Matthews (T C)		I've added about 300 mathematics pages, many biographies, and lists of mathematical topics. I now also work on other areas of WP, but a well-organised and credible collection of mathematical articles is very much what is needed. We now pretty much have the house style and topic classification in place; there are some missing areas, and a great need to explain current research areas, as well as good history. I'm a sysop - one of not too many on this list.
Chas_zzz_brown (T C)	abstract algebra, group theory	My knowledge of topics outside of group theory is a monotonically decreasing function of their relationship to abstract algebra.
Mark Dominus (T C)
FunnyMan3595 (T C)	abstract algebra	I'm a freshman majoring in mathematics, but I already have quite a few courses under my belt. My specialty is abstract algebra.
irrªtiºnal (T C)		Let ε < 0 (hehe...) I am a highly unsuccessful mathematician. I am a man. I am single. I am free. I am an existentialist, therefore I am not.
Jeff (T C)	dynamical systems, complex systems, real analysis	I love to edit.
Kevin Baas (T C)		I started the fractional calculus section. Though it is still embryonic, it is very much 'my style', which is still under development. -Also started Information geometry section. I am just learning about this, though.
Ling Kah Jai (T C)		I have contributed an interesting article called last stone game.
LittleDan (T C)	geometry, group theory, vector spaces	I know up through geometry, and a fair amount of group theory and vector spaces. I can usually pick things up from wikipedia articles, if not from mathworld, then I can edit wiki articles for clarity.
Markus Krötzsch (T C)		I think many math articles still lack: general intros/motivation, links to relevant literature, objective account of alternative definitions (even if one definition is prefered in Wikipedia).
MarSch (T C)	geometry, category theory, physics
Miguel (T C)		How come Toby didn't tell me about this?
Pierre Abbat (T C)
Ram-Man (T C)
Revolver (T C)		Hi, I'm back.
Taku (T C)
Toby Bartels (T C)
Tomo (T C)

Notes: ¹ User's talk page; ² User's contributions

Any comments? Paul August ☎ 22:40, Mar 11, 2005 (UTC)

Much better, go for it -- so long as people aren't scared off to add their own entry. --stochata 14:36, 13 Mar 2005 (UTC)

Yes I had wondered about that. Figuring out the table syntax might discourage some. Although, perhaps we could consider a kind of IQ test, sort of like figure out the next term in this sequence … ;-) I'd be willing to write some instruction and/or provide a template. What do others think? It is a bit of work, so I don't want to undertake it if it is not deemed useful, or if we think it will put people off unnecessarily. Paul August ☎ 14:49, Mar 13, 2005 (UTC)

Well, trying to overcome the apathy...

I am against the table. I never learned the syntax of the Wiki table (all those absolute value signs everywhere :) and never plan to. And I don't see the gain of the table, ~~besides the obvious rosy background.~~ :)

Other thoughts? Oleg Alexandrov 16:21, 13 Mar 2005 (UTC)

PS And the background ain't even rosy! :) Oleg Alexandrov 16:21, 13 Mar 2005 (UTC)

Well I guess the main advantage of the table, in my mind, is that it encourages participants to enter fields of interest, plus it is eaisier to read, and I think the links to the user's talk page and contributions is helpful, for me at least. I'd be glad to help anyone with the syntax — or add a "rosy background" if that would help ;-) (Oleg: tables are fun! :) Paul August ☎ 16:56, Mar 13, 2005 (UTC)

I like it. Tomo 23:21, 13 Mar 2005 (UTC)

OK, although the response has been somewhat limited, I've decided to go ahead with the new format. Three users have expressed support, stochata, Tomo and MarSch (on my tak page). Oleg's was the only dissenting voice, but he has since warmed up enough to the idea to create a script to generate the table from the existing list ;-) So he is hoist on his own Perl petard, so to speak ;-) I would have preferred to have heard from some of the more senior participants (Charles Matthews, are you listening? ). Hopefully people are at worst indifferent. If anyone doesn't like it we can always revert it ;-) Paul August ☎ 21:41, Mar 18, 2005 (UTC)

"monotonicity" merged with "monotonic function"

After some discussion on talk:montonicity involving me, Toby Bartels, Michael Hardy, and Markus Krötzsch, it was agreed that monotonicity should be merged with monotonic function, which I have now done (monotonicity now redirects to monotonic function).

However there was a bit on a generalized notion of convergence for function between posets, which Toby thinks is worth keeping, but which I don't think necessarily belongs in the monotonic function article. Toby has suggested that perhaps it should be moved to its own article titled "order convergence". I made a stab at converting the orphaned text into a first draft for such an article (see: talk:montonicity) but I'm unfamiliar with this concept and am reluctant to actually create the new article myself. So If anyone knows anything about this, and would like to salvage this now orphaned content please do so.

Here is the text under discussion:

(Beginning of quoted text)

The notion of monotonicity allows one to express the principal instances of convergence (to a limit):

Given that a commensurate difference relation is defined between the members of S; that is, such that for any four (not necessarily distinct) members g, h, j, and k of S, either g − h ≤ j − k, or g − h ≥ j − k, and given that M from T to S is a map of equal monotonicity, then the values M(s) are called converging (to an upper limit), as the argument s increases, if either:

the set T has a last and largest member (which M maps explicitly to the corresponding limit value l in set S); or
for each member m of T, there exists a member <n > m such that for any two further members x > y with y > n, M(n) − M(m) ≥ M(x) − M(y).

As far as the set of all values M(s) does therefore have an upper bound (either within set S, or besides), and as far as every set which is bounded (from above) does have a least upper bound l, the values M(s) are called converging to the upper limit l as the argument s increases.

Similarly one may consider convergence of the values M(s) to a lower limit, as the argument s decreases; as well as convergence involving maps of opposite monotonicity.

(End of quoted text)

Paul August ☎ 21:13, Mar 14, 2005 (UTC)

Algebraic solution

Could someone here confirm that this new one sentence article is correct? An algebraic solution is a solution that is either a number or can be computed. That strikes me as so general as to be essentially meaningless, but google's been no help & I'm not competent in this area. Thanks. Michael Ward 03:06, 18 Mar 2005 (UTC)

It seems the definion does not make sense unless the term computation is explained. Maybe one should add a reference to or redirect to algebraic number or algebraic equation. Tomo 06:54, 18 Mar 2005 (UTC)

I've redirected this to closed-form solution. Charles Matthews 08:34, 18 Mar 2005 (UTC)

periods at the end of formulas -- request for comment

This is an edited version of my conversation with Omegatron, about periods at the end of sentence. I just wonder, what are your opinions about this? Thanks!

Is there a consensus that [period] is needed? looks bad to me. - Omegatron 00:19, Mar 19, 2005 (UTC)

I wonder if the reason it looks bad has to do with a peculiarity of using TeX on Wikipedia, as opposed to using TeX in the usual way. That is that if you put the period or comma outside the math tags, it gets mis-aligned. If you put it inside, however, it looks good. Michael Hardy 23:45, 19 Mar 2005 (UTC)

Period at the end of formula is the universal style in math. I am aware that in engineering for example, people do not do that. Did it happen that I modified something outside math (I try to stick to math, but sometimes the links from the list of mathematics topics lead into related subjects). If you would like, we can have a wider discussion about this. Oleg Alexandrov 00:24, 19 Mar 2005 (UTC)

Yeah it was an electronics article common drain, and they weren't sentences, either. I think even in mathematics articles it doesn't look good. I don't remember seeing it in my math books. It looks like a symbol, which could certainly confuse me; I don't know about other people. $Q \cdot Q .$ $\dot Q .$

...,1,2,3,....

Perhaps it's something from typesetting that doesn't carry over perfectly to the web? - Omegatron 00:30, Mar 19, 2005 (UTC)

I just pulled two math books off my shelf (math math, not engineering math) :-) and they are different. One has no punctuation next to formulas unless they are inline with the sentence. The other has periods the way you are using. - Omegatron 00:35, Mar 19, 2005 (UTC)

I just randomly pulled 5 applied math and probably books off my shelf. They all use period at the end. Would you like us to discuss this at Wikipedia talk:WikiProject Mathematics. Or would you take my promise that I will not mess up with any articles which are not either linked from list of mathematics topics, or in some math category, or listed as a math stub? Either way is very fine with me. Oleg Alexandrov 00:41, 19 Mar 2005 (UTC)

The encyclopedia of physics uses periods, too. :-) You are winning my bookshelf 2 to 1 so far. The engineering books don't, as you said. - Omegatron 00:42, Mar 19, 2005 (UTC)

If it's standard mathematics practice I guess go for it, and leave the engineering articles without. Of course, there are some articles that exist on the intersection between these two worlds. Has there been any discussion about it before you started adding them? - Omegatron 00:44, Mar 19, 2005 (UTC)

No, I did not consult anybody [about this]. But, I am already at letter "C", and at at least 5 Wikipedians I know had one or more of those on their watchlist (well, I assume so, as they contributed to those). I can certainly stop until we talk this over at Wikipedia talk:WikiProject Mathematics. All up to you. Oleg Alexandrov 00:47, 19 Mar 2005 (UTC)

Let's just move this conversation there and see what other people have to add, and you can keep going with the math articles. - Omegatron 00:49, Mar 19, 2005 (UTC)

I don't care for them when the formula is on its one line (I see a lot of "cleanup" on my equations). Inline with sentences is fine like this $\sum_{x=0}^{N-1}f(x)^2$ . But the period *not* inside the math tags. Cramér-Rao inequality is mixed with and without periods: Cramér-Rao inequality#Single-parameter proof doesn't but Cramér-Rao inequality#Multivariate normal distribution does.

In the end, I don't see you can really justify either no more than if why it should be Jones' or Jones's. Entirely style. Cburnett 02:13, 19 Mar 2005 (UTC)

I did not get to Cramér-Rao inequality yet. I think one needs to be consistent at least on a per-page basis. Oleg Alexandrov 02:33, 19 Mar 2005 (UTC)

That's primarily from one section having already been there. Might as well wait and see what results from this discussion. :) Cburnett 04:33, 19 Mar 2005 (UTC)

Yes, this is standard style in mathematics textbooks. But on screen I think it looks clumsy, is potentially confusing, and is unnecessary - I think the effect on continued fraction, for example, has not improved the article. My vote would be not to do this - and certainly to stop until you have a consensus. Gandalf61 13:46, Mar 19, 2005 (UTC)

I am reluctant to comment on this rather trivial matter, but I think the convention to treat formulas as part of the text for the sake of punctuation rules is useful and logical, and widespread in maths style guides. So I support Oleg's efforts. I don't see Gandalf's point that there is a distinction between maths in books and maths on the screen in this matter. -- Jitse Niesen 15:36, 19 Mar 2005 (UTC)

Agree. Charles Matthews 17:20, 19 Mar 2005 (UTC)

Also agree. Now may I get a pardon from Oleg for being one the worst offenders against this commandment? CSTAR 18:56, 19 Mar 2005 (UTC)

Penance required - start the Weil representation article ... Charles Matthews

OK, OK I suppose that's better than saying 500 padre nuestros.--CSTAR 18:00, 11 Apr 2005 (UTC)

From User talk:CesarB

I am now doing myself a bad service, but there is discussion going on at Wikipedia talk:WikiProject Mathematics about period at the end of formula if formula is at the end of sentence. So, you can go there and put your vote (which will be against me). I would like to ask you to specify there your background. It seems that mathematicians are mostly for period at the end of formula, while engineers (and now I see, computer scientists) are against.

In the future, I will avoid modifying non-math articles, like bra-ket notation, which is physics. I try to stick to math, but sometimes non-math articles (again, like bra-ket notation) are put in a math category, and then this kind of disagreements arise. Cheers, Oleg Alexandrov 19:42, 19 Mar 2005 (UTC)

I don't care either way, as long as it's obviously separate from the formula (like a big fat period). You not only added a period which looked like part of the formula, but you added it inside the <math> tags, which made it even more like part of the formula. cesarb 19:45, 19 Mar 2005 (UTC)

Often all it takes is to precede the period by a little bit of space and it no longer intrudes on the formula. --Zero 12:07, 20 Mar 2005 (UTC)

Agreed. Of course, how much space is needed depends on the formula (a formula full of whitespace would need more space than a formula with no whitespace at all). cesarb 13:42, 20 Mar 2005 (UTC)

I am for proper punctuation of formulae. BTW the bra-ket article is a really bad example IMHO, since it has lots and lots of miniscule formulae, which would probably benefit from inlining.MarSch 15:27, 20 Mar 2005 (UTC)

Period before or after </math> -- please comment on this as there are opinions on both sides.

It seems that the opinion leans (I would say overwhelmingly) towards putting period at the end of formula. There are situations in which there needs to be some space between formula and period, and in some situations one could be better off without a period if that would confuse things, but these are rather special cases, when careful and individual judgement needs to be made.

There is another quite dividing issue which needs to be settled. Shoud the period before or after </math>?

I would agree with Michael Hardy that the period should be before </math> so that it becomes part of the PNG image. Otherwise, if the period is separate, if the formula is at the edge of browser window, the period moves to the next line. Also, this introduces a big space between formula and period (and comma) which can look quite unnatural (I don't mean one quarter space, like \, in LaTeX, rather a full space).

On the other hand, Cburnett believes that (taken from his talk page):

I'm vehemently opposed to having to make an article work around bugs or unexpected behavior (see discussion above to see what I mean [there Cburnett argues that one should put one category and language link per line, even if that causes some extra space at the bottom]). I did get my browser to wrap periods to the next line with equations (images really). However, I don't readily see this as a WP issue but rather a browser issue. Either way, whatever is decided on the wikiproject page I'll go with. Just can't promise I'll always remember. :) Cburnett 04:04, 19 Mar 2005 (UTC)

I wonder what everybody else thinks. Comments would really be much appreciated. Thank you. Oleg Alexandrov 17:21, 20 Mar 2005 (UTC)

Another point to go for after </math> is like with the new grammar bot. Rending the period in the tags means a bot might see the period if HTML rendered or might not if PNG rendered. It makes for an inconsistency even if the period is placed consistently. If placed external to the tags then it will always be there. And, no intention of insulting here, you have to be ****extremely**** pedantic to worry about a browser wrapping a period. :) Cburnett 18:32, 20 Mar 2005 (UTC)

About the bot thing. The bot does the queries based on the wiki source, not the final html, so will have no problems sticking its nose in math formulas. Oleg Alexandrov 02:48, 21 Mar 2005 (UTC)

The grammar bot (I forget the exact user name, perhaps User:GrammarBot) ignores math tags because of the commas. If you're going to require a bot to parse math tags then you've just added more complexity to it......to keep a period from wrapping. Cburnett 03:26, 21 Mar 2005 (UTC)

I think so far GrammarBot was very sucessfully messing inside of formulas. Maybe it will be a new feature that it will not do that anymore. Now, about your concern. Let me tell you that the bot I wrote to put periods at the end of formulas semiautomatically had to deal with issues similar but worse than that (there is lots of variabitity to how people type formulas). Besides, the GrammarBot has nothing to do in or around a math formula anyway, since after the period (or comma) in an aligned formula one goes to a new line. Either way, I think our concern for bots should probably be the last thing to worry about. Oleg Alexandrov 03:59, 21 Mar 2005 (UTC)

If the bot is to detect sentences without a period then it'll have to parse inside and around formulas. Really, though, if you want to worry about wrapping periods then I'll worry about bots. Both are equally pedantic and both are concerned about a mundane detail instead of actually writing or editting articles. Cburnett 04:05, 21 Mar 2005 (UTC)

If you are not pedantic yourself, and if you don't care if there is a period at the end of formula to start with, why are you so pedantic about where the period is? :) I think you are right. We are wasting time here. You can do what you love most, editing articles, and I will continue with the issue which has been concerning me me for at least one month, that is, proper punctuation of math articles. How's that? :) Oleg Alexandrov 04:18, 21 Mar 2005 (UTC)

Try rereading what I wrote. Notably, the second sentence. Cburnett 04:27, 21 Mar 2005 (UTC)

You are right again. I focused on your very provocative third sentence. So let us not imply that what the other is doing is irrelevant, because then you should not take part in this discussion to start with.

On your second sentence, I do not buy the bot argument. We will probably not agree on this. Let us see what others have to say. Oleg Alexandrov 04:32, 21 Mar 2005 (UTC)

When did I call it irrelevant? Cburnett 05:06, 21 Mar 2005 (UTC)

My fault. I overreacted. I read it (the third sentence) to mean that some people spend their time in an useful way writing good articles, and some other people have nothing better to do than argue about pedantic issues ultimately of little importance. But I had time to think about it, and agree that what you said can be interpreted as saying that there are two kind of issues, one of writing articles and the other one of taking care of the fine details. So, sorry!

Either way, I think better arguments can be found than the bot thing, and it seems that ultimately nobody really cares about this issue except us two and cesarb. Let us see if more developments happen. Oleg Alexandrov 05:12, 21 Mar 2005 (UTC)

I would put it after </math>, because it's not part of the formula. Only things that are part of the formula should be inside the tags. As a bonus, it gives some extra spacing before the period.

I found an easy way to prevent breaking: the element. Since it's not supported by mediawiki (and in fact not part of the HTML standard), I created a template nobr using the standard way of doing a (and in fact, the way used by Mozilla's default HTML stylesheet).

Here's how to use it:

$1+1=2\;$ .

I disagree with Cburnett about it being pedantic; with some large formulas (I've seen formulas that take more than half of my screen, and I use a huge resolution), it's quite easy when using lower resolutions to end up with a period by itself in the next line.

A more extreme example (you can comment it out after the discussion is over, it will cause scrollbars to appear):

$a+b+c+d+e+f+g+h+i+j+k+l+m+n+o+p+q+r+s+t+u+v+w+x+y+z+a+b+c+d+e+f+g+h+i+j+k+l+m+n+o+p+q+r+s+t+u+v+w+x+y+z+\;$ .

cesarb 19:40, 20 Mar 2005 (UTC)

Oh, and by the way, if this is too verbose, it would be easy to create a template to simplify it, containing something like:

{{subst:nobr|<math>{{{1}}}</math>.}}

cesarb 19:57, 20 Mar 2005 (UTC)

Vote for after. We should not compromise logic. There should be better workarounds. Isn't there a Unicode character specifically to glue parts together? – Sebastian 05:33, 2005 Mar 21 (UTC)

If you are thinking of the non-breaking space, it won't work (it would only work if it was replacing a space character; there is no space character). The nobr template I made works. --cesarb 10:01, 21 Mar 2005 (UTC)

The template cesarb suggests would work. However, I don't see it getting widely adopted (it is hard enough to convince people to care about putting that period to start with).

I agree with Sebastian about the logic thing. When I type LaTeX papers I don't like the period to be inside of the formula. However, on Wikipedia we have just three options (a) put the period after /math and not worry about misalignment, as this is a browser bug — this is what Cburnett says (b) put the period after, but do some kind of quick fix like a template, which cesarb suggests and (c) put the period inside, which is kind of a hack too.

Dealing with numbered formulas, like

$\int_a^b f(x)\, dx = F(b)-F(a) \quad\quad\quad\quad (1)$

does not make things easier. Here, probably the period should go before (1) rather than after (with some spacing between the formula and the period in some situations — if necessary — but probably not in this case).

So, no perfect solutions, but I would still think the third option is better than the first two. Oleg Alexandrov 12:50, 21 Mar 2005 (UTC)

I don't see the problem with the numbered formulas. The number is not part of the formula. In fact, it usually is written in the same font as the text. Sometimes you even find a name for the equation before the number - so it should really be outside of the . Moreover, it is not uncommon to put the punctuation after the the number, which I also regard as more logical. Example: Eddington, The Constants of Nature in The World of Mathematics, Vol. 2. — Sebastian 09:45, 2005 Mar 22 (UTC)

Well, it is not standard to put the period after the equation number. (Actually, LaTeX does not even give you a choice.)

It seems that people are pretty split about this (2 for period inside, 3 for period outside), and there were not as many people involved in this as could have been.

So, I guess a solution would need to wait until the browser and display technology will advance — do you hear that Cburnett? — like switching to MathML where hopefully this will not be an issue.

However, there was broad agreement that sentences with formulas at the end must have a period. Unless I hear any objections, in several days I will resume putting the periods. I will put them inside the math tags, as again, it seems to me that this is the least problematic way. But, I will not attempt to convert the formulas where the period is there, but outside the math tag, as I had originally planned.

If, again, I hear no objections, I am aware that there could be disagreements about individual instances, where one might feel there needs to be some spacing between the period and the formula, or that a period does more harm than good in that instance. Since my work will be semi-automatic anyway, just feel free to revert or change those cases. In most situations however, I do not expect these to be an issue.

Anyway, let us see how it goes. Oleg Alexandrov 21:18, 23 Mar 2005 (UTC)

Objection. The (admittedly narrow) majority voted for outside, and it's technically feasible with the stub mentioned above; so there's no reason to put them inside. I also disagree with using LaTeX's inability as an argument. Our criterium should be what we deem most straightforward logically. — Sebastian 22:09, 2005 Mar 23 (UTC)

Vanity references?

I wanted to alert everyone to some edits I've just noticed. Take a look at IP 84.94.98.49's contribution list: [13]. Notice that all of the edits were adding links to abstracts or papers by someone named " J.Foukzon". They were not, as far as I could tell, particularly relevant to the articles (I could be wrong). I'm wondering if someone might be engaging in something which could be called "vanity references". This could be a particularly insidious form of vandalism. One that could be difficult to deal with, since it can be hard to verify that a reference is really relevant. Paul August ☎ 20:37, Mar 20, 2005 (UTC)

Certainly references like both the ones on Path integral formulation (now only visible in the history) are unnecessary and, while broadly 'relevant' to the subject at hand, at best add nothing to the article and at worst distract from more suitable references. The Foukzon references in that article are in fact conference papers that have not yet been presented (appearing July 2005); sheesh! Well spotted, Paul. Ben Cairns 22:06, 20 Mar 2005 (UTC).

I would say, delete without further fuss. Oleg Alexandrov 22:16, 20 Mar 2005 (UTC)

Structure of math articles

I have seen some mathematics articles that suffer from too narrow a perspective, like laplace operator, which completely ignored generalization to forms and still ignores a discription in terms of covariant derivatives so it would apply to all tensors. The laplace article is still very far from decent since it does not say anything usefull about the (general) Laplace operator, but that's another issue.

Also I have seen some mathematics articles which are now physicist territory, like Noether's theorem and Lagrangian. I think that a good article should start at it's highest level and then explain how lower levels are special cases of it. These lower levels may then also have their own page if necessary. And if something has application to physics or anything else, these should then be treated. Sometimes people say that this is an encyclopedia as a reason for excluding certain information that is considered too specialised/difficult. I don't see their point. Any comments? MarSch 16:07, 26 Mar 2005 (UTC)

I agree that we should discuss generalizations. However, I strongly disagree with your statement that "a good article should start at its highest level". Instead, we should "start simple, then move toward more abstract and general statements as the article proceeds" (quote from Wikipedia:WikiProject Mathematics). This has the advantage that we don't scare away people that are not interested in the generalizations; people that do want to read about the most general case will understand (and skip) the lower levels. For instance, I think the article on the Laplace operator should start with the definition

$\Delta f = \sum_{i=1}^n \frac{\partial^2 f}{\partial x_i^2}.$

But by all means, proceed to treat the definition

Δ = d d * + d * d

The split mathematics/physics should be handled on a case-by-case basis. I definitely agree with you for Noether's theorem and I would be very happy if somebody will tackle this article. For another view, read Wikipedia:Village pump (miscellaneous)#where are the chemists?, from which I quote: "Turning to physics, I often find articles which appear to have been hijacked by mathematicians, causing them to loose insight into _physics_ principles." -- Jitse Niesen 22:31, 26 Mar 2005 (UTC)

Ugh. I completely disagree with the form of the recent edits to Laplace operator by User:MarSch. As a geometer, I like the fact that the full abstract definition has been added, but it should appear later in the article, after a simpler high-school/college-level definition.

Please keep in mind why people come to Wikipedia in the first place: to learn something new, to refresh thier memory, to look up a forgotten formula. There is nothing worse that one can do to a reader than to overwhelm them with abstractions they don't understand. For example, any chemist, who may have had a few semesters of quantum, would be lost in this article as it currently stands. Ditto for any structural engineer, or electronics engineer. These are people who would use wikipedia, and frankly, they outnumber the geometers by a hundred to one. The article should cater to that level of understanding first, and then, only later, turn to the more abstract definitions. As an example of where this works, see the definition of the discrete laplace operator, which appears at the end of the article, not at the beginining. linas 02:02, 27 Mar 2005 (UTC)

Agree with Jitse and Linas. Most people will not appreciate seeing things in their higher perspective upfront. Besides, bottom-up, from particular to general, is the natural way of learning things. Oleg Alexandrov 02:44, 27 Mar 2005 (UTC)

Thanks for your comments. My above viewpoints reflect my feeling of a lack of modern math content. I agree that by making the article more difficult I have, hopefully temporarily, made Laplace operator worse, because there wasn't and still isn't any informal stuff. I have been reading the project pages on structure of mathematics articles and searching for a good example article, and I have not been able to find what a good article should look like. I have given it some thought and I think what is most lacking from, as far as have seen, all articles is a good motivation at the beginning of the article (everything before the TOC) of why that article is interesting to read. After that should come a good informal treatment with few or no formulas and still after that should come the formal treatment. After this section should come some applications. What i was trying to say earlier was about the formal section, it should be as general as the article title warrants and then reduce to some special cases. At the moment Laplace operator has only a formal section, which is why it is very difficult to understand right now. Writing good motivational and informal stuff is probably one of the most difficult things one can do, because they require a very clear understanding of a subject. MarSch 11:34, 28 Mar 2005 (UTC)

I think we will all agree that math articles here need more motivation, more applications, more connections with other articles and relevant real world examples. This is mentioned at Wikipedia:How to write a Wikipedia article on Mathematics (maybe not in such uncertain terms as MarSch would like). However, I think no amount of motivation or explanation is going to make Laplace operator a good article, if instead of starting with the Laplacian as a sum of partial derivatives one goes right to the Laplacian on manifolds, a huge number of formulas, and a very general abstract treatment. I think that some kind of consensus was reached that going from most general to the particular is not the way to go. Oleg Alexandrov 18:29, 28 Mar 2005 (UTC)

The ideal on Wikipedia is to give a 'concentric' treatment: brief lead paragraph, then more details, then further details for the reader who needs them ... and even link to other pages when the extra details become very long. This is actually the opposite of the Bourbaki idea that you start with the supposedly 'correct' general definition. Now, we as mathematicians have some problems doing it that way; but in the end it is better to give an accessible treatment. Charles Matthews 15:00, 1 Apr 2005 (UTC)

This discussion and the one on Laplace operator have changed my mind. All parts of the article should start simple and end very very hard ;) -MarSch 14:34, 4 Apr 2005 (UTC)

encouraging references for formulas

formulas and constants are especially vulnerable to malicious vandalism. adding a square root, changing a single digit, etc. how do we fight it? two possible treatments:

encourage references for every formula
encourage people who know the formulas and numbers well to watch the pages

see Fourier_transform#Continuous_Fourier_transform for an example where I included an image from another site as a reference in comments after an anon removed an erroneous sqrt sign.

- Omegatron 16:01, Mar 28, 2005 (UTC)

the square root probably went over the 2pi? This is just a problem of definition. Do you want the Fourier transform and it's inverse to "look the same". It is a convention. You should probably mention that two versions exist.

In general I guess we gotta watch our formulas. If we use them to derive a few simple properties or prove something then mistakes will be spotted sooner.-MarSch 17:26, 28 Mar 2005 (UTC)

You're right. It was just over the 2pi. But I've seen other small changes here and there that were incorrect. - Omegatron 17:35, Mar 28, 2005 (UTC)

It's tricky to reference formulae as we often want to fit in with the style of related articles within Wikipedia, meaning we might use a "paraphrased" formula rather than one directly from a paper or book. (As a trivial example, we might write "sum nx" rather than "n sum x".) Just as for any other topic, that means those that know the subject need to watch the pages and check for subtle changes. --stochata 21:27, 28 Mar 2005 (UTC)

I agree in principle with Omegatron. I've added a section to Wikipedia:WikiProject_Mathematics/Proofs specifically deal with this type of issue. linas 03:58, 3 Apr 2005 (UTC)

Apr 2005 – May 2005

This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

Educational trampoline

I'd like to propose the creation of a new WP math policy (and category) concerning articles that are of particular educational value. I have in mind articles, such as Pi and Torus, which, if properly written and edited, could be accessible to pre-teens and still be interesting and fun for experts. Articles in this category would provide a portal for bright kids or teens (or even college freshmen) to launch into sophisticated math topics. For example: torus: when I was 9 years old, my teacher wrote formulas for a sphere, cylinder and torus on the blackboard: this is clearly a topic accessible to youth. Yet the article continues on to mention Lie groups and cohomology (and links to modular forms), which are advanced undergrad or grad-student topics. If this article is properly structured, it could provide a fine entrance to many fantastic topics in math.

The suggestion here is then only to create and apply some special editorial guidelines to articles in this class, and to create a special category so that educators could easily find them and thus suggest them for brighter students. If there is general agreement, I'd like to make this an official WikiProject Mathematics policy. linas 03:49, 3 Apr 2005 (UTC)

I'm very confused. Why does the inclusion of Lie groups and cohomology, esp. later in the article, make the elementary discussion any less accessible?? If an article is not accessible enough for the audience you talk about, then what is needed is more attention to the elementary presentation, not a deletion or excision of the advanced material. Of course, if the advanced material starts to overwhelm the entire article, a split may be called for. But not including things about the advanced properties is a disservice to those who are looking for this. The point is, if the elementary treatment is first, then the audience you are talking about it will read it, go as far as they can, and then turn away when they're overwhelmed by terminology or abstraction. And the people looking for an abstract treatment will be mature enough to recognize the various levels presented and navigate around the article. If we're worried about scaring people off simply by presenting an advanced treatment in addition to a wonderful elementary treatment, then we're underestimating the readers. "Knowing where you starting to get lost" is sort of a skill itself that will become more and more important as the information age goes on. And besides, why should we guess where a reader's "level" stops? They might read the elementary part, come back a year or two later and read more, and a year or two after that and read the advanced. The article could become an old friend rather than an enemy. And for me, at least, reading about things I don't quite yet understand often leads me to investigate further and I sometimes end up learning quite a bit I didn't know before. Maybe there are precocious undergrads (or evne high school students) who are really interested what the heck a Lie group is, or what cohomology is. It's not Why close these opportunities off? Revolver 14:36, 12 Apr 2005 (UTC)

It would be very nice to have such articles. I suggest you choose one article to convert/improve as an experiment. Hopefully this could lead to improved structure of all our articles. -MarSch 14:25, 4 Apr 2005 (UTC)

It's Wikibooks that is the designated place for textbook development. The suggestion seems to be along the lines rather of the material in the kind of popularising, accessible book that really does have a chance of interesting readers without much background. Still, it does sound more like a Wikibook, to me. Charles Matthews 14:52, 4 Apr 2005 (UTC)

I don't believe in wikibooks. Yet. I like linas vision of the future of WP. -MarSch 13:51, 7 Apr 2005 (UTC)

Providing an introduction for math articles (or wikipedia articles in general) is a good thing. It makes the articles accessible to a wide range of people. But writing an article which can be used for studying a certain topic is an entirely different matter. Wikipedia is an encyclopedia as such is primarily used for looking up information. The structure of the articles should reflect this and present the information in an accessible and neutral way. A textbook on the other hand should be structured according to pedagogical principles. These principles vary from author to author as does the selection of material. MathMartin 15:25, 7 Apr 2005 (UTC)

I agree with MathMartin. We need to keep the encyclopedic style. So, several styles (described below) which were mentioned in places in the discussions on these pages are not quite encyclopedic. They are:

(a) Writing very concise articles containing just formulas and listing theorems (a la Abramowitz and Stegun)

(b) Writing things in a top-down approach.

(d) For that matter, putting proofs in the articles, unless they are useful to the statement of the theorem or are otherwise instructive. Oleg Alexandrov 17:05, 7 Apr 2005 (UTC)

If you want encyclopedic then that is the Bourbaki way and thinigs should be top-down. Nobody wants this. Instead everybody wants our articles to be easily understandable. I believe linas proposed to make some articles _extremely understandable_ and thus accessible to children. In addition he proposed to make these articles more interesting by providing connections with other subjects. Don't we want interesting understandable articles? Also proofs are always usefull, and if someone is not interested than they can be skipped, but they provide a way of checking that a result is properly stated and should always be included. MarSch 12:49, 12 Apr 2005 (UTC)

These generalisations are always only indicative. It is pretty clear that some proofs should be included, others not, and so on. Some articles, particularly on recent work (from the past 40 years, maybe) are likely just to be surveys. Something no one has said yet, I think: accessible often will mean visual, so one direction in which to concentrate efforts is to add many more diagrams, not more words (waffle). Charles Matthews 12:52, 12 Apr 2005 (UTC)

I think Revolver got my meaning completely reversed; I wholly agree with him. In fact, I intended to suggest that an article like "torus" could safely include more links to various complex topics. I also wanted to suggest, that the progression from simple to complex be made a tad less challenging, so that the article becomes slightly easier to follow. However, one must stop short of writing a book. Borwein wrote a book about Pi, but if you look at his book, much of the material in it is already covered by various wikipedia articles. For example, Borwein's book on Pi has a chapter on modular forms or something like that (not sure); whatever that connection is, via Ramanujan's series, it could be spelled out in a a few sentences, followed by a wiki link. Similarly, a torus is a great example of a simple Teichmuller space. We don't have to write the book; but adding the words to establish the link would be good.

Very few articles in Wikipedia have the opportunity to bridge from simple to complex. Pi, Torus and modular arithmetic are a few that come to mind. Most of the rest of the articles cover topics that are either too advanced, or have no natural ties to a wide range of topics. This is why I wanted a special category for the few articles that have this magic property of being broadly relevant. linas 15:27, 13 Apr 2005 (UTC)

Disagree with some of this. As far as I know a torus isn't a Teichmuller space. You can relate π to modular forms if you want; you can relate it to Buffon's needle too - I'd be surprised if there was anything you couldn't relate it to, in mathematics. I'm not here to sell anything specific, and I think Wikipedia policies make it better just to build up 'core material' in a steady way. Charles Matthews 18:40, 19 Apr 2005 (UTC)

Error in rendering of html math

''Lp'' gives L^p (rendered as Lp)

''L''''p'' gives L^p (rendered as Lp)

Apparently, for a lot of users, these expressions are identical but I see something close to Lp for the second (where the p is slightly smaller font). I use the konqueror browser version 3.2.1. My question is: is this a bug in the wiki software or in my browser?

''L''p renders the way I would expect: L^p Jan van Male 18:45, 12 Apr 2005 (UTC)

They look the same in Firefox. I^believethis^is the _correctbehavior^fornested tags.

(Although the wiki software seems to remove nested tags! Interesting. Because it assumes they are mistakes? What if you need to print x^f_s? Oh. That works. But nested supers do not: x^fs) h^{e_{h^{e_h^e}}} - Omegatron 19:12, Apr 12, 2005 (UTC)

I use Konqueror, they look the same to me. (and both look good). Your choice of default fonts, maybe? linas 15:31, 13 Apr 2005 (UTC)

Using different fonts does not help here. I'll see whether the konqueror bug database turns up anything usefull. Jan van Male 16:22, 13 Apr 2005 (UTC)

Yes. Nested sup/sub tags are broken in MediaWiki!! :( Vote for bug #599 and maybe it will get some attention and be fixed. Dysprosia 03:02, 20 May 2005 (UTC)

Articles needing diagrams

Is there a page listing mathematics articles which are in need of diagrams? If not, we should create one somewhere. There are plenty of articles which could be listed. I am handy at doing commutative diagrams and don't mind doing them but I'm completely inept when it comes to anything requiring artistic talent. I'd like a place where I could put up some requests and handle others. -- Fropuff 17:02, 2005 Apr 14 (UTC)

Well, there already is Wikipedia:Requested_images#Mathematics. - Omegatron 19:20, Apr 14, 2005 (UTC)

There are presently no requests in there. Maybe I'll try populating it and see if I get any turnaround. -- Fropuff 22:04, 2005 Apr 21 (UTC)

I think a separate page for mathematics-related articles would be a good idea. Fredrik | talk 22:08, 21 Apr 2005 (UTC)

Template:MacTutor Biography — what about Template:MathGenealogy like it?

I have noticed a recently created Template:MacTutor Biography — looks like a cool idea. I've found 26 articles on people linking into the Mathematics Genealogy Project database, and thought about creating a template to link to it, similar to the MacTutor one. Does anybody have any objections against me going ahead and doing it? BACbKA 18:54, 16 Apr 2005 (UTC)

Update: I have done the above. Please use the template when linking to the mathematical genealogy project database entries; also you're welcome to improve the template text. BACbKA 12:50, 17 Apr 2005 (UTC)

Plutonium recalculations

Can someone please redo the calculations involving the half life of Pu on pages RTG and Voyager program to reflect the proper half life of 87.7 years instead of 85 year current value? thx.--Deglr6328 01:55, 17 Apr 2005 (UTC)

Have done this on RTG. -MarSch 12:49, 19 Apr 2005 (UTC)

Several proposals to modify the List of mathematical topics

The List of mathematical topics is a very useful resource, as from there one can track the recent changes to all the listed math articles (try Recent changes in mathematics articles, A-C). Its only weakness is that quite a lot of math articles are missing from there (in addition to the 3537 articles listed at the moment, there are at least 2000 not listed — and this is a very conservative estimate, the actual number could be as high as 3000 or more).

Now that we have the math categories, and most math articles are categorized, one idea is to add to List of mathematical topics by harvesting the articles listed in the math categories. I would be willing to do that, especially that I already have written some scripts which do most of the work.

One issue would be how to sort the articles, this is discussed at Talk:List of mathematical topics, and seems to be a tractable problem, even if one needs to sort the mathematicians by last name.

That was the first proposal. I wonder what people think. Now, the second proposal. Charles Matthews suggested (see again Talk:List of mathematical topics, at the bottom), to remove the mathematicians listed there altogether, as they have their own list, List of mathematicians. So, some feedback on this is also needed.

Now, to the third proposal, closely related to the above. You see, adding lots of new articles will make the lists quite big, and even now some are big (for example, List of mathematical topics (A-C) is 58KB, with almost all contents being links). This causes issues when the server is slow, and when updating with new entries (it happened in the past that the lists actually got corrupted because of that). It can also be hard to check the diffs if lots of changes happen. So, the proposal is to further split the lists, with each letter getting its own article.

Backward compatibility can be ensured by using a template-like thing. If we have the articles List of mathematical topics (A), List of mathematical topics (B), List of mathematical topics (C), one can insert in List of mathematical topics (A-C) the lines:

and the appearance of this list would be as before, and can be also edited as before. The link Recent changes in mathematics articles, A-C will still work (I tried these).

So, I wonder what people think of these proposals. Note that they are related, but a decision on one of them need not affect the decision on the other ones. Oleg Alexandrov 02:33, 19 Apr 2005 (UTC)

All the above seems fine to me. Paul August ☎ 02:57, Apr 19, 2005 (UTC)

Having heard no objections, I will proceed. I will also create a List of mathematics categories, which I will populate as I move along. I will try to work on this this weekend, or either way do it by next Wednesday. Oleg Alexandrov 21:40, 21 Apr 2005 (UTC)

All three proposals sound good to me. The template trick is rather nifty; I had no idea that worked. -- Fropuff 22:02, 2005 Apr 21 (UTC)

Scanned math monographs of Polish mathematicians

Today after following an external link from Lebesgue-Stieltjes_integration I found the following gem [14]. On this page journals and monographs from Polish mathematicians can be downloaded free of charge. (for example the complete french translation of Stefan Banachs Théorie des opérations linéaires.) If nobody objects I would like to start a section in Wikipedia:WikiProject Mathematics with a list of webpages where older mathematical monographs and journal articles can be accessed. I know there are simialar projects in France and Germany going on. I think it is fantastic that many important math journal articles can now be found online making it possible to link them directly from the relevant wikipedia articles.MathMartin 21:24, 19 Apr 2005 (UTC)

Gathering together our conventions

The new page Wikipedia:WikiProject Mathematics/Conventions is to collect up our current set of working conventions. Please add any more to it, and use its talk page to discuss the adequacy or otherwise of those conventions. Charles Matthews 11:13, 23 Apr 2005 (UTC)

Renaming the List of lists of mathematical topics ?

There is a discussion at Talk:List of lists of mathematical topics#Renaming this list. I wonder what you think about those suggestions, and which, if any is preferred. Thanks. Oleg Alexandrov 00:31, 24 Apr 2005 (UTC)

VfD

Someone has listed Pearson distribution for deletion:

Wikipedia:Votes for deletion/Pearson distribution

For some reason this is picking up a few delete votes, and I don't understand why. It's not my field but I know this is a fairly popular distribution nowadays. Any help with cleanup, keep votes, etc, welcome. --Tony Sidaway|Talk 02:18, 28 Apr 2005 (UTC)

"Things to do" section?

I'm thinking about adding a "Things To Do" section to the project page, some thing like:

Things to do

Looking for something to do? There are several places on Wikipedia where mathematics related requests, suggestions and tasks have been collected together:

What	Where
Suggest or edit a mathematics article needing attention	Pages needing attention: Mathematics
Suggest or edit a statistics article needing attention	Pages needing attention: Statistics
Suggest or write a mathematics article	Requested articles: Mathematics
Expand a mathematics "stub"	Mathematics stubs
Suggest or edit a redirect which could have its own article	Redirects with possibilities: Mathematics
Help move PlanetMath content onto Wikipeia	PlanetMath Exchange

Any comments? Paul August ☎ 18:26, Apr 28, 2005 (UTC)

Sounds fine with me. Some of these links already show up at the bottom of Wikipedia :WikiProject Mathematics. The PlanetMath Exchange link shows up somewhere higher on the same page. To integrate all of these nicely would be good. Oleg Alexandrov 18:41, 28 Apr 2005 (UTC)

Ok I've added the above to the project page. Paul August ☎ 22:03, May 3, 2005 (UTC)

Template:Calculus -- is that needed?

Topics in Calculus

Differentiation

Integration

Vector Calculus

Tensor Calculus

I just wonder, are things like Template:Calculus so useful? I put it to the right just for illustration.

(Note: the template refered to above is now at Template:Calculus2 the first template displayed to the right is the "old" template, the "new" template, now at Template:Calculus is displayed below. Paul August ☎ 02:19, May 10, 2005 (UTC))

To me, as I followed its evolution, it looks like an ever growing monster of links, popping up in many places. Besides, it is very long and wide, taking up lots of room even on a 19" monitor with high resolution. Also, I thought the category system should take care of linking articles to each other.

I would suggest this template be eliminated, or otherwise be trimmed to the true calculus, which is integrals and derivatives on the real line, no vector calculus, tensor calculus, and what not. Opinions? Oleg Alexandrov 23:08, 29 Apr 2005 (UTC)

I do not like the template. The scope is too broad and it takes up too much space in the article. So either trim down radically or delete entirely. MathMartin 10:03, 30 Apr 2005 (UTC)

My attitude: I have removed it in a number of places. I think it might actually be useful to some readers; but it doesn't need to be on every calculus article. Charles Matthews 12:49, 30 Apr 2005 (UTC)

I agree. It takes up too much space. I think the vector and tensor calculus stuff should go. Perhaps moved to their own templates. Paul August ☎ 13:23, Apr 30, 2005 (UTC)

I have an idea. We could put Vector Calculus and Tensor Calculus as topics under Topics in Calculus, get rid of all the subtopics that were under those two headings, and then make the overall sidebar narrower. I think that might sufficiently trim it down. Sholtar 21:25, May 3, 2005 (UTC)

I've made a template to show what it would look like the way I suggested. It's located at Template:Calculus2 (now at Template:Calculus see note above Paul August ☎ 02:19, May 10, 2005 (UTC)). If you compare it to the former one, I think this one is much more reasonable in size and would be adequate as far as links are concerned as well. What do you all think? Sholtar 22:21, May 3, 2005 (UTC)

Looks good, thanks! But I can't promise that at some later moment I won't feel like trimming more the template. :) By the way, what do you think of creating a Category:Vector calculus? That will put the related topics in the same box. Same might work for the tensors. Oleg Alexandrov 22:25, 3 May 2005 (UTC)

Hmm... yeah, having a Vector calculus category and a Tensor calculus category would probably help. Should they have sidebars, or just categories? Sholtar 22:46, May 3, 2005 (UTC)

I thought the very purpose of categories is to group similar subjects together. And my own humble opinion is that one does a better job that way than by using templates (sidebars, that is). One day, when I get to it, I will carve out Category:Vector calculus as a subcategory in Category:Multivariate calculus. Oleg Alexandrov 22:59, 3 May 2005 (UTC)

This is true, but templates do make for somewhat easier navigation between topics within a category. Anyways, unless there's any disagreement, I'm going to put the slimmer template in to replace the current one and back the current one up in Calculus2 if it's needed for future reference. Sholtar 23:10, May 3, 2005 (UTC)

I suggest limiting the use of templates to articles most likely to be read by high-school and college students, and then only on articles that are widely and broadly taught. They have pedagogical value for a student trying to master the material. Thus, the fat template might actually be a lot more useful than the thin template. However, it should be used on only a few pages. linas 17:02, 14 May 2005 (UTC)

Now on VfD: Evaluation operator

The mathematical article evaluation operator is now on VfD; see Wikipedia:Votes for deletion/Evaluation operator. It is claimed to be original research. Unfortunately, it is now too late for me to investigate it. Related articles are multiscale calculus and theta calculus. -- Jitse Niesen 00:39, 10 May 2005 (UTC)

I should have added that I spotted this while listing an another article, namely John Gabriel's Nth root algorithm. Its VfD entry is at Wikipedia:Votes for deletion/John Gabriel's Nth root algorithm. -- Jitse Niesen 08:15, 10 May 2005 (UTC)

Reminds me of this group: eucalculus, differation, atromeroptics. These seem to be personal definitions/original research, and should presumably go to VfD. Charles Matthews 08:47, 10 May 2005 (UTC)

The evaluation operator surfaced on the german Wikipedia, was discussed at de:Portal Mathematik and put to VfD there. After assuring myself that only the original author uses this term but was rather busy creating a net of articles here, I put it on VfD here. --Pjacobi 09:58, 2005 May 10 (UTC)

I listed eucalculus on VfD, after verifying that I could not find a peer-reviewed article about it. The VfD entry is Wikipedia:Votes for deletion/Eucalculus. -- Jitse Niesen 22:57, 12 May 2005 (UTC)

Discussion on german Wikipedia seems to indicate, that Theta calculus and Multiscale calculus, at least in their current form, are original research by User:Dirnstorfer. Opinions? VfD? --Pjacobi 15:26, 2005 May 13 (UTC)

Evaluation operator has now been deleted, and the other two articles are listed on VfD; their entries are at Wikipedia:Votes for deletion/Theta calculus and Wikipedia:Votes for deletion/Multiscale calculus. -- Jitse Niesen 22:24, 17 May 2005 (UTC)

Major fields of mathemtics

I've added an 'Major fields of Mathematics' template to the Matematics Categories page. It's based on the classification used in The Mathematical Atlas. Any comments or suggestions? --R.Koot 13:38, 10 May 2005 (UTC)

The template in question is at Template:Mathematics-footer.

Now, first of all, the style here is not too use that many capitals. That is, one writes "Linear algebra" instead of "Linear Algebra", and "In mathematics" instead of "In Mathematics".

About the template. I myself do not think it is a good idea. There is already a Areas of mathematics article, having good information.

I would like to note that the very purpose of categories is to group related subjects together. As such, navigational templates should not be used that much, they just become link farms showing up all over the place.

This is my own personal thinking, and I am somewhat biased against templates for the reason above. I wonder what others think. Oleg Alexandrov 20:36, 10 May 2005 (UTC)

On this one, I'm going to have to agree with Oleg Alexandrov. I like templates personally, but they have to be used with moderation. I just don't think this one is neccessary. Sholtar 23:23, May 10, 2005 (UTC)

I agree with Oleg. I am against using a template for this category. Note: I believe that templates are useful and nice in certain pedagogical settings, see debate on the calculus template above. However, a template is inapporpriate for this cat. linas 17:30, 14 May 2005 (UTC)

To be honest I think that this template shouldn't be neccessary, I had two (good) reasons for creating one. The first is that is is also done in the Category:Technology and more importantly, the current categorisations of articles is quite a mess, which makes it very difficult for the non-mathematicain to quickly get an overview of mathematics major fields. --R.Koot 00:32, 11 May 2005 (UTC)

The Category:Mathematics is not a mess. Math has many more facets than just subject areas. The categories reflect this. Oleg Alexandrov 00:47, 11 May 2005 (UTC)

We should probably come to a consensus about whether or not to do this in all categories, but just because someone did it for technology doesn't seem to be a feasible reason to do it for mathematics. I think unless a consensus is reached about the subject, default to whether or not it's neccessary. This one I just don't think is neccessary, especially because there's an article about the major fields. Sholtar 05:23, May 11, 2005 (UTC)

I agree that mathematics is much richer than it's fields. Therefore the template is biased, but adding more links to it make it lose it's purpose so I suggest the following:

Remove the template.
Put all the articles that are categorized direcly under mathematics in a subcategory, except for the Mathematics article itself, and maybe a select group of introductory articles like Areas of mathematics (articles that help navigate you quickly and would propably be found in a real encycolpedia).
Rename a lot of the categories from Mathematical foo to Foo_(mathematics), this would make the index more readable and is the prefered Wikipedia style, I believe.
Design a good categorization system and make people aware of it. A suggestion

   Logic             Computer Science                   Literature
   Set Theory        Signal Processing                      Journals
   Arithmetics           Digital Signal Processing      History
   Combinatorics         Transforms                     Recreational Mathemtics
   Number Theory         Wavelets                           Games
   Algebra           ...                                ...
   ...

Now you could either put all the categories in the three columns together under Category:Mathematics or put them in their own subcategory (Pure Mathematics, Applied Mathematics), resulting in a rather tiny index, whcih would probalbly be my preference, but I think this might be a bit too controversial? --R.Koot 10:52, 11 May 2005 (UTC)

(This was written before I saw R.Koot's comment above.) At the moment, we have several ways to navigate through the articles:

Wikilinks. This works well, but requires the user to read a lot of text to find the link he is interested in.
Categories. They are very useful, but in my opinion not very user-friendly. I actually agree that Category:Mathematics is a bit of a mess; part of the problem is that the list is sorted alphabetically, another part is the lists mixes very different kinds of subcategories, like Cellular Automata (a small subfield), Geometry (a big subfield), Formula needs explanation (a category meant for editors) and Theorems.
Lists like list of linear algebra topics. They provide more flexibility (one can sort articles as one wants, introduce subheadings, annotations), but the experience shows that these lists are difficult to maintain.
Navigational boxes. Again, I think these can be useful, but they take up space (especially when implemented as sidebars instead of footers) and they tend to grow out of control.

Unfortunately, none of these is perfect. I believe Charles Matthews has written a whole piece comparing these navigational aids, but I cannot find it anymore. But it would be good to build some sort of consensus on which to use where. -- Jitse Niesen 11:10, 11 May 2005 (UTC)

The point about our existing systems of lists and categories is that they have grown up organically, in line with the articles. They are not an imposed, top-down categorisation. I support strongly the idea of doing it this way. After all, where do top-down lists come from? They are basically a bureaucratic idea, and not very compatible with wiki self-organising principles. What we need are a few structures to support the existing system. For example, a 'guide' page outlining the category system, and some project page on which to discuss areas where the coverage remains weak. Charles Matthews 08:55, 13 May 2005 (UTC)

This is a very good point. MathMartin 16:44, 14 May 2005 (UTC)

I see that R.Koot went ahead and performed the edits anyway, despite the discussion. I disagree with a number of the edits. About a month ago, Category:mathematics had approx 300 articles. I categorized almost all of them, leaving behind about 30 articles that gave a flavour of mathematics, that dealt with topics that were broadly applicable to all branches of mathematics, or that were inter-disciplinary, giving a sense of the relation of mathematics to broader society. While not perfect, the remaining lone articles in combination with the list of categories, gave a pretty good overview of what math is about. I am rather distressed that the collection of individual articles were shorn out of the category (I started reverting last night, I plan to continue when my spirits increase). linas 17:46, 14 May 2005 (UTC)

As to the 65 subcategories of mathematics, its certain that this list could be cleaned up a bit and shortened; but I'm sure I'd shit the proverbial brick if it was not done correctly. linas 17:46, 14 May 2005 (UTC)

vote for MarSch's adminization

Please visit Wikipedia:Requests for adminship and vote on my application. I want to do some edits on protected pages, but I have too few edits yet to get enough anonymous support, so since you guys know me a little better I'm hoping that my edit count will be less of an issue. So please take a look. -MarSch 14:43, 13 May 2005 (UTC)

Hoaxer is back

Kimberton's Poppages Theorem, now deleted, was the Bryleigh (Cayley/Newbirth) hoaxer again. Not possible to do a long-term block on the IPs used. Everyone please look out for hoaxes. Charles Matthews 14:08, 14 May 2005 (UTC)

Is there a way of monitoring what articles are added to (or removed from) a category? I'm wondering how you discovered the existance of the above page. (No doubt, you're aware of my recent bout of categorization and thus interest in such things.) linas 17:54, 14 May 2005 (UTC)

It's possible to monitor added articles, but not removed articles; see m:Help:Category#Detection_of_additions_to_a_category. Daniel 18:26, 14 May 2005 (UTC)

mathbf or boldsymbol?

Typically, bold font is used for vectors, as in $\mathbf{x}=(x_1,\ldots,x_n)$ . Note that $\mathbf{\xi}$ does not have the desired effect. I think it would be better to use \boldsymbol as in $\boldsymbol{x}(t)=\boldsymbol{f}(t,\boldsymbol{\xi}(t))$ (Igny 23:52, 15 May 2005 (UTC))

Well, we'll use whatever works. We can use mathbf, and when it doesn't work, we can use boldsymbol. Observe also that $\boldsymbol{x}$ does not show up the same as $\mathbf{x}$ , which may be undesirable. Dysprosia 23:49, 15 May 2005 (UTC)

I didn't know about boldsymbol, but I like it. Use whatever is more appropriate. -MarSch 11:43, 16 May 2005 (UTC)

Vector valued variables should be written bold but not italic so you should use \mathbf not \boldsymbol --R.Koot 00:37, 17 May 2005 (UTC)

Agree with R.Koot. Oleg Alexandrov 01:18, 17 May 2005 (UTC)

Problem with the "what links here" feature, affecting the recent changes to list of mathematical topics

If you check what links to the article Osculating circle, one can see that it linked from the List of mathematical topics (O). However, it does not look as if it is linked from list of mathematical topics (M-O), which is very strange, because if you click on that page you will certainly see the article listed.

On the other hand, if you look at what links to Alan Turing, you will see a link from List of mathematical topics (S-U), which is wrong, as if you visit List of mathematical topics (S-U) you will not see Alan Turing listed there. I removed this article from there a long while ago (since it shows up in list of mathematicians).

As such, the "what links here" feature does not show links which exist, and does show links which do not exist. This affects the "rececent changes" from list of mathematical topics. I find this very strange. Anybody having any ideas with what is going on? Oleg Alexandrov 19:15, 18 May 2005 (UTC)

I seem to remember that there are some bugs with What links here when combined with templates. I think you should look in the list with wikimedia bugs for details, or wait and hope that somebody gives you a more precise answer. Jitse Niesen 21:06, 18 May 2005 (UTC)

I've been seeing stuff like this in more than Mathematics, but I can't really help you out in knowing what the problem is. It's probably just some kind of bug with the overall feature, as Jitse said. Sholtar 04:13, 2005 May 19 (UTC)

I went to List of mathematical topics (J-L) and just inserted a comment and saved the thing. Miraculously, the "what links here" feature worked just fine afterwards! The moral I think is that every once in a while applying a dummy edit will refresh the database, and quirks as above -- where linked articles did not show as linked and unlinked articles showed as linked -- will not show up. Oleg Alexandrov 19:39, 21 May 2005 (UTC)

Move of "Mathematical beauty" to "Aesthetics in mathematics", comments?

(Discussion moved to Talk:Mathematical beauty#Move of "Mathematical beauty" to "Aesthetics in mathematics", comments?. — Paul August ☎ 20:00, May 27, 2005 (UTC))

Covariant, contravariant, etc.

Here is some discussion from my talk page. -- The Anome 14:57, May 20, 2005 (UTC)

User:Pdn wrote:

The entry Contravariant has a notice: "This article should be merged into covariant transformation. If you disagree with this request, please discuss it on the article's talk page." I very much disagree. I wrote something on the discussion page but the notice is still there, so here I go.

The term covariant has two very different meanings. In relativity theory (and probably differential geometry) it refers to the invariance of a quantity (generally a measurable one) when coordinates are changed, including changes among relatively moving reference frames. For example, the velocity of light is covariant, and the rest mass of an object can be determined in a way that does not depend on coordinate system or reference frame, i.e. a covariant way. But covariant also refers, unfortunately, to certain components of a vector or tensor that do usually change very much when the coordinates change. The simplest example is the vector from one point to another in ordinary three dimensional geometry. In the usual Euclidean metric, the numerical values of the contravariant and covariant versions of the vector are identical. If we perform a coordinate transformation doubling all the coordinates, (x',y',z') = (2x,2y,2z) then all the contravariant coordinates double but the covariant ones are cut in half. The distance, which depends only on the products of the coordinate differences (contravariant times covariant) (summed, and then the square root taken) does not change. It is covariant, but the covariant coordinate increments were all cut in half. The transformation is a covariant one, but does not preserve the covariant components. The invariance of the distance relates to the discussion of "covariant transformation" while the discussion of the changes in individual coordinate values, contravariant vs covariant, belongs in "contravariant". Thus, the notice suggesting merge should be removed. If you want to match "contravariant" with something, then you should create a page "covariant component" as opposed to "covariant transformation." Else you could rename "contravariant" as "Contravariant and covariant components" and I will port some of this discussion in there. These very concepts are rather passé now, at least in relativity theory, as the use of differential forms is supplanting old fashioned tensor analysis, but some folks still use tensors for fluid and continuum mechanics [15], rheology [16], mechanical vibration, crystal optics [17] and other fields not so suitable for the fancier newer maths so the entries should not be dropped. Simple tensor analysis is helpful when a cause (force, mechanical stress, polarized optical beam, e.g.) produce an effect imperfectly aligned with it. Such usages do not lend themselves as much to exterior differential form analysis so there's no reason to toss old-fashioned tensor analysis. Pdn 13:48, 19 May 2005 (UTC)

[...time passes...]

Dear Anome (sorry to put this as a trailer on some vandalism , but I do not know how to create new messages without appending to old.) I'm afraid that the two usages of "covariant" are so very different that your concept of parallel disambiguation pages won't fly. I have never heard of a "contravariant transformation", though you could ask a person more expert than I in differential geometry or differential forms. As I explained, "covariant components" and "contravariant components" are two faces, so to speak, of the same thing. The second one, in the case of the differentials of coordinates (hope I restricted my remark to that case) is an integrable quantity, a thing many people do not realise. Thus, if one totals the contravariant component of "dx" around some closed curve one gets the change in x, a property not generally shared with the covariant component of dx. I do not know how "covariant" came to be used for vector components, but I do not see it as related to the invariance under transformations. The devil of it is that we can't just change "covariant transformation" to "transformation with invariants" for many reasons, including wide usage probably started by Einstein. You could make up a disambiguation page for "covariant" pointing to "covariant transformation" on the one hand and "covariant tensor components" on the other. Unfortunately you cannot just use names like "covariant tensor" and/or "contravariant tensor" because these are two faces of one item. So you would have to work with "covariant tensor components" and make up a page like the existing one for "contravariant" for that case, so you could change "contravariant" to "contravariant tensor components." Actually, now that I think of it you could rename "contravariant" as "contravariant and covariant tensor components" and I'd be glad to fill in the "covariant" portion - you can leave a stub. Then the disambiguation page would fork between "covariant transformation" and "contravariant and covariant tensor components."

I think we probably need to discuss this at the Wikipedia:WikiProject Mathematics I agree with you about the covariant and contravariant components of tensors; tensors seem to be a particularly tricky subject here for some reason. The term "contravariant transform" seems to have been used: see Google for a few examples of what seem at least at first sight to be valid uses. The other terms really need some thought; you've certainly convinced me that a simple merge/redirect alone will not do the job. To that end, I'm copying your recent comments and this reply into the Wikipedia talk:WikiProject Mathematics page. -- The Anome 14:51, May 20, 2005 (UTC)

Some confusion here. Differential forms, which are always contravariant, can only 'replace' tensors that are already contravariant and antisymmetric with respect to interchange of indices. The "components" terminology causes more confusion than anything else in this area, I think. In the presense of a metric you can indeed 'raise and lower indices', so have the option of taking the components of the variance you want; but that is very much not the basic situation with tensors. Charles Matthews 15:14, 20 May 2005 (UTC)

When physicists say covariant, they mean tensorial as far as I know. Since tensors exist without reference to any coordinate system they don't transform.

This is a fine mess we have here. I think the article about covariant transformations is really about coordinate transformations. Then the components of tensors transform co(ntra)variantly as per their nature. Perhaps we should merge the lot with tensor or tensor field. You can only take covariant components and contravariant components of a (co)vector when you have a metric.--MarSch 15:34, 20 May 2005 (UTC)

I am afraid you maths guys are taking the definitions and discussion too far away from what is used by engineers and the more pedestrian of physicists. I have taught relativity using differential forms, but not for a while and had forgotten that part about their always being contravariant. Engineers would be floored by trying to use differential forms and I am not even sure they are useful for elasticity, fluid mechanics in Newtonian theory, birefringent optics, and so on. In all the cases normally used by physicists and engineers, you do have a metric. So the math is getting far afield by discussing cases with and without metric. There are some anomalous theories in physics where the metric is affected by another field (e.g. Brans-Dicke theory and other "conformal" theories,) and it may be that branes can make the usual usage of a metric muddled (path dependent) but you are getting so far from what can be used in most colleges and in university courses in physics or engineering up through second year graduate school, that I am getting queasy. In relativity, we distinguish general covariance and covariance under the special theory of relativity. In the latter case, measurable quantities have to be invariant to the Lorentz transformation (in the most general sense, including translations and rotations, as well as [constant] velocity differences, but not to time-varying rotation). In the former, the measurables must be locally invariant to change to systems in relative acceleration, including time-varying rotation. While coordinate changes are not measurables in the strictest sense, distances are. By "the strictest sense" I mean that a reliable measuring tape or clock does not measure a coordinate, but it measures the distance, including the metric. I will stop here or the debate entries will become too long. Anyway, to physicists "covariant" does not mean "tensorial" in my opinion, it means invariant to certain coordinate and reference frame changes as I described above. Pdn 14:42, 21 May 2005 (UTC)

I'm confused by the confusion. A covariant transformation is the thing that changes the coordinate system on a covariant tensor component on a (mixed) tensor. Ditto for contra. Mass and speed of light are invariant and not covariant. The people who study branes and Brans-Dicke know differential geometry inside-out and upside-down, so I'm not worried about them. The above seems to be implying that there is something else out there, not yet documented in WP, that is called a "covariant transformation" ?? what is that thing? linas 00:19, 22 May 2005 (UTC)

You are absolutely right - sorry - there is no such thing as a covariant or contravariant transformation. If one wants to make up separate names for the operations on covariant and contravariant components, one could use these names, but that would obscure the fact that (when there is a metric) both kinds of components are just different aspects of one thing, the tensor. So I would think that the two items could be combined into one about how to transform tensors, in component form. And also you are right that I should have used "invariant" for scalars that remain fixed in transformation. I just now referred (way) back to Peter Bergmann's book "Introduction to the Theory of Relativity" (Prentice-Hall, 1942) and my memory is returning: equations can be covariant under certain kinds of transformation; the transformation is not the covariant thing. When the equation (such as $G_{ab} = R_{ab} - {R \over 2} g_{ab} + \Lambda g_{ab}$ ) is preserved under coordinate transformations it is covariant. I also agree, and I am glad you agree, that people doing advanced work such as branes and conformal theories do not need any help from Wikipedia; that is why I wanted to steer away from cases where there is no metric, which were referred to by MarSch on May 20. So I suppose we need entries for tensors and their transfromation rules, covariant and contravariant components, and covariance of equations - the exact titles are not clear to me. In regards to the previous comment (also by MarSch): ":::When physicists say covariant, they mean tensorial as far as I know. Since tensors exist without reference to any coordinate system they don't transform." I agree in part - the tensor is "there" and we just see different views of it when we take components in different systems, but we need to retain some of what was taught to engineers, physicists and maybe even some differential geometers, who can't easily be weaned from components. I am now probably going to cease writing here because there is, indeed, so much confusion over covariant, covariant transformation and contravariant, and you mathematicians should be the ones to settle it. I just hope you leave something useable by scientists and engineers who do not want to learn more advanced mathematics than they have to, but want to use tensors.Pdn 03:12, 22 May 2005 (UTC)

Yes I agree, three articles on essentially one topic is too much. All three, covariant, covariant transformation and contravariant should be merged. Yes, the expression "covariant transformation" is a poor choice of language, and the new article should be purged of this expression. Oleg is right, there are times when a metric doesn't exist, or the metric is not invertible, but these cases should be treated in distinct articles (non-invertible metrics occur in subriemannian geometry; a special language exists for this case.). The component notation is just fine for the merge article. (The metric-less and componenent-free case is already dealt with in the pullback/pushforward articles.) Not sure what MarSch is going on about with this component-less thing; I'd like to see him write a computer program that graphs pictures of tensor quantities without using components ;-). If an equation is invariant under a change of coordinates, one calls that equation invariant in modern terminology, not covariant. I guess some folks might still use the term "covariant" in this case, but suspect its anachronistic. I'm not planning on doing any merging myself. linas 06:40, 22 May 2005 (UTC)

Oh, and I do see one point of confusion: the "transformation" of tensors under changes of vector basis is related to, but not at all the same thing as the "transformation" of tensor fields under change of coordinates. Unfortunately, these two distinct concepts often do get conflated. linas 06:48, 22 May 2005 (UTC)

I do not see any difference between a tensor and a tensor field, unless the former is a very special case, being defined at only one point, and therefore of little use. I do not consider terms like "covariant" (for invariance of an equation under special-relativistic transformations) and "generally covariant" for invariance under more arbitrary transformations in GR (I say "more arbitrary" because I want to keep the light cones etc preserved) to be out of date. That's what Einstein used so it is worth preserving; otherwise people need to ask the mathematicians who changed the definition what Einstein meant. This kind of thing is often tried by well-intended people who like, nevertheless, to play "follow-the-leader." One outstanding case was the late (I believe) Parry Moon of MIT. He wrote the article on illumination in the 1956 Encyclopedia Brittannica, wherein he tried to replace ordinary concepts like brightness, illumination, luminous flux, the lumen etc by a new breed of terms such as "pharosage","lamprosity" (sounds like something that invaded the Great Lakes, killing many gamefish), "blondel," "stilb" and "apostilb." The terms have not stuck very well but can be found here and there. Moon and collaborators (such as Domina Eberle Spencer and Euclid Eberle Moon) wrote many bizarre papers. Early on, Moon and Spencer claimed, in J.Opt.Soc.Am. 43,635(1953), that according to relativity, light from distant galaxies could reach Earth in a few hours or days. This was picked up by young-earth creationists, and stil is, but it is nonsense. More recently, the indomitable trio published items supporting a ballistic theory of light in Physics Essays, and for the latest see this: [18]. So be careful about renaming things like the covariance of an equation. It may be a sign of impending senility. OK, nowadays a janitor is a "building engineer" and an overweight person is "gravitationally challenged," but that's harmless, while to side-track people who want to understand the writings of Einstein, Minkowski, Weyl, Pauli, and many capable if not illustrious successors by requiring them to consult Wikipedia talk pages to find out that the "covariance" of an equation is now called "invariance" is uncool. The forgoing was not a filibuster and I am not a filibusterer [19]. One final point: Somebody (I believe he was named Kretschmer) once pointed out that you can make anything into a tensor by defining it in one system and transforming it to any other by tensor transformation rules. So, reflecting on that, we see that "covariance" of a physical quantity or scientific equation means that the same measurement process used to measure it in one system will measure the transformed version of in (transformed using tensor rules) in another system. For example. E^2-B^2 where E is electric field and B magnetic is covariant. E-B is not, but if you measure E-B in one frame and then transform it to other frames by brute force with tensor rules you can claim that it is covariant or invariant etc. So "general covariance" has more to it - that the physical content is carried over to new frames - not just math.Pdn 05:09, 23 May 2005 (UTC)

What I don't like about merging into covariant and contravariant is that those are adjectives, so the article is about a descriptor instead of a thing. As a physicist I came across covariant transformation long before covariant, but that's because we usually define co(ntra)variant vectors by how they transform. If they're going to be merged into one article, how about at least something like covariant tensor. But personally this differential geometry talk is above my head, and I'm just pulling for them ending up somewhere that makes sense to physicists, too. --Laura Scudder | Talk 22:41, 26 May 2005 (UTC)

Since this issue is being clouded by various points-of-view, I think we need to talk structure and organisation first. Nouns are better than adjectives, as Laura implies: so we need to treat covariance and contravariance in some central place. I suggest making covariance and contravariance the 'top level', most general article, and hang things like tensor field (all those indices) off it. Charles Matthews 09:17, 27 May 2005 (UTC)

Talk:Squaring the circle

Perhaps my fellow math-nerds should look at Talk:Squaring the circle. I have taken the position that the article is about the legitimate mathematical problem of squaring the circle and the proof, published in 1882, that it is impossible; that although it should mention crackpots who continue working on squaring the circle, nonetheless that that topic is at most tangential (to the circle?)Pdn 15:10, 21 May 2005 (UTC). As nearly as I can tell, a Wikipedian named Sebastian Helm is saying that squaring the circle is a topic invented by crackpots rather than a legitimate mathematical problem. He seems very angry at my assertion to the contrary, which he called "BS". Michael Hardy 04:06, 21 May 2005 (UTC)

I am sorry about the misunderstanding. What i called BS was your "example of a conspiracy of space aliens". I never said that "squaring the circle is a topic invented by crackpots". And i got angry because you keep putting words in my mouth which i never said or meant (on three counts including this one). You don't even have to assume good faith, if you just stick with the facts. — Sebastian (talk) 16:30, 2005 May 21 (UTC)

I think all of this started with Sebastian putting Squaring the circle in Category:Pathological science, which is kind of undeserved. Oleg Alexandrov 17:45, 21 May 2005 (UTC)

I agree with Michael and Oleg in questioning the appropriateness of the category "pathological science", for this article. In fact, I think that "pathological science" is a problematical name for a category. The description given here seems to imply as much, and Sebastian seems to agree, quoting from here: "I don't like the name "Category:Pathological science", either, but this was the closest i could find." A good category name should be self-explanatory, which this one is not. It should not require a paragraph to define, and then still be not quite clear (to me at least). Having said that, there is some merit to what this category is trying to describe. And it does have some relationship to this article. And there are other mathematical topics which might share this relationship, for example other impossible contructions like angle trisection (do people still try to do this?).

As to the somewhat unpleasant discussion between Michael and Sebastian, I think there has been some misunderstanding going on. I do not see that Sebastian said or implied that "squaring the circle is a topic invented by crackpots rather than a legitimate mathematical problem". Nor do I think he meant to imply that by assigning the article to the category "pathological science", although I can see why Michael might have thought so. I think everyone agrees that "squaring the circle" was a legitimate problem considered by serious and reputable mathematicians, prior to the proof that it is impossible. However, that people nevertheless are still trying to square the circle, is an interesting phenomenon, which is deserving of some thought and discussion, and perhaps even a category. Paul August ☎ 21:08, May 21, 2005 (UTC)

Yes, I agree. This is exactly what i meant! Thanks for getting back on topic! Possible names include:

pointless scientific efforts
misguided scientific endeavours
research which flies in the face of facts

— Sebastian (talk) 22:10, 2005 May 21 (UTC)

Squaring the circle is not the right article for a more-than-tangential mention of mathematical crackpots. Certainly a separate article could treat that. Michael Hardy 01:24, 22 May 2005 (UTC)

Micheal, I think the request is to come up with a catchy category name that says "this topic is a legit topic that tends to attract crackpots"; not just math but in general. free energy and casimir effect spring to mind. linas 06:56, 22 May 2005 (UTC)

What exactly is the motivation behind creating a category bringing together subjects 'attracting crackpots'? Surely not to attract crackpots more effectively. It seems kind of unencyclopedic to give these things too much attention. Charles Matthews 20:51, 27 May 2005 (UTC)

Perhaps category:pseudoscience is the category which Sebastian is looking for. Although I don't think it would be appropriate for Squaring the circle. And pseudomathematics could be the right place for a more lengthy description of the phenomenon represented by the continued attempts to square the circle. Paul August ☎ 21:19, May 27, 2005 (UTC)

I'll say first of all that it's clear all this resolves around the aggressively named category "Pathological science". Let me draw a more modern parallel.

In complexity theory, a classical result is that the class NL, and indeed the entire log-space hierarchy, collapses to NL — that is, NL is closed under complement. I've read papers predating this discovery by the most eminent of researchers, still alive today, that claimed that most researchers reasonably believed that the log-space hierarchy did not collapse, and they based some of their results on this. A similar thing happened with the discovery that SL is closed under complement, widely believed to be false not so long ago and now trivial as a consequence of L=SL.

The short of it is, very smart and very reasonable people have good reasons to believe that things that are false. Neither they nor the goals they pursue are "pathological" or even "misguided"; rather, they are reasonable actions based on available knowledge.

Finally, one more example: I can't remember the name, but one of the founders of noneuclidean geometry actually believed that Euclid's parallel postulate could be derived from the remaining axioms — in other words, his aim was to disprove the existence of any alternate geometry. He assumed that the axiom was false for purposes of contradiction, going on to write a large book deriving many results from noneuclidean geometry, eventually uncovering a "contradiction" which was actually an error and proclaiming the theorem proved. Was he a crackpot? No. Was his effort pointless? Not at all! He didn't achieve the unattainable goal he set, but he discovered a lot of useful things in the process. You don't tell a kid they'll never be an astronaut.

So what's a good category? I vote for Category: Disproven conjectures.

Deco 09:44, 28 May 2005 (UTC)

Possible crackpot pages

Seems that User:Laurascudder has unearthed a cluster of physics pages of highly dubious content. I'm not sure what to do with them. I'd suggest VfD except that I don't quite know that process.

Coherence condition
Electromagnetic jet
Extended Yukawa potential
Nonlinear Coulomb field
Nonlinear magnetic field
w-field

and possibly also

Quantization of the pionic interaction

although this last one almost does make sense.

As a whole, these pages seem to be filed with errors, ommisions, indecipherable formulas, a mixture of trite and deep statements, notation pulled from many different areas of physics and mashed together in highly non-standard, incoherent ways. My gut impression is that most of this stuff is dubious "original research" by an out-of-work Soviet nuclear technician who has a strong grounding in physics, but was unable to master quantum field theory as it is taught today. So what's the WP process for stuff like this? linas 16:39, 22 May 2005 (UTC)

Linas, I recommend heading over to Wikipedia:Votes for deletion and going to the bottom of the page, there are instructions there for listing on VfD. Even if these pages end up being worth keeping, it's still a good thing to know. Sholtar 17:11, May 22, 2005 (UTC)

These are all created by the same guy - Rudchenko (no user page, so link shows all contributions to date). Maxwells nonlinear equations looks especially suspect to me... (I always understoof Maxwell's equations are the whole and the entirity of non-quantum electromagnetism). I will try contacing people I know to get some definate answers. Tompw 17:07, 22 May 2005 (UTC)

Gluonic vacuum field should also be looked at. It seems to belong to the same cluster of articles. Paul August ☎ 03:28, May 23, 2005 (UTC)

Well, it seems they have gone to VfD anyway, which is a process hard to stop once it is started. Rather than theorising about the author, I think it is important to focus on what we know about the content. Which is indeed about an alternate line of field theory, to standard QFT. There is a key passage on one of the pages, which I will cite when I find it. Charles Matthews 10:01, 23 May 2005 (UTC)

Right, the place to begin is certainly w-field, with its reference to an approach to field theory attributed to Gustav Mie. One approach is to assume that all essentially all these pages are working out consequences of that idea. Original research they may be - I wouldn't know enough about this corner of theoretical physics to know. I don't think they should be deleted simply because the approach is different from standard QED. Charles Matthews 10:08, 23 May 2005 (UTC)

Hi Charles, I'm the one who VfD'ed it. The reason for this is not so much that they're non-standard (you should know by now that I have a weakness for non-standard things), but rather 1) they're pretending to be something they aren't: one could formulate a non-linear electrodynamics, but this isn't what's being done here. 2) They're filled with deductive errors. Sure, the pionic field is pseudo-scalar, (it changes sign under parity), but to argue that this means that the associated (non-relativistic) potential is purely imaginary is bizarre/wrong; the (non-relativistic) Hamiltonian wouldn't be hermitian, which is wrong. I suppose one could try to build up some quantum theory with non-Hermitian pseudo-Hamiltonians, but you'd have to lay oodles of groundwork first, and it might not work out in the end. 3) The same formulas show up in gluonic vacuum field and quantization of pionic field. That's wrong. If it had been called pionic vacuum field, that might have flown, but gluons are non-abelian, they belong to the adjoint rep of su(3); they're very different than pions, which would be a singlet of su(3). One musn't write an article about gluon-anything without saying su(3) at least once. 4) Multiple instances of the usage of the non-relativistically covariant Schroedinger equation, followed by remarks such as "we can use the Klien-Gordon equation". 5) article on coherence condition: one can't write down a kinetic term that way, at least not without oodles of justification. The 'coherence condition', a purported variational minimization of the Lagrangian, is missing a few terms. The presentation turns incoherent shortly thereafter; the variation δ s should not be thought of as "non-fixed numbers".

As far as I'm concerned, this stuff is a word salad of formulas, the likes of which is common in the underworld of flying saucer theory. Sure, one can build alternative theories, but one needs to lay a groundwork, define terms and the like. One mustn't say "D^2s=0" without first explaining what "D" is. And next, one must point out in the preface that these are "alternative theories", rather than pretending that Maxwell had invented some kind of non-linear equations (and thereby implying legitimacy). That's why I VfD'ed them; these articles are beyond repair. linas 14:49, 23 May 2005 (UTC)

FWIW, here's why I expound so confidently: my PhD thesis was on the Casimir effect inside of protons/neutrons, so I know a lot about the quantum vacuum state and QCD in general. This quark vacuum was coupled to a topological soliton made out pions. That's how I got my grounding in math. As to pions ... somewhere (misplaced) I have a copy of the "Pion-Nucleon Interaction", signed by the authors, Andy Jackson (my advisor) and Gerry Brown, (his advisor). Gerry, unwelcome in the US, spent the McCarthy years running around Europe setting up nuclear research centers; one might say things like RHIC and the neutron star equation of state are his legacy. You can find a few of my lame publications from that era on scholars.google.com. e.g. "Justifying the Chiral Bag", cited by 21, hot damn!linas 15:15, 23 May 2005 (UTC)

One more quickie remark: The standard formulation of a non-linear version of Maxwell's equations is known as Yang-Mills theory, which these days is understood to be a principal bundle with fiber SU(N). Rudchenko's attempts seem to be an effort to use SU(2), given the appearence of the cross-product. Until he explains how it differs from the 'standard' SU(2) formulation, its just bunk. linas 16:51, 23 May 2005 (UTC)

The articles are of such low quality they would have to be rewritten anyway. Further, the only person that seems to know anything about it Rudchenko stopped contributing several months ago. And last but not least I could not find any papers on the subjects (except for w-field and nonlinear magnetic field) meaning this will never be verifyalbe. So I'm in favor of a delete. --R.Koot 12:45, 23 May 2005 (UTC)

Rudchenko is still contributing but is using anon IPs, see: 194.44.210.6, and probably: 195.184.220.198 and 213.130.21.162. Paul August ☎ 16:52, May 23, 2005 (UTC)

I'm confused. From 195.184.220.198 and 213.130.21.162 he tweaked some formulas, which you wouldn't do if this was a hoax. While he has been creating a link farm and given some very strange replies on talk pages from 194.44.210.6. (If your known similar calculation please give sign here. Rudchenko.)? --R.Koot 18:27, 23 May 2005 (UTC)

inetnum: 194.44.210.0 - 194.44.210.255

descr: Donetsk Regional General Scientific Library

country: UA (Ukraine)

inetnum: 195.184.192.0 - 195.184.223.255

country: UA

address: Scientific & Technological Centre FTICOM

inetnum: 213.130.21.0 - 213.130.21.255

descr: Dial-up pools and interface addresses. FARLEP-TELECOM-HOLDING, a subprovider of Farlep-Internet in Donetsk, Ukraine

country: UA

I think it is more likely that these articles are original research than hoaxes. Paul August ☎ 19:07, May 23, 2005 (UTC)

Extended Yukawa Potential, Yukawa Potential. Maybe this is of some use to anyone? --R.Koot 13:04, 23 May 2005 (UTC)

Be aware that google and even scholar.google is blissfully unaware of most modern physics and math. Dead-tree media still underpins the dominant publishing paradigm. linas 16:07, 23 May 2005 (UTC)

Revert to an old version of manifold

(Moved to Talk:Manifold. Oleg Alexandrov 16:59, 27 May 2005 (UTC))

Use of this page

It is better, I think, if discussions on page content are left on the talk pages of the articles. It is perfectly fine if, in the case of an article of basic importance to mathematicians, an invitation to participate is made on this page. I really don't think long discussion threads on specific content issues are correctly placed here. Charles Matthews 10:11, 27 May 2005 (UTC)

Right. Sorry, I did not think it will go that far. Not again. Oleg Alexandrov 15:33, 27 May 2005 (UTC)

I agree with Charles. For obvious reasons, page-specific discussions, usually best occur on that page's talk page. I think there is a tendency to raise page-specific issues here, in order to reach a potentially wider audience, which I must say I do find useful, both as one who wants to "reach", as well as be reached. But as Charles implied, that can, to some extent at least, be accomplished by posting a notice (perhaps together with an excerpt of an ongoing discussion) here, with a request that further discussion occur there. In any event, any page-specific discussions which do occur here, should, at some point, be copied or moved to the associated talk page, so as to preserve a more complete historical record there. To that end, unless anyone objects, I will move the above section "Move of "Mathematical beauty" to "Aesthetics in mathematics", comments?", which I initiated, to Talk:Mathematical beauty. Paul August ☎ 16:32, May 27, 2005 (UTC)

By the way, I also wanted to say that I quite value this project's active and vibrant discussions. The more we do it, the better we should get at it. A project needs a certain critical mass of activity to remain viable. This is a great project and it has a great group of participants, and if it takes an occasional "off-topic" discussion to keep it active or to assure ourselves that some of us are still alive and kicking, then it is worth it ;-) (Perhaps, from time to time, we should take attendance!) However, as this page's only archivist, Charles may have mixed feelings about the volume of discussion ;-) — so I pledge to help out with that task in the future and also in accord with my earlier comment, I volunteer to go through all of this page's archives, and copy any page-specific discussions to the appropriate talk page. Paul August ☎ 18:02, May 27, 2005 (UTC)

I think we should create a section on this page to note important discussions: obviously if big edits to mathematics, manifold and so on are being mooted, it is of general interest. Charles Matthews 18:07, 27 May 2005 (UTC)

Should there be a distinct math-related VfD page? Are VfD's common in math? At any rate, if any come up, I think announces should be posted at least here. linas 20:34, 27 May 2005 (UTC)

They are not so common. There have been a few 'crank' pages in the past. Mostly poor material can just be dealt with by redirecting. Also, it is not always clear when topics are technically wrong: who knows enough to be an expert in all branches of mathematics? So my policy is not to rush to VfD. Of course sometimes we need it. Charles Matthews 14:08, 30 May 2005 (UTC)

Two math pages set for deletion

Algebra I has been submitted for deletion, and I did the same thing today for Algebra II. They are about courses with the same name. I think does not look encyclopedic. But either way, here are the links:

Oleg Alexandrov 00:10, 30 May 2005 (UTC)

Might I direct your attention to Long-tail traffic as well. It has a VfD banner on it, but isn't on the list. At least one of the pictures seems to be scanned and the rest of the article gives that impression too. Reference [1] are lecture notes on ELEN5007 so this is probalby someone who put his paper on Wikipedia. --R.Koot 00:27, 30 May 2005 (UTC)

This article is part of a collection of articles, which are all part of a class project. They are being discussed here: Wikipedia:Deletion_policy/Teletraffic_Engineering. Paul August ☎ 01:45, May 30, 2005 (UTC)

Thanks, I missed that. Very strange though... --R.Koot 11:40, 30 May 2005 (UTC)

Vfd for space mixing theory

The page on space mixing theory seems to be unpublished work. I called for a vote for deletion. I hope this is the right forum for announcing that. If not, I apologize, and would really appreciate it if someone could point me to the right place to discuss deletion of unreal science. Bambaiah 10:39, May 30, 2005 (UTC)

Current active content discussion

Please edit this section to keep it up to date (major topics only)

See

for some of the more important content discussions now active in this WikiProject.

Nominated article

It has been proposed that every WikiProject choose a single article which represents what the Project members hope each article will eventually look like, so that interested onlookers can see where a Project is heading. If this project is ready to choose such an article, please do so and link to it after the Project name at Wikipedia:WikiProject. If there are no articles ready for this yet, you may wish to focus as a group on an article which is close and/or will be relatively easy to research.

I nominate Lebesgue integral. Charles Matthews 08:17, 19 Feb 2004 (UTC)
- Hello Charles. I do like the Lebesgue integral article, although it gets bogged down toward the end -- it seems like the discussion sections can be tightened up quite a bit. Comments? Wile E. Heresiarch 02:33, 8 Apr 2004 (UTC)
  - Always room for improvement. I chose it mainly because it touches all the major bases (motivation, some history, towards applications, picture, real content), so is quite a good template. Charles Matthews 06:31, 8 Apr 2004 (UTC)
I second the nomination for Lebesgue integral. I'll also nominate Bayes' theorem. Wile E. Heresiarch 02:33, 8 Apr 2004 (UTC)

Other articles I think are good in their ways are Boy's surface (graphics) and Nicholas Bourbaki (perspective and NPOV - I have worked on this one). Charles Matthews 09:19, 15 Jul 2004 (UTC)

Wikipedia:Classifications of mathematics topics

Seems this page was not updated in ages. And right on top is a suggestion to maybe delete. Indeed, what people think? We already have areas of mathematics, list of lists of mathematical topics, and list of mathematics categories. So, Wikipedia:Classifications of mathematics topics seems kind of reduntant. Or does this article have a purpose? Oleg Alexandrov 02:15, 22 May 2005 (UTC)

It proposes 2 categorizations one of which is original work and the second is included in areas of mathematics. Looking more closely this seems to be a talk page not an article? --R.Koot 15:24, 22 May 2005 (UTC)

What do you mean by original work? Oleg Alexandrov 16:01, 22 May 2005 (UTC)

I meant original research. --R.Koot

For now, I redirected Wikipedia:Classifications of mathematics topics to areas of mathematics, as the two aritcles have exactly the same purpose and the latter is more compete and better written. Both pages seem to be concerned with classifying the math on Wikipedia based on the American Mathematical Society's math subject classification, MSC2000.

Also, some content in Wikipedia:Classifications of mathematics topics makes me think that this page was either vandalized, or otherwise very sloppily edited.

By the way, I have a feel that areas of mathematics would need some work, but I don't know exactly what kind of work; it just feels somewhat unfinished. Any ideas on what to do with this page? Oleg Alexandrov 00:22, 2 Jun 2005 (UTC)

question about formatting of standard symbols

I am wondering whether there is any policy in this project about formatting for standard symbols like Q (the set of rational numbers). I sometimes see Q, sometimes Q, sometimes just Q, and on a few occasions the blackboard-bold version wrapped in <math> tags, i.e. $\mathbb{Q}$ . It's particularly jarring when these different versions appear in the same article (or sentence). I realise that if a single article uses both inline and <math> formats, then some inconsistency in appearance is unavoidable. Also I realise there's some conflict here between freedom and rules, with the concomitant effects on productivity. Still, I'm wondering if at least there is some consensus on the 'ideal' notation. Dmharvey 18:47, 31 May 2005 (UTC)

I think one needs to use either Q or $\mathbb{Q}$ . The first is preferable in inline formulas, as the second yields an image, which is undesirable, see Wikipedia:How to write a Wikipedia article on Mathematics. The second one is more preferrable in big formulas I think. Now, to use Q or plain Q for the rationals is not correct; it needs to be changed to one of the two if encountered.

Now, all this is my own opinion, but this seems to be the unwritten tradition. Oleg Alexandrov 01:46, 1 Jun 2005 (UTC)

I like to use both Q and $\mathbf{Q}\;$ . The blackboard bold should be reserved just for that: the blackboard. --MarSch 16:22, 1 Jun 2005 (UTC)

I think I agree that $\mathbf{Q}\;$ is a definite improvement on $\mathbb{Q}\;$ . Certainly in my regular work with LaTeX I stick to $\mathbf{Q}\;$ . Although usually it doesn't turn out so huge. And it could be argued that, in certain important respects, WP has a lot in common with the humble blackboard :-) If other people agree, perhaps the math(s) project needs somewhere for this kind of notational suggestion to belong. Does it belong under Wikipedia:WikiProject Mathematics/Conventions? Dmharvey 17:38, 1 Jun 2005 (UTC)

I always prefer using blackboard bold even in typeset work, as bold is used for too many things. This will always be a matter of opinion though; there will always be those who disagree. If more browsers supported it I would use ℚ in all my articles. For the time being I stick to Q and $\mathbb Q$ . -- Fropuff 18:25, 2005 Jun 1 (UTC)

I'd stick with blackboard bold, not only because I find it more pleasing aesthetically, be because it's a defacto standard. Maybe Wikipedia's policy of no original research should be extended to no original typesetting? --R.Koot 22:07, 1 Jun 2005 (UTC)

I personally like the LaTeX rendering, but I think it would be best to use only when it is not disruptive to the general flow. If an effort were made to set formulae aside from other text, perhaps making the statements first in "math lingo" and then restating what was just stated in TeX with standard English perhaps the entire issue could be resolved. Guardian of Light 5 July 2005 14:46 (UTC)

Jun 2005 – Jul 2005

This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

Featured list nomination

Please see Wikipedia:Featured_list_candidates#Nominations.

I have nominated list of lists of mathematical topics (not to be confused with list of mathematical topics) to be a featured list. Please go to that nomination page to vote for or against it. Michael Hardy 01:22, 1 Jun 2005 (UTC)

PLEASE VOTE ON THIS at Wikipedia:Featured_list_candidates#Nominations. Some of the opinions expressed there are from persons who are naive in more ways than just mathematically. If you doubt this, see the accompanying discussion page at Wikipedia_talk:Featured_list_candidates#Nominations. Michael Hardy 00:59, 2 Jun 2005 (UTC)

$\uparrow$ VOTE! $\uparrow$

why are the latex images so big anyway?

Again: why are the latex images so big anyway? I generally have my browser text set pretty large, yet the latexs still often look rather silly. Is there some kind of preference setting to adjust the rendering size? If not, is it technically possibly for somebody to do that? Dmharvey 17:45, 1 Jun 2005 (UTC)

In my work browser images look same size as text, while at home the images look much bigger. I don't know the reason. It might have to do with the screen resolution besides font sizes. So we again arrive at the time-established truth that one should not use latex images mixed with text, only on a separate line. That's why, back to the question of $\mathbb Q$ versus Q, one should use the latter when inline. Oleg Alexandrov 23:13, 1 Jun 2005 (UTC)

If only the MathML mode worked... --cesarb 23:32, 1 Jun 2005 (UTC)

OK, let's try something:

$\int_{-\infty}^0 1\,dx$

Consider the integral $\int_{-\infty}^0 1\,dx$ which is blah blah blah .....

(1) Look at this here equation: $AX^2+B=0.\,$ So there!

(2) Look at this here equation: AX² + B = 0. So there!

(3) This renders all right: $A X 2 + B = 0.$ So ereht!

No, it does not. It looks exactly identical to (1) above; the characters are comically gigantic. Michael Hardy 01:44, 2 Jun 2005 (UTC)

FYI For me, (1),(2) and (3) are exactly the same size, and (2) and (3) visually look identical. I have a 1600x1280 monitor so use large fonts.linas 03:04, 3 Jun 2005 (UTC)

I generally use the format (2) rather than (1) for two reasons: the math notation in (1) is ridiculously too big, and it gets mis-aligned. Possibly this could be overcome by using a different browser or altering my preferences. I have long said that TeX looks good on Wikipedia when it is "displayed", but often looks terrible when embedded in lines of text. Note also: 1+2 does not look as good as 1 + 2; n + 2 is better than n + 2; and also better than n + 2. Michael Hardy 00:57, 2 Jun 2005 (UTC)

Number (3) render pretty good here (but this might look horrible if you have a larger/smaller font). This is actually quite an interesting question. What if rendering of math becomes unbroken in a future version of MediaWiki? You'd rather have the stuff between <math></math> than marked up using html. --R.Koot 01:21, 2 Jun 2005 (UTC)

See the link Archive4(TeX) at the very top of this page, discussing this in as much detail as one can get. Oleg Alexandrov 01:32, 2 Jun 2005 (UTC)

(3) looks exactly identical to (1) from my browser. Michael Hardy 01:43, 2 Jun 2005 (UTC)

Hmmm.. It looks SO good over here (Firefox/SuSE 9) that I thought it was a PNG, but it isn't it's HTML

<span class="texhtml"><i>A</i><i>X</i><sup>2</sup> + <i>B</i> = 0.</span>

The problem must be with the class="texhtml"? --R.Koot 01:56, 2 Jun 2005 (UTC)

Interestingly, the font in the TeX output is smaller on Wikicities. See example at [20]. Would this look better on Wikipedia? One problem is that it may be harder to read. - Fredrik | talk 01:49, 2 Jun 2005 (UTC)

Looks better inline but equations are MUCH harder too read. However is you could manually select the size (with two separate tage like <math> and <equation> for example it might work? --R.Koot 02:08, 2 Jun 2005 (UTC)

I was thinking the same thing. Also, clicking the image could show a very high resolution version in addition to the wrapped TeX code. Fredrik | talk 02:11, 2 Jun 2005 (UTC)

For me, the LaTeX images are slightly smaller than the surrounding text. But then, I'm using a 12pt font at 132DPI. Since most Windows boxes are at 96DPI (since a lot of Windows programs look weird if you try to change it), I can see how it can look huge. --cesarb 02:23, 2 Jun 2005 (UTC)

You will never get text in images and text not in images to mesh well for everyone. Saying it should be done one way or another because "it looks better" is just nonsense. It looks better to you on your screen, maybe; that says nothing about how it looks to everyone else. (BTW, I must interject at this point that the font used in the TeX images changed several months ago and I really preferred the old font!) The best solution, perhaps, would be to add a preference setting to scale LaTeX images to a (user-) specified relative size — for example, "80%" or "110%", etc. — so that each user could, if they cared, have the images scaled to match the size of the regular text in their own browser (I guess this would also have to include a vertical-shift option, as well, if that's possible to implement). The only problems I can see with this plan would be: (1) server load, since every (TeX) image would have to be tagged with height and width calculated using the user's scaling preference; and (2) readability since some browsers probably have terrible algorithms for scaling images. - dcljr (talk) 11:11, 2 Jun 2005 (UTC)

For me, (2) and (3) are identical. Only (1) looks bad. I think this is because I have selected "HTML if very simple or else PNG" in my prefs - it is not determined by my choice of browser. L upin 12:32, 2 Jun 2005 (UTC)

(3) is the best, because I think using images for any kind of text is not a good thing to do.--Reubot 10:19, 5 Jun 2005 (UTC)

Thanks everyone for your comments and examples. I think I now understand a little better why this is such a complicated issue.

I have a question: how good is MathML at rendering inline equations (as opposed to displayed equations)? Does it handle things as well as LaTeX, like line wrapping?

Dmharvey Talk 12:56, 2 Jun 2005 (UTC)

I think the previous suggestion of a user-definable relative size attribute is quite nice. Note also that CSS (I don't know if this is true for "old style HTML attribs") allows for sizes given in "ex", e.i. the height of an "x" in the current font. maybe this could also used to fix the problem. But I also agree that (maybe unless you have a 1600x1200 screen, which is still rather exceptional - maybe wiki has statistics on screen resolution...) the images are always way too big w.r.t. the text, so a fix should definetly be provided. (Maybe also alternate style files (at worst through user prefs) could allow to cope with this issue.) — MFH: Talk 22:32, 20 Jun 2005 (UTC)

tangent bundle and vector field

I would really like to know your opinion on what these articles should be about. Since the tangent bundle is basically the collection of vector fields, it would be useful to make it clear what info should go where. --MarSch 14:26, 2 Jun 2005 (UTC)

These articles certainly need a lot of work. For example, the vector field article should also have a more "introduction to several variables"-level version, with explicit formulae in terms of partial derivatives etc. There should be a version of tangent bundles in terms of submanifolds of euclidean space, as well as the more abstract version there currently. Dmharvey

Talk 14:52, 2 Jun 2005 (UTC)

Tangent bundle should cover the holomorphic version, the version in algebraic geometry, too. There are also replacements (microbundles) to consider; and mappings on tangent bundles (not on vector fields - see the notorious push forward talk page discussion). Vector fields in plane regions is already an interesting area. So there seem to be reasons to have two pages. Charles Matthews 15:48, 2 Jun 2005 (UTC)

Wikipedia:Mathematics Collaboration of the Week

So what is happening there? The tag has been taken down from tensor, which was current. I don't see another nomination has been made. Charles Matthews 16:00, 2 Jun 2005 (UTC)

Copyright

I'm sorry if this is the wrong place, but I wonder if there's copyright on proofs? Can I copy some proof from my lecture notes (in my own words)? Hugo 08:30, 2 Jun 2005 (UTC) (Moved from Wikipedia:WikiProject Mathematics/Proofs by Oleg Alexandrov)

Try asking at Wikipedia:Village_pump and then summarize the answers you get; I'd like to know myself. linas 01:07, 3 Jun 2005 (UTC)

(I'm not a lawyer) You will have to make a distinction between the structure of the proof and the text of the proof itself. The stucture is not copyrightable only patentable, and that is not possible because you can't patent mathematics. Whether the/a text is eligible for copyright depends on wheter or not is considered original. A proof consisting mainly of formulas, "let ... denote ...", and "from which we conclude", could hardly be considered orginal (and would be very hard to prove in court). However this might change if the proof contains original/creative explanations of the proof. Note that even rewiting the text in your own words is considered plagiarism (this might again be hard to prove in court but you or other Wikipedians might (should) have some moral problems with this). The safest would likely be to ask the author of the lecture notes if you could copy part of it to Wikipedia. --R.Koot 19:11, 3 Jun 2005 (UTC)

I would like to mention that if some theorem is missing a proof, that might be on purpose. Some of us (if not the majority) think that proofs should be a part of the article only if they ellucidate the article, and if they are not too hard. So, proofs for their own sake are not very encouraged. Discussion on this is under way at Wikipedia:WikiProject Mathematics/Proofs. Oleg Alexandrov 04:18, 4 Jun 2005 (UTC)

R.Koot, you are mistaken, it is possible (in the US) to patent pure mathematics when the math is the embodiment of some functional procedure or algorithm. Examples include the RSA encryption algorithm and the inversion procedures used in MRI scanners. So while in general you can't patent a proof there may be occasional exceptions if that proof is somehow a necessary component in the description of some otherwise patentable process. Such cases are likely to be very few and far between however. Dragons flight 01:15, Jun 23, 2005 (UTC)

Wikipedia:How to write a Wikipedia article on Mathematics

There are some interesting discussions going on at Wikipedia talk:How to write a Wikipedia article on Mathematics. I believe as many of us should be involved in that as possible, as that article is the main document defining how math is to be written. So, comments welcome. Oleg Alexandrov 22:25, 2 Jun 2005 (UTC)

Conjecture for deletion

According to newly created polygon sum conjecture article,

The Polygon sum conjecture is a geometric conjecture that states that the sum of the interior angles of a polygon are equal to 180(N-2), where N is equal to the number of sides that the polygon has.

I almost put it in Category:Conjectures, when I realized conjectures in elementary geometry do not happen that often... :)

Anyway, see Wikipedia:Votes for deletion/Polygon sum conjecture. Oleg Alexandrov 01:21, 3 Jun 2005 (UTC)

Also see Wikipedia:Votes for deletion/Roman letters used in mathematics Oleg Alexandrov 01:28, 3 Jun 2005 (UTC)

complex multiplication and e^(pi sqrt(163))

Dear all, I have added the fascinating fact concerning e^(pi sqrt(163)) to the article on complex multiplication. It doesn't really fit very well at the moment, but hopefully one day that will change. The only reason I mention this here is that I'm not sure if this formula appears anywhere else in WP, perhaps it is already stated elsewhere. Thanks peoples. Dmharvey Talk 01:32, 3 Jun 2005 (UTC)

I've added the equation to Pi, under "Numerical approximations of π". Fredrik | talk 05:00, 6 Jun 2005 (UTC)

There is currently an "explanation" with links to modular form and something else, which is quite frustrating because nothing is explained there. I would appreciate a more precise indication on "how", even if w/o details. — MFH: Talk 12:58, 23 Jun 2005 (UTC)

I agree the explanation is drastically lacking in detail. I will try to do something about this at some point, but I don't promise anything soon. The problem is, to make this work sensibly would require an article on complex multiplication considerably more in-depth than the presently existing one. Dmharvey

Talk 15:00, 23 Jun 2005 (UTC)

long-term of future of mathematics in wikipedia

(copied from the talk page of Charles. This is an interesting discussion, and I wonder what others would like to say Oleg Alexandrov 04:37, 3 Jun 2005 (UTC))

I am wondering what your opinion is of the possible long-term future of maths in wikipedia? In particular, do you think that wikipedia (or some other wiki-based medium) has the capacity to (eventually) become an authoritative source on well-understood material? I guess 'authoritative' and 'well-understood' are somewhat rubbery terms. For an arbitrary starting point, perhaps 'well-understood' might mean "material that has made it into book form by 2005", and 'authoritative' might mean that a professional mathematician might consider making WP their first port of call for learning material they are unfamiliar with. I appreciate your insight, you seem to have had a lot of experience on WP. Dmharvey 17:21, 30 May 2005 (UTC)

To try to sum up my take on this - mathematics is short of good survey articles, and not really short of textbooks, except for things that are quite recent. It is quite hard to get a good historical perspective, from the technical literature alone; and much harder to understand what is going on in the Russian or Japanese perspectives, than in Paris or Princeton. We ought to be trying to give a good broad coverage, by survey article standards, with reasonable references. We ought to be giving the sort of background that makes the current preprints more accessible (so, basic definitions to answer 'what the hell is X?' questions). We should reach for a good overview of the whole tradition, and what is going on globally. I don't think it is so sensible to aim to compete directly with the conference literature, say. WP ought to complement academia, and make the effort to explain 'how it all fits together' and 'why any of this matters' - which academics generally don't find the time for. Charles Matthews 21:01, 30 May 2005 (UTC)

Interesting. (BTW thanks for your time in answering these questions; you must be a pretty busy guy.) I certainly agree with your last sentence, i.e. that WP should help explain 'how it all fits together', I'm very keen on that. I'm also very keen on giving historical perspective. On the other hand, it seems that WP provides an ideal vehicle for a piece of writing to start off as a survey article, but then slowly morph into something providing textbook level detail, while nevertheless remaining a survey article to a reader not concerned with details or proofs. (They just don't have to follow all the links.) Mathematics seems to be a subject area especially suited to this, since there tends to be less disagreement about correctness than in most other academic discplines.

I'm sure this meta-wiki discussion has been had by plenty of people already :-). Perhaps I should spend some time reading what everyone else has had to say. As I am a wiki newbie, I am probably suffering from some kind of wiki-thrill, believing that WP can solve all of humanity's problems. It does seem to me to be a genuinely new form of communication/publishing media, which as you can tell I find very exciting.

WP can do some good, no question. Trying to audit quite how much progress is interesting, taxing and sometimes chastening. The first five years, for mathematics, is going to look like 10000 pages with much 'core' material. Chronologically the solid coverage can get us into the 1950s, mostly; but not past 1960. I would project, that in 2010 it would look more like 1970 rather than 1960; and even that is ambitious and would require much more expertise in the 'rarer' topics (algebraic geometry and topology, for example) than we currently command. I'm quite upbeat, but it is still very easy to find the gaps. Charles Matthews 10:13, 31 May 2005 (UTC)

Hi Charles, Dmharvey. I don't mean to butt in on this conversation, but I've enjoyed reading both of your thoughts in this and the above section (the "multiple audience" issue particularly), and I would expect others involved in Wikipedia:WikiProject Mathematics would find these discussions interesting and beneficial as well, and perhaps even want to join in ;-) However if you prefer to keep this a private discussion, I respect that. Paul August ☎ 15:13, May 31, 2005 (UTC)

As far as I'm concerned, I'm not saying anything private - go ahead, Paul. Charles Matthews 15:27, 31 May 2005 (UTC)

Charles, yes, I didn't really think that what you were saying was meant to be private (I was just trying to allow for the possibility that you or Dmharvey might prefer to have a two-person conversation). And anyway there isn't anything I really want to add to the discussion — yet. I just think that you guys have been having a couple of interesting discussions that others would be interested in also. So I was trying to encourage you to consider discussing these ideas on Wikipedia talk:WikiProject Mathematics. (By the way thanks for your vote in support of my admin nomination ;- ) Paul August ☎ 16:45, May 31, 2005 (UTC)

As far as I'm concerned, nothing on WP is private :-) (Unless of course you're using PGP, but that, as they say, is just not cricket.) I'm quite happy for anybody to move the above text to an appropriate venue, or to do whatever is appropriate. Dmharvey 18:22, 31 May 2005 (UTC)

Wow, yes, agree with both Charles and Dmharvey. Realistically speaking, WP has huge gaps in just about any topic, and will need to grow at least 50-fold to fill these gaps in. It will take many many years for this to happen. But I also agree with Dmharvey in that it seeems inevitable that WP will become the authoritative reference in a decade if not sooner; its already beyond mathworld.com in many areas.

But please note that we will have to tackle many serious structural issues first; and if these are not solved, then it will make growth harder. For example: Charles "survey" articles are already outnumbered by more "mundane" articles that mostly list facts. (I myself generate "mundane" articles because I'm not knowledgable enough to write surveys in any but a few fields, and those fields bore me...). I would like to see some system that somehow makes the survey articles more visible, more prominent. They tend to be lost in the mire.

I don't know how to fix this. Maybe have different classes of articles? This is kind of like the "proofs" discussion, but in reverse. With proofs, the problem is how to hide this third-tier material so that it doesn't impede article flow. With "survey articles", the problem is how to highlight them above and beyond the rest of the bulk.

Note also the existing tension between "simple" and "advanced" treatments of the same material is going to get worse. We'll need to devise some mechanism for dealing with this, as I wonder if the current ad-hoc approach can last. I've had Oleg delete some of my edits because they were too advanced, I've had Fropuff delete some of my edits because they were too trivial. I'm not complaining, I'm rather trying to make note that this is a potential problem area that will recur in WP and is worthy of attention. linas 00:19, 4 Jun 2005 (UTC)

Yes, the greatest problem I'm having is where to put things. I really think we need to structure all our articles hierarchically and make it clear what should go where. --MarSch 10:50, 4 Jun 2005 (UTC)

In the context of Wikipedia, I think I have come to the opinion that the issues being discussed do not really raise any problems.

Suppose that we have an article X that discusses topic Y. There are lots of people who might end up looking at page X. A priori, they might be arriving there with a huge range of different levels of mathematical experiences. However, I claim that the gap between

The lowest level of experience a person could have before they conceivably could get anything on that topic; and
The highest level of experience a person could have and still be interested in that topic,

is actually not that large. It may seem large, but there's some kind of "logarithmic scale" operating here. I think it is possible to have a well-written introduction that can simultaneously branch off to cover many different levels of pre-experience. Obviously, not everyone will be able to write that introduction, since some people simply don't have the background to see it all in context. But, almost by definition, someone will have that context, and will (eventually) supply it. Dmharvey Talk 11:34, 4 Jun 2005 (UTC)

Mostly agree, just please note that there are some exceptional pages: Torus and Laplacian operator are examples. Torus can run the range of middle-school "volume of a torus" to grad-school "Teichmuller space". Laplacian runs from engineering school to harmonic analysis. Maybe these can be treated on an ad hoc basis. Somewhere I suggested an "educational trampoline" for things like "torus", since it can be a doorway to higher math for younger students. linas 17:03, 4 Jun 2005 (UTC)

One way to deal with it is to take advantage of Wikipedia's subsection facility. The first paragraph is a corse overview, which should be understandable to the journeyman, and will probably have little valuble content for the expert. It's allright it the total novice is a *little* floored by it, because the first proper section starts on the ground floor and explains things simply. Linkouts are good, but we shouldn't expect even a novice to have to search 10 links deep in order to understand something. Following sections can build up from there. Experts who know everything can skip to the bottom, where the heavy theory lies, and the novices can stop after a section or two, when they have a good overview of the topic, but before they get into the deep math. The trick is to compromise, and cede the top of the article to the complete novices, and only put the Masters level theory at the bottom. (Summary: Novice on top, Intermediate in the middle, Expert on the bottom.) 15:35, 22 Jun 2005 (UTC)

I would also like to mention something else about "authoritativeness" of WP. It seems to be widely acknowledged that there are issues with reliability in WP, and that this seems an insurmountable barrier to WP becoming useful to the academic community (in the present discussion, the academic mathematical community). I agree with the first half of the sentence but not the second half. Something can be useful even if it's inaccurate. And it seems that WP has a strong tendency to become more accurate over time, at least on topics that are not too sparsely covered. In the real world, no one source is enough anyway. When I want to learn about a maths topic I don't know much about, I don't just get a book out of the library. If I really want to learn something, I get at least three books or journal articles, and talk to my colleagues, asking them what their point of view is on the whole subject area, and where they think is a good place to read about it. Dmharvey Talk 11:34, 4 Jun 2005 (UTC)

I'm wondering if some semi-formal peer-review/voting/audit-trail type system might help with authoritativeness. I'd like to mark up a page or a portion of a page to somehow state "yea verily I have reviewed this and attest to its accuracy". Kind of like wear marks. Have no idea how to implement this. linas 17:03, 4 Jun 2005 (UTC)

I've sometimes wondered if a symbiosis with Planet Math might work; they'd hold peer-reviewed content, which the public cannot edit. It could be copied from WP after some sufficient quantity of review. linas 21:35, 4 Jun 2005 (UTC)

That's why the project we have here is called Wikipedia:WikiProject Mathematics/PlanetMath Exchange (please note the word Exchange; it was hoped that the map from PlanetMath to Wikipedia is invertible, and PlanetMath people could use our stuff). Oleg Alexandrov 23:56, 4 Jun 2005 (UTC)

On the other hand, on the more general topic of "long-term future of mathematics in WP", I have some other concerns. My first concern regards typesetting. I summarise by saying that in the present situation, I don't think WP has sufficiently sophisticated typesetting for serious mathematical work. This may become a long term problem, because one important group of people we would like to attract to write articles, serious mathematicians, will be put off by something that visually looks amateurish. For those who don't believe me, I suggest trying to write a complete paper in LaTeX. It's incredible how LaTeX is able to make even completely incoherent babble look like the most brilliant piece of mathematics written since the 16th century. This might improve if browsers improve, I'm not sure.

A second concern is that there are other interesting things that a WP-like system could conceivably do, but which the current software does not support. For example, it would be lovely for WP to support a parallel development of some kind of formal proof system; i.e. symbolic manipulation software where people could enter formal proofs which are checked automatically for correctness. I don't believe such a system exists yet, except in fairly primitive forms. I think there have been a fair number of attempts, but I haven't heard of any that have scaled up well. I think in time, the collaborative nature of something like WP will solve the scaling-up problem. Then, if you believe the axioms that the system is founded on, and you believe that WP is doing its proof checking correctly, then you can be happy that the theorem you are looking at is OK. (Please don't take this paragraph too seriously; there are ENORMOUS problems, both theoretical and practical, with automated proof systems, and I just wanted to throw it up as a random thought.)

OK I've really chewed up enough bandwidth now. Dmharvey Talk 11:34, 4 Jun 2005 (UTC)

That's an interesting concept (mixing automated reasoning with mathematical exposition), but that's another beast entirely, in my opinion. You probably are thinking of Mizar or Isabelle? Proofs there tend to be long and not easy for the non-expert user to construct.--CSTAR 14:59, 11 Jun 2005 (UTC)

The proofs do tend to be longer, but the difference is getting smaller nowdays. I put a small pdf file at [21] with an example of modern declarative formalized proof style (generated by Isabelle). Having a link to a formally verified proof of a theorem certainly increases "authoritativeness". Formalized proofs of many theorems mentioned in Wikipedia:WikiProject Mathematics are accessible on the web. --Slawekk 23:49, 14 December 2005 (UTC)

Wallpaper groups

Dear peoples, I have spent quite a number of hours the last few days working on Wallpaper groups. It looks almost completely different now, and I hope it is an improvement.

The only thing I plan to do with it for the next few days is finish labelling the pretty pictures. Apart from that it is in all of your capable hands.

Then I need to take a break from wikipedia, so I can do some other things.

I will return in a few weeks.

Dmharvey Talk 17:09, 4 Jun 2005 (UTC)

Wow! Paul August ☎ 18:31, Jun 4, 2005 (UTC)

That is indeed stunning. --14:51, 11 Jun 2005 (UTC)

banner for talk pages

I've just come across a nice template slapped onto talk pages of chemistry ({{chemistry}}):

Image:Glasswareb.gif

This article is supported by the WikiProject on Chemistry, which gives a central approach to Chemistry and related subjects on Wikipedia. Please participate by editing the article WikiProject Mathematics/Archive Index, or visit the project page for more details on the projects.

Should/do we want to have something similar? Might bring more people to the project. --MarSch 18:06, 5 Jun 2005 (UTC)

Some reaction might be nice. Any reaction. --MarSch 13:24, 12 Jun 2005 (UTC)

I didn't react since I don't have much of an opinion either way. It is quite a bit of work, and I think our current approach of inviting people personally to have a look works much better; on the other hand, it doesn't do any harm, and it will rake in some more people, so go ahead. -- Jitse Niesen 20:45, 12 Jun 2005 (UTC)

Personally, I hate banners. Ditto for topic templates, and such. I suggest that you just watch a lot of pages. If you see the same person making good edits on a number of pages, invite them here. I made hundreds of edits before I even bothered to look at this page, and am deeply suspicious of anyone who would be interested in process who hadn't been an active editor first. linas 04:16, 13 Jun 2005 (UTC)

List of lists of mathematical topics

There is a proposal at Talk:List of lists of mathematical topics to reformat that list according to subdivisions of math. Comments welcome. Oleg Alexandrov 19:51, 5 Jun 2005 (UTC)

WP etiquette question

There has been a recent addition to Pythagorean theorem by 67.86.108.32 which although appears to be in good faith, I feel is unnecessary. I tried for a while to think of a way to rephrase it so that it would fit, but eventually decided it just shouldn't be there. What's the best thing to do in a case like that? Thanks Dmharvey Talk 11:59, 6 Jun 2005 (UTC)

Write to the talk page explaining your reasoning and why you're going to delete it. Then be bold and delete it. Be firm but polite. If the editor clarifies or suggests alternative wording, be reasonable. --Tony Sidaway|Talk 12:45, 6 Jun 2005 (UTC)

OK thanks. I'll try that. Dmharvey

Talk 13:02, 6 Jun 2005 (UTC)

Try moving it somewhere else (another article), if it is information. If it's just words then delete. --MarSch 14:57, 6 Jun 2005 (UTC)

Assuming that you have the time and find the right spot, that's a good idea. Otherwise, just moving the text to the talk page, together with your explanation for why you moved it, is perfectly fine. Deleting the text altogether, with an explanation also works. Oleg Alexandrov 15:09, 6 Jun 2005 (UTC)

One of the exasperating things about WP is suddenly to find an article changed in totally bizarre ways. It 's very very hard to be polite in these circumstances. --CSTAR 15:55, 11 Jun 2005 (UTC)

It can be exasperating, but you have to expect it. There will always be new users coming into Wikipedia who will act in very unusual ways. It is just the price we pay for the open model, which has been so enormously successful. And of course politeness is always the best strategy, no matter the circumstances or the exasperation level. Paul August ☎ 16:47, Jun 11, 2005 (UTC)

carmichael's theorem

Is my brain broken, or is this theorem just silly? It seems to be saying that the definition of the carmichael function is, in fact, identical to the definition of the carmichael function. Surely the theorem should instead say something like, "the recursive formula given for the carmichael function is correct, i.e. satisfies the property alluded to in carmichael's theorem"? Really these should go into the same article with a redirect on one of them. (And then one day I'll write something about larger examples of carmichael numbers, and of its relevance to primality testing, and fix up some nasty markup.) Dmharvey Talk 23:57, 6 Jun 2005 (UTC)

Aaah. Just found Carmichael number, strangely enough not linked to either of the above articles. That makes life easier. Dmharvey Talk 00:01, 7 Jun 2005 (UTC)

The recent total re-write of list of lists of mathematical topics

(NOT to be confused with list of mathematical topics)

User:Samohyl Jan has completely re-written this list of lists, with some input from me as well.

Please vote on list of lists of mathematical topics at Wikipedia:Featured_list_candidates#Nominations. Michael Hardy 00:23, 9 Jun 2005 (UTC)

I'm tempted to support, but I'm not really into featured lists. --MarSch 10:49, 9 Jun 2005 (UTC)

math-wikify

What about a specialized wikify template for mathematics articles? This might make it easier to keep our to-do-lists recent. See also the discussion at TFD about some of these templates: Wikipedia:Templates_for_deletion#Template:Foo-wikify --MarSch 10:58, 9 Jun 2005 (UTC)

I really think this would work much better than Wikipedia:Pages needing attention/Mathematics since categories automatically keep an uptodate list of articles. If you still want to vote, you can do so at Wikipedia:Categories_for_deletion#Category:Foo_articles_that_need_to_be_wikified. --MarSch 13:23, 12 Jun 2005 (UTC)

I am not sure about a Category:Math articles that need to be wikified, for the reasons given in the CfD discussion (everybody can wikify), but a Category:Math articles needing attention does seem to have some use. -- Jitse Niesen 20:04, 12 Jun 2005 (UTC)

Article on VfD

I nominated topic-based vector space model for deletion because this is a method proposed in a paper in 2003 (see the external link in the article), so it is very new and too early to say if it is proeminent. So I think it is not yet something to be included in an encyclopedia. But I am not 100% sure. I wonder if other mathematicians would visit that article, then post their opinions on the VfD page. Oleg Alexandrov 03:37, 10 Jun 2005 (UTC)

I would vote "merge as a note in the VSM article and redirect". Pcb21| Pete 07:45, 10 Jun 2005 (UTC)

vector space model is by the same author... --MarSch 09:39, 10 Jun 2005 (UTC)

WikiProject logic

Encouraged by User:Paul August on Talk:Aristotelian logic, I'm posting an invitation to comment on the idea for a WikiProject for Logic. I have a draft proposal at User:Chalst/WikiProject Logic proposal, and I am interested in:

Indications of interest
Criticisms of the what is on the page

Many thanks in advance for your comments. --- Charles Stewart 15:59, 10 Jun 2005 (UTC)

Related articles with similar content and unclear interrelations are the biggest problem I am facing. A mild version of this is the group, group theory combo which can usually be sorted out, although I think this has often not happened yet, but what to think about: vector (spatial), vector field, vector space, tangent bundle, tangent space, and the also to these related scalar, scalar field, tensor, tensor field, Tensor_(intrinsic_definition), Intermediate_treatment_of_tensors, Classical_treatment_of_tensors and maybe more. What I would like to know is which you think the possible content of these articles should be in. Possibly using templates subarticleof}} and seesubarticle}}. I would welcome any ideas. --MarSch 14:00, 12 Jun 2005 (UTC)

For now I don't have the time to take a look at all the articles; but on principle, I would think that the fact that the articles are loosely organized (with repetitions occuring in places) is a good thing as this allows for reading one article independent of the other. Also, from what I saw, vector (spatial) is a less abstract/more physical/geometrical article as compared to vector space, and integrating the two could be a mistake. In short, I am for some anarchy on Wikipedia. :) Oleg Alexandrov 14:32, 12 Jun 2005 (UTC)

The problem with anarchy is that it is not clear where information can be found and by extension also not clear where information should be contributed. If the efforts were a little better organized all of these articles might have already been featured, instead of the cluttered form most are now in.--MarSch 15:10, 12 Jun 2005 (UTC)

Yes, well, be careful. These articles treat similar topics, but not the same topic. Vector bundles are not vector spaces; and the former links to the later in the introductory sentence. Vector bundles are a kind-of fiber bundle ... I discovered early on that attempting to make large re-organizational edits can often sink a lot of time, while failing to improve quality. I'm surprised you're not sensing this yet ... Personally, I prefer smaller articles, with a given topic spread out across multiple articles, than trying to jam everything into one article. As to some repetition, that's OK, too. I'd prefer to see articles grow "organically" by accretion. After lots of accretion, they may look poor, in which case they can be restructured. However, trying to optimize content across multiple articles makes me very nervous. In particular, such a re-organization implies that you are trying to impose your world view on something that had evolved quite differently to begin with. Catholics and Protestants are both Christians, but neither would agree to the restructuring suggested by the other. linas 04:02, 13 Jun 2005 (UTC)

I agree that articles on both vector spaces and vector bundles (I didn't even mention this one) are warranted and also tangent bundle, but probably not vector (spatial), vector field and tangent space. Vector (spatial) really about vector spaces and some Euclidean metric, vector field ought to be part of vector bundle and tangent space should redirect to tangent bundle. --MarSch 14:34, 13 Jun 2005 (UTC)

I agree very much with Linas. MarSch, I think you should proceed with caution, if at all. And please consult frequently with some of us; it is good that whatever you do have the community support.

Now, in my view, the biggest problem the math articles face is not what you mentioned above. Many articles just need careful reading, fact checking and minor fixes. One should also watch a lot for vandals, trolls, or just misguided, misplaced or poor edits. If you feel full of energy, instead of rewriting and reorganizing things, I would suggest you check more often the recent changes to the list of mathematical topics (go to that link then you will see what I mean). Janitorial work is not very glamorous, but much needed. Oleg Alexandrov 14:17, 13 Jun 2005 (UTC)

Janitorial work is all very nice, but it doesn't improve article. --MarSch 14:34, 13 Jun 2005 (UTC)

I agree with Linas and Oleg that most of these articles should remain separate. Tangent space and tangent bundle should remain separate for the same reasons that I mentioned on Talk:Cotangent space. Vector fields are often studied by advanced calculus and physics students long before they've every heard of things like manifolds, let alone vector bundles. Vector (spatial) — also known as vector (physics) — is how vectors are treated in freshman physics courses (where they almost never worry about vector spaces as such) — this article should definitely remain separate. I do think that the articles on tensors are rather scattered and could do with some more cohesion. However, this needs to be done carefully, with much discussion, to avoid alienating certain user groups. -- Fropuff 16:15, 13 Jun 2005 (UTC)

Kettle Principle

I ran into this article, and don't know what to do about it. Any opinions? Oleg Alexandrov 05:25, 16 Jun 2005 (UTC)

A very bad version of the "tea making joke", probably vfd or even d --MarSch 15:43, 16 Jun 2005 (UTC)

I've heard of the joke (and there is a better version in Mathematician), but I've never heard of the "Kettle Principle" (no google hits), unless someone can come up with a reference, I would support deletion of the the page via VFD. Paul August ☎ 20:31, Jun 16, 2005 (UTC)

I first wanted to turn Kettle Principle into a redirect to Mathematician, which wouldn't require listing it on VfD, but on second thought I don't even want the redirect. I don't see why it would be a candidate for speedy deletion (which of the criteria of WP:CSD applies?), so I listed it on VfD. Please vote at Wikipedia:Votes for deletion/Kettle Principle. -- Jitse Niesen 23:08, 16 Jun 2005 (UTC)

Vector space example x

Vector space example 1 and Vector space example 2 and Vector space example 3 are really horrid. They are complete verbosity. Maybe we should delete them. --MarSch 15:48, 16 Jun 2005 (UTC)

Yes, I wrote examples of vector spaces as a replacement for these pages. But they are still lingering around. I would VFD. -- Fropuff 15:54, 16 Jun 2005 (UTC)

I would support their deletion. Paul August ☎ 19:53, Jun 16, 2005 (UTC)

All three are now listed on Wikipedia:Votes for deletion/Vector space example 1. -- Jitse Niesen 23:08, 16 Jun 2005 (UTC)

Pulation square on vfd

The article pulation square, which in my opinion is a perfectly fine math stub, has been nominated for deletion here. Please share your thought there. Thanks. Paul August ☎ 15:30, Jun 18, 2005 (UTC)

This is not a legit VfD. Its an act of vandalism by an extremely foul-mouthed 14-year old newcomer to WP (User:Big al kicks ass). I reported it as such to Wikipedia:Vandalism in progress. linas 17:34, 18 Jun 2005 (UTC)

Category:Physics: general/basic/introductory concepts

We're currently having a brain storm on Category_talk:Physics about the following questions:

How best to distinguish the articles that genuinely cover general topics from those that have been moved into the main physics category recently and jsut aren't specified yet.
What to call a category for mathematical tools, such as tensors, and if this makes sense at all.

You're cordially invited. — Sebastian (talk) 07:50, 2005 Jun 20 (UTC)

Democratic peace theory

An excessively original believer in this piece of social science questions the following observation, which seems trivial to me:

(... The proper odds to judge a set of data which satisfies a theory deriving its parameters from that [identical] data is the chance that the data would satisfy the theory using, not those particular parameters, but any possible parameters.)

If one of you can think of an exact source, contact me or comment on the article's talk page. Now at bottom. user:Pmanderson

With due respect to the person who actually wrote the quote above, it seems to me of little value and poorly phrased. Oleg Alexandrov 16:13, 21 Jun 2005 (UTC)

Amateurishly phrased, and trivial; but apparently not allowed for by the political scientists in their calculations, and denied by User:Ultramarine. Septentrionalis 17:27, 21 Jun 2005 (UTC)

I think this is highly non-trivial, even ignoring the fact that the GUT is supposed to have no parameter freedom. It does not mention by what probabillity distribution that chance is to be calculated. By incorporating that distibution into your theory you can fix the outcome of the judgement to probably a very great extent. Thus I think the statement is highly ambiguous or even non-sensical. Also why does it say "judge a set of data"? Surely the theory is what you want to judge. Theories are judged by their predictions, their intuitive explanatory power and Ockham's razor. --MarSch 09:51, 22 Jun 2005 (UTC)

Thank you. I think the following phrasing is what I mean: see if you can object to the following:

Using a set of data to determine the parameters of a theory, and then validating the theory by applying it to the same set of data is a weak form of proof. Normal statistical tests assume the theory is independent of the data. Septentrionalis 16:13, 22 Jun 2005 (UTC)

I'll object. I know very little about statistics, but it was my impression that this is exactly how statistics is done. When a medical trial tests the effectiveness of drugs, they don't try to fit parameters to some of the data, and then try to validate with another chunk of the data. They try to fit all of the data; they validate the theory by looking at the standard deviation and the correlation. So its not a weak proof at all, its the standard way by which statistics is done. I thought User: Michael Hardy was into statistics. linas 00:42, 23 Jun 2005 (UTC)

medical tests just try to find out which out of a few treatments works best. There is no parameter fitting and hardly any theory, just facts that have been measured.--MarSch 10:39, 23 Jun 2005 (UTC)

So far I'm still finding this very vaguely expressed. I'm not sure what Septentrionalis a.k.a. user:Pmanderson, is trying to say. Michael Hardy 01:48, 23 Jun 2005 (UTC)

The context is in this version; the section called Significance. Rummel, a political scientist, is trying to prove a statement about all "sufficiently nice" democracies: to wit, that they don't go to war with each other. He narrows his sample of democracies by excluding those states with less than a certain proportion of voters, and less than a certain age. These are parameters, in the real sense of the word.

It is possible that he chose his values parameters precisely to get as many democracies, and as few wars, as possible. Let us suppose this true. If so, he is then testing the resulting theory against the historical record for the same period. I believe that this is a weaker test than if he had chosen his parameters a priori and then looked at the historical record.

This seems to me actually a fairly trivial observation, but it is the one that was challenged. (And my statistics may be rusty; I was an actuary some years ago, after all.) Septentrionalis 02:41, 23 Jun 2005 (UTC) -and after previewing I see the error of agreement in the paragraph.

<sigh>

Allright, let me say some things. I think what we are talking about here is not a theory at all, since it has no predictive power, but just a statement of fact. The fact that if you define liberal democracy so and so, then there is so and so much war. If you define it somewhat differently you may get a different picture. For an informed picture you should present a few of these statements ranging from a restrictive to a broad def. If you don't like that picture then you can leave out some data (a few statements) thereby deceiving people into thinking what you want them (and possibly yourself also) to think. This you might call fitting the parameters. Looking at a single set of parameters is surely better than this, but also leaves much to be desired, as I explained.--MarSch 10:56, 23 Jun 2005 (UTC)

OK, I understand now. What Rummel should have done is to graph number of wars as a function of parameters (voting age, population size, etc.). If he finds that the graph is flat (i.e. independent of the parameter) then he has a theory. If there is a strong correlation between the parameter and the number of wars, then he has no theory until he explains why there is a strong correlation. So maybe there is indeed an error of methodology. Either that, or a misinterpretation of Rummel's work. linas 15:44, 23 Jun 2005 (UTC)

I mostly agree with the Significance section. If you only have one set of data and you have to first deduce a theory, you normally randomly split the data set. The first part is used to find a theory, including the parameters, and the second part is used to verify the theory.

I think it's a valid theory and might be true, but so far it's not proven, there is a deep flaw in the statistical argument. Future will show if the theory is right. Markus Schmaus 18:35, 23 Jun 2005 (UTC)

Morton's theorem

I ran into this article today. From what I see, this article is the thoughts of a certain Andy Morton about poker posted on rec.gambling.poker (Usenet) around 1997. It seems that his post was rather word for word pasted in this article, and that this article is not encyclopedic. How about voting it for deletion? Oleg Alexandrov 19:53, 25 Jun 2005 (UTC)

My first impression is not that it should be deleted. However, it may be a copyright issue, so I asked the user who posted it if this could be clarified, see User talk:Fekko. If I do not receive an answer, I will list it on WP:CP. You may also want to confer with User:Revolver, who is apparently responsible for our article on the Fundamental theorem of poker. -- Jitse Niesen (talk) 20:56, 25 Jun 2005 (UTC)

First of all, although it's math-related, it's not really a "theorem", so I deleted it from that category. One thing that's not made clear, is that the first paragraph appears to me to be Caro's words. This makes a big difference in reading the post. But, it is definitely a legitimate concept, in fact, it may be one of the most important concepts in all of poker. I'll try to summarise the gist of the post, esp. the example, so as to minimise the potential copyright problems. But, it's definitely encyclopedic. Revolver 13:20, 26 Jun 2005 (UTC)

Birthday distribution

Here's another article on which input is needed. Probabilists out there, do you think this is rescuable? So far, it looks like a table of data obtained by using a paper from 1981. Oleg Alexandrov 20:13, 25 Jun 2005 (UTC)

This is a copy of http://www.mathcad.com/library/LibraryContent/puzzles/soln28/exact28.html, but I doubt that it is copyright-able as it's basically a table of numbers. However, I don't see much encyclopaedic value in it. -- Jitse Niesen (talk) 21:04, 25 Jun 2005 (UTC)

Proof of... articles

Any objections to moving Proof of Leibniz formula to Leibniz formula and Proof of Viète formula to Viète formula? I moved Proof of Wallis product earlier, but didn't notice these two. Are there any other proof of X articles without a main X article that should be handled similarly? - Fredrik | talk 21:22, 25 Jun 2005 (UTC)

Actually, it seems that Leibniz formula should more properly be a disambiguation page... - Fredrik | talk 21:22, 25 Jun 2005 (UTC)

No objections. --MarSch 10:22, 26 Jun 2005 (UTC)

Hyper generalized orthogonal Lie algebra

A badly written article should not be deleted, rather cleaned up. That is the conventional wisdom, but this particular article is trying my patience. Could anyboyd knowing this stuff take a look and say if this at all makes sence? Thanks. Oleg Alexandrov 22:07, 25 Jun 2005 (UTC)

The mathematics is probably OK. It's about explicit expressions of things like the Lie algebra of the Poincaré group, which is a semidirect product, in a block matrix way. Which is perfectly sensible. There is some odd language, but it is really mostly about writing things down in a 'dimensionless' way (c=1, that sort of thing). I wouldn't vouch for the title being standard. Charles Matthews 22:27, 25 Jun 2005 (UTC)

italic "i"s for the imaginary unit are being changed to non-italic, please comment

Wurzel is proposing here that the imaginary unit be represented using a non-italic i, and has been changing articles accordingly. The first seven books I've just pulled from off my shelves, all use an italic i. Please share your thoughts on the appropriate talk page(s). Paul August ☎ 17:04, Jun 26, 2005 (UTC)

scope of derivative article

There's an interesting discussion going on at Talk:Derivative concerning the scope/audience of the article. I'd be interested if anyone supports what I have to say. Alternatively, if you disagree with me, please add your voice. When I hear enough I'll shut up :-) Dmharvey Talk 00:25, 27 Jun 2005 (UTC)

The discussion in question is at the ==Scope of derivative article== heading and below it. Comments are very welcome (requested), since the issue of what to expect from the audience reading our articles is (I think) one of the more pressing ones this project faces. Oleg Alexandrov 03:06, 27 Jun 2005 (UTC)

Relaunch of Mathematics COTW

For those who don't know, the Mathematics Collaboration of the Week has been re-launched. Please nominate and vote for articles to focus on each fortnight. Both stubs and articles that are not stubs, but are confusing or poorly written, are acceptable. NatusRoma 29 June 2005 05:42 (UTC)

Please vote!

Please vote at Wikipedia:Featured picture candidates/Ford.circles.gif. The selection criterion includes the following:

the images featured on Wikipedia:Featured pictures should illustrate a Wikipedia article in such a way as to add significantly to that article

and stated that merely being a spectacular picture is not a sufficient qualification. This picture will probably not be considered spectacular; it's very simple. But it can make clear to ordinary laypersons the concept explained in Ford circle that would otherwise probably be understood by few other than mathematicians. <hubris> Thus in "illustrat[ing] an ... article in such a way as to add significantly to that article" I think it excels. </hubris> Michael Hardy 30 June 2005 23:10 (UTC)

Renaming the derivative article

There is a proposal at Talk:Derivative#move to differentiable function to move that article to Derivative (high school version) or some other similar sounding title. The reason seems to be that the derivative article as now written is not representative about what derivative is in mathematics, rather, it focusses on the most elementary calculus definition. Comments welcome. Oleg Alexandrov 1 July 2005 02:20 (UTC)

Don't say derivative (high school version); say derivative (elementary calculus), or something like that. Michael Hardy 5 July 2005 01:02 (UTC)

The ugly theorem

I found this article about a rather elementary fact in number theory. Anybody heard it called that way? Google yields nothing about this particular theorem. Oleg Alexandrov 1 July 2005 03:04 (UTC)

I don't understand what the "theorem" or elementary fact aspect is. It just looks like a property possessed by three particular numbers. Can anyone elaborate? (Google no help to me either) Kinser 1 July 2005 03:50 (UTC)

Checking the page history, it looks like an anonymous user with a tenuous grasp of English just typed up some info about something they found in a book or online, which then got copyedited into the current version by other people. The original version of the article didn't actually claim that Masahiko Fujiwara named the result the ugly theorem, though it does suggest that the "theorem" is that only the given three numbers have this property. In the absence of any other information about it, I would be inclined to delete the article on the grounds that the information has not been able to be verified. - dcljr (talk) 1 July 2005 05:13 (UTC)

I cannot verify it. Let's get it deleted. --MarSch 1 July 2005 11:43 (UTC)

Errors in articles

I don't know if this is the right place to comment on this; please move if you know a better place.

About 3 months ago, I added an intentional error to the page about "Distribution", date/time "21:33, 31 March 2005 82.157.131.133 (→Formal definition)". Of course the type of convergence is weak, not strong. Jitse Niesen was so kind to move the error part in the text, and has been unnoticed until now.

If such a major error in a basic mathematical article can survive this long, how much errors will there be in the more advanced subjects? For me this is enough proof not to trust Wikipedia articles. Hugo 1 July 2005 11:37 (UTC)

you shouldn't trust anything that you've not seen the proof of. --MarSch 1 July 2005 11:46 (UTC)

I don't trust your statement. I even don't trust my own statements. With such an argument there is no need to make a precise encyclopedia. I was in doubt about adding a statement like "Don't just say you can never trust your sources" but I hoped such a non-argument wouldn't be said. Hugo 1 July 2005 12:01 (UTC)

How's this for a non-argument: If you're intentionally introducing errors into articles, why should anyone engage you in serious discussion? In any case, see Wikipedia:Replies to common objections. - dcljr (talk) 2 July 2005 01:39 (UTC)

There is sad truth in what Hugo is saying above. But this is not surprising. There are 7000-8000 math and math-related articles on Wikipedia (7995 items on the list of mathematical topics as of now). There is not enough time and man power to check all contributions for mathematical correctness. There is not enough manpower even for style fixes. Besides, I am sure that a good chuck of those articles represent "dark matter", articles which are not on the watchlist of any active Wikipedians. One of course can check the changes to them from the list of mathematical topics, but again, who has the time? So, while Wikipedia can be lots of fun for editors (me at least :) and a useful source for readers, ultimately it is not much more reliable than a lot of other information on the internet. And there is not much to be done about this. Oleg Alexandrov 2 July 2005 02:21 (UTC)

There are lots of errors in wikipedia articles, we just corrected a subtle error in linear independence, but as a survey showed, many textbooks contained the same error. I found wikipedia very helpfull in several cases, but you're free to trust or not to trust any source you want to. Markus Schmaus 2 July 2005 03:18 (UTC)

Perhaps you might be polite enough to fix the error, now that it has been spotted, and now that the point has been made :-) (Although I see that there would be additional mileage gained by not fixing the error, since then you could point out that the error has not been fixed even after explicitly pointing it out in a discussion forum like this....)

But seriously... I agree that this is a problem, but probably not as big of a problem as you are making it out to be. You said: "For me this is enough proof not to trust Wikipedia articles." I agree: you shouldn't trust wikipedia articles. That should have been clear from the first moment you heard of the concept of wikipedia. And I don't think it is at all a non-argument to say "don't trust your sources". I genuinely believe in that argument. Trust is not black and white. It is possible to have a spectrum of trust in things you read, and a lot of it depends who wrote it and what your opinion is of them.

You also said: "With such an argument there is no need to make a precise encyclopedia." In my opinion, this is a vacuous statement; it is impossible to make a precise encyclopaedia. Precision is an ideal; I think generally wikipedians strive towards it, and they do a reasonable job, but I'm under no illusions of it being completely attained. However, it is possible to make a useful encyclopedia. And I think wikipedia is already such an object, and becomes more useful every day. An article can still be useful, even if it contains errors. (And I think most articles do not contain deliberate errors – the most insidious kind). For this reason, I still welcome your contributions, as long as the bulk of them are useful :-) Dmharvey Talk 2 July 2005 12:48 (UTC)

I sometimes wonder what percentage of Wikipedia's inaccuracies are there because someone felt the need to make this point. Isomorphic 2 July 2005 19:00 (UTC)

I concur with the above posts: I trust Wikipedia generally far less than textbooks or mathematical papers (which does not mean that they are perfect), not only because of the anonymous edits but also because most articles are not written by experts and most are not reviewed by experts. Furthermore, I personally am more careful when writing a mathematical paper than when editing the Wikipedia, and I guess this is true for most of us. It is highly unfortunate that Hugo mentions a weakness on which most of us agree without offering any suggestion for overcoming this weakness, and also that he hasn't tried yet to amend the error he deliberately introduced. For reference, this is all about the following sequence:

"The space D'(U) is turned into a locally convex topological vector space by defining that the sequence (S_k) converges towards 0 if and only if S_k(φ) → 0 for all test functions φ; this topology is called the strong (operator) topology."

Here, D'(U) is the (continuous) dual of the space of test functions. The topology is certainly not the strong operator topology because the space D'(U) does not consists of operators. Hugo seems to claim that it's the weak topology, but my impression is that it's the weak* topology. Can he (or anybody else) explain this? -- Jitse Niesen (talk) 2 July 2005 20:09 (UTC)

Lets get real. It appears that User:Hugo doesn't understand the process by which mathematics is actually done, and how research is published, much less how WP articles are written and corrected. A WP article can only be corrected when someone who is knowledgable and interested in a topic spots an error and corrects it. The error was presumably not corrected because there were no readers who were capable and interested in pursuing the particular claim. There's two ways to spot the error: one way is to be extremely knowledgable on the topic, and spot it instantly when the vandalism occurs. Clearly, there is no such person watching this article. The other way is for someone who is weak on the topic, but is interested in it, to be engaged in the processes of performing research, to eventually notice the error. Seems that was not the case, either. There is a third class of readers; those who didn't notice and didn't care. I think the above analysis shows that what Hugo really discovered is something about the quantity and type of readers of WP math articles, and not about the quality of the articles themselves.

If User:Hugo was actually performing research, and actually using WP as a source, then if there were errors in the articles that Hugo was reading, he would have eventually found them. I presume that he'd eventually find them, since I presume he double- and triple-checks his work. If not, and he publishes his work with errors and erroneous conclusions, then he is a fool, and has only himself to blame and not WP.

Ethical norms are such that anyone who is intentionally misleading, such as Hugo was, has crossed an ethical boundary, going in the wrong direction. Equally, if someone was deceived by his deceptions, they can blame Hugo. But, on the other hand, if WP contains honest mistakes (which it does), and someone is lead astray by these errors, then they are unfortunate or dumb or both. Hugo has only demonstrated that one can fool some of the people some of the time; this is hardly new.

If Hugo is interested in refereed math referneces, he should perhaps engage in thinking a bit about the WP and PlanetMath Exchange. We've talked about this here, before.

Everyone who has done research has found errors in published articles and books; some minor, some major. Errors on WP have the opportunity to be corrected, those on the printed page do not. Take a look a look at Talk:Bessel function for a real-world example of an error in a famous and highly-respected book that failed to propagate into WP. We actually have a chance to do better. linas 3 July 2005 00:04 (UTC)

Linas: well said. Dmharvey

Talk 3 July 2005 01:04 (UTC)

graphs

I've been teaching myself how to make pretty graphs in gnuplot and maxima. Is there a guide to this somewhere? If not, there should be. I will gladly contribute what I have learned today and yesterday. See commons:Image:Weighting curves.png and commons:Image:Hilbert_transform.png for examples. - July 2, 2005 17:48 (UTC)

A guide would be wonderful. I also hope MediaWiki gets support for gnuplot integration some day. Fredrik | talk 2 July 2005 20:17 (UTC)

Such a guide would certainly be very useful, so please start it. I had so many problems getting nice graphs with gnuplot that I reluctantly switched to Matlab (see Commons:Image:Schwarz-Christoffel transformation.png for my latest contribution), but judging from your graph to the right, gnuplot can also make nice pictures. -- Jitse Niesen (talk) 2 July 2005 22:07 (UTC)

A guide would be great; but don't make it into a guide for gnuplot, make it rather a set of "suggested" line weights, styles, etc. for WP, and how to set those things. I note that the above graph looks very nice, whereas the gnuplot default settings look quite poor on WP. linas 2 July 2005 23:12 (UTC)

We have been trying to standardize plots for probability distributions. A summary of the latest definition of a "standardized plot" is at Template talk:probability distribution#Standard Plots. See normal distribution for an example. A basic trick is to make the plot very large, like 6000 pixels on a side, using size 48-64 font size and 17 pixel line thickness, then reduce down to about 1000 pixels on a side using bicubic interpolation. This give a plot with no jagged lines. It is, however, big enough so that someone could download it and use it for projection purposes without pixellation. The display size for the plot is about 325 pixels for the Wikipedia article. Plots are as language free as possible, and uploaded to Wikimedia commons, so that they may be used in any language version of Wikipedia. PAR 3 July 2005 00:01 (UTC)

Any way to do the Gaussian blurring and bicubic interpolation without using PhotoShop? Can GIMP or Matlab do this? -- Jitse Niesen (talk) 3 July 2005 03:03 (UTC)

Aha! Those graphs look really great, and I based mine off of one without realizing they were standardized. Also instructions from MarkSweep. The two I linked to above have instructions in the commons page for reproducing them. One is in gnuplot and the other is in Maxima. I used GIMP to do the blurring and resizing. I wonder if there's a way to get gnuplot to generate the graph the way we want directly to PNG? - Omegatron July 3, 2005 03:25 (UTC)

I did a quick write-up at Wikipedia:How to write a Wikipedia article on Mathematics#Graphs. It would be great if somebody added the specific commands to do this in gnuplot, matlab, gimp, photoshop, and other programs. -- Jitse Niesen (talk) 4 July 2005 14:42 (UTC)

Something about graphs (very shortly) is mentioned in another paragraph in Wikipedia:How to write a Wikipedia article on Mathematics (up several sections). Do you think that part and what you wrote could (should) be merged? Or otherwise, the short part above could mention that more detail is below? I don't know myself how to proceed. Oleg Alexandrov 4 July 2005 15:31 (UTC)

I don't see the two sections. Were they already merged? I will add the instructions for gnuplot and maxima (which outputs to gnuplot) later today. Or you can do it. I included it in the linked images. Too busy right now. - Omegatron July 5, 2005 14:57 (UTC)

The first section is just two sentences in "Main part" (1.2 if you have numbering turned on), starting with "A picture is a great way of bringing a point home". I had already added a reference to the Graph section. -- Jitse Niesen (talk) 5 July 2005 15:26 (UTC)

Dotted framebox around formulas

What do people think of framing important formulas as in this example encountered at differintegral

definition

${}_a\mathbb{D}^q_tf(t)=\frac{d^qf(t)}{d(t-a)^q}$
$=\frac{1}{\Gamma(n-q)} \frac{d^n}{dt^n} \int_{a}^{t}(t-\tau)^{n-q-1}f(\tau)d\tau$

I myself find it not very pleasing. Oleg Alexandrov 3 July 2005 01:09 (UTC)

The template {{ImportantLabeledEquation}} has been put up for deletion on WP:TFD. I've subst'ed the template here for readability, and so that it will be preserved in case of deletion. --Quuxplusone 23:17, 28 July 2005 (UTC)

No I can't say I like it much either. Paul August ☎ July 3, 2005 03:51 (UTC)

Not a fan. Doesn't look especially nice, plus it adds extra formatting, which I consider a Bad Thing unless absolutely necessary. Isomorphic 3 July 2005 06:18 (UTC)

I don't care for that particular example either. But as it happens, I have been mulling over introducing equationbox templates for my project of improving the General relativity articles. See the talk page for exact solutions of Einstein's field equations. I would be grateful if anyone has any ideas. Also, I just used a table in the section on Lie algebra of the Lorentz group in my new revision of the article on the Lorentz group. I think the information there is useful in an encyclopedic way, but it would be nice if the table could be shrunk a bit. This problem exhibits the problem I am having in devising equationbox templates; existing infoboxes display some kinds of data in a generally vertically stacked way, but for equations one typically needs a more horizontal array which someone avoids interrupting the main flow of text. Maybe my notion is too quioxitic to be worth pursuing, but if you have any ideas, please add them to the above cited talk page. TIA---CH (talk) 3 July 2005 06:27 (UTC)

I don't really like this particular example. Keeping an open mind for other examples. Also I don't like the definition text in the corner. If you want to define something you should use := or =: for absolute clarity. --MarSch 3 July 2005 13:25 (UTC)

Paul Erdős moved to Pál Erdős

What do people think about the recent move of Paul Erdős to Pál Erdős? Paul August ☎ July 3, 2005 04:14 (UTC)

In general, articles should be at the title most commonly used in English. See Wikipedia:Naming conventions (common names). The new title may be more "correct" in some sense, but it's not what most books have. Until "Pál Erdős" becomes the generally used form, I would rather stick with "Paul". Isomorphic 3 July 2005 06:15 (UTC)

I agree with Isomorphic, although I do think the English-language article should mention the Hungarian form of his name.---CH (talk) 3 July 2005 06:29 (UTC)

I've put a mention of the Hungarian form in the intro, and moved the article back to its original title. Isomorphic 3 July 2005 06:32 (UTC)

I can understand why Russian names are not at their original name, although they probably shold be, but I cannot understand this at all. What's worng with Pál? --MarSch 3 July 2005 13:37 (UTC)

See Isomorphic's response: the problem with Pál is that it is not used that often in English. -- Jitse Niesen (talk) 3 July 2005 14:58 (UTC)

I think the English name should be used. That's how I always encountered this guy in the English mathbooks. Same thing as with John von Neumann who orignally was Janos. Oleg Alexandrov 3 July 2005 15:38 (UTC)

Anyone who publishes scientific articles is urged to choose one name, and one name only, under which to publish, so as not to confuse readers and in order to make bibliographies easier to assemble. Under what name did Paul Erdos publish? Shouldn't the article be under the name he himself chose? -- linas 3 July 2005 15:46 (UTC)

I didn't even know John von Neumann is actually named Janos. How stupid is that. Or did he change his name upon becoming an American? --MarSch 3 July 2005 16:09 (UTC)

I took a quick search on MathSciNet. Everywhere I saw Paul. The only exception is

Surányi, J. Remembering Pál Erdös. Paul Erdös and his mathematics, I (Budapest, 1999), 47--49, Bolyai Soc. Math. Stud., 11, János Bolyai Math. Soc., Budapest, 2002. 01A70.

So, even the Hungarians call him Pál only to emphasize that he is their guy, while the formal name is Paul. Oleg Alexandrov 3 July 2005 16:17 (UTC)

Why do I prefer Isomorphic's criterion to Linas's criterion? I think biographies in en:wiki should be named according to the name English language readers are most likely to encounter, particularly in searching on the web. Usually, this will agree with the name the person went by in his own writings (such is the case with Paul Erdos), but there are exceptions, such as some Russian mathematicans whose names appeared in print in various German and French language journals with transliterations which would now be regarded as archaic, like Tschebycheff. So an article on Chebyshev should use the currently most popular spelling in English language sources, but should of course mention other forms of the name which a reader might encounter. Any questionable cases should probably be resolved by asking what choice of name is least likely to confuse the average Wikipedia reader. So for example, some modern transliterations of Chinese names or Russian names might actually be more confusing than using the most commonly encountered name. Case in point: you all probably know who Shing-Shen Chern was (if not see [22]), but the wiki biography is called Shiing-Shen Chern. I am told this is a more accurate transliteration, but it is neither what he most often went by nor the form of the name which English language readers are most likely to encounter in web searches.---CH (talk) 3 July 2005 20:26 (UTC)

P.S. An example of another common naming problem: Émile Picard went by Émile, not Charles, but his biography appears under his full name, which readers are unlikely to encounter except at the popular MacTutor Archive [23], which uses full names exclusively. This practice always makes me think of the quip that triple barrelled names always seem to denote either murderers (Lee Harvey Oswald) or philosophers (John Stuart Mill). ---CH (talk) 3 July 2005 20:45 (UTC)

Maths COTW: Manifold

As mentioned above, we are witnessing an attempt to revive the Mathematics Collaboration of the Week (which should probably be renamed to Collaboration of the Fortnight since it seems to run over two week periods). I am pleased that manifold was chosen to be the target of the collaboration and I'd like to invite all of you to contribute to this article. Note that we are currently rewriting the article at manifold/rewrite. Please put further comments on Talk:manifold/rewrite. -- Jitse Niesen (talk) 4 July 2005 13:26 (UTC)

Hierarchy in the math articles

What people think of the article tangent bundle having on top the notice that it is a subarticle of differentiable manifold? Or of the planned topological manifold article being thought as a subarticle of the manifold article? I find this terminology introduced by MarSch a bit unusual. It implies that some articles are subordinate to others.

Also, I am not a native speaker of English, but doesn't the phrase

Tangent bundle is a subarticle of differentiable manifold

imply the former is a chunck of text contained in the latter, rather than a standalone article is it is now? Oleg Alexandrov 4 July 2005 15:43 (UTC)

I am not a big fan of the hierarchy thing. It is only in very rare cases that I would approve. This is not one of them. I bet that the term "tangent bundle" is probably used in other areas of mathematics that have nothing to do with differentiable manifolds, or at least are only loosely analogous to them. I think algebraic geometry might be an example, but I'm not an expert. Perhaps someone else can expand on this. (Oleg: I'm not even sure if "subarticle" is a real english word :-) Dmharvey

Talk 4 July 2005 20:06 (UTC)

With few exceptions, no article should be subordinate to any other article. I can imagine some kind of "subarticle of" relationship perhaps being useful, but I don't think it should be a hierarchical parent-child relationship. We would certainly want an article to possibly be a "subarticle of" more than one article, and perhaps even two articles to be "subarticles of" each other, both of which however run counter to the usual notion of "subness". In short I don't think it is probably a very good idea. Paul August ☎ July 4, 2005 21:06 (UTC)

The terminology is indeed confusing, but I like the idea of having a prominent link at the top of tangent bundle pointing to differential manifold. How about a phrase like "See differential manifold for more background." -- Jitse Niesen (talk) 4 July 2005 21:15 (UTC) (via edit conflict with Paul)

Definitely agree there should be such a prominent link. Dmharvey

Talk 4 July 2005 21:17 (UTC)

Wikipedia is not heirarchal. If you start building linked lists and trees into the software through templates, you are breaking the design of Wikipedia. It has purposfully been designed NOT to be heirarchal. This discussion has been gone over many times allready in the past 4 years and there are rules against it. If you want to draw attention to another article, you do what every one else does: write it into the text of the article, explain why, and provide context for the reader.

Keep in mind, articles can be copied anywhere, in any format, including paper, it has to be assumed that the reader is not reading the article using software and a computer, and thus does not have access to links. Thats why Wikipedia style guidelines are the way they are, articles are self-contained units with no dependencies or heirarchies. Stbalbach 5 July 2005 03:11 (UTC)

Basically a differentiable manifold is a topological manifold, so there is a section of topological manifold about #differentiable manifolds. This section cannot contain all information on diff. manifolds so there exists now a full article on them (complete with intro and everything), with the most important parts in the section of top. manifolds. This is policy. For this situation were created the templates {main} and {seemain}. One to go in the section and one to go at the top of the corresponding article. Unfortunately the wording of these templates was identical and is still almost. Therefore nobody could knew which was which and they were used interchangeably. Consequently somebody listed them at tfd, because the seemed to be forks. Their creator SEWilco explained that they have different purposes. I voted to keep at first, but then I went and read their talk page descriptions and I found it very difficult to understand which was which. Basically because each uses main in a different meaning. Main as in has the most information and main as in is more general and thus has less information. So I started a discussion and proposed new templates with a clear distinction. These are {subartcleof} and {seesubarticle}. Their names are clear and their wording is clear. You may not like that wording though. The use of two such templates implies a acyclic graph structure. It is possible to have multiple subarticles and also to have multiple superarticles, just as it was with {main} and {seemain}. Stbalbach may rage against the {subarticle} templates, but the fact is that he uses the {main} versions which basically have the same purpose and also imply a hierarchical structure whether he realizes it or not. These templates are not intended to connect articles on the same level. If you want that then you need another template such as {siblingarticle} which does not exist yet. This is hardly an argument against {main} and {seemain} or {subarticle}s. So I can only understand all this by assuming you dislike the current wording. --MarSch 5 July 2005 10:45 (UTC)

Since the word subarticle seems to cause problems. What about two other templates

{details}: For more details on this topic, see the article {1}.
{background}: For more background on this topic, see the article {1}.

Please discuss at Wikipedia:Templates_for_Deletion#Other_wording --MarSch 5 July 2005 13:41 (UTC)

Just in case people have not noticed, {{Template:subarticleof}} is up for deletion at Wikipedia:Templates_for_Deletion#Template:Subarticleof. Oleg Alexandrov 6 July 2005 03:41 (UTC)

Paul: such multiple relationships are possible. Horizontal grouping cannot be done with these, you need another template for that. So those are not two arguments against this template.

Dmharvey: I don't understand why you do want the prominent link, but not the hierarchy. What is the difference?\

Oleg:What about subcategories? Are they somehow not standalone?

That's the very point of it. Categories were meant to replace any other form of hierarchical relationship. No need for more. Oleg Alexandrov 6 July 2005 15:23 (UTC)

Jitse, what do you mean by prefer written out in full? What is wrong with a template? Do you want local variation? --MarSch 6 July 2005 11:25 (UTC)

My problem with templates is that they are not transparent. If I see a template when I'm editing an article, it's not immediately obvious what it does. It's not a big problem, but I also think it's not a big gain to write it out all the time (use subst: if you are too lazy). I understand that this may lead to variation, but that is quite okay with me. But let me iterate that this is really a miinor issue for me. -- Jitse Niesen (talk) 6 July 2005 19:55 (UTC)

I want the prominent link because anybody looking up tangent bundle should realise that the idea comes from differential geometry. I don't want the hierarchy because tangent bundle may apply to settings other than differential geometry. As I said above, I'm not an expert, and I don't know much about these other settings. However, take a look at [24] on planetmath. Towards the bottom of the article, you'll see a discussion of how you define a "tangent bundle" over a scheme (mathematics), which is a pretty abstract version of tangent bundle, and has nothing to do with differential geometry. Dmharvey

Talk 6 July 2005 12:56 (UTC)

I think sometimes the link is clear from context. Sometimes different wording should be used. I very much agree with Jitse (see Wikipedia:Templates_for_Deletion#Other_wording) that mindlessly slapping templates on articles illustrating its dependencies is not the way to go. Oleg Alexandrov 6 July 2005 15:23 (UTC)

Dmharvey, the link is the hierarchy. I guess you object to my calling it a hiereachy and using the word subarticle. But I can only guess, since you haven't explained yet. Do you like my proposed alternatives any better?

Oleg, there is nothing mindless about slapping a template on something. Mindless is not an argument. This is one relation that I would like to highlight and I don't see what would be gained by doing that in a different way each time. Saying templates are mindless implies you want all templates to go away.--MarSch 6 July 2005 15:38 (UTC)

Oh, and forgive me for forgetting, but I can't believe I have to say this yet again. There is nothing to prevent tangent bundle from having another link to scheme. --MarSch 6 July 2005 15:41 (UTC)

Hi again, there seem to be a lot of proposed alternatives floating around, and I'm not quite sure I understand what they are. The problem I see with having a message like "this is a subarticle of differentiable manifold" on the "tangent bundle" page is that you would then require also "this is a subarticle of scheme" and so on. It just seems unwieldy and unnecessary. My preference is to have an introduction on Tangent bundle which discusses the tangent bundle in relation to differentiable manifolds as the simplest and most important case, mentions the fact that tangent bundles have analogues in quite different settings (for example in schemes), and then the main article focusses on the differentiable manifold case, and perhaps later we have a section that expands on the various generalizations of the tangent bundle concept. (This discussion reminds me very much of the ongoing debate about Derivative, which is perhaps not a coincidence, given the close relationship between derivatives and tangent bundles :-) ) Personally I would be unable to write such an article because my knowledge of generalisations of tangent bundles is extremely limited.

I think the best reason to avoid "subarticles", "main articles" and so on, is that it introduces too much unnecessary rigidity into the structure of the whole encyclopaedia. You really can't predict what people will want to expand on later. Dmharvey

Talk 6 July 2005 16:21 (UTC)

Mathematics Subprojects, Anyone?

I'd like to point out that there are already some projects which can be described as subprojects of this one, and to suggest some new ones:

listing key publications in the history of mathematics (actually, I think this one is a quixotic task),
adding suitable citations to all mathematics articles (I see this as much more painless and feasible, but encourage participants to try hard to add only really suitable citations to articles on topics for which they know the textbook literature),
themes of mathematics: examples include multiplicity of representations, levels of structure, local to global, classification, categorification, (all but the last two just came up in the manifold/rewrite discussion--- I'd say that manifold is a concept in mathematics, but classification theorem is a theme, and a big one),
classification theorems could be a category in itself, which would include for example Thurston's classification theorem and Bianchi groups,
actually, Bianchi group could itself be a category, since I for one believe that these guys are worthy of indidivual articles (which I plan to write), and similarly for other classifications (e.g. an article on H² should be accessible in one click to someone searching for manifolds of constant curvature, sometimes called space forms).

The goal of the proposed themes of mathematics subproject could be to ensure that any reader who comes to the math pages here will be likely to encounter at least one of these "big ideas", and will be encouraged to read more about it. At present, many articles adequatley describe a concept but fail to point out that this concept exhibits certain themes, an oversight which I think should be systematically rectified. For some examples of how big ideas can be incorporated into articles, see my discussion in the talk page for the manifold/rewrite article.

Categorification seems to be a notion some mathematicians hate with a passion, but what I have in mind for the categorification subproject is something I expect we could all agree on: many articles describe concepts but fail to point out that they are examples of categorical notions, and these often arise from an attempt to capture in formal language some theme. So the categorification subproject could have two complementary goals:

ensuring that articles mention (probably near the end!) when a concept is an example of a (usually much more general!) concept in category theory, such as a pullback square,
ensuring that articles on concepts such as pullback square link to articles on important examples of pullback squares.

By the way, the article on Thurston's classification theorem should clarify the relation with uniformitization. It should probably cite the little book by Andrew Casson.

--CH (talk) 4 July 2005 20:41 (UTC)

I would say we don't have enough mathematicians (post-doctoral, say) to indulge in subprojects. What is a big deal for us is still getting the top-down view right: fill obvious gaps, list articles, categorise, add biographies, and generally pull things together so that reading the English Wikipedia on mathematics can constitute a liberal education on it. Charles Matthews 08:38, 13 July 2005 (UTC)

Puzzle articles on VfD

Several articles on puzzles such as burr puzzle, mechanical puzzle and packing problem are up for deletion in two mass listings on VfD here and here. —Blotwell 5 July 2005 00:31 (UTC)

Thanks, many of them listed aren't the crap that they are thought to be. --MarSch 5 July 2005 16:16 (UTC)

Yes I agree, I have voted to keep these. Paul August ☎ July 5, 2005 18:19 (UTC)

Templates for thought

In a magic country far far away, there lived four templates, explaining what math is all about. They were named "quantity", "space", "change", and "structure" (note that "quantity" is actually about numbers). Here they are in full glory.

Template:Structure

I would like to generate some discussion on whether these templates are useful, whether they should be trimmed, or even eliminated, replaced by categories. Wonder what people think. Oleg Alexandrov 03:23, 13 July 2005 (UTC)

(From talk:Transcendental number, copied here by Oleg Alexandrov 03:23, 13 July 2005 (UTC))

While I agree that these templates are a bit weird and of dubious utility, I'm not sure I completely support their removal. I might, but I probably need more convincing. The fact that lots of other technical subjects seem to have similar templates means that removal from the math pages would damage the consistency of wikipedia across technical subjects, and I do think we should value some uniformity of format at this project. So what am I saying, either we have to delete all the templates or none of them? No, that's probably too severe.

How about this Oleg, can you imagine a mathematics template which we could agree may be useful? Maybe a much coarser template, and only a single one instead of four of them. And maybe not organized so bizarrely (structure, quantity, change, and space???? wtf!). I'd feel better if we still had one organizing template, to ensure consistency with the other technical subjects. -Lethe | Talk 17:31, July 11, 2005 (UTC)

I despise templates. I like categories. I can make only one argument in support of templates: if one is learning calculus or trigonometry for the first time, they are a handy tool for trying to cram a whole bunch of facts into your mind at the same time. But once you're no longer cramming for school ... no. They're ugly, they're inaccurate, they chew up space, they impart little knowledge. linas 04:58, 13 July 2005 (UTC)

Templates are unpopular, justly. I think we only need a few templates, and those for pedagogic purposes. So, no bi-complex numbers, for example. Charles Matthews 08:33, 13 July 2005 (UTC)

I prefer the simple "See Also" section at the bottom of an article. Dmharvey

Talk 11:38, 13 July 2005 (UTC)

I nominated the templates {quantity} and {strucutre} which have a lot of articles and which are not very related, for deletion. See Wikipedia:Templates_for_deletion#Template:Quantity and Wikipedia:Templates_for_deletion#Template:Structure. Oleg Alexandrov 23:09, 14 July 2005 (UTC)

I recently saw for the first time the {{mathematics-footer}} template

Major fields of mathematics v • d • e
Logic • Set theory • Algebra (Abstract algebra - Linear algebra) • Discrete mathematics • Combinatorics • Number theory • Analysis • Geometry • Topology • Applied mathematics • Probability • Statistics • Mathematical physics

in my opinion, that's all the template we need for mathematics for consistency. Right? -Lethe | Talk 03:32, July 16, 2005 (UTC)

Kill 'em all. -- Dominus 04:55, 16 July 2005 (UTC)

Well, I got embolded and nominated for deletion the other two of the four templates. See Wikipedia:Templates_for_deletion#Template:Change and Wikipedia:Templates_for_deletion#Template:Space. Oleg Alexandrov 06:43, 16 July 2005 (UTC)

Fwiw, see also {{mathematics}}. —msh210 00:22, 26 July 2005 (UTC)

Redirects on rfd

Recently I moved Infinite tree (graph theory) to Tree (set theory), because the trees in question don't have to be infinite and don't have much to do with graph-theoretic trees. For the same reasons I have proposed that the two redirects, infinite tree and infinite tree (graph theory), be deleted. --Trovatore 04:19, 13 July 2005 (UTC)

Infinity-Borel set

I'm having a great argument with myself on the above-named page, and it'd be great if one/some of y'all would come referee. --Trovatore 04:38, 15 July 2005 (UTC)

Think I've sorted it out now. Still welcome to come take a look, though. --Trovatore 02:25, 16 July 2005 (UTC)

In fact please do come look at it, particularly the Alternative definition section on the Talk page. Opinions solicited on which definition is clearer/better. --Trovatore 02:52, 16 July 2005 (UTC)

Template:Quantity and Template:Structure

Template:Quantity and Template:Structure have both been listed for deletion at Templates for deletion. I don't know enough about mathmatical topics to know how coherent the topics are in either template, so I am requesting that some editors with some math knowledge visit TFD and offer their input to the discussion. BlankVerse ∅ 07:25, 15 July 2005 (UTC)

H numbers

Hello. The article H numbers looks like original research to me. Article links to this web site [25]. Mathworld hasn't heard of H numbers and I can't find any relevant Google hits. Comments? Thanks for your help, Wile E. Heresiarch 08:32, 16 July 2005 (UTC)

It looks like patent nonsense to me. Dysprosia 08:37, 16 July 2005 (UTC)

Not nonsense, necessarily. One can define such an algebra, I guess. But prima facie it is OR, and the link page just confirms that. Charles Matthews 08:39, 16 July 2005 (UTC)

Perhaps I use the term a little too loosely -- it appears to have some rather naive reasoning anyway afaics. Regardless, should be VfD'd for original research, plus it looks like an attempt to legitimize this by having a link from the hnumbers website back to us, and is in a sense advertising. Dysprosia 08:44, 16 July 2005 (UTC)

I agree. It looks like original research to me. Paul August ☎ 12:03, July 16, 2005 (UTC)

I don't think I'd call it research, but anyway let's get it deleted. Markus Schmaus 12:19, 16 July 2005 (UTC)

absolute value article rewrite, RFC

I've just completed a major revision of the absolute value article. I've described the changes I've made here. I'd appreciate any comments/criticisms anyone might have. (Please respond here) And a good proofread would be greatly appreciated (my eyes now glaze over when I attempt to read it). Paul August ☎ 19:56, July 16, 2005 (UTC)

On my browser (Mozilla 1.7.8 running under Debian Sarge) the Wikipedia logo shows up in the article itself, on top of some of the text of the article. And the navigation, search and toolbox boxes are nowhere to be found. Something to do with this line?

[[Image:Absolute value.png|frame|The graph of the absolute value function for real numbers.]]

No, that line isn't the problem. I copied the article to my sandbox and deleted that line; problem's still there. --Trovatore 20:28, 16 July 2005 (UTC)

--Trovatore 20:14, 16 July 2005 (UTC)

I take back the "nowhere to be found" part--they show up at the very bottom of the article, in case that helps in debugging. --Trovatore 20:19, 16 July 2005 (UTC)

Just tried it in Konqueror -- same result.

Hmm I'll have a look. I forgot to say that any comments (specific to that article) should probably be directed to that talk page. Paul August ☎ 20:58, July 16, 2005 (UTC)

It works ok for me in Safari, Firefox And IE on a MacOS 10.3. Paul August ☎ 21:02, July 16, 2005 (UTC)

Same problem in Netscape 7.1 (Windows XP). I've noted it on the talk page for the article. --Trovatore 21:21, 16 July 2005 (UTC)

Works fine for me with Firefox, Mozilla, and Konqueror on Fedora Linux. Works equally well with Mozilla and Internet Explorer on MS Windows. Oleg Alexandrov 22:30, 16 July 2005 (UTC)

Yes, but that's after Paul's latest fix. Try this version: [26]. Clearly there's an issue with the Rf and Ent templates that someone needs to look at. --Trovatore 22:34, 16 July 2005 (UTC)

That one also works for me with Firefox on both Linux and Windows (did not try the other browsers now). Oleg Alexandrov 22:37, 16 July 2005 (UTC)

Well, Paul said Firefox worked. I don't have it to check. Doesn't work in Mozilla 1.7.8. --Trovatore 22:43, 16 July 2005 (UTC)

Ok I can see we are having a multipage discussion. My fault really. let's continue any future discussions at Talk:absolute value. I'm heading there now ... Paul August ☎ 22:47, July 16, 2005 (UTC)

Merging of Portal and Category

Has anybody noticed the new Category:Mathematics? --R.Koot 19:54, 17 July 2005 (UTC)

Nice job, visually. I'm a bit concerned, though, that the formalist view is presented in a way that might suggest it's the default. This may not have been the intent, but possibly should be addressed. --Trovatore 20:30, 17 July 2005 (UTC)

Actually, that bit used to be in the main mathematics article - now we have something more mushy, and I miss it. Charles Matthews 20:58, 17 July 2005 (UTC)

By the bye, it led me to an interesting discussion that I hadn't seen before, and I cast my "yes" votes on math being a science and emperical. See Talk:Mathematics#Is Mathematics a science? and Talk:Mathematics#Is Mathematics empirical?. --Trovatore 20:30, 17 July 2005 (UTC)

The big challenge is to keep the portal thing up to date. I myself am no big fan of a Wikiportal, whether stand alone or embedded in the category. Oleg Alexandrov 20:39, 17 July 2005 (UTC)

One of my two main objectives. See User_talk:DavidLevinson#Category Mathematics --R.Koot 21:45, 17 July 2005 (UTC)

I redirected Wikipedia:Wikiportal/Mathematics to Category:Mathematics now that the contents has been merged. I do agree that the latter is more visible, as there is a link to it from the main Wikipedia page. I also put a note on Wikipedia talk:Wikiportal/Mathematics saying that the math talk usually takes place on this page, Wikipedia talk:WikiProject Mathematics, and not there. I plan to put the same note on Category talk:Mathematics. Oleg Alexandrov 17:51, 18 July 2005 (UTC)

I've put Template:MathematicsCOTW on TfD as is superseded by Template:Wikiportal:Mathematics/Opentask]. --R.Koot 18:41, 18 July 2005 (UTC)

Definable number

The definable number article is in pretty bad shape. Whatever it is that the article is talking about, it makes some true and useful assertions about--but it's very unclear what it's talking about. See the talk page. --Trovatore 04:40, 19 July 2005 (UTC)

I've rewritten the page. See talk page for discussion. --Trovatore 05:15, 21 July 2005 (UTC)

BTW why isn't there a template for "math accuracy disputes" or "math articles needing attention" or some such? I put the {{accuracy}} tag on it and believe I'm completely justified--but that only puts it in the "Accuracy disputes" category, where it could wait forever for a mathematician to notice it. It would be nice to put it in a more specific needs-attention category. But then again I suppose that's part of what this page is for. --Trovatore 04:40, 19 July 2005 (UTC)

I decided to see, replaced {{accuracy}} with {{Math-accuracy}}, meant to hit Alt-P but hit Alt-S by mistake, got the red template link, and now it won't let me change it back. Something going on with the server?--Trovatore 05:03, 19 July 2005 (UTC)

OK, I think I'm done with it for now. Anyone here who knows about forcing is invited to check my proof that it's consistent with ZFC that there are only countably many OD reals (or better, find a reference). --Trovatore 03:10, 22 July 2005 (UTC)

Forgot to mention, the proof's not on the main page; it's on the talk page. --Trovatore 03:40, 22 July 2005 (UTC)

The article isn't perfect but at least it no longer gives the false impression that there's a univocal, mathematically well-understood notion of what it means to be a not-further-specified "definable" real. Unfortunately there are lots of pages that link to the page, and some of them do give that impression. Not sure what to do about that yet. --Trovatore 03:10, 22 July 2005 (UTC)

Mnenta

Anybody here heard of mnenta? It's the only contribution from some IP address, I cannot find it in MathSciNet or OED, and none of the 14 pages returned by Google is relevant, so unless somebody speaks up it will go to VfD. -- Jitse Niesen (talk) 19:39, 19 July 2005 (UTC)

Sounds like the sort of thing Clifford Pickover does; but I don't remember it specifically. Whether this should, if true, save it from VfD is another question. Septentrionalis 19:43, 19 July 2005 (UTC)

This is a dicdef at best without some relevance to the rest of mathematics; I say VFD. --Kinser 23:16, 19 July 2005 (UTC)

If someone knows Pickover well enough to e-mail him, I say go for it; maybe the article can be brought up to a level worth keeping. But if there's no serious, immediate prospect of improvement, I'll vote delete--the article as it stands is very uninformative. --Trovatore 23:52, 19 July 2005 (UTC)

Without a source, this is unverifiable and should be deleted. Paul August ☎ 03:47, July 20, 2005 (UTC)

Sounds like a mini-consensus. Jitse, why don't you put it on VfD and get the ball rolling? If the article has defenders, that'll concentrate their minds. --Trovatore 04:12, 20 July 2005 (UTC)

Went ahead and did it myself--hope you don't mind. --Trovatore 05:48, 21 July 2005 (UTC)

Puzzle VfD ... Its baaaack ...

The puzzle articles are under renewed attack.

I am concerned that these VfD's are being pushed by someone who has it in for puzzles. I am concerned that the people voting to delete never actually contribute to math or physics articles. In a moment of heated anger, were I to actually get that heated, then I would say that these people are anti-social vandals, and should be treated as such. But everyone knows I'm not a hot-head, right? linas 15:38, 20 July 2005 (UTC)

I think they all contain valid encyclopedic content. This is getting tiresome. Paul August ☎ 18:27, July 20, 2005 (UTC)

Yeah, -Ril- started some sort crusade Karl Scherer after he added 'spam' to some articles (which it barely was imho). --R.Koot 18:47, 20 July 2005 (UTC)

It should be noted that the articles are up for VFD as neologistic categorisation by Karl Scherer. Coupled with a distinct lack of non-categorisation content, existing only to fluff the categorisation enough to have an article for each class. The 100+ that have already been VFD'd were done so for predominantly the same reason.

Wikipedia is meant to be an encyclopedia, and not something to push your POV of how things should be categorised. Neither is it a collection of all information under the sun.~~~~ 22:10, 20 July 2005 (UTC)

You have to categorize articles one way or another. And I think Karl did a pretty good job. --R.Koot 22:19, 20 July 2005 (UTC)

Dotted box template up for deletion

I nominated Template:ImportantLabeledEquation up for deletion (this was a bit discussed above, see Wikipedia talk:WikiProject Mathematics#Dotted framebox around formulas). I myself think that dotted box looks ugly, and indenting should be enough to display a math equation or defintion. Oleg Alexandrov 18:43, 20 July 2005 (UTC)

The vote for deletion is at Wikipedia:Templates for deletion#Template:ImportantLabeledEquation. Oleg Alexandrov 18:44, 20 July 2005 (UTC)

Somewhere there one also can find Template:Calculus2 which is not necessary anymore, as it is just an old version of Template:Calculus. Oleg Alexandrov 00:40, 21 July 2005 (UTC)

Category:Integer sequences

(Moved to here from my talk page.) linas 17:17, 24 July 2005 (UTC)

I notice you recently recategorised quasiperfect number to 'integer sequences', but it seems odd to mark it as such given that no such numbers are known to exist. Do you see the categorisation as extending to any boolean property defined on integers (or maybe the naturals)? (I ask in all humility - it isn't clear to me whether the categorisation is appropriate or not.) Either way, it may also merit a clarification on Category::Integer_sequences. Hv 16:30, 24 July 2005 (UTC)

Hi Hv, If you know of a better category, please recategorize as appropriate. I was attempting to do a broad cleanup; the articles I placed in Category:Integer sequences I had found scattered about Category:Numbers, Category:Integers, Category:Number theory, Category:Number sequences, a few in some odd corners, and a few without any cats at all. Rather than having them scattered all about, I thought I'd at least pull them into one place. There may be a better way of organizing these, but I don't know of one/can't think of one at this time. If you have ideas, let me know. At any rate, quasiperfect number seemed a better fit there than elsewhere. linas 16:44, 24 July 2005 (UTC)

Hm, maybe Category:Divisor-related sequences, since there seems to be a dozen or so that can be loosely defined in this way, e.g. abundant number. linas 17:05, 24 July 2005 (UTC)

And then, there's Category:Totient-related sequences as well; e.g. highly cototient number. Is there a common name for these things? linas 17:13, 24 July 2005 (UTC)

Sequences can be finite, of course, but this category might be better named Category:Kinds of integer (or Types or Classes). Sequences should be kept for those where the order matters, like Fibonacci sequence or John Conway's Speak-and-say sequence. Septentrionalis 19:39, 24 July 2005 (UTC)

I agree. I saw Linas put primitive semiperfect number in Category:Integer sequences and I thought that it was very odd to call it a sequence, but I forgot to follow up on it. How about something like Category:Divisibility properties? -- Jitse Niesen (talk) 19:58, 24 July 2005 (UTC)

I'm not sure it's a divisibility property. How about Category:Properties of natural numbers? Or maybe a List of properties of natural numbers. --Trovatore 20:10, 24 July 2005 (UTC)

Something in the spirit of Category:Properties of natural numbers looks good to me. But can one shorten this in some way? Oleg Alexandrov 21:08, 24 July 2005 (UTC)

Category:Integer properties is shorter, if a bit looser. But presumably a description could explain that it is appropriate for properties defined over more restricted sets as well, such as naturals or positive integers. Hv 23:35, 24 July 2005 (UTC)

Or just make sure the articles somewhere say the property only applies to non-negative/positive integers. They probably should anyway. Septentrionalis 23:39, 24 July 2005 (UTC)

I'd prefer Category:Properties of integers. Somehow "integer properties" sounds like something that's an integer and at the same time a property. --Trovatore 00:16, 25 July 2005 (UTC)

I like Trovatore's suggestion. Oleg Alexandrov 01:33, 25 July 2005 (UTC)

Well, there are 75 articles in Category:Integer sequences; and it would be appropriate to introduce some subcategories, such as Category:Divisor-related numbers and Category:Totient-related numbers. The first seems to be a category over at mathworld, the second a neologism. I was fishing for a commonly-used, commonly-accepted name for these two cats. In all cases, I assume that the category will also contain "theorems pertaining to divisor-related numbers" and "properties of numbers that are in the divisor-related number category". I think we can add wording stating this explicitly,once we know the correct, commonly accepted cat names. linas 02:20, 25 July 2005 (UTC)

Personally I think "Divisor-related numbers" is horrible. Every number is divisor-related (for example, it has divisors, is a divisor of other numbers, etc). The things in the category are not numbers, but rather properties of numbers, and the name should reflect that. --Trovatore 01:43, 27 July 2005 (UTC)

And just in passing, I really wouldn't look to MathWorld, or PlanetMath either, as an example of how to do anything. --Trovatore 01:47, 27 July 2005 (UTC)

A category such as Category:Divisors of integers would be useful, and could be a subcategory of both the 'integer sequences' and 'number theory' categories. It would not just hold sequences, but I think people get a bit hypnotised by the sequence thing. Charles Matthews 10:11, 27 July 2005 (UTC)

Taken literally, which categories usually are, this would be coterminous with Category:Integer. I presume this is not what is meant; but what is meant? Septentrionalis 14:35, 27 July 2005 (UTC)

Quite a lot of number theory takes an integer n, looks at its set of divisors (a multiset, if you want) and then defines some function f(n) via that multiset. So, it's a substantial topic, and not really a tautologous thing either. Charles Matthews 14:43, 27 July 2005 (UTC)

Perfectly true (pun unintentional). And now I see what you mean. If the whole category becomes Category:Properties of integers, the subcat should be Category:Properties of divisors or even Category:Properties of divisors of integers (although I'd rather not go there). I will propose a move of the whole category now, to move that part of this discussion where it will do something. Septentrionalis 15:15, 27 July 2005 (UTC)

There is some misunderstanding; its about "numbers related through functions of the divisor function", and not whether or not numbers have divisors.linas 17:34, 27 July 2005 (UTC)

Which is precisely why "divisor-related numbers" is a bad name. If you have a category called "foo numbers", the individual articles should logically be about individual foo numbers. (So we shouldn't have any categories called "foo numbers".) (Maybe that was your point--I can't tell from the comment above and haven't bothered to trace through the history to see which comments are yours.) --Trovatore 06:20, 31 July 2005 (UTC)

There is a Category:Prime numbers which contains articles about related theorems. linas 23:53, 1 August 2005 (UTC)

I vote we keep the discussion here, instead of CfD, since almost no mathematicians hang out on CfD. I promise to make the changes myself, if we can build a reasonable consensus on what the naming should be. linas 17:34, 27 July 2005 (UTC)
- Fine; CfD has been notified in case anyone there cares. The category talk page will refer them here. Septentrionalis 01:59, 2 August 2005 (UTC)

3.14

The article for this number is up for deletion at Wikipedia:Votes for deletion/3.14. Uncle G 02:01:35, 2005-07-25 (UTC)

Visualstatistics.net

User:Cruise (talk • contribs) has recently added a number of links to Visualstatistics.net and vstat.net. A number of the pages on this site about social science topics (e.g. slavery) are a mix of facts and patent nonsense, and I have thus removed them. I have no idea about the quality of the math and statistics pages linked, e.g. at multiple correlation, but it would be a good idea if someone double checked them. - SimonP 03:20, July 25, 2005 (UTC)

the Multiple correlation link looks somewhat simple-minded but not utter bilge, at least at a glance. Septentrionalis 22:34, 25 July 2005 (UTC)

PNG vs HTML

I have a disagreement over at cardinal number about using inline TeX which becomes HTML. I argue against it (that is, use HTML if TeX gives PNG), while the other opinion seems to be that if one really want HTML then one should set up the browser settings that way. Wonder what people think on this issue. Thanks. Oleg Alexandrov 22:40, 26 July 2005 (UTC)

The advantages to using markup like "<math>|X| \le |Y|</math>" rather than "| ''X'' | ≤ | ''Y'' |" which in turn is automatically turned into HTML such as | X | ≤ | Y | are numerous, by writing formulae in an abstract markup language they can be turned into HTML, PNGs (and in the future MathML) on the fly rather than being restricted to just one of those options, it's not future proof, it's restrictive and it's bad for accessability to use html rather than the math module.

If you have a problem with how the math module is converting LaTeX into HTML please file a bug at http://bugzilla.wikimedia.org/ . —Ævar Arnfjörð Bjarmason 22:59:06, 2005-07-26 (UTC)

This is an issue which comes up frequently and generates long discussions; see e.g. Wikipedia talk:WikiProject Mathematics/Archive4(TeX). The majority of mathematicians seem to prefer HTML, as documented on Wikipedia:How to write a Wikipedia article on mathematics.

My personal opinion is that given this situation, the author of an article gets to decide, which for cardinal number means that the HTML should not have been changed into <math> (if my cursory skim of the history is correct). However, I care so little about it that I won't even revert. I think the only permanent solution is technical, and that it would be more constructive to find out how to achieve a technical solution (of course, just filing bugs won't help much). -- Jitse Niesen (talk) 23:24, 26 July 2005 (UTC)

I found out in a discussion with Pmanderson that ℵ doesn't show up correctly for everyone. I think that by itself is a pretty good argument for LaTeX. Being able to use the aleph symbol inline is indispensible. --Trovatore 23:56, 26 July 2005 (UTC)

Right, if you have no choice then you use PNG. If you have a choice, you use HTML. Oleg Alexandrov 03:30, 27 July 2005 (UTC)

Thankfully the HTML-<math> renderer uses the proper fonts now, so it wouldn't be bad if <math> was used in articles (judiciously of course as it spontaneously springs to PNG if it is used a little too liberally) as it looks decent now, but I would suggest that PNG be reserved for inline as it has been. Dysprosia 12:13, 5 August 2005 (UTC)

Number articles up for deletion

List of numbers ordered by Google rating (discussion)
99999999 (discussion)
List of numbers that are not primes (discussion)
31999998 (discussion)

The aforementioned articles are all up for deletion. Uncle G 02:18:02, 2005-07-27 (UTC)

I voted to delete them all. Paul August ☎ 03:35, July 27, 2005 (UTC)

Symmetry

I noticed that there is no Category:Symmetry. Should there be? Charles Matthews 10:13, 27 July 2005 (UTC)

I think it is a good idea. Here are a bunch of articles which could go there:

Axis of symmetry -- Broken symmetry -- Circular symmetry -- Freiling's axiom of symmetry -- Homological mirror symmetry -- Mirror symmetry -- P-symmetry -- Plane of symmetry -- Rotational symmetry -- Spacetime symmetries -- Spontaneous symmetry breaking -- Symmetry -- Symmetry group

(maybe not all of them). Oleg Alexandrov 15:47, 27 July 2005 (UTC)

Not Freiling's axiom of symmetry, I think. [In fact, if this and Symmetry group are removed, I see a good Category:Physical symmetry. 17:13, 27 July 2005 (UTC)] Septentrionalis 16:10, 27 July 2005 (UTC)

Hmm. Are you sure? This lumps together a bunch of otherwise unrelated topics. In physics, p-symmetry and spontaneous symmetry breaking are ... well, related, but in a subtle way. And these have little to do with some of the math concepts of symmetry ... If we create this cat, then we need to rethink the VfD for template:Numbers which lumped together a bunch of "unrelated" articles with the word "number" in the title. However, I think its lots of fun to have a list of all math articles with the word "number" in the title and it would be fun to have a similar list for symmetry. linas 17:05, 27 July 2005 (UTC)

I agree about not including Freiling's axiom of symmetry. Let us keep this geometric/physical. So for example, the article symmetry of second derivatives should not be there either. Oleg Alexandrov 17:24, 27 July 2005 (UTC)

And this asks an interesting question. If we adopt this cateogry as mathematical, putting it in the list of mathematics categories, should all the physics articles in category:symmetry be added to the list of mathematical topics? (For example, CPT symmetry.) Oleg Alexandrov 17:24, 27 July 2005 (UTC)

Not very harmful, I think. One can trust the physicists eventually to bend any mathematical concept to the breaking point. But if you think about rotational symmetry and circular symmetry, for example, it is a bit perverse to say that one is mathematics and the other isn't. Charles Matthews 05:42, 28 July 2005 (UTC)

Thanks Charles. Oleg Alexandrov 15:29, 28 July 2005 (UTC)

Proposal: rename Category:Math lists

The word Math (as opposed to Maths) is quite jarring for many Brits, and to me it feels somewhat too informal for a category title anyway. How about moving articles in this category to Category:Mathematical lists? This is a task which bots can perform fairly easily, I believe. L upin 23:32, 27 July 2005 (UTC)

Fine with me. If agreed on the change, my bot can take care of it. (However, under no circumstances will I rename my bot from mathbot to mathsbot :) Oleg Alexandrov 00:13, 28 July 2005 (UTC)

Of course it should be renamed (the category, not the bot), see Category talk:Mathematics stubs for a precedent. -- Jitse Niesen (talk) 12:18, 28 July 2005 (UTC)

I think Category:Math lists better be renamed to Category:Mathematics lists, rather than Category:Mathematical lists. Any objections to that? :) Oleg Alexandrov 15:29, 28 July 2005 (UTC)

Picking nits, "Mathematics lists" could be interpreted by someone who knew nothing as being "Lists of various (kinds of) mathematics". I can't think of a meaning for "Mathematical lists" other than "lists of a mathematical nature". So I slightly prefer the latter. But I'm really not that bothered. L upin 15:34, 28 July 2005 (UTC)

I see your point about mathematical instead of mathematics (and I agree). Lupin, I think you will need to submit a formal request at CfD for Category:Math lists to be deleted, and the articles moved to Category:Mathematical lists. I expect no problems with that, and then I can start the move. Oleg Alexandrov 22:06, 28 July 2005 (UTC)

I actually already moved the articles. Should we formally ask for the Category:Math lists to be deleted, or can an admin among us just quickly get rid of it? Oleg Alexandrov 02:41, 29 July 2005 (UTC)

blahtex: a LaTeX to MathML converter

Someone called "kate" once said to me:

the best way to get this implemented is to write the code :-)

I took her advice. Following a few weeks of down-and-dirty coding, I would like to announce blahtex version 0.1, a LaTeX to MathML converter designed specifically for Wikipedia (or more generally for the MediaWiki environment).

You can try it out interactively here. You can also see some samples extracted from Wikipedia here.

Important note: Your mileage may vary depending on OS/browser. I will get back to this in a moment. For now, I'll just say that your best bet is Mozilla/Firefox on Windows; if you're on a Mac then I'm afraid the world of MathML is rather inaccessible right now; if you're on Linux or another Unix then I really have no idea, I'm guessing Mozilla will be your best bet.

Before getting to more details, let's just check out this screenshot of blahtex plugged into MediaWiki:

Screenshot

Here's the wiki markup I used for this:

'''Archimedes''' was a [[Greek]] [[mathematician]] who is best known for the myriad mathematical
[[notation]]s that he invented, most of which are still in use today. His earliest work included
devising simple [[inline equation]]s such as <math>\sin x = \cos^2(y+t)</math> and
<math>x^2 + y^2 = -e^{-\theta}</math>. He pioneered the use of greek symbols such as
<math>\alpha</math> in English writing. While performing complicated calculations such as
<math>\sum_{i=1}^3 i^2 = 47</math>, he noticed that despite the baseline of the equation
lining up nicely with the surrounding text, the so-called [[displayed equation]]
: <math>\displayed\sum_{i=1}^3 i = 46, \qquad \textrm{unless} 46 \not= 47</math>
was probably better value. A similar effect occurred for integrals such as
<math>\int_0^1 \sin^2 x \, dx</math>. He marked this up using the kludgy "\displayed"
command, although he suspected that later and greater thinkers would come up with something
better. When he couldn't make up his mind he would write
: <math>\displayed F(x) = \begin{cases} \left\uparrow\frac{\partial^2 G}{\partial u \partial v}\right\}
& \textrm{if the sky was \bf blue}, \\ A_0 + \cdots + A_k & \textit{if Troy was on the attack.}
\end{cases}</math>
He also invented the polynomial rings <math>\mathbf{R}[x]</math>,
<math>\mathcal{C}[y]</math> and <math>\boldsymbol{\mathcal{C}[z]}</math>, and being
fluent in Chinese he was comfortable writing things like
:<math>\displayed 钱 = \sqrt{不好},</math>
although historians have debated whether his Chinese really was all that good.

How did I get this screenshot? I installed MediaWiki on my laptop (an iBook G3), and fiddled around with a few bits of the code to change the MIME type etc, and redirected the math code so that it fed into blahtex instead of texvc. A rather ugly hack. It doesn't really work. I don't recommend it. But it's enough to get something like the image above. The browser was Mozilla running on a Windows XP machine.

Blahtex's main features

backwardly compatible with texvc

In other words, all the equations already present on Wikipedia won't break.

Hmmm. A big claim. Probably not entirely true. In any case, a proposition capable of empirical testing.

Here's how I tried to test it. First, I downloaded a database dump of the current content of the English Wikipedia, from http://download.wikimedia.org/wikipedia/en/pages_current.xml.gz. (I got the file dated 14th July 2005. It's 3.4 GB uncompressed, 1GB compressed.) Then I wrote some code to suck out everything surrounded by <math> tags. After throwing out some junk caused by people enclosing <math> tags inside nowiki tags :-), and discarding duplicates, we are left with 50193 distinct equations (71561 including duplicates; we lost about 80 "equations" as junk). If you want to play with them, you can get the full list here, one line for each equation. I set my poor laptop the task of running texvc on all 50193 equations, which took about nine hours. (About 1800 of them failed to work with texvc; casual inspection suggests these are things in people's personal sandboxes, and markup being discussed on talk pages.) Then I ran blahtex on all the equations as well (under ten minutes :-)). Actually I did this several times during development, to gauge progess.

For ease of comparison, I have collected the result together here (36 MB). Uncompress it and load up "index.xml" in your browser. You'll find the entire corpus of English Wikipedia equations, divided up pseudo-randomly into 256 pages (each containing about 200 equations), with the LaTeX, PNG output from texvc, and MathML output side-by-side for handy comparison. As mentioned earlier, I've put one sample page up on the web here.

(Warning: there are about 50000 small files in there, so if your filesystem is anything like the one on my mac, it could take up to 200 MB of hard drive space, even though there's only about 100 MB of data.)

So you can have a look yourself to see what blahtex's strengths and weaknesses are.

I should mention that I studied portions of the texvc code quite carefully to work out exactly what it was doing, and which LaTeX commands it accepts.

displayed and inline equations

Blahtex has command line options for choosing either inline equations (for use in running text) or displayed equations.

In my opinion, Wikipedia's greatest math rendering weakeness at the moment is the inability to do inline equations well. You can do simple stuff with HTML (although it renders inconsistenly with the displayed PNGs), and you can sure try to do PNGs inline, but they look pretty awful. In contrast, one of MathML's wonderful features is that it automatically lines up baselines and fonts with the surrounding text.

As you can see from the markup I gave above, I used the "\displayed" command to get displayed mode. This is just a temporary fix because I don't know enough about MediaWiki internals to make up another math tag (e.g. <mth>, or something like that). If blahtex is ever plugged into MediaWiki on a real site, I don't expect "\displayed" to be used.

You might point out that the font sizes don't match properly in the screenshot above, but I'm pretty sure this is more a result of my complete ignorance about CSS and stylesheets and MediaWiki internals, rather than any fault in MathML or the browser's rendering. As soon as someone who understands these things gets involved, the font size matching problem will go away.

unicode happy

As you can also see from the screenshot, blahtex is quite happy to accept Unicode characters. Try typing some chinese characters into the interactive form, either in math mode or inside text blocks (like \textrm). I'm sure that our friends at the non-English Wikipedias will find this very pleasant. Since MathML is based on XML, which in turn uses Unicode, it seems a bit silly not to support it.

Blahtex accepts input in UTF-8, and output is pure ASCII, but all internals are done with wide 32-bit characters, so it should be trivial to implement different input/output encodings if necessary.

GNU GPL

I will be releasing the code under the GNU GPL, probably in the next week or so. I just need to remove various profanities from the code and generally clean it up. Stay tuned.

written in C++

Except for a yacc parser, it's all written in C++, with a healthy dose of STL. Probably C++ isn't the best choice of language from a technical point of view, but it has the advantage that I know it, and so do lots of other people. I think this will encourage collaborative hacking in a way that is not possible for texvc, which is written in OCaml, which not many people know.

Browser compatibility issues

So far all is well and good. Now we come to the hard stuff.

There are actually two completely separate questions concerning browser compatibility.

The first question is: how does the browser know that it should be trying to translate MathML tags? In an ideal world, the following would happen. Joe loads up a Wikipedia page with equations on it. If he's running Mozilla or Firefox, everything just works. If he's running internet explorer and has MathPlayer installed, then everything just works. If he doesn't have MathPlayer installed, he gets a dialog box telling him that he should install MathPlayer; if he chooses not to, he gets the next best alternative (e.g. PNGs). If he's running a completely MathML-unaware browser (like Safari), then he should just get the PNGs again (perhaps with a message telling him to get a different browser!!)

I don't know how to make this happen. For various technical reasons that I don't understand very well, it seems like a very difficult problem. I will leave this to the experts to sort out.

The second question is: assuming our browser does understand MathML and knows that it should be doing so, how does its rendering look? Does it render things "correctly"? Do different browsers give different renderings?

Let me summarise my current understanding of the situation here. Overall, I think the best browser I've played with is Mozilla/Firefox on Windows. It does have a bunch of bugs (which I will say more about on another day), but it does give the best overall effect. You'll notice that there is a radio button for "Mozilla tweaks" on the interactive site. This activates a bunch of tweaks to the output to compensate for some of Mozilla's bugs. Almost all of my testing has been on Windows Mozilla. MathPlayer for Internet Explorer is occasionally competitive, but its pixelation doesn't get corrected by XP, which is a major disadvantage, and sometimes it does some really weird stuff with spacing.

(NB: if you're on Windows and your equations look pixelated in Mozilla, you might want to try turning on ClearType. On XP, go right-click on desktop, then Properties, then Appearance, then Effects, then "Smooth edges of screen fonts" should be set to "ClearType".)

Sadly, on the Mac, you don't really have anything very good. Mozilla's support got broken a few versions ago. I'm not sure why they're taking so long to fix it. You could try running an old version (I think 1.3 is ok), but it doesn't look that great. Despite being a big mac fan, I concede that currently Windows kills the Mac in this department — you have no idea how hard it was for me to admit that :-)

As for other OSes, I'm pretty ignorant. Maybe someone else can report on the situation.

You could also try Amaya. It's a bit frustrating to work with (the mac version anyway), but sometimes helpful for debugging.

What to do now

I need your help. Play with blahtex and help me find and squish all those evil bugs.

Of course it would be fantastic if a MediaWiki developer knows how to plug blahtex into MediaWiki (at least the "MathML - experimental" option). Drop me a line if that's you.

I am going to run a blahtex development page at http://meta.wikimedia.org/wiki/Blahtex. Probably the best place to continue this discussion is over there. In particular you can report bugs there.

now I'm off to bed

Goodnight guys and gals, I hope you enjoy playing with blahtex.

Dmharvey Talk 02:17, 28 July 2005 (UTC)

Comments

"If he doesn't have MathPlayer installed, he gets a dialog box telling him that he should install MathPlayer"

Nooooooooooooo!

He gets a note on the top of the page that it would look better with Mathplayer, but it displays PNGs for now, letting him decide that he wants to install it when he gets around to it. :-)

Otherwise, very very cool.

I don't know much about mathML, but is it possible that little spacing issues could be from your code? Or is that just the browser's interpretation of the mathML? Specifically,

Moved to m:Blahtex/Bugs and feature requests

(HTML id tags would be helpful.) :-) - Omegatron 05:51, July 28, 2005 (UTC)

Hi Omegatron, thanks for your interest. I'd appreciate it if you could list the bugs on the page I mentioned at meta.wikipedia.org. Right now I want to concentrate on getting the source to a level appropriate for release. I'll come back to those bugs in a little while. Dmharvey

Talk 12:05, 28 July 2005 (UTC)

Very promising. Almost all formulas are understandable in my browser at work (Firefox 1.0 on Linux with Fedora Core release 2), though the spacing is often wrong; almost certainly the browser fault. Re 99d1d9133a0a5551e047a9560783aedc, there is a special latex code which should have been used, I think \ll, so it's not blahtex's fault. I hope dmharvey forgives me for saying that my personal opinion is that translating latex to mathml is the easy part and there is a lot that needs to be done, but as I said, it's a very promising start. I poked a bit around in the mediawiki code lately, going through some of the texmf bugs, and I'd be quite willing to lend a hand (within my time constraints, of course). -- Jitse Niesen (talk) 12:11, 28 July 2005 (UTC)

Yes, I forgive you :-). I agree it's probably the easy part, but not quite as easy as I had thought it would be several weeks ago when I started trying to write the code. :-) There are of course other translators out there, but in my opinion they have a lot of weaknesses, and I hope that eventually blahtex will be better. Anyway, maybe having a working translator will spur other people on to fix the MediaWiki end of things. Your assistance is appreciated. Dmharvey

Talk 12:35, 28 July 2005 (UTC)

I don't understand why it's difficult. They already have rudimentary mathml output in the preferences, and blahtex looks like it works for everything. So isn't it just a matter of swapping blahtex in place of the older experiment? Could still leave the "experimental" tag on it, but it would be a better experimental. (And I'd start using it all the time.) - Omegatron 23:10, July 28, 2005 (UTC)

The problem is that your browser probably won't know that it's supposed to interpret the MathML as MathML unless the server sends out some additional information. You should try splicing some of blahtex's output into a page with wikipedia's standard headers and see if that works. I suspect it won't, although I haven't tried it myself. Maybe if you save it as a file with a xhtml extension, and fiddle with the file headers then that might work, or something like that. (btw, "rudimentary" means: it can handle equations as complicated as "x+2" but not as complicated as "x^2" :-)) Dmharvey

Talk 16:38, 30 July 2005 (UTC)

Yes, I know; I've played with it. But if they can already get my browser to display mathML for

x + 2

, and a Tex-to-mathML converter has been written, why can't they combine the two? It sounds like the rudimentary mathML support already does all the "hard stuff" like MIME or XHTML or whatever other strings of capital letters. - Omegatron 00:48, August 4, 2005 (UTC)

Your browser (probably) doesn't really display the MathML for

x + 2

For example, I often use Safari, which doesn't know anything about MathML. The MathML code for "x+2" is <mi>x</mi><mo>+</mo><mn>2</mn>. So safari just ignores the tags like <mi> and just prints the conents inside the tags, which turns out to look ok (i.e. looks like "x+2"). But for anything more complicated it's useless. For example to do something like "x^2" it sees <msup><mi>x</mi><mn>2</mn></msup> and it just prints something like "x2".

Now here's the thing. Even a browser like Mozilla, which knows about MathML, will just print "x2", UNLESS you put a whole bunch of headers at the beginning of the page, which Wikipedia doesn't currently do. So, although it would be very easy to simply plug blahtex into the mediawiki software to do the conversion, it would presently be useless, because no-one would be able to see the MathML output. (Unless they manually changed the headers on every page they downloaded, which is ridiculous). Until Wikipedia is able to send out the right headers, or unless there is some other way to coax everyone's browsers into interpreting the MathML, there isn't any point in just "plugging it in". Dmharvey

Talk 10:55, 4 August 2005 (UTC)

Aha. Well, is it really that hard to plug in the appropriate headers? Is it a server-side MIME kind of thing as well or is it something that could be added with a clever user.js or greasemonkey script? If the current experimental mathML can't add the headers either, then what's the harm in plugging in the new converter? - Omegatron 17:08, August 4, 2005 (UTC)

n-th versus nth

There are quite a few articles that use "n-th", "n-th", and/or "nth" (similarly for "ith", etc). All of the literature I checked uses "nth" (and occasionally "n^th"). The only justification for "-th" that I can see today is if you don't have italics available, such as in a newsgroup. Based on the articles I've seen, I think that "nth" is more common in Wikipedia than "n-th" and "n-th", but I didn't do a formal count.

I think the standard style should be "nth". Bubba73 22:14, July 28, 2005 (UTC)

I prefer nth; but I could understand an editor deciding that it was unclear. A standard, but not a mandatory one?

But then, I spent today watching the anti-Communist revert wars and the &^$%&$ AD/CE revert wars, so I'm a little more laissez-faire than usual. Septentrionalis 22:40, 28 July 2005 (UTC)

I prefer n-th. I guess it was my edits which brought Bubba73 in here. If many people say they like nth, I will obey. :) Oleg Alexandrov 23:07, 28 July 2005 (UTC)

nth IS CLEARLY THE ONLY SOLUTION AND I WILL not TOLERATE THIS POV CULTURAL IMPERIALISM CHRISTIANITY-HATING U.S.-BIASED FASCIST CONSPIRACY!!1! - Omegatron!!!11!! 23:18, July 28, 2005 (UTC)!1!!!

Should be n^th. Bit of a pain to type, but if you have to use it in a lot of places, copy and paste (or write nth and do a global change). --Trovatore 14:36, 29 July 2005 (UTC)

Would be nice if we had a wiki shortcut for super and subscripts. I've been using T_{E}X (=T_EX) markup in my greasemonkey scripts, although that might be confusing when alongside the same thing inside math tags?

Also things like 220+-5% becomes 220±5%, ==> becomes ⇒, 100degC becomes 100°C, and so on. - Omegatron 16:11, July 29, 2005 (UTC)

My personal preference is for n^th too, and that is sometimes used in the literature. However, nth is much more common in the literature.

Another argument in favor of nth is that TeX has a function "\nth{<number>}", which makes 1st, 2nd, nth, etc, although it isn't implemented in WP. Furthermore, TeX interprets "n-th" as "n - th". Since math formulas are rendered in TeX, I think we should use nth to be consistent. Bubba73 16:08, July 29, 2005 (UTC)

I think n-th is marginally easier to read. I think i-th, for example, is definitely easier to read than ith. I think (n − 1)^th is not a sensible piece of notation, for example; and the sort of thing that shows we should mostly aim to be clear and readable. Charles Matthews 16:34, 29 July 2005 (UTC)

Well, (n − 1)^th is just jarring to my ear; I prefer (n − 1)^st. I can see the point that maybe it should be (n − 1)st or (n − 1)-st, to keep people from trying to evaluate it as an exponentiation (although the latter two choices could be, respectively, multiplication or subtraction). --Trovatore 16:39, 29 July 2005 (UTC)

That's a good argument against n^th. nth and (n − 1)th look the best to me, so far, though it seems there's a better solution for n-1 out there somewhere. - Omegatron 16:46, July 29, 2005 (UTC)

But in my experience nobody (or almost nobody) actually says "en minus oneth". We say "en minus first". Conflict between euphony and logic, perhaps--in this situation I vote for euphony. --Trovatore 16:50, 29 July 2005 (UTC)

Quoting Charles, "I think n-th is marginally easier to read. I think i-th, for example, is definitely easier to read than ith" (ditto for i). Readability is the reason I prefer n^th over nth. But nth seems to be almost universal in the literature and I haven't found n-th in the literature. My feeling is that WP should be more like the literature in style than that of newsgroups and email. Bubba73 17:50, July 30, 2005 (UTC)

vfd

Wikipedia:Votes_for_deletion/Log/2005_July_29#Arc_Sine --R.Koot 14:24, 29 July 2005 (UTC)

Law of information

Is this article salvagable; does it even make sense? Law of information --R.Koot 15:18, 31 July 2005 (UTC)

I couldn't make any sense out of it. When I searched the internet I found a discussion on a wiki about evolution. Markus Schmaus 17:11, 31 July 2005 (UTC)

I put it on VFD here. Samohyl Jan 17:15, 31 July 2005 (UTC)

Aug 2005

This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

Other_names_of_large_numbers

I find Other_names_of_large_numbers a rather dubious article. Google will only find a lot of the names here inside this article. --R.Koot 00:02, 1 August 2005 (UTC)

hmm, it does seem pretty arbitrary --MarSch 17:57, 14 August 2005 (UTC)

I concur -- Arthur Rubin 22:13, 16 August 2005 (UTC)

meta: help formulae

Has anyone else noticed what's happened at http://meta.wikimedia.org/wiki/Help:Formula? Someone has added a whole bunch of stuff which might be reasonable but I don't think it's the right place for it. It's certainly not what people should see when they go looking for help on TeX markup. I'm not really sure where it should go though. Dmharvey Talk 20:50, 1 August 2005 (UTC)

You might have noticed that I moved it to the talk page. The suggestions contain a lot of tweak factors, which are probably very specific to the browser and configuration. They are totally out of place at meta:Help:Formula and to be honest, if he can't be bothered to put them in the right place, neither can I. -- Jitse Niesen (talk) 17:00, 4 August 2005 (UTC)

I agree that they don't belong there at all. I think that was the point, though. Wanted them to be seen. Who's in charge of TeX markup, anyway? - Omegatron 17:05, August 4, 2005 (UTC)

The m:Developers are in charge of the software and hence also of the TeX markup (no surprise here). As far as I can see, there has been very little work done on it in the past two years, so I guess nobody is taking responsibility for the TeX markup specifically. That's why I'm pretty confident that just putting some comment on m:Help:Formula will anger people but not yield any improvements. -- Jitse Niesen (talk) 17:22, 4 August 2005 (UTC)

So no one in particular? Just kind of this thing that's there but no one ever touches or has anything to do with? - Omegatron 17:55, August 4, 2005 (UTC)

E (mathematical constant) moved to Euler's number

Ed Poor has moved E (mathematical constant) to Euler's number. Is everyone ok with that? I have no strong feelings either way, but the move has created a lot redirects which should be fixed (especially the double redirects). I don't know as yet if Ed intends to to do that. I'd be willing to help with the redirects, but i want to be assured that we have a consensus for the name change first. Please respond on Talk:Euler's number. Thanks, Paul August ☎ 19:55, August 2, 2005 (UTC)

Why should it be moved? I think I'll move it right back. Charles Matthews 20:01, 2 August 2005 (UTC)

No, I'm not happy with the move. It is rarely called Euler's number, I think. Bubba73 20:06, August 2, 2005 (UTC)

Good move. Leave it at Euler's number. - Omegatron 20:56, August 2, 2005 (UTC)

I think it would be best if everyone responded at Talk:Euler's number. Thanks Paul August ☎ 21:08, August 2, 2005 (UTC)

blahtex version 0.2 released

Blahtex is a new LaTeX to MathML converter designed specifically for MediaWiki.

More information is available at m:Blahtex.

At the blahtex download page may be found an interactive demo, samples of equations from Wikipedia, and the source code.

I invite everyone to participate in the discussion on how on earth to make MathML work in MediaWiki.

This message will be cross-posted on Wikipedia:Village pump (technical) and on the Wikitech-l mailing list (as soon as I figure out how it works).

Cheers Dmharvey Talk 13:37, 3 August 2005 (UTC)

Deletion of VfD

This isn't strictly an issue for this project, but I thought it was about such a fundamental part of Wikipedia that it should be widely publicized. It concerns the Vfd process (and as it turns out this page has been involved in several VfDs recently). There has been considerable recent discussion about possibly eliminating VfD see:

An RFC about the recent deletion of the VfD page (since undeleted): Wikipedia:Requests for comment/Deletion of VFD.
A vote and discussion on the deletion of the VfD page: Wikipedia:Requests for deletion.

Paul August ☎ 15:19, August 3, 2005 (UTC)

Ongoing discussion at Wikipedia:Deletion reform and its subpages; my proposal is on Wikipedia:Deletion reform/Proposals/Speedy redirect Septentrionalis 01:29, 24 August 2005 (UTC)

Inline PNG formulas - a poll requested

There was a discussion right above about PNG-fied TeX vs HTML. It looks to me that the arguments for inline PNGs there were the same as in Wikipedia talk:WikiProject Mathematics/Archive4(TeX), but that the consensus nevertheless seemed to be that HTML is preferred to PNG.

However, the issue does not seem to die out, with some kind of silly revert war going on at cardinal number. I would like to see an informal poll to figure out what people think and if there is some consensus about it; and whether the issue is that important at all. I for one prefer HTML formulas inline if the TeX formulas become PNG images, unless HTML is unable to render the formulas correctly. Oleg Alexandrov 15:27, 3 August 2005 (UTC)

I've gone both ways on this. At first I put equations in as HTML if they were simple enough and used TeX for the more complicated stuff. However, it didn't look good to me to have some equations in one and some in the other, since they look so different. Secondly, in some fonts at least (including the one I use) the HTML Greek letters are not very close to the way I'm used to seeing them. Therefore, if some of the equations on a page were in TeX I want to do all of them in TeX. A drawback if TeX is that the characters are thin and not of uniform thickness, at least on my system. Bubba73 15:45, August 3, 2005 (UTC)

*sigh* — if only MathML was working, we could leave this debate behind.... (hint hint see above :-) Dmharvey

Talk 15:52, 3 August 2005 (UTC)

Yes we know that MathML will cure all the ills. :) But it is at least 5 years away I would say. What is your position on inline PNGs in the meantime? Oleg Alexandrov 15:35, 4 August 2005 (UTC)

Haven't we been through this?

I can see both. Ideally we would use math tags for everything, and the inline PNGs and HTML and mathML generated from that code would look good no matter what. See m:Help_talk:Formula#Maynard_Handley.27s_suggestions for more about inline TeX tweaks, including appropriately-sized PNGs that resize along with text, etc. - Omegatron 15:41, August 4, 2005 (UTC)

Oleg, you're much more pragmatic than me :-) My position is: both inline PNGs and HTML look awful, but I am forced to concede that inline PNGs are worse. Therefore, in the current software environment, I think inline PNGs should be forbidden under all circumstances. As displayed equations, they are fine (if a little rough around the edges). I also think that inline HTML should be avoided if at all practical. Such equations should be made displayed if at all possible. In other words, I really don't like any of the options currently available for inline equations.

In response to some other points: (1) I'm not sure exactly what you're referring to when you saying that MathML is five years away. There are browsers out there that do a half-decent job. (Perhaps not decent, but half-decent anyway.) Besides, there are moves afoot. For example, the Stix fonts project is supposed to reach a major milestone later this year. (2) I'm concerned about the portability of Maynard Handley's ideas. I would like to see them up and running on a test wiki, so that I can try them out in a few browsers. Dmharvey

Talk 16:10, 4 August 2005 (UTC)

In response to (1) and (2). What matters is when Microsoft's Internet Explorer will have default and goood MathML support. And I doubt that will happen soon. Oleg Alexandrov 22:13, 4 August 2005 (UTC)

I agree that IE won't have default MathML support soon (if ever). That's a shame. I also agree that the current plugin support (i.e. MathPlayer) leaves a lot to be desired. However, I don't think requiring a plugin is necessarily a bad thing in itself. For example, lots of people view PDFs in their browser, even though browsers generally don't have default support. (Correct me if I'm wrong about this.) There is some mechanism that lets the browser inform you when you need an appropriate plugin for something.

Yes you are right. :) So let us hope MathPlayer will work soon, and work not only for IE. Oleg Alexandrov 23:47, 5 August 2005 (UTC)

May I add that my position on inline PNG would change drastically if Wikipedia had MathML support enabled. If MathML was there and working, I would *encourage* people to do inline equations in <math> tags, and hope that this encourages people viewing those pages to switch to a better (!) browser. Dmharvey

Talk 22:32, 4 August 2005 (UTC)

Separated from other text, I think TeX looks a lot better than HTML. However it's use inline is problematic. I usually try to avoid inline TeX, and I think there has been a consensus for this view. But to me it is also problematic to mix inline HTML with non-inline TeX, so sometimes when I want to use non-inline TeX, I also sometimes use inline TeX (for example for variable names, see absolute value). I would hate to see a hard and fast "rule" about this. Paul August ☎ 16:39, August 4, 2005 (UTC)

Agree about not wanting a hard and fast rule about it. But why would one use as in cardinal number the PNG $\{1,2,3,\dots\}$ instead of simply the html {1, 2, 3, ...}? Oleg Alexandrov 22:13, 4 August 2005 (UTC)

I agree that doesn't make a lot of sense. Paul August ☎ 02:51, August 5, 2005 (UTC)

Please see my comments on this issue at: Wikipedia_talk:How_to_write_a_Wikipedia_article_on_Mathematics#Too_much_HTML.3F. - Gauge 03:48, 21 August 2005 (UTC)

The blind, with screen reading software and with some kinds of HTML enabled software, have some hope of making sense of the page if HTML us used. Unless appropriate "alt=" attributes are required, they have no hope with PNG. Nahaj 02:35:26, 2005-09-08 (UTC)

If you would have checked yourself, the TeX in math tags is in the alt text. Dysprosia 02:41, 8 September 2005 (UTC)

The section is PNG formulas, and I understood the question to be HTML or PNG. Since my browser doesn't speak TeX, I'll guess you are referring to a PNG produced from the math tags? And I give, how is it that you expected me to tell PNG from a PNG produced from the tags so that I would have noticed this? Nahaj 02:51:08, 2005-09-08 (UTC)

I think you are misunderstanding how PNG formulae are generated. The formulae images are not manually created, users do not upload regular images of formulae. Formulas are written in the TeX language and are placed inside <math> tags. If the formula is very simple, the TeX representation of the formula is converted into HTML and displayed. Otherwise, if it is complicated, the TeX representation of the formula is converted into a PNG image and is displayed. The alt text of the PNG image is the TeX representation of the formula. For example, the PNG formula $S_{\mathbf{p}}(\mathbf{a})=\alpha\mathbf{v}_1+\beta\mathbf{v}_2$ will have "S_{\mathbf{p}}(\mathbf{a})=\alpha\mathbf{v}_1+\beta\mathbf{v}_2" as the alt text. So the issue of 'appropriate "alt=" tags' is responded to, and thus some provisions at least are made for accessibility.

If you would have investigated this issue yourself, by either playing around in the sandbox, or having a look how some mathematics articles are typeset, and viewing the alt text of PNG formulae, you would have found out all this yourself.Dysprosia 10:40, 8 September 2005 (UTC)

Ten thousand articles waiting to be written ...

Looking for something to do? WikiProject Missing encyclopedic articles has made a list of missing science topics, containing articles on Weisstein's MathWorld that have no corresponding Wikipedia article. There are more than ten thousand entries (but a considerable number is due to different capitalization conventions), including the intriguing Algebra of Chinese Characters (unfortunately, it is just an empty article on MathWorld). On a side note, remember that there is also the PlanetMath exchange. -- Jitse Niesen (talk) 22:39, 3 August 2005 (UTC)

CiteSeer citations

I've created a template you can use for CiteSeer citations. If they ever change the URL again, only the template needs to be updated.

{{citeseer|View-based and modular Eigenspaces for face recognition|pentland94viewbased}}

View-based and modular Eigenspaces for face recognition

--R.Koot 22:28, 4 August 2005 (UTC)

I've also created one for links to MathWorld

{{mathworld|Register machines|RegisterMachine}}

Eric W. Weisstein, {{{title}}} at MathWorld.

--R.Koot 03:33, 5 August 2005 (UTC)

The second one duplicates Template:MathWorld - Fredrik | talk 19:09, 6 August 2005 (UTC)

Did I say Template:Mathworld? I meant Template:ScienceWorld ofcourse. ;) --R.Koot 19:29, 6 August 2005 (UTC)

minus or negative infinity?

"linearly towards minus infinity" or "linearly towards negative infinity" or "linearly towards −∞"? - Omegatron 22:35, August 4, 2005 (UTC)

Negative infinity sounds right to my non-native speaker ear. Oleg Alexandrov 00:41, 5 August 2005 (UTC)

I think either of the first two are ok. The second sounds slightly more formal, but I once had a professor who couldn't stand people even saying "negative three", it was only "minus three" for him. Dmharvey

Talk 00:56, 5 August 2005 (UTC)

I use minus infinity in speech, which sounds better, but that may only be so because it's closer to what it is in Dutch. I think I prefer negative infinity in writing, however. --R.Koot 01:02, 5 August 2005 (UTC)

I am a native speaker (UK English), and only ever use "minus", be it three or infinity. (I doubt I am Dmharvey's professor!). --stochata 21:32, 6 August 2005 (UTC)

To me, "negative three" sounds like the script of a Holywood B-grade. I'm a "minus 3" type of person. --Zero 13:43, 11 August 2005 (UTC)

IMO, they are different. minus infinity is a number, negative infinity is a place. -- SGBailey 22:04:53, 2005-09-08 (UTC)

Jitse's math news page

I don't know if you noticed, but Jitse Niesen made a bot to output the following page each day: User:Jitse_Niesen/goim. Here, listed are new math articles in the list of mathematical topics and list of mathematicians, new requests for math articles, fulfilled requests for math articles, articles in need of attention/on vfd, etc.

I believe this page should be a very useful resource for math articles editors (that is, us). I would suggest adopting this page to the project, that is, renaming it to Wikipedia:WikiProject Mathematics/recent changes or something, but I can't come up with a good name.

Any ideas of what else such a page can contain or what other things itchy bot writers like Jitse and me could do to improve the math wikiproject? Oleg Alexandrov 00:41, 5 August 2005 (UTC)

how about Wikipedia:WikiProject Mathematics/Current activity?

I've sometimes wondered whether it would be possible to write a "non-reciprocated link finder" script. If A links to B then in many cases B should link to A. Would be nice to find these more easily. But I can think of lots of reasons that it wouldn't really work. Dmharvey

Talk 01:00, 5 August 2005 (UTC)

I could write such a script, and generate a list of pairs of math articles which have links going on only in one direction. Is that what you want? Oleg Alexandrov 23:47, 5 August 2005 (UTC)

I guess I would be interested to see that. My only reservation is that I expect there to be a very large number of links that we discover only really make sense in one direction, and that the links we are really interested in are actually hard to spot within such a list, and therefore that you'd be spending a lot of time writing a script that turns out not to be useful. So if your best guess is that it wouldn't be worth the effort, then don't bother. Otherwise, please go right ahead! (by the way, where is some information on how to write such robots? I might be interested in trying my hand one of these days.) Dmharvey

Talk 23:51, 5 August 2005 (UTC)

To write the script would be very easy. It will not be a bot, rather a perl script analyzing all the math articles which I have stored locally on my machine (and I have all of the articles in the list of mathematical topics, updated daily). But I am not myself sure how helpful that would be. The total number of pairs would be in the tens of thousands. Maybe we should sleep on this idea for a while, and wonder if anything useful will come up. Oleg Alexandrov 00:05, 6 August 2005 (UTC)

I agree. Leave it for now. Dmharvey

Talk 00:34, 6 August 2005 (UTC)

I moved User:Jitse_Niesen/goim to Wikipedia:WikiProject Mathematics/Current activity. Did you know that 2451 of the 8979 articles are (marked as) stubs? Rather depressing, really. -- Jitse Niesen (talk) 01:48, 6 August 2005 (UTC)

How did you find 8979 articles? I count 8227. Oleg Alexandrov 02:06, 6 August 2005 (UTC)

My first guess is that I include List of mathematicians and you do not. This gives me 746 links, and 8227 + 746 = 8973, which is close enough. I can send you the complete list if you want. -- Jitse Niesen (talk) 13:00, 6 August 2005 (UTC)

other languages

hi I'm just wondering if there are math(s) project pages like this in other languages? It sounds like a lot of people who hang around here actually are quite multilingual. I speak only English (and a pathetic amount of mandarin chinese). Dmharvey Talk 01:28, 5 August 2005 (UTC)

I could not find anything in Romanian or Russian. Oleg Alexandrov 02:22, 5 August 2005 (UTC)

Dutch: no mathematics project.

German: http://de.wikipedia.org/wiki/Diskussion:Portal_Mathematik.

French: http://fr.wikipedia.org/wiki/Discussion_Wikip%C3%A9dia:Projet%2C_Math%C3%A9matiques and http://fr.wikipedia.org/wiki/Discussion_Wikip%C3%A9dia:Projet%2C_math%C3%A9matiques_%C3%A9l%C3%A9mentaires (both not very active.) --R.Koot 02:40, 5 August 2005 (UTC)

Italian: http://it.wikipedia.org/wiki/Wikipedia:Progetto_Matematica

Spanish: http://es.wikipedia.org/wiki/Wikipedia:WikiProyecto_Matemáticas

Swedish: http://sv.wikipedia.org/wiki/Wikipediadiskussion:Projekt_matematik

Japanese: http://ja.wikipedia.org/wiki/Wikipedia:ウィキプロジェクト_数学

Some are, inevitably, more active than others. And some of them were already linked together, I would never have been able to find the Japanese one myself. —Blotwell 13:08, 7 August 2005 (UTC)

request

Could an admin exchange Random Access Machine and Random access machine for me, please? Thanks, --R.Koot 02:40, 5 August 2005 (UTC)

Done Paul August ☎ 03:00, August 5, 2005 (UTC)

Another one: Mathematical reviews should go to Mathematical Reviews as it is the title of a journal, see Talk:Mathematical reviews. -- Jitse Niesen (talk) 12:25, 7 August 2005 (UTC)

Done Paul August ☎ 23:58, August 8, 2005 (UTC)

EXTRAPOLATION METHOD I would be grateful if the mathenaticians would be kind enough to look at my extrapolation method on www.AIDSCJDUK.info to determine whether it is suitable for a link from Wikipedia. Copy of earlier E-mails with Wiki. are below. Edward G. Collier MBCS CITP

Unfortunately, it seems that one cannot paste E-mails into this area. My method was devised in 1987 and wasexplained in detail at a Royal Statistical Society special meeting on AIDS forecasting that year. It was briefly written up in the Jornal of that Society Vol 151 Part 1 1988 Although the professors, statisticians and epidemiologists present also explained their proposed methods, my simple (but not simplistic) mathod was the only one that ever produced any viable forecasts and is still being used today as can be seen from the web site. I also have used the method for several years in forecasting variant CJD in the UK. The SEAC sub-committee with responsibility for overseeing the progress of vCJD asked me to get the method published. However, the various mathematical bodies and journals that I approached declined to publish it as I had no references. As a retired engineer and not an academic, I had no way of finding appropriate references and in any case I had not referred to any as the idea came into my own head. I am sure that there are many people who could make use of the method - even in control engineering- if you can publicise it in the excellent Wikipedia. Thank you, Edward G. Collier Edwardhfd@aol.com

Peer review is not a perfect process, but Wikipedia is explicitly not supposed to be a way around it. See WP:NOR. --Trovatore 20:06, 13 September 2005 (UTC)

Project subpages

As some of you have noticed, partly in honor of Jitse's great new Current activity page — way to go Jitse! — I have created a new section on the project page to list and describe the various project subpages. I know they are all mentioned somewhere else on the page, but I thought it would be good to also list them together. At any rate that got me to thinking about these pages:

Wikipedia:Naming conventions (theorems)
Wikipedia:How to write a Wikipedia article on Mathematics (proposed)
~~Wikipedia:Algorithms on Wikipedia (proposed)~~

Should these also be subpages of this project? I could see some benefit to bringing these all under one banner so to speak. Paul August ☎ 17:38, August 6, 2005 (UTC)

Guidance on style

Manual of Style
Supplementary manuals
Abbreviations Biographies Capital letters Command-line examples Dashes Dates and numbers Headings Legal Links Lists of works Mathematics Music Pronunciation Spelling Text formatting Titles Trademarks Writing about fiction
Special article styles
Disambiguation pages Arabic transliteration China-related articles Ethiopia-related articles Ireland-related articles Islam-related articles Japan-related articles Korea-related articles Latter Day Saints Medicine-related articles Portugal-related articles
Other guidance
How to edit a page Guide to layout Captions Categorization Categorization of people Cite sources Explain jargon Footnotes Writing better articles Lead section Lists Music samples Naming conventions Overlinking Picture tutorial Proper names Sections Sister projects Technical terms and definitions Words to avoid

I think we should not make them subpages, as these pages are not just about our project. So, our style manual, Wikipedia:How to write a Wikipedia article on Mathematics, might be better off standing on its own rather than

Wikipedia:WikiProject Mathematics/How to write a Wikipedia article on Mathematics.

I agree though that it is better to list some of those pages together, as there is quite a bit of duplication now on the project page, with things listed multiple times.

On a more general note, I would think the project page needs a bit of overhaul. Wonder what people think. Oleg Alexandrov 19:35, 6 August 2005 (UTC)

YES. Dmharvey

Talk 12:29, 7 August 2005 (UTC)

On a related note, I think the name of the style manual, Wikipedia:How to write a Wikipedia article on Mathematics, is rather long and not so pretty. Maybe a renaming it to something else could be a good idea. Oleg Alexandrov 19:35, 6 August 2005 (UTC)

Actually, I think it could well be a subpage, like Wikipedia:WikiProject Mathematics/style. Or rename it to Wikipedia:Manual of Style (mathematics). Anyway, please do something, as I rarely type the title correctly at the first attempt. The other two pages should not become subpages: Wikipedia:Naming conventions (theorems) falls into the Wikipedia:Naming conventions (...) series and Wikipedia:Algorithms on Wikipedia is more computer science than mathematics. I also agree with Dmharvey above. -- Jitse Niesen (talk) 12:49, 7 August 2005 (UTC)

The shorter the better. :) I hope more opinions will come in as how to rename it, since it is an important document. Oleg Alexandrov 23:24, 7 August 2005 (UTC)

I agree that Wikipedia:Algorithms on Wikipedia should not be a project subpage. I hadn't really looked at it, just copied it from the project page —now I'm wondering if it belongs there either? Also I like either of the page titles Jitse suggested for the "How to …" page. Paul August ☎ 17:23, August 7, 2005 (UTC)

What about just Wikipedia:Mathematical writing or Wikipedia:Writing mathematics Dmharvey

Talk 19:36, 8 August 2005 (UTC)

I think if we do not want to make it a subpage of this project, then it should probably be called Wikipedia:Manual of Style (mathematics) (per Jitse) since that would be consistent with other "Supplementary Manuals of Style" listed on Wikipedia:Manual of Style (see table to right.)

I agree with Paul and Jitse about naming it Wikipedia:Manual of Style (mathematics). By the way, I truly hope that the fat style template to the right will not make its way in our manual of style, it is just so long, and not so helpful (for example, why would we need in our manual of style a link to how to write China-related articles).

Oh, and we can make the shortcut WP:MSM point to the new location, to save some typing when referring to it. Oleg Alexandrov 20:30, 8 August 2005 (UTC)

Agree that Wikipedia:Manual of Style (mathematics) is good. Dmharvey

Talk 01:51, 9 August 2005 (UTC)

Moved. Oleg Alexandrov 20:37, 9 August 2005 (UTC)

blahtex: now compiles on linux

Blahtex 0.2.1 has been released. It now compiles and runs on Linux thanks to Jitse Niesen.

Jitse has had some initial success with integrating blahtex into mediawiki: check it out.

Source code, online demo and samples here.

More info and bug reports at m:Blahtex.

Dmharvey Talk 01:53, 9 August 2005 (UTC)

Style: *-algebras

I was editing the *-algebra, B*-algebra, C*-algebra etc. pages for consistency of style and I noticed some pages had tags around the * in these expressions, thus giving (e.g.) C^* rather than C*. This looks horrible (and increases leading) on my browser (Netscrape 7) and the majority of pages didn't have it, so I took out those I found. But I assume someone had a reason for putting them in: is there any browser for which this looks better? Our proposed style guide should address this one way or the other. (This is different from the superscripting issues discussed at Wikipedia:How to write a Wikipedia article on Mathematics already because it relies on the * character appearing superscripted by default.)

And while I'm here: our preferred spelling seems to be C*-algebra (not C* algebra, C-star algebra, C star algebra, etc.) The exception is that our page on *-algebras is currently at star-algebra. Is there any reason for this, for example, is it usually spelled this way in the literature? —Blotwell 04:58, 9 August 2005 (UTC)

mentions of categorical considerations

I wrote the section on morphisms in the article on projective spaces, and it occurred to me that while using the language of category theory to describe maps between projective spaces is extremely convenient, it might be off-putting for the undergrad who's never studied any category theory, and just wants to know about projective spaces. -Lethe | Talk 07:13, August 9, 2005 (UTC)

I agree. I don't think you can assume that the person reading about projective spaces knows about category theory. However, that doesn't mean you should throw out what you've done. I think the article needs both versions. (The baby one first.) Dmharvey

Talk 11:03, 9 August 2005 (UTC)

I agree with Dmharvey, we can have our category theory and eat it too! (of course this come from someone who was a categorical topologist in a past life ;-) Paul August ☎ 19:55, August 9, 2005 (UTC)

But the thing is, for the example I'm thinking of, there aren't "two versions". I just say "in the category of ____ the morphisms are ____". there really isn't any category theory there that can be separated out. just some terminology that can be used or not used. -Lethe | Talk 22:07, August 9, 2005 (UTC)

Hmmm. A question: what title would you give the section if you chose to write it without categorical language? Would you still call it "morphisms"? Or something like "Projective linear transformations"? Are you worried that without the categorical language, it is difficult to motivate why these particular types of maps between projective spaces are important? Dmharvey

Talk 22:16, 9 August 2005 (UTC)

It seems like only someone with category theory in mind would, immediately after describing a new mathematical construction, then describe maps between such constructions. I imagine that if I didn't have that language available, I also wouldn't have the mindset to take time out to describe the maps. So I guess it's probably OK this way? -Lethe | Talk 22:59, August 9, 2005 (UTC)

I'm not convinced. I think that for a reader interested in learning about projective spaces, but without the category theory background, it is still useful for them to hear the fact that the "right" kind of maps between such spaces are the projective linear ones, even if they don't quite have the context to understand what "right" means. Anyway, why is this the right category? What about algebraic maps between projective spaces? Dmharvey

Talk 14:33, 10 August 2005 (UTC)

Sub and super markup feature request

I've requested that markup be added to simplify entering sub and superscript at Bug 3080. It's just TeX markup with mandatory brackets. I think it will clean up the markup and be a lot easier to type than HTML.

Examples:

x^{3} → x³ (powers)
CO_{2} → CO₂ (carbon dioxide symbol)
1^{st} → 1^st (ordinals)
^{2}H_{2}O → ²H₂O (isotopes)

I can't think of anything this would conflict with, can you? Vote for it if you like it. Suggest a different syntax if you don't. Other syntaxes were suggested, which I really don't like. - Omegatron 19:39, August 9, 2005 (UTC)

I am not really happy with new notation. You can just use math tags to do the same thing. Oleg Alexandrov 20:25, 9 August 2005 (UTC)

There are lots of uses for super and subscripts that aren't math, like $CO_2\,\!$ or " $1^{st}\,\!$ place". There's really no need to type 17 characters to output 3. My markup is 6 characters; shorter and quicker and easier than both math and HTML markup. Math markup isn't appropriate for everything, and there's a lot of contention about whether it should be used inline with text at all.

And regardless of whether math markup is the way things should be done, HTML markup is the way things are done, in most cases (as in these featured mathematics articles: 1, 2).

This could save time and effort for those reading and writing the markup this way. - Omegatron 21:25, August 9, 2005 (UTC)

I agree that for things like CO2 and 1st it would be nice to have simpler markup. I disagree in the case of x^3, since this should have the semantics of a mathematical expression, but let's not go there, because that always seems to open up a can of worms :-). However, I'm quite uneasy about adding your modifications to the wiki markup. How are you going to handle the fact that there are probably quite a few ^ and _ and { and } characters hanging around in existing articles? Dmharvey

Talk 22:25, 9 August 2005 (UTC)

It doesn't matter if there are ^, _, {, or } characters hanging around in the markup. It only matters if there are ^{ ... } or _{ ... } hanging around outside of math tags. If there are, I doubt there are many. The only article I can imagine having them is m:Help:Formula. There aren't even any in the TeX, ASCII art, or obfuscated code articles. (I checked!) I'm sure whoever would implement this also has the capability to search for the few that might be out there and surround them with nowiki tags first (or math tags, since they're probably mistakes). - Omegatron 23:46, August 9, 2005 (UTC)

FWIW, I like it, seems like a good idea. As to the stray-markup issue, what about articles that contain sample source code? I thought I saw an article that showed how to compute factorials in 18 different programming languages. linas 00:00, 10 August 2005 (UTC)

I have to admit it's starting to sound tempting. Have you suggested this to the people who work on chemistry articles? Dmharvey

Talk 00:30, 10 August 2005 (UTC)

Yeah, I suggested it at Wikipedia:WikiProject Chemistry. :-)

As for stray markup, just track it down and put <nowiki> tags around it before implementing the markup filters. I'm not sure how that works for preformatted text, though:

Testing testing 1² 3<sup>4</sup> 5^{6} 7^{8}

Looks like it works for those, too. - Omegatron 02:47, August 10, 2005 (UTC)

AKS primality test cleanup

I've expanded the article with information about the algorithm itself, and some detail about the proof. I'm not happy with the look of the <math> sections though - this is my first attempt at a significant amount of mathematical markup - so some help in cleanup would be appreciated.

Eventually this article should probably include the full algorithm in programming terms (rather than only in mathematical terms), and describe the complete proof. But I need to learn a bit more about finite fields and group theory before I can hope to do that myself.

As far as I can see, the only markup forcing things to PNG are the use of \sqrt(r) and \equiv. Hv 13:39, 10 August 2005 (UTC)

Thanks. It's an important algorithm, which caused quite a stir when it appeared. I cleaned it up a bit. In particular, you should use \log for logarithms in <math> mode, and \ge instead of >= (incidentally, \ge and \le are other commands that force PNG, which is rather strange as they can be rendered rather easily in HTML). Look at my changes for details. Oh yes, if you reference articles like Lenstra 2002, they should also be put in the references. Cheers, Jitse Niesen (talk) 15:05, 10 August 2005 (UTC)

Thanks; I didn't know about \log, but I've noticed that I tend to miss the < and > operators; the references to more recent papers are not mine (though among my next tasks is to track those down and try to read them).

I'm not convinced I like the mix of <math> and inline HTML, but I accept there is no ideal solution at the moment - Bubba73's comments in the Inline PNG formulas discussion above resonated strongly with me. Hv 16:59, 10 August 2005 (UTC)

As I say in that discussion, I usually don't change PNG to HTML (though I do make the change sometimes when I don't think enough), but since you made the request, I thought it would be okay. Anyway, I changed it back. I hope you don't mind my changing the \forall in text. Sorry about assuming that you put the references in there; I should have checked that. -- Jitse Niesen (talk) 17:20, 10 August 2005 (UTC)

Apologies if my lack of clarity here caused you to waste time. I can claim only ignorance and foolishness; I'm trying to catch up with the options and arguments on formatting, but I haven't located consensus yet on anything beyond no current solution is ideal, and wouldn't it be nice if MathML were here already, and it's a mess.

In summary, I don't know what is best for that page, and don't trust that what's best for me (my browser, my OS, my installed fonts) would be best for the majority, so I can only hope for and defer to someone better able to judge. Hv 18:10, 10 August 2005 (UTC)

Move of Inclusion (mathematics) to Inclusion map

I am proposing moving Inclusion (mathematics) to Inclusion map. For my reasons and how I plan to go about it see Talk:Inclusion (mathematics). If you have any thoughts on this move please comment on that talk page. Thanks. Paul August ☎ 18:42, August 10, 2005 (UTC)

I found this on VfD

Wikipedia:Votes_for_deletion/Hyper_generalized_orthogonal_Lie_algebra --R.Koot 03:45, 11 August 2005 (UTC)

Mathematics and space

Over at the Talk:Space#On arranging stuff in this article page there's a discussion about whether the section on Mathematics and space could be rewritten to contain a brief summary of how space works in maths, as at the moment it is pretty much a list of links. Could someone take a look at Space, which it is hoped will be a big picture article taking in the various uses of the concept of space, and see if work can be done on the Mathematics and space section. Thanks for any help or thoughts. Steve block talk 07:58, 11 August 2005 (UTC)

VfD for Mathematics and God

The article Mathematics and God is up for deletion. I voted to keep, here's the VfD page: Wikipedia:Votes for deletion/Mathematics and God. — Paul August ☎ 19:36, August 11, 2005 (UTC)

Of course, anybody watching Wikipedia:WikiProject Mathematics/Current activity would have discovered this a few days ago (sorry for the shameless plug, but Paul gave me a perfect opportunity). I moved the section "Articles on VfD" up to make it more prominent. By the way, it quite worries me that the article got a dozen delete votes and none of them bothered to comment on the reasoning brought up subsequently — I understand Ed Poor's frustration better now. -- Jitse Niesen (talk) 11:37, 12 August 2005 (UTC)

Yes that's how I discovered it by checking up on Wikipedia:WikiProject Mathematics/Current activity (I had forgotten to put it in my watchlist) And I agree about the comment on VfD. Paul August ☎ 16:50, August 12, 2005 (UTC)

BTW, its not showing up on Wikipedia:WikiProject Mathematics/Current activity any more ... maybe the time limits should be increased to more than a week? When I'm not in wiki-holic mode, more than a week can pass before I look at stuff. linas 23:58, 16 August 2005 (UTC)

The idea is that VfD discussions are supposed to last only seven days, so I thought it wouldn't be useful to list it longer. However, as you noticed, some discussions are not closed after that period, so now VfD pages are kept for ten days. I'm still trying to find the right balance on how long to keep the material. Of course, you can always look in the history of the page. -- Jitse Niesen (talk) 17:33, 17 August 2005 (UTC)

The VfD is closed. Keep won, though I'd hardly call it a concensus. The NPOV tag remains in the article itself (correctly, in my view). China, India, and the Arabic world have produced more notable mathematicians than just Ramanujan; those who voted to keep might help by finding quotations from other non-Western voices. Mathematicians like Russell and Clifford are well-known for their writings on God; I have added their remarks, and would invite others to add more of the kind. Especially nice would be more fun contributions like Erdős and (my addition) Hardy. --KSmrq 20:01, 2005 August 19 (UTC)

Category:Mathematician Wikipedians

I created Category:Mathematician Wikipedians as a subcategory in Category:Wikipedians by profession and categorized myself in there. Company is welcome. :) Oleg Alexandrov 23:28, 11 August 2005 (UTC)

What about Category:Wikipedian mathematicians? --R.Koot 23:56, 11 August 2005 (UTC)

Will people list themselves there or can anyone list them there? If the former, the list may be so incomplete as to be useless. Michael Hardy 21:28, 18 August 2005 (UTC)

If anybody is willing to go through mathematicians user's pages and add them to one or the other category, I will not mind. :) Oleg Alexandrov 01:28, 19 August 2005 (UTC)

Do you think that the others would? I think a directory is a great idea but perhaps the listing should be voluntary. Or maybe you could just leave someone a note on their talk page when you have added them (to give them the option to be unlisted). What do you think? --Kooky | Talk 19:13, 19 August 2005 (UTC)

To rephrase myself, if anybody is willing to go through mathematicians talk pages and mention to them about one or the other category, I will not mind. :) Oleg Alexandrov 19:56, 19 August 2005 (UTC)

There must be only one. If we do not merge these now, someone will do it later and more clumsily, and with much more work. There seems to be no standard, and Category:Wikipedian mathematicians is more idiomatic to my ear, so I propose we use that one. Septentrionalis 14:01, 19 August 2005 (UTC)

Category:Wikipedian mathematicians also fits better with Category:Wikipedians by profession. My vote is with Septentrionalis. I've added Wikipedian mathematicians to Category:Wikipedians by profession, so at least it is now obvious there are two conflicting page titles. --stochata 20:05, 19 August 2005 (UTC)

Don't know about you folks, but my profession seems to change every few years. (Three years ago, I was a "businessman". Now I'm an "engineer".) Classification by areas of interest, past and/or present, might be more accurate than whatever (non-)career is one is fated to, given the caprecious winds of the economy and slipperiness of the rungs of the social climbing ladder. linas 21:31, 19 August 2005 (UTC)

According to this, WP is not a directory. However, many categories for Wikipedians already exist. Since all the listings appear to be voluntary ones, I have no further comment on the subject. Oleg: Sorry about the misinterpretation. =) --Kooky | Talk 22:32, 19 August 2005 (UTC)

OK, I moved myself to Category:Wikipedian mathematicians. If more people feel to prefer this one, we will need to nominate Category:Mathematician Wikipedians for deletion and move the other people in there to Category:Wikipedian mathematicians. Oleg Alexandrov 05:48, 20 August 2005 (UTC)

I've now nominated Category:Mathematician Wikipedians for deletion. Note that the yokels don't seem too happy about the other page either (as per Koooky's comment above). --stochata 15:34, 26 August 2005 (UTC)

stochata, thanks. It seems there is a likelyhood both categories will be deleted, so you could go vote on that. Oleg Alexandrov 16:08, 27 August 2005 (UTC)

Announcing Jise's RfA

I would like to announce that I have nominated Jitse for adminship, and I am here shamelessly encouraging everyone to vote (in support I hope ;-). To vote or comment go here: Wikipedia:Requests for adminship/Jitse Niesen. — Paul August ☎ 16:58, August 12, 2005 (UTC)

Paul's nomination was successful, so I have now access to the admin tools. Thanks to everybody for voting. -- Jitse Niesen (talk) 12:28, 20 August 2005 (UTC)

Jitse, shouldn't you update your blurb in the participants list to reflect your newly elevated status? ---CH (talk) 00:04, 24 August 2005 (UTC)

PNG rendering improvements

Maynard Handley has put up a wiki demonstrating some improvements he has made to the LaTeX => PNG rendering process.

With his permission I offer you the URL: http://name99.org/wiki99/. It will disappear within about a week so check it out soon.

In my opinion, some of the improvements are great (Wikipedia should definitely use them), some are so-so, and some are, let's say, ambitious.

I'd like to hear some opinions. Dmharvey Talk 21:39, 12 August 2005 (UTC)

The rendering looks worse to me. Dysprosia 03:21, 13 August 2005 (UTC)

Those are all terrible on my system (Firefox on KDE/linux with 1024x768 res) -Lethe | Talk 03:35, August 13, 2005 (UTC)

Correct link to the zip-file: wiki99.zip

There is a particular, uncomfortably large, font size at which the rendering is readable (although still worse), otherwise the rendering is unreadable (Firefox 1.0.4 and IE 6 SP2 on Win XP HE SP2, LCD screen 1680x1050). I think the way it scales with font size is cool though. --nosfractal 04:21, 13 August 2005 (UTC)

The auto-scaling feature is indeed interesting, but the actual rendering, as noted above, does resemble an atrophied 16th century manuscript. (I'm using Konqueror.) linas 22:42, 16 August 2005 (UTC)

Having a stronger TeX->HTML conversion would make autoscaling irrelevant, however. A good first step has been taken in ensuring that the HTML text is the same font as the rest of the document, but the conversion is still so weak as to render less than signs in PNG and not use HTML (iirc). Dysprosia 22:52, 16 August 2005 (UTC)

Actually, in my browser (Safari 2.0, also with Firefox 1.0.4 for mac),

x y z

is rendered (via HTML) in a different font to xyz. Am I doing something wrong? Dmharvey

Talk 23:18, 16 August 2005 (UTC)

Dave, go to User:Dmharvey/monobook.css and add

span.texhtml { font-family: sans-serif; }

See User:Jitse Niesen/monobook.css for an example. Unless anybody disagrees that this is a good idea, I will try to get this in the site-wide stylesheet. -- Jitse Niesen (talk) 10:24, 17 August 2005 (UTC)

Looks like your skin. It looks quite nice and consistent in Cologne Blue, where math is in the same font as italics. Dysprosia 11:45, 17 August 2005 (UTC)

Not for me, if I switch to Cologne Blue, then

x y z

(<math>xyz</math>) is rendered in a different font than xyz (''xyz''). Perhaps a browser thing, or something to do with the browser settings? More research needed. -- Jitse Niesen (talk) 11:59, 17 August 2005 (UTC)

That's quite bizarre. The fonts should be the same, anyway. Dysprosia 12:15, 17 August 2005 (UTC)

Hmmm. I've applied Jitse's suggestions (about User:Dmharvey/monobook.css). Now I get matching fonts in Firefox, but not in Safari. I've tried clearing caches and restarting the browser, and as far as I can tell Safari isn't trying to apply its own style sheets, so I have no idea what's going on. Ah well, no big deal. Incidentally, I don't often use Firefox, but now I'm looking at it, the italics in normal text look awful. The spacing after a word in italics is much too small. Dmharvey

Talk 12:32, 17 August 2005 (UTC)

Number articles up for deletion

1984 (number) (discussion)

The aforementioned article is up for deletion. Uncle G 15:42:27, 2005-08-16 (UTC)

I've voted to delete this article. I agree with the sentiments expressed here: User:Uncle G/Wikipedia is not infinite. Paul August ☎ 16:59, August 16, 2005 (UTC)

New section: "Mathematics featured articles", comments?

I've added a new section: "Mathematics featured articles" to the project page. I might expand it a bit with some information on "Featured articles" and the FAC process. It might also be nice to track down and add the date when each article became an FA. Comments? Paul August ☎ 18:48, August 16, 2005 (UTC)

Ok I've made some changes to the "featured articles" section. In particular I:

added a list of "former features articles"
added the date when each article was "featured" and "de-featured"
linked the date to the "featured" or "de-featured" discussion (for those I could find, older articles don't have nicely organized and archived discussions)
used a tabular format rather than a list format.
changed the section title to reflect the addition of "former" articles.

Paul August ☎ 20:28, August 18, 2005 (UTC)

Mathematical notation in articles

I'm new here, and I'd like clarification about use of mathematical notation, specifically in set theory and mathematical logic. For example, my new stub of Transitive set uses the ∈ (∈) symbol, which the guidelines suggest should be replaced by the text "is in". Arthur Rubin 00:29, 17 August 2005 (UTC)

Generally speaking, you would want to follow the guidelines. However, my opinion in your case is that using ∈ is fine, essentially because the audience for that article would be expected to be familiar with standard set-theoretic notations already. Dmharvey

Talk 03:23, 17 August 2005 (UTC)

Two distinct concerns apply, both of which argue for "is in". The first is whether a reader can properly view the character in their browser. This would not be a problem for a PNG image, but that's ugly inline. The second concern is audience comprehension. For this brief article there is little to be gained by technical notation; "is in" may invite more readers.

The implications of these two concerns vary among articles. We can only hope that the character set problem will go away soon, but meanwhile the list of "Insert" characters below the edit window is considered safe. In the case of a long, technical article like Kripke semantics, proper notation is essential, so use it — though as little as possible in the lead paragraphs, and in <math></nomath> brackets elsewhere. --KSmrq 04:46, 2005 August 17 (UTC)

Good points by Dmharvey and KSmrq. Oleg Alexandrov 15:16, 17 August 2005 (UTC)

more about improving inline PNGs

I've been trying to improve on what Maynard Handley did with the PNGs.

There are still severe problems (mostly relating to Windows), and it's not good enough for deployment, but I think it's starting to get somewhere, and I'd appreciate some opinions.

Check out User:Dmharvey/Inline_PNG_discussion.

Dmharvey Talk 17:15, 17 August 2005 (UTC)

Requested move

Could an admin move Menelaus theorem to Menelaus' theorem? Note that the page's principal author User:Tokek has left a note on talk:Menelaus theorem regarding the choice of title, but as I read it it doesn't seem that Tokek would find this change objectionable. —Blotwell 06:57, 20 August 2005 (UTC)

I did it. Now Menelaus theorem is a redirect to Menelaus' theorem. Hope that was a correct move. --Zero 08:28, 20 August 2005 (UTC)

Framed box around formulas

Yesterday I removed with my bot framed boxes around formulas wherever I could find them. I mean, boxes of the form:

This is a theorem, or a formula.

I based my reasoning on the discussions at Wikipedia_talk:WikiProject_Mathematics/Archive10#Dotted_framebox_around_formulas and Wikipedia_talk:WikiProject_Mathematics/Archive6#A_little_note_on_using_purple_dotted_boxes but Paul rightly pointed out that a preliminary discusion would have been good. So, belately, I wonder, what do people think of these boxes? Thanks. Oleg Alexandrov 18:46, 20 August 2005 (UTC)

I don't feel strongly one way or the other, but I never use the boxes. I think they should probably be left out unless something really needs to be emphasized. Bubba73 19:28, August 20, 2005 (UTC)

I don't much like them. I think it would be good to remove them, at least in the cases I've seen. Perhaps there might be a use for some more visually pleasing way (not purple dotted lines) to set off certain text. But it would be best to use such devices sparingly, if at all. Paul August ☎ 19:36, August 20, 2005 (UTC)

I think the borders are gaudy and obtrusive, but I'm not going to bend anyone's arm either way. --Kooky | Talk 20:28, 20 August 2005 (UTC)

Can we have hot pink with circulating neons? --Zero 02:44, 21 August 2005 (UTC)

Characterizing Notability of Mathematicians

Hi all, I am a non-member dropping by to alert you all to an ongoing VfD discussion.

The issue is: which mathematicians should have biographies in the Wikipedia? I think a simple and common sense rule of thumb (the title is a joke; of course I don't expect a mathematically precise criterion) should be:

a wikibiography of mathematician M, which claims no non-mathematical notability for M, should explain or at least describe at least one clearly notable mathematical achievement of M.

I am no doubt hardly the first to point out that with thousands of person obtaining a Ph.D. in math every year, and gadzillions of math professors around the world, and tens of thousands of members of SIAM, AMS, MAA, and other mathematical societies around the world, simply earning a Ph.D. or publishing some research papers probably shouldn't qualify one for a biography.

Here is a more bizarre possibility: suppose the article claims that M is notable because he won the Y Prize, it should link to the formal English language Y prize citation for M. If that doesn't exist (in English), at the Y Foundation website, and if there is no other grounds for M's alleged notability, I question whether M should have an entry in the English language Wikipedia.

No, I didn't make that up. This is exactly the argument some nonmathematician made in a VfD. (Quick now: has anyone here ever heard of the Zois Prize? Before reading the preceding sentence?)

Yesterday, I happened across several biographies listed in Category:Algebraic graph theory which I think violate my simple rule:

Aleksander Malnic
Dragan Marusic
Tomaz Pisanski

I have nominated them for deletion as non-notable. I think the first two are clear cases, the third maybe a bit less clear. Just to be clear, in each case, I would be equally happy with either of the following outcomes:

the article is deleted on the stated grounds,
someone comes up with a useful description of a truly notable mathematical achievement of the subject.

I hope many of you will drop by those pages and vote one way or the other, but I'd also like to see any comments on the bigger issue raised in the subject line: how can one characterize which mathematicians are notable?

In retrospect, I probably should have considered trying to contact authors/editors of these articles before making my VfD nominations. Has anyone had some good experiences along these lines to share? Or advice on how to proceed if a similar situation arises in the future?

Someone raised another issue: these three men all happen to appear on a List of Slovenian mathematicians, so there might be some, er, patriotic rationale for creating these biographies. I don't want to get involved in Balkan politics, so I'd just say that I did recognize one name on that list, Josef Stefan, and I would certainly agree that Stefan is notable and should have a biography here. I'd like to see the others include an explanation of some clearly notable mathematical accomplishment, or else I think they should probably go.---CH (talk) 21:50, 22 August 2005 (UTC)

Oh dear: to forestall misunderstanding, of course I did not mean to imply that whether or not I recognize a name is an adequate criterion for mathematical notability. But if none of the members of this project know anything about mathematician M, and the biography doesn't help, I would say that biography should probably go.

Another thing: I overlooked another name I recognize: Josip Plemelj. Ironic I missed that, because I am gearing up to write about something he was involved with.---CH (talk) 22:04, 22 August 2005 (UTC)

P.S. Someone commented in the VfD to the effect that the fact that some towering figure doesn't yet have a biography, while some lesser figures already have ones, is not by itself grounds for deleting anything. I agree; clearly, Wikipedia's growth is haphazard so this will be a not infrequent occurrence. The balance issue raised in these three cases goes far beyond that, I think, but all I am really trying to say is that, IMO, the average reader of a biography on Wikipedia should not be left with serious doubt that the subject is indeed notable, as I was after reading these three biographies. Again, I'd be happy if someone who knows more than I do about them can convince me I am wrong by telling us all (by expanding the biographies) about some clearly notable accomplishment. But some prize I have never heard of? Doesn't help me. Some very rough analogies (not very serious):

earned a Ph.D.: made the local Little League baseball team
serves on the math faculty at some uni: plays minor league professional baseball
won tenure or an obscure award: got a pat on the back from the team after a big game
made a major contribution to mathematics: set a significant major league baseball record
won an internationally known mathematics award: won the MVP award
won the Field's Medal: entered the Hall of Fame

(I should confess that I don't know much at all about baseball, I'm just trying to, er, play along with a favoriate analogy among Wikipedians.)---CH (talk) 23:58, 22 August 2005 (UTC)

JYolkowski has suggested several times (if I understand him correctly) that the mere verifiability of stated facts in an biography is sufficient grounds for keeping it (see my talk page). This doesn't make sense to me: name person X, birthdate, and birthplace, and someone can probably verify that information. Does that alone qualify X for inclusion? I think it should be rather the notable substance of stated facts (or lack thereof) which qualifies X (or not) for having a biography here.

I seem to be trying to summarize, er, notable comments recieved elsewhere. I have to take the blame for this. Due to the accidental way I got into this (and my inexperience in Wiki discussions of this kind), various useful (or bizarre) comments are now scattered over the talk pages of the three articles, my user talk page, and the vfd pages. Sorry for the confusion!---CH (talk) 00:35, 23 August 2005 (UTC)

Jitse actually found the citation (in Slovenian, I guess) of some obscure award to Marusic :-) So I did the obvious thing and awarded the very first Biographical Barnstar for Brain-numbingly Obscure Web Research to Jitse Niesen. Congrajulations, Jitse! This is such an obscure award that until a few minutes ago it didn't even come with a bronze plated pewter star. But you can verify that Jitse won it!-- just look here! Anyway, if some kind person can translate this well enough, maybe I will change my own vote. Even better, said kind person can add a description (in English) of Marusic's notable achievement in the original article.---CH (talk) 01:02, 23 August 2005 (UTC)

Hi CH, by posting here, you are now officially a member. You might be interested in considering the positions of the Association of Inclusionist Wikipedians as well as the Association of Deletionist Wikipedians. There are some serious philosophical battles on these issues. Amazingly, WP is filled with oodles of non-encyclopedic, non-notable material, e.g articles on ancient soviet submarines, underwater electrical cables, television shows, Pokemon characters, and rock-n-roll bands. linas 04:57, 23 August 2005 (UTC)

Hi CH, to add to what Linas said above, the issue of notability on Wikipedia is unsettled, see: Wikipedia:Notability, Wikipedia:Importance, and Wikipedia talk:Fame and importance. Since Wikipedia is not paper, I lean toward the inclusionist idea that "verifiability" is the more important concept, since it is a necessary condition to be encyclopedic, and being that it also implies a certain minimal amount of notability, is arguably sufficient. (For what it is worth, I believe this is the view held by Jimbo Wales). Paul August ☎ 16:11, August 23, 2005 (UTC)

OK, some anon has translated the now notorious Zois prize citation of Marusic, which led me to guess that if he is internationally recognized, some papers by him would appear in a review paper I happened to have at hand. This turned out to be the case, so I changed my own vote in the VfD to a lukewarm keep.

I'd like to try to summarize a few more valuable points which came up:

if someone knows of a mathematician who rarely if ever publishes in English but has done extraordinary work (every mathematician can think of examples), of course we all agree that this person should have a biography in the English language Wikipedia, because such a person has clearly made a notable contribution to the body of human knowledge.
exhaustive lists of Lusitanian mathematicians might be appropriate in the Lusitanian language Wikipedia, but should be discouraged in the English language Wikipedia, which clearly has a special responsibilty to students all over the world because English currently plays the role of the scholarly lingua franca.
the problem with exhaustive lists is that they impede navigation by the generic reader, who wants to find and absorb information on a specific topic; particuarly in a deeply and confusingly interconnected subject like mathematics, eliminating cruft is essential if these pages are to become (remain?) a valuable resource for students and the general public all over the world, which I take it is our goal in the EN language Wikipedia.
the sports metaphor breaks down here, because reading about mathematics is far more challenging and daunting than reading the sports pages, and we have a special responsibility to help people find useful and intriguing information about mathematics, which inevitably means taking them places they didn't expect in other parts of the math pages. We must avoid disorienting them or landing them in a huge and amorphous category. So if exhaustive lists "for the sake of keeping exhausting lists" must be kept out, or at least in special categories.
how ironic (if unsurprising) that the mindless drones are not the mathematicians--- who were alleged in the popular culture of the first part of the last century to spend their time poring over long lists of meaningless numbers--- but the sports fans! The mere fact that no non-mathematicians expressed surprise at our concern for organization, sanity, good judgement and balance, might suggest that the general public now knows better, or has a new set of misconceptions about us, but probably it only means that the non-mathematicans who dropped by weren't in a contemplative mood.
a prize citation by itself means little; mention in a review paper by an international authority is a much more reliable indication that person X, working in some field in which one is not oneself expert, is a major player.

Paul August: up above I think I expressed my take on inclusion; fine by me as long as it doesn't intrude upon the learning experience of the generic user. My concern is to keep that from happening. A mixture of discouraging cruft (hopefully by the art of gentle persuasion) and segregating it is probably the best answer.

Two points, first, "providing a learning experience" for our readers is a noble goal, but strictly speaking, that is not the mission of an encyclopedia, and second, If we are sufficiently creative, having subjects with low notability, should not "intrude" upon such a goal anyway. Paul August ☎ 23:02, August 23, 2005 (UTC)

Linas: OK, I'm adding back my name, but I need to focus on the GR WikiProject at least for the rest of this year, because I promised to get some serious work done on that. Yes, I'm talking to you, and all is forgiven, but Linas, I really hope that in the future, you in particular will pay attention to clues that you might be getting on my nerves (or keep an eye on the wikistress meter on my user page), OK? If that happens, I'm sure I'll try to tell you, so if you just remember to be a good listener when interacting with me all should be fine.---CH (talk) 22:27, 23 August 2005 (UTC)

Can more people help me out?

I have a question/problem/something-I-don't-understand that has been bugging me for years. I have posted it at the bottom of Talk:Infinity. Thank you already to Paul August. --Lord Voldemort ^{(Dark Mark)} 17:20, 23 August 2005 (UTC)

weird vandalism

There have been some rather strange edits to Galois theory in the last few weeks, all emanating from IP address 64.136.26.235, just deletions of large random chunks of text. What is especially odd is that this IP address appears to be making genuine edits to other articles. Any ideas? Dmharvey Talk 18:49, 25 August 2005 (UTC)

This is the IP address of a cache server fom United Online, so is most likely used by a lot of different users. --R.Koot 18:58, 25 August 2005 (UTC)

"Tav (number)" article

Take a look at Tav (number). Is this valid? Salvageable? The original article is credited to an IP (which has no other math-related edits), and subsequent edits by others have left the basic text unchanged. Obviously, this article needs either a rewrite or deletion. — Nowhither 13:50, 26 August 2005 (UTC)

It has a valid basis but is so poorly written as to be incomprehensible. See the footnote on page 3 of this Postscript document. Here is Tav: ת --Zero 14:11, 26 August 2005 (UTC)

Talk:Sigma-algebra

The notations used by the cluster of articles close to sigma-algebra are inconsistent with one-another; I'd like to fix this, but only after some agreement on a unified notation. Please see Talk:Sigma-algebra for details. linas 13:58, 26 August 2005 (UTC)

Sheaf

Almost a million (well, nearly) pages still point to sheaf rather than to the moved sheaf (mathematics). There were good reasons not to move it. Charles Matthews 20:33, 26 August 2005 (UTC)

There's an entry for it on the disambiguation page. What's wrong with that? --Kooky | Talk 20:53, 26 August 2005 (UTC)

Well first, the article at "sheaf" should be about the mathematical kind if that is the "primary" meaning of the word (see: Primary topic disambiguation). Of course that the mathematical meaning is the "primary" one is debatable, but the great number of links to it vs. the others is suggestive that it is (at least for the here and now). But if it is decided that it should stay at "sheaf (mathematics)", then the links to "sheaf" which want "sheaf (mathematics)" need to be changed. Paul August ☎ 21:17, August 26, 2005 (UTC)

Actually, there are 109 articles listed on the "what links here", of which TWO are not mathematics-related. I vote to change it back. Dmharvey

Talk 21:25, 26 August 2005 (UTC)

to Paul August: I see. That makes sense. I'd be willing to work through all the mathematical articles that point to sheaf and redirect them to sheaf (mathematics). If it were decided later on that the mathematical definition were no longer the "primary" definition, wouldn't it have to be done anyhow? --Kooky | Talk 22:18, 26 August 2005 (UTC)

If you can make a good case that the primary definition of "sheaf" is moving away from the mathematical one, then I might be persuaded to change my mind. However, the overwhelming proportion of wikipedia articles are presently pointing to the mathematical meaning of Sheaf, and this seems to be evidence pointing the other way. Dmharvey

Talk 22:42, 26 August 2005 (UTC)

Gauge, who moved it, contributes to mathematics articles, and I see no discussion anywhere calling for a move. So I can't imagine there will be an outcry if we just quietly move it back, or whatever administrators do. --KSmrq^T 22:58, 2005 August 26 (UTC)

The meaning to which the most links point should perhaps not always be considered primary. For example, the word sheaf was probably chosen for use in mathematics to be suggestive, precisely because the word has another, non-mathematical meaning. The effectiveness of the mathematical usage to some extent depends on that other meaning. Michael Hardy 22:51, 26 August 2005 (UTC)

Almost no one outside of math actually uses the word sheaf; what, pastoral literature? Move it back. linas 00:37, 27 August 2005 (UTC)

Change it or leave it, it's all the same to me. --Kooky | Talk 01:12, 27 August 2005 (UTC)

Agree to move it back to sheaf. Oleg Alexandrov 16:03, 27 August 2005 (UTC)

Sorry, I don't know how I missed the remaining links. I will contribute to fixing them or moving them back, based on what we all decide here. Regarding the move, I was thinking that "sheaf" is a common enough word that it could have many possible current (and future!) meanings. Personally, I don't see any harm in having a more specific link to the mathematical definition (so long as the remaining links are fixed). However, if you'd like to go back to the old link, that's fine with me too. - Gauge 16:58, 28 August 2005 (UTC)

I have fixed the remaining old mathematical links to point to the new location. Apparently at least a couple of articles have already referred to sheaves in the agricultural sense. - Gauge 04:40, 2 September 2005 (UTC)

Aged requests

Some of you may remember that in August 2003 a user began adding a huge number of missing math topics to Requested articles. There were well over a thousand requests added, but through the labour of our math people all but seven of them have now been filled. These last few requests are now listed on Articles requested for more than two years. Since they have taken so long to be filled they are probably very obscure and difficult to write about, and certainly need some expert knowledge. It would be great if some math people could take a look at Articles requested for more than two years and try to clear these final relics. - SimonP 23:28, August 26, 2005 (UTC)

Math Babel

I've just made a comment on the category deletion pages for Category:Mathematician Wikipedians about a Math version of the Babel project. Then I realised it's actually only an extension of the Babel project. Below are some sample categories for discussion, and we could make up a pretty box template like the babblers:

Math native speaker of math. This person works as a math professor or similar role in industry.
Math-N near-native speaker of math. This person is either engaged in a math doctorate, or works where a very high level of math is required e.g. as a physicist, etc.
Math-3 very high level of math. Works where a high level of math is involved (e.g., actuary, computer science, etc), or is engaged in a higher level degree in math, physics or other math related subject.
Math-2 has taken or is taking an undergraduate degree, in math, physics or other math related subject.
Math-1 basic mathematical ability and literacy. Typically working in an environment where an understanding of math or logic is desirable, such as an accountant.

If we preferred it could be a proper equivalent of Babel, where statisticians, applied mathematicians and pure mathematicians have their own boxes, and people like me can be Pure Math-1! --stochata 11:12, 27 August 2005 (UTC)

Not sure I like this fine level classification. OK, if one wishes to do that, one could. But those Babel thing are ugly and take a lot of room on the page. Oleg Alexandrov 16:10, 27 August 2005 (UTC)

The only problem I have with that classification is that it doesn't distinguish different types of math-nativeness. For example, I might be classified as "native" myself, but when it comes to articles on algebraic topology, numerical analysis, several complex variables, or any number of other topics, my understanding is really probably somewhere between Math-3 and Math-N at most. In other words, a lot of the time, the level would depend on the particular subject itself. Revolver 21:52, 2 September 2005 (UTC)

I think those categories are setting the bar too high. After all, we don't make up separate categories for "native speaker of english", "native speaker, additionally is studying english literature at PhD level", and "native speaker, additionally teaches english literature and phonics at university level". I think what you have as "Math-3" is the highest level I would be willing to categorise on babel. After that there are just too many problems with specialised areas, as Revolver notes. Dmharvey

Talk 22:10, 2 September 2005 (UTC)

I did wonder about the height of the bar, especially as compared with "native speaker of English" (which covers perhaps 300 million+ people), as opposed to perhaps a few thousand math professors in higher education. However, sometimes I feel it is worth knowing that X is actually a math professor, rather than a doctoral student. I also agree that specialised subdomains complicate thing. I would also be Math-3 (alternatively, Graph Theory-N, Number Theory-1, Statistics-2) under this classification, but then I do feel that others are better qualified than me, and would appreciate knowing who is who (and would also like other editors to know that my math isn't always 100%, and needs checking). --stochata 12:33, 4 September 2005 (UTC)

A math(s) professor may advertise themselves as such on their user page without a babel notice, if they so choose. Perhaps what you really want is a "Mathematical Wikipedians, classified by area of specialisation" page. The difficulty is that often people categorise themselves too high because they don't know any better. For example, there would be a fair few high school students who would describe themselves as accomplished in "geometry and algebra", despite not knowing the first thing about what real mathematicians in these areas actually do. Dmharvey

Talk 12:54, 4 September 2005 (UTC)

Merge sigma additivity into measure (mathematics)?

The article sigma additivity used to be a redirect to measure (mathematics). As part of the PlanetMath Exchange project I copied over the article "additive" to sigma additivity, replacing the redirect. User:Blotwell is now suggesting that sigma additivity be merged into measure (mathematics). I feel like the topic is deserving of its own article, but this is not my area of expertise, (not that I have one ;-) and I would appreciate if other knowledgeable editors could help decide what the best thing to do is. Please comment here. Thanks — Paul August ☎ 19:21, August 27, 2005 (UTC)

New math categories

As part of working on categorizing articles copied from PlanetMath — the PlanetMath Exchange project, I noticed that there might be a need for more math categories from subjects listed in the Mathematics Subject Classification (2000 edition). Here's the categories I have in mind:

Category:associative rings and algebras as subcategory in Category:Abstract algebra, as per MSC 16-xx, Associative rings and algebras
Category:nonassociative rings and algebras as subcategory in Category:Abstract algebra, as per MSC 17-xx, Nonassociative rings and algebras
Category:Difference equations and Category:functional equations as subcategories in Category:Equations, as per MSC 39-xx, Difference and functional equations
Category:Global analysis and Category:analysis on manifolds, subcategories in ???, as per MSC 58-xx, Global analysis, analysis on manifolds
Category:Sequences, subcategory in Category:Mathematics, as per MSC 40-xx, Sequences, series, summability
Category:Mathematical biology as subcategory in both Category:Mathematics and in Category:Biology, as per MSC 92-xx, Biology and other natural sciences

I am aware that the Mathematics Subject Classification is not directly applicable to Wikipedia math articles, still, probably it can give some inspiration. I am most uneasy about the global analysis and analysis on manifolds thing. Any suggestions and discussion of the above are very welcome. Oleg Alexandrov 22:57, 27 August 2005 (UTC)

Category:Nonassociative algebra would be good. Nobody can remember categories A&B, so let's not have any more. Category:Global analysis was 'big in the 1960s' but I think should probably not be used here - cover by means of other ones (possibly one on infinite-dimensional manifolds, one day). Category:associative rings and algebras is really just ring theory, which we have. Charles Matthews 09:45, 28 August 2005 (UTC)

Charles, should it be Category:Nonassociative algebras, meaning plural? Oleg Alexandrov 15:36, 28 August 2005 (UTC)

(I changed the list to a numbered one, to make referring to it easier). I think (1) and (2) should be under ring theory, as I find it hard to see there being enough articles to justify addiational catergories. Similarly for (3) - I don't think there's enough articles to justify additional catergories. For (4), it seems the seqeunce catergory is broadly equivilant to the catergory you suggest putting it under. On the other hand, I definately agree with doing (5) as you suggested. It is important to remember that the MSC classification is designed to classify maths papers, not maths itself. Tompw 11:50, 28 August 2005 (UTC)

So: Category:associative rings and algebras can be just replaced with Category:Ring theory, and probably Category:Difference equations and Category:functional equations are premature, with Category:Equations being enough. However, I would argue though for creating Category:Sequences. It could contain as subcategories Category:integer sequences and Category:mathematical series. Any comments on this? Oleg Alexandrov 01:54, 30 August 2005 (UTC)

Fibonacci numbers subscript style

I raised this question on Talk:Fibonacci number a while back, but didn't get any comments, and since this also concerns other articles, I'll bring it up here. The Fibonacci number article uses the notation F(n), but my impression is that F_n is far more common in other works (both versions are used more or less randomly around Wikipedia). Which one should it be? Consistency would be desirable. Fredrik | talk 18:56, 28 August 2005 (UTC)

I think I prefer F_n, both PlanetMAth and MathWorld use that notation. And Fibonacci number uses both! I would vote to change it to F_n everywhere for consistency. Paul August ☎ 20:15, August 28, 2005 (UTC)

Agree with F_n as the preferred notation. Oleg Alexandrov 20:46, 28 August 2005 (UTC)

I agree too. I think subscripts are preferred when you have them available. some literature uses f instead of F. Bubba73 22:54, August 28, 2005 (UTC)

Both notations are common and should be defined. F(n) notation is better for complex expressions such as F(n-3) or worse I think. For simple expressions I prefer F_n though.--MarSch 16:01, 30 August 2005 (UTC)

Game theory wikiproject

Hello all - In the interest of standardizing and growing wikipedia's coverage of game theory, I have started a WikiProject on game theory. We could use some mathematicians help over there. (For instance, we could use an article on the Kakutani fixed point theorem which is used in the proof of the existence of Nash equilibria.) I hope that some folks will come join in! --best, kevin ···Kzollman | Talk··· 02:22, August 30, 2005 (UTC)

featured math articles template

I've templatized the math FAs, although thanks to Paul it doesn't add much :) Any ideas about this? --MarSch 15:41, 30 August 2005 (UTC)

I have objected on Wikipedia talk:Featured articles. --RobertG ♬ talk 15:41, 30 August 2005 (UTC)

I doubt how much use a template is. Oleg Alexandrov 15:59, 30 August 2005 (UTC)

At the time I created the FA section on our project page, I thought about suggesting this at the FA talk page, and decided not to, since I thought it would be easy enough to maintain our list separately (at least for the foreseeable future). I also figured (correctly as it turns out) Raul wouldn't much like it ;-) Paul August ☎ 19:54, August 30, 2005 (UTC)

Math equations to plain english

There is an interesting thread at Wikipedia:Village pump (proposals)#Math equations to plain english. Oleg Alexandrov 19:02, 30 August 2005 (UTC)

Map between AMS math articles classfication and Wikipedia categories

Based on the feedback above, I created a table listing how Wikipedia categories are in correspondence with the AMS Mathematics Subject Classification. Again, this is needed for automatic categorization of articles imported from PlanetMath but would be a curious thing to look at in general. See link at User:Mathbot/Wikipedia categories and AMS MSC classification. Any feedback welcome. Oleg Alexandrov 23:22, 30 August 2005 (UTC)

Are you not aware of areas of mathematics? My only complaint is that it links to articles, when I think it should link to categories. The other complain is a lack of the next level of detail: at one point, I attempted to also add a list of categories corresponding to subcats of MSC 11, but was rebuffed. linas 04:12, 1 September 2005 (UTC)

I am aware of that list, and it was very helpful in compiling my list of categories. No, I would not think that page should link to categories — linking to the article is more informative, and from there the link to category is one click away. But maybe a wider discussion is needed on this. Oleg Alexandrov 04:56, 1 September 2005 (UTC)

Rewrite of Boolean algebra, or new article?

There is a discussion going at Talk:Boolean algebra about rewriting it, or perhaps writing a new article. Several people think the article is too technical and difficult to understand, and User:Plugwash (who says he doesn't understand the current article at all) has made an attempt at rewriting it & mdash; that has been reverted (by me!). Please join in the discussion ;-) Paul August ☎ 17:12, August 31, 2005 (UTC)

I've concluded that the article for mathematicians (the current one) needs to be separated from the article for non-mathematicians, which I wrote and placed under Boolean logic. It may need to be moved again, though, as I am getting considerable complaints from PhDs over it's placement there. StuRat 19:45, 18 September 2005 (UTC)

the state of "product/sum" articles

It is my personal belief that all of the "product" articles collectively are in a confusing and sorry shape. Some things are misnamed, some articles have no apparent reason for their content organisation, other things aren't clarified enough, etc. At the heart of the matter seems to be a failure to organise, name, and clarify topics by keeping in mind their category theory meaning. This doesn't mean you have to know category theory to understand anything, but category theory does point a clear direction of how things should be organised, and it's not the direction we're going.

There are 4 major ideas going on in all these articles, based on 2 criteria with 2 options each: first, product or coproduct/sum; second, external or internal. That makes

(External) product
Internal product
(External) coproduct/sum
Internal coproduct/sum

A lot of things are named "sum" that are really products, and a few things that are "internal" aren't clearly identified that way (so could be confused with the "default" external case). For example, direct sum of groups is not about the (external) direct sum, or free product, it's actually about the internal weak direct products of groups. Also, in many cases, you can form the product/sum like you do the sum/product, as objects, but it's not a universal object. Similarly, you can take the "abelian" sum of arbitrary groups, but it's not universal. This is sometimes called the "weak direct product" or "restricted direct product". This distinction between what is an object and what actually is universal is missing in many places. You don't have to mention it directly, but it seems it should guide the presentation. Revolver 21:01, 31 August 2005 (UTC)

The universal and unconditional applicability of category theory is a PoV. I believe the definition complained of is Jacobson's, but I will check. Septentrionalis 01:33, 1 September 2005 (UTC)

After looking around some places, the point is taken. There seems to be a conflict in terminology between researchers in pure group theory and others. Even people writing general algebra books (Jacobson is a bit old to guide current usage, it seems to me), the tendency seems to shy away from "direct sum". But a number of people seem to use it, and for those that use it often, I can imagine how the longer name would get old after a while.

Just to put my comment in context, my first immediate reactions upon reading the term "direct sum of groups" were (honestly)

I've never heard of that before.
There shouldn't be such a thing.

But apparently, the term is used fairly commonly among group theorists. I had no idea about this. For the reasons I said above, I think it may seem counterintuitive or contradictory to many people. Perhaps a strong statement expressing that although the term "direct sum" is commonly used when discussing decomposable groups and so on, it should not be confused with the "direct sum" concept of abelian groups, modules, Banach spaces, abelian varities, representations, etc. which most people are more familiar with. Revolver 05:00, 1 September 2005 (UTC)

Besides direct sum of groups (which does indeed sound crazy at first blush), can you wikilink the other articles you are talking about? Its quite an undertaking to make all the various articles more category-like and at the same time point out the various colloquial flavours in each. A uniformity of style would be better achieved by one person combing over all of these articles, which is no small task. linas 05:12, 1 September 2005 (UTC)

One of the used to be direct sum, which was mostly about direct sums of modules, but also had other stuff. The case of groups was cited as a special case of modules, which isn't true, so I changed it to abelian groups, renamed the article direct sum of modules, and added some other remarks. Direct product seems redundant to me, and could probably be used as a disambiguation page, moving most of the material to separate articles for the cases of groups, vector spaces, and topologies. The only thing distinguishing why these are collected together here vs. others which are not is that they are called "direct product", that's why I think a disambig is good. Beyond this, just a clear distinction between internal/external products in some of the cases, comments on alternative terminology (e.g. I had always heard "weak/restricted direct product", etc.), and checking to see that statements made for the finite case really hold for the infinite case (I already corrected one of these at direct sum of groups.) Revolver 16:46, 1 September 2005 (UTC)

I'm not so much interested in "making them more category-like" then I am about making alternative terminology clear and making the non-category vs. category discussions more clear-cut. For example, in the case of a finite collection of abelian groups, the direct sum and direct product are the same as objects, so in the first discussions of what these terms mean (as objects), there's no need to qualify the statement. But, when moving to the category discussion, it should be pointed out that these are not the same thing, even though the objects are the same. The distinction between objects/limits doesn't belong in the primary discussion, but it should belong somewhere. Revolver 16:53, 1 September 2005 (UTC)

Revolver, I think all of what you are saying is eminently sensible. A lot of work though! :-) Dmharvey

Talk 17:29, 1 September 2005 (UTC)

Yes, and being the one who mentioned it, I feel I should try to do something. That's the thing about complaining — it carries responsibility! Revolver 21:52, 2 September 2005 (UTC)

Sep 2005 – Oct 2005

This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

Games and determinacy

There's some fairly good work on WP about determinacy, but it's a bit haphazard. The axiom of determinacy article doesn't explain very clearly what a game or a strategy, or in particular a winning strategy, is. Winning strategy itself tries to be all things to all people. See my remarks in Talk:Axiom of determinacy and Talk:Winning strategy#Organizational questions for some thoughts with no clear conclusions, but I think a good starting place for trying to get the (nonexistent) category into better shape.

A couple of things of which I recently became aware have given me a little more sense of urgency about this. There's a Wikipedia:WikiProject Game theory, and they added winning strategy to it, which may be appropriate if that article should be ceded to the game theorists, and another written for the determinacy theorists (I'm thinking of writing a Game (set theory) article to subsume a whole bunch of these things, and change links from other articles to it). See my remarks in User talk:Kzollman#Game theory wikiproject.

Also there's apparently a category, Category:Combinatorial game theory, which deals with John Horton Conway type games.

I think this needs to be sorted out before it becomes an irretrievable mess. Would anyone be willing to work on a Wikipedia:WikiProject Determinacy?

On further reflection, I think the central article of the Determinacy category should just be called Determinacy. It's a much more general topic than Axiom of determinacy, which currently serves the purpose of a central reference point. You can see an outline at User:Trovatore/Sandbox/Determinacy. --Trovatore 01:45, 2 September 2005 (UTC)

So the article is far from finished, but there's enough there to put it in article space I think, and I've done so. --Trovatore 04:33, 2 September 2005 (UTC)

Axioms of an equation

I like the intent of this new stub, but I think this material really belongs in Elementary algebra. In a sense, the material is already there, but Elementary algebra seems to already assume that the reader is familiar with the semantics of "=". In other words, Elementary algebra is not quite as elementary as it could be. The new article Axioms of an equation appears to be attempting to fill the gap for, say, late primary or early secondary school students, by explaining more explicitly how to work with "=". Dmharvey Talk 02:57, 3 September 2005 (UTC)

We have equals sign and equality (mathematics), and various other pages on equations, no doubt. The Axioms page should really be re-styled as an easy introduction to those topics. Charles Matthews 09:00, 3 September 2005 (UTC)

Any quantity can be added to both sides. Some equations came from physics, and you can not add joules to meters. For algebraic equations, I would rephrase it to something like "validity of equation holds if you add same thing to both sides". Besides what's about adding two equations?(Igny)

Well, getting picky about that, any dimensionless quantity can be added to both sides of an equation in dimensionless form. But in algebra everything is dimensionless anyway. Adding two equations, ie add A = B and C = D to get A + C = B + D, should follow in two steps A + C = B + C and 'substituting equals for equals'. Charles Matthews 19:43, 3 September 2005 (UTC)

You can also raise both sides to a power, apply the logarithm on both sides, take the square root on both sides (be careful with the signs though)... this article isn't very complete, or could just be summed up in one line. --R.Koot 19:47, 3 September 2005 (UTC)

Hehe, which I've just done, but this stuff should really be merged somewhere. --MarSch 10:27, 5 September 2005 (UTC)

This discussion is already archived, but I want to report that I've merged the article into Equation. Melchoir 00:18, 27 November 2005 (UTC)

Length of a stub

Exactly how long should an article be before it stops being considered a stub? I removed [Digamma function]] and earlier (before Linas's major edit) Harmonic number from Category:Mathematics stubs, but I am not currently sure if articles such as Omega constant are still to be considered stubs or not. Scythe33 01:57, 4 September 2005 (UTC)

The criteria for "math-stubbiness" have baffled me for some time. I don't think it should purely be a question of length - I think the question of whether anything more can be said about the subject should be a criterion as well. But this inevitably becomes subjective. For example, I don't think quartic should be classified as a stub, even though it is very short. It defines the word in question and gives links to quartic equation and quartic function - I struggle to see what else could be added to make it non-stubby. But that is just my opinion. Does anyone have any objective criteria for determining stubbiness ? Gandalf61 10:25, September 4, 2005 (UTC)

Opinions differ (as always). I think that stubs are articles for which it is immediately obvious that they are missing something. An article with just a definition is a stub, an article with more than a definition probably not, an article with definition and some discussion on why this concept is important is never a stub. Some examples: Digamma function and Harmonic number were not stubs when Scythe33 removed the message and Omega constant is not a stub either; on the other hand Peetre's inequality, Egon Pearson and Cauchy surface are stubs. I consider Artin reciprocity and cylindrification as boundary cases; if forced to decide, I'd classify only the second as a stub. Of course, there are exceptions: quartic is not a stub because I consider it as a disambiguation page. You can use {{expansion}} for articles which are not stubs but still need expansion; you'd probably also need to specify what needs to be added. This is all just my opinion of course; I just had a discussion with an editor of a very different opinion. See also Wikipedia:Stub#Identifying a stub. And of course, don't start a fight about whether an article is a stub. -- Jitse Niesen (talk) 12:05, 4 September 2005 (UTC)

Category:Mathematics in India

I just discovered this new category as a subcategory in Category:Mathematics. While I have nothing against Indian mathematics, I wonder if it is wise to have such a category. Next thing we know is Category:Mathematics in United States followed by 100-200 more subcategories in Category:Mathematics. What do people think of this? Oleg Alexandrov 23:16, 5 September 2005 (UTC)

So my main objection to this category is this nonsense notion that an article shouldn't be both in a category and in a subcategory of that category. Following that ridiculous guideline, which it should be a high priority to delete ASAP, if an article is placed in Category:Mathematics in India, it ought to be removed from Category:Mathematics, and that would be silly. But the silly thing is the guideline, not the category. --Trovatore 05:32, 6 September 2005 (UTC)

Perhaps it would be better titled "Indian mathematics" instead of "Mathematics in India"; there may be use to put stuff like Vedic stuff in there. Dysprosia 08:46, 6 September 2005 (UTC)

I can imagine having a category for history of mathematics in India for Vedic stuff, and having this as subcategory of Category:History of mathematics. I struggle to see why present-day mathematics in India should be put in a separate category. Oleg's problem can be resolved by collecting Category:Mathematics in India, Category:Mathematics in United States, &c in something like Category:Mathematics by country. By the way, I quite like the guideline Trovatore mentions. -- Jitse Niesen (talk) 12:46, 6 September 2005 (UTC)

It seems to me that, if B is a subcategory of A, you may put an article in B for reasons involving a small piece of the article. If the rest of the article would by itself qualify as category A, then the article should stay in category A, otherwise not.

A slightly different issue is that a reader may be interested in seeing all articles in a category without having to know which subcategory to look in. If I browse Category:Mathematicians it's reasonable to expect to see John von Neumann without having to know that he was Hungarian or American or what century he worked in. --Trovatore 15:10, 6 September 2005 (UTC)Septentrionalis

The reason for the rule is that only 200 articles will be visible in a single category; Septentrionalis

Well, that should be changed. Let's get a feature request in. --Trovatore 22:07, 6 September 2005 (UTC)

Having tried to find things in large cats, I oppose the existence of larger ones. A cat of the thousand great mathematicians would be very slow to load and, by me, almost useless. Septentrionalis 22:23, 6 September 2005 (UTC)

The user interface needs some thought, to be sure. Possibly when a cat comes up very large, there should be some sort of page where the user decides what to do about it (view only subcats, split up by first letter, etc). But the classification question shouldn't be decided primarily by this sort of technical issue, much of which will change as servers get better, more users get broadband, etc. --Trovatore 22:32, 6 September 2005 (UTC)

and there are (thoughout history) a good many mathematicians even of v. Neumann's quality. Therefore Category:mathematicians includes by reference Category:American mathematicians Category:Hungarian mathematicians and Category:Game theorists and v. Neumann should be in all three of them.. Septentrionalis 21:46, 6 September 2005 (UTC)

As I see it, it is a guideline and not a hard rule, thus one may disregard it if one has a good reason. The first case mentioned by Trovatore could be a good reason; I'm less convinced by the second case. -- Jitse Niesen (talk) 22:18, 6 September 2005 (UTC)

Sure, I understand that it's not a hard rule. The problem is that too many editors follow it when they shouldn't. This is the reason, when I created Category:Determinacy, that I didn't make it a subcategory of Category:Set theory, even though it logically should be. I didn't want articles disappearing from the latter category just because they had some relevance to the former. --Trovatore 22:20, 6 September 2005 (UTC)

I asked the creator of this category to comment about it. Oleg Alexandrov 22:29, 6 September 2005 (UTC)

I appreciate that this is a rather odd category. I created it to clear the main menu in Category:India - something which has already been done for the United States and United Kingdom, and should be done for all countries (the problem with clearing most articles from a national category, but leaving a few awkward cases is that it highlights a few minor articles, whereas if any articles are to be left in the main national menus, they should be the most important). I don't mind what you do with this category, so long as you don't put the contents directly into the main India category. CalJW 22:32, 6 September 2005 (UTC)

I see. I would support renaming this to Category:Indian mathematics (per Dysprosia). I will post this on CfD today. Oleg Alexandrov 15:14, 7 September 2005 (UTC)

I posted this for deletion or renaming at Wikipedia:Categories for_deletion/Log/2005_September 7#Category:Mathematics in_India. I myself voted to delete it as I don't see any special need for such a category. Oleg Alexandrov 19:26, 7 September 2005 (UTC)

Table of Lie algebras & groups

I am vaguely thinking of starting an insane and hopeless task, and that is to create a page listing low-dimensional, non-supersymmetric Lie groups and algebras, thier properties, isomorphisms, topologies, etc. I despair, because this seems like a collossal project trying to describe a hopelessly tangled web of inter-relationships. I was irked because what I really wanted was a list of (examples of) infranil manifolds. Any suggestions on how to minimize the pain and maximize the gain? linas 15:19, 6 September 2005 (UTC)

There is a start to this project at the list of simple Lie groups; this still needs some work in filling in the properties of these groups. This will not help much if you want to know about nilpotent groups. R.e.b. 20:31, 6 September 2005 (UTC)

There is also table of Lie groups which I somehow blindly didn't see at first. linas 04:37, 7 September 2005 (UTC)

10000 math articles

The drinks are on me!

According to Wikipedia:WikiProject Mathematics/Current activity there are now 10029 mathematics articles and mathematician biographies. Now, around 500 of them are redirects, a bunch are arguably more physics or related than math, and a rather good chunck are stubs. Still, this is something of a milestone.

This also makes me think (again) that with so many articles, there is just not enough manpower to even check articles for vandalism and style, not to talk about the mathematical correctness and if articles are coherent rather than just a bunch of text put together by different contributors.

This is probably a good moment to think of where we are, and wonder what the future will hold. Oleg Alexandrov 22:59, 6 September 2005 (UTC)

Well, so far the pessimists have been wrong - badly wrong - about WP in general. It's bigger, and it's better, and articles are generally longer and better written. And more people come to look, and some stay to help. About the only thing that gets worse is the proliferation of tags (including unresolved clean-up). Charles Matthews 16:23, 8 September 2005 (UTC)

I think we should raise a glass in celebration. Paul August ☎ 16:54, September 8, 2005 (UTC)

Indeed! An excellent idea! A bit of celebration is in order. Cheers! linas 23:45, 9 September 2005 (UTC)

I am glad to see that Wikipedia is exceeding my previous expectations. When it came to joining this project, the choice was between here and Planetmath. I chose to work here, primarily for the reason of having all of the information in one place, instead of scattered across multiple sites with conflicting standards. What if there were separate sites "PlanetLinguistics", "PlanetZoology", "PlanetBotany", etc? I personally cannot tolerate this kind of fragmentation. I hope that people on Planetmath begin to feel the same way, and move their work over to this site to avoid duplication of effort. By the way, maybe with 10,000 articles we now have the leverage to ask for some tools to create commutative diagrams on Wikipedia (again: I mean the kind you can edit along with the rest of the article, not just uploading images). Wishful thinking ;-) - Gauge 21:32, 9 September 2005 (UTC)

What did the non-abelian dalek say? Charles Matthews 21:42, 9 September 2005 (UTC)

(Umm, did Charles have a little bit too much to drink?) linas 23:45, 9 September 2005 (UTC)

What did the non-Abelian Dalek say? linas 23:47, 9 September 2005 (UTC)

He says: "DOES - NOT - COMMUTE … DOES - NOT - COMMUTE" Paul August ☎ 00:00, September 10, 2005 (UTC)

Have we sunk so low? (And shouldn't that be K9? Daleks are organic.)

Q: What is purple and commutes?
A: An abelian grape.
(As told by non-mathematician) Q: What is purple and travels to work?

Hey, I didn't start this! Cheers indeed! --KSmrq^T 23:57, 13 September 2005 (UTC)

Gauge, are you aware of our PlanetMath Exchange project? Paul August ☎ 23:17, September 9, 2005 (UTC)

I am aware of the PlanetMath Exchange. You can guess in which direction I prefer to port articles. Btw: What do you call a commutative semigroup?

A: A carpool. :-) - Gauge 02:14, 14 September 2005 (UTC)

If you start copying articles from Wikipedia to PlanetMath, you will get a commutative diagram. Oleg Alexandrov 02:26, 14 September 2005 (UTC)

That reminds me I forgot to comment on Gauge's idea of a commutative diagram tool. I've yet to contribute in any significant way to the category theory articles, (ostensibly one of my areas of expertise) because I can't work up the gumption to create those diagrams by hand. I would really love such a tool. Paul August ☎ 03:20, 14 September 2005 (UTC)

What happens when you get kidnapped by the mathematical mafia? Dmharvey

Talk 02:24, 14 September 2005 (UTC)

I give up. What does happen? Paul August ☎ 15:44, 14 September 2005 (UTC)

They make you an offer you can't understand. Dmharvey

Talk 22:37, 18 September 2005 (UTC)

Why are fields immoral? --Trovatore 23:05, 18 September 2005 (UTC)

lemma moved to lemma (mathematics)

The article lemma was moved to lemma (mathematics), with the former being made into a disamibig. I disagree with the move, as the absolute majority of pages linking there are about the mathematical term. And even if one agrees with the move, one needs to disambiguate the links, and having them point to the correct destination. I asked the person who did the move to comment here. Other opinions welcome. Oleg Alexandrov 21:58, 8 September 2005 (UTC)

It should be moved back. This should be a case of "primary disabiguation". The primary meaning is the mathematical one. Paul August ☎ 00:26, September 9, 2005 (UTC)

I agree - the mathematical meaning is likely to remain primary. Charles Matthews 07:08, 9 September 2005 (UTC)

I think we should maybe tread a little lightly. It's true that a large majority of the links are mathematical, but that could reflect the vigor of the mathematics project, our 10k articles and all that. If it's an important term for linguists, maybe they should get equal time in the dab page. (Like Alice, I only said "if"--I don't know enough linguistics to know how important a term it is.) --Trovatore 03:16, 9 September 2005 (UTC)

And the OED has another set of definitions entirely: ranging for "motto" to "basic definition" in lexicography. Go comment on that talk page, but we should not be rash. Septentrionalis 03:46, 9 September 2005 (UTC)

As the editor who moved the article, my main concern was to fix the lemma page that looked like this at the time. So the main purpose was to create a disambig page. I decided to move the page because (as others here have already pointed out) experts in other disciplines link to lemma with the same confidence that they know what it means. If that article is a {{disamig}} page, that will be noticed and fixed by Wikipedia:Disambiguation pages with links (because internal links should not go to dab pages). — That said, I anticipated that some might not agree with the move I made, so I created direct links to lemma (linguistics), but didn't fix articles to point to lemma (mathematics). In other words, it's easily undone if you don't like it, but please bear in mind that the WikiProject Mathematics may be a tad biased, and it's going to be more expensive to fix if you wait until the other disciplines realize that they've been had :-). Algae 06:27, 9 September 2005 (UTC)

I think it is probably better this way. --MarSch 11:12, 9 September 2005 (UTC)

The best solution is to have the mathematical sense as the main article, and use a disambiguation on that page (ie. See Lemma (disambiguation) for other uses). The mathematical sense is far more commonly used than the linguistics sense. Dysprosia 11:45, 9 September 2005 (UTC)

Dysprosia's solution is in line with the official policy: Wikipedia:Disambiguation#Page naming. Oleg Alexandrov 15:22, 9 September 2005 (UTC)

Well, that's assuming that the mathematical meaning really is the primary one. Is it? It's certainly my primary meaning, but then I'm a mathematician. I think we should hear from some linguists about how much they really use the term. --Trovatore 16:01, 9 September 2005 (UTC)

By the way, I suggest that this discussion (that is, all the above text) be moved to, and continued at, Talk:Lemma. That's a better place for people to find it in the future, and it's "neutral ground" so to speak. --Trovatore 16:41, 9 September 2005 (UTC)

Copied to Talk:Lemma

This discussion should follow.Septentrionalis 17:24, 9 September 2005 (UTC)

Connected, connectivity, etc.

For several months, I have been doing occasional clean-up work on the pages related to connectedness, connectivity, etc. Things are still a little messy, but I am not sure what to do about some issues. In particular:

The word "connected" has similar meanings in many fields of mathematics. Thus we have connected space, connected graph, and connected category. Do we want to consider "connected" as a mathematical term, independent of what field it is used in? Currently, there is a link to connected from List of mathematical topics (C). I consider this link to be somewhat inappropriate, since connected is a disambig that also points to nonmathematical usages. Should there be a page called "Connected (mathematics)"?
"Connectivity" is a slippery word. I have heard a number of mathematicians use it as a synonym for "connectedness". In graph theory, of course, it has a very precise meaning; thus, we have connectivity (graph theory). In some semi-mathematical fields, like cellular automata, image processing, and robotics, it seems to be used in the sense of how cells arranged in a grid are considered to be adjacent to each other. Thus, automata researchers might speak of "4 connectivity" (I guess). The word is used in the article Image processing, and I think this is what it means there, but I am not sure. In any case, there is no good place for that link to go; currently, it goes to connected. What should we do about this? Should there be a page about this meaning of the word, and if so, what should it be called? Maybe "Connectivity (grid)"? Is there a better word than "grid"? I have heard of "lattice connectivity". Is this the same thing?

— Nowhither 00:01, 9 September 2005 (UTC)

In image processing on a square grid, a pixel is connected North, South, East, West (4-connected) to its neighbors. Many algorithms, such as flood fill (propagating a color to neighbors), offer the optional inclusion of the diagonal neighbors NE, SE, SW, NW (8-connected). --KSmrq^T 03:38, 2005 September 9 (UTC)

Connectedness should be developed, since we prefer nouns. Connectivity can imply things about the topology. Charles Matthews 07:11, 9 September 2005 (UTC)

Good point about "connectedness". On the other hand, I think there is still a need for the connected page to be a general disambiguation, since there are pages that would not fit well with "connectedness", for example, Connected (album).

So, how about this scheme:

Connectedness will be an article, pitched at a relatively non-technical audience, giving an overview of mathematical uses of the word. It will refer to the more technical articles connected space, connected sum, connected graph, and connected category. At the top will be an italic note pointing at connected for non-mathematical usage.

Connected will stay much as it is now: a general (mathematical & non-mathematical) diambig. It will include links to connected space, connected graph, etc., just as it does now, and it will also link to connectedness.

Connectivity is still a sticky issue. User:Kku has just made it a disambig, with the former content at connectivity (computer science). I agree that this is an improvement, but I am not sure if it is optimal.

I still think there needs to be an article about the definition of connectivity as it is used in image processing, cellular automata (?), and possibly robotics, parallel computing, etc. But I still do not know what to call it, or which of these fields use the same definition.

— Nowhither 00:30, 10 September 2005 (UTC)

News flash: I wrote the connectedness article. See New "connectedness" article, below. — Nowhither 03:13, 12 September 2005 (UTC)

Omega?

Do we have a specific math article on Omega? The specific one that states that mathematics can't be strung together and that discoveries are just luck? It also states that its goal is to try and find the halting possibility of a computer when faced with an infinite answer.

Omega doesn't "say" that; it's just a number. But Wikipedia does have an article on it: Chaitin's constant. — Nowhither 00:11, 10 September 2005 (UTC)

Math in the dock

See Wikipedia:Village_pump (miscellaneous)#Riemann_zeta_function. Oleg Alexandrov 03:56, 11 September 2005 (UTC)

At analytic continuation, some decent diagrams would help. For example of overlapping circles, showing how analytic continuation by re-expanding a power series can gain a fingernail-shaped area of definition. Charles Matthews 06:30, 11 September 2005 (UTC)

This kind of discussion gets my goat. It's absolutely ridiculous that people without prior experience in a field read an article about a topic in that field and then complain that it's the article's fault that they don't understand it. I know little to nothing about quantum mechanics or geology for example, but I wouldn't complain if I didn't understand the spin (physics) article or the Quantum Hall effect article. Wikipedia articles are not self-contained instructional works. Sure, an article can try and explain as much as reasonably possible for someone with some assumed knowledge, but the important fact remains that Wikipedia is a reference work and not an instructional work (compare Wikibooks). This is doubly inappropriate for mathematics works, where the very nature of the topic depends on having assumed knowledge to understand deeper and more complex work. Dysprosia 07:40, 11 September 2005 (UTC)

I'm not exactly fond of the comment or commentator. There aren't many mathematical articles where the exposition is perfect; nor is the coverage anything like complete in 'core' topics (whatever those are). So the chances are that matters can be improved. Charles Matthews 08:26, 11 September 2005 (UTC)

Oh, absolutely, I'm not disagreeing that pages can be improved -- many of the math articles could do with improvement from what I've seen, but it's the sort of "I don't understand the article, so it must be a bad article" attitude that irritates me. Dysprosia 09:00, 11 September 2005 (UTC)

As one of the laypeople who responded to that "survey", I'd like to chip in. Please understand that I mean this as constructive criticism and not as bashing or saying that you guys are going about things in the wrong way -- on the contrary: I'm impressed that we've got such thorough coverage of these topics in the first place.

Of course not every math article is going to be 100% comprehensible to the layperson. On the other hand, it is possible for every math article to make clear to the layperson why its subject is important. Not everyone who reads that article will be a mathematician. A large number will presumably be people who were reading about something else that mentioned the Riemann Zeta Function and want to get at least a basic sense of why the Riemann Zeta Function is such a big deal.

I've got a 4-year college degree, including two years of math: so probably a stronger math background than 90% of Americans -- and I still get lost in the first two sentences of most math articles on Wikipedia. Anyone in this wikiproject knows more math than I, and that's necessary for this project to be possible. On the other hand, it may make it more difficult to see things from the perspective of someone who doesn't already have a firm grasp of the concepts you're discussing.

If a layperson doesn't understand an article, it doesn't mean it's a bad article. It may, however, be an indicator that there are areas of the articel that could still be improved. I think it would be possible to improve the comprehensibility of many of the math and science articles on this encyclopedia. If I knew anything about the subjects, I'd work on it myself -- as it is, I'd be happy to give any assistance I can to anyone in this wikiproject who is interested in attempting to do so. -- Avocado 14:54, September 11, 2005 (UTC)

I think both Charles, Avocado, and Dysprosia have very good points. A great many math articles are written for an audience which knows at least as much as the person writing the article. In many cases there is no motivation, no intuitive explanation, no gradual development from easy to complex, no pictures, no examples, and the list can go on. If one would teach in college with the same attitude, one would get quickly fired (well, ideally :)

However, there is only that far one can go in making a topic acessible. For example consider the meromorphic function article, which now has a {{technical}} template slapped upon. If you know anything about the complex plane and about functions, you should understand from the examples and the picture that a meromorphic function is roughly a fraction of two functions, with the denominator going bad every now and then. However, if you say that you don't understand the statement:

In complex analysis, a meromorphic function on an open subset D of the complex plane is a function that is holomorphic on all D except a set of isolated points, which are poles for the function.

then that's your fault. You cannot possibly understand meromorphic functions unless you know what holomorphic functions and poles are. Oleg Alexandrov 17:30, 11 September 2005 (UTC)

"A meromorphic function is roughly a fraction of two functions, with the denominator going bad every now and then."

I understand that that phrase is probably an oversimplification and not 100% accurate, but it makes it a million times more clear to me what a meromorphic function is, even without my knowing much of anything about the complex plane. A few more plain-english explanations might be helpful. I don't need to understand meromorphic functions any more than I need to understand the internal workings of my cellphone's AC adapter, but having an idea of what they are or what makes them interesting is possible. -- Avocado 17:54, September 11, 2005 (UTC)

suggestion

Please note that there are now 10,000 math articles on WP (making it as large as Wolfram's mathworld, it seems), and that maybe 80% of these articles require at least a math major, and many require considerable post-graduate studies. Its impossible to make these 80% understandable to non-mathematicians; even math professors trained in one field might not understand articles written in another field. So what can we do?

I suggest a new category, Category:Overview of mathematics, that would contain articles from any branch of math, but with the requirement that these articles be comprehensible (and enjoyable) by anyone with no more than a year or two of college math education. For example, what's knot theory and why would anyone care? How about soap bubbles as minimal surfaces? Of course chaos belongs there, as does gravity, and something along the lines of Riemann zeta revealed. Furthermore, these articles could be written as "educational trampolines", starting at the most basic level, e.g. torus, and rocketing the reader into very advanced topics (the torus opens the door to things like Albanese variety) if the reader is diligent enough. In some sense, Category:Overview of mathematics would be the math version of "featured articles", with the bar set maybe only a little bit lower. linas 17:39, 11 September 2005 (UTC)

(Corollary: "too technical" labels will be unceremoniously stripped from articles that are not in Category:Overview of mathematics, e.g. the meromorphic function article.) linas 17:48, 11 September 2005 (UTC)

It sounds good to me. I do think we should be careful that this solution not become a way to remove all pressures to add intuition and motivation, though. In my own case, I know that my Prewellordering article is guilty of the offenses Oleg mentions, particularly the Prewellordering property section.

The other side of that is that it is better to have something than nothing, I think. Prewellordering needs to be motivated, but for me at the moment finishing the Determinacy article is a higher priority, and I do have non-Wikipedia tasks as well. In the mean time I think it is better that there be an unmotivated article on the prewellordering property than none at all. --Trovatore 18:00, 11 September 2005 (UTC)

In theory it would be possible for a high school student to learn linear algebra from the articles on wikipedia, in practice this wouldn;t work, because s/he wouldn't know were to start and in what order to read the articles. So we could create an article called learning linear algebra. On the articles we could slap some prerequisites such as linear algebra and comples analysis which link to those articles. (Unsigned comment by User:R.Koot 18:02, 11 September 2005)

No. Wikipedia is a reference work, not an educational one. Learning mathematics from an encyclopedia would be extremely difficult, because the encyclopedia material is not geared for learning, it is geared to be a reference work. Wikibooks is for educational material. Dysprosia 23:20, 11 September 2005 (UTC)

I can find nothing above with which I disagree ;-) Per Euclid, There is no royal road. But we need to keep trying to make the road as short and smooth as possible. Paul August ☎ 18:53, September 11, 2005 (UTC)

Having math overview articles aimed somewhat lower than the normal math articles is a good idea. My suggested "connectedness" article (see "Connected, connectivity, etc." above) could be one of these. However, I must agree with Dysprosia, that educational works belong in Wikibooks. In fact, the linear algebra tutorial suggested by R.Koot has already been started there; see wikibooks:Linear algebra. — Nowhither 00:31, 12 September 2005 (UTC)

I may as well throw in my 2 cents: I have been developing an idea that certain topics in mathematics have a certain intrinsic minimum complexity which cannot be reduced in any exposition. In this sense, one can either present the material as simply as possible while retaining accurate content, or lose accuracy for the sake of readability. I agree with Linas that the current Riemann zeta function article may in fact be too simple rather than not simple enough; an accurate description of the zeta function and its properties is complicated business, no matter how you present it. I tend to write articles as reference works aimed at graduate students and researchers. I recommend (to those who are interested) the creation of an article Riemann zeta function (overview) or something similar for those who want a less technical exposition. There is certainly room for both perspectives (research-oriented and pedagogical).

Also some nitpicks that I have with the current article:

The Easier proof for the layperson section really belongs in another article if we are to make this article the more technical one. The technical proof is shorter and more elegant.
The "Importance of the zeros" section needs elaboration and appears in an odd place (before "basic properties"?). It should be moved further down into the article.
I wonder if the physics applications of the Riemann zeta should have its own separate article? I have a feeling that there are enough applications just in physics to warrant such an article...
If this article does become the more technical one, we should place a warning at the top pointing readers to the "easier" version as well.

- Gauge 02:34, 12 September 2005 (UTC)

So what's the plan?

I like Linas' suggestion at least in principle (with the caveat that it not become an excuse to avoid adding motivation to articles). I'd suggest further that there be a uniform naming scheme for the simpler articles, say Foo (introduction) or Foo (elementary) for the beginners' version of Foo. But it does seem like something of an "unfunded mandate"; I'm not personally volunteering to produce these articles for the hundreds if not thousands of topics that'd need them. Any further thoughts? I hate to see the matter just dropped, without a clear decision. --Trovatore 20:13, 13 September 2005 (UTC)

One more idea

As a less radical measure, how about updating just the introductions of some of the math articles to be more accessible. For instance, something to the effect of:

The Riemann Zeta Function is a mathematical function discovered by Whatever-his-first-name-is Riemann in 1822. It is important in number theory because it demonstrates some property of prime numbers, as was proven in 1903 by whoever.

< template of some sort >

What follows is a technical discussion of the properties of the Riemann Zeta Function. This discussion assumes familiarity with meromorphic functions, the Euler Product Formula, basic forcing, and whatever else.

< / end template >

-- Avocado 21:29, 13 September 2005 (UTC)

It's all a question of perspective

From the back-jacket information for Itay Neeman's book on The Determinacy of Long Games, which I will likely cite:

The book is largely self-contained. Only graduate level knowledge of modern techniques in large cardinals and basic forcing is assumed.

--Trovatore 18:41, 11 September 2005 (UTC)

That's a good one! Only very basic forcing is assumed, right? As far as I am concerned it means that I will have no clue whatsoever about the very first section in the book. :) Oleg Alexandrov 23:04, 11 September 2005 (UTC)

That's cute. FWIW, I know a Ph.D. student who did his dissertation on forcing. Apparently the first question at his defence was, "So, what's 'forcing'?" He said he immediately knew he was going to pass. — Nowhither 03:00, 12 September 2005 (UTC)

New "connectedness" article

As suggested above in a couple of places, I have written a new article: connectedness. This is supposed to be an overview of mathematical uses of the term (and similar words), written at a somewhat lower level than most mathematical articles. I would be interested in hearing what people think about:

Is this a good article to have?
Is it written at a low/high enough level?
Should there be other similar articles?

By the way, I also put a note linking to the new article in connected, which is a general (non-mathematical) disambig. And I removed "connected" from the List of mathematical topics (C) and replaced it with "connectedness". And ... I'm still wondering what to do with connectivity.

— Nowhither 03:12, 12 September 2005 (UTC)

Looks useful to me; but, like most readers at this page, I cannot tell what it would look like to a non-mathematician. You should take this question to the Village Pump, or, despite the fact you actually want cmments, WP:RfC

Was Bertrand Russell Welsh?

And, speaking of RfC, one of the topics there is:

Was Bertrand Russell Welsh and does he belong in Welsh Wikipedia:categories? (He was born in Monmouthshire, and lived there until his parents died - when he was four.)

I'm not making this up; if anyone has an opinion on the matter (I did) do go share it with Talk:Bertrand Russell; maybe we can drown out the various contending nationalisms. Septentrionalis 22:46, 12 September 2005 (UTC)

How important is a list of publications?

Currently, List of publications in mathematics has at the bottom 31 mathematics categories. Some explanation for that is here. The whole thing seeems to be an effort by APH as part of Wikipedia:WikiProject Science pearls. I truly doubt that there is any article under the wiki Sun so important as to be included in that many categories. Oleg Alexandrov 06:24, 13 September 2005 (UTC)

I agree; this is an inherently PoV effort to make a list do the work of a category. Unmaintainable, controversial, naturally incomplete - and if completed, useless. AfD? Septentrionalis 03:28, 14 September 2005 (UTC)

AfD, seems a bit drastic. I don't think I could support that. Lists have several well discussed advantages over categories, for example they can be annotated, as this one is. (By the way just out of curiosity, a show of hands, how many people know that VfD has been renamed?) Paul August ☎ 04:49, 14 September 2005 (UTC)

I don't want that artilcle deleted either, just put in two to three relevant categories and link to it from other places. Oleg Alexandrov 04:56, 14 September 2005 (UTC)

I know what you are implying when mentioning AfD. I agree with renaming the VfD but I think the decision was taken very fast and without public consultation. Uncle G, can you clarify us in here? (Uncle G's bot did the move.) Oleg Alexandrov 04:56, 14 September 2005 (UTC)

I sort of agree with Paul the list could be valuable. Right now IMO it's overly weighted to publications of historical importance; what's really more needed is a bibliography of reference works and textbooks. Maybe with BibTeX entries too? That'd be great.

On the other hand the book reviews that make up much of the content could be problematic. I just wrote one today for Kunen's set theory book, but it occurs to me that a book review is almost on its face original research, or at least original journalism. Still, WP has lots of 'em. --Trovatore 04:58, 14 September 2005 (UTC)

I'd like to respond to the ideas above. First, I'd like to point out that I also think that the use of a list is problematic. I see it as an initial phase before creating an article for every publication and connecting them using categories (See more details at the project description). Note that in the next phase the problem that bothers Oleg will be solved too. An article about logic won't be in the topology category. The description of the publication shouldn't be an original research. Most of the times, something quite similar to the publication abstract will do. BibTeX entries is a great idea. APH 05:37, 14 September 2005 (UTC)

Isn't there a larger issue here? What we have on List of publications in mathematics, especially near the bottom, is a list of papers. But mathematical research papers are being published at a rate of something like 100 per day (rough estimate — and that's only the ones that make it into Math Reviews). It is ridiculous to expect to sort through these and point out those that ought to be listed, whether in a big list, as separate articles in a category, or whatever. The problem with this page is not misuse of categories, or anything like that, but that it is aimed at an impossible task, the magnitude of which boggles the mind. The page very badly needs a more focused purpose. — Nowhither 01:16, 16 September 2005 (UTC)

Science pearls

Hello, Please notice this project. I hope that the List of publications in mathematics, List of publications in statistics and List of publications in computer science will be adopted by the mathematics project. Thanks,APH 06:48, 13 September 2005 (UTC)

Converse

It seems to me that the article on logical converse is incomplete. It has the schoolbook definition of the converse, which is that the converse of a statement of the form (A → B) is the statement (B → A). But I think that "converse", as the term is used by mathematicians, is actually a more subtle and complex concept. I've put some simple examples at Talk:Converse (logic).

I think that if we actually look at examples, we'll find all sorts of different forms that the converse can take, and that this information should be incorporated into the Converse article.

I hope people will assist me in this. -- Dominus 13:32, 14 September 2005 (UTC)

Boolean algebra, redux

Once again someone has been trying to rewrite the Boolean algebra article based on the preconception that it's about the logical calculus sometimes called "Boolean algebra". I'm afraid I got into a mini-editwar with him; he got tired of it and went to write his own article called Boolean algebra (basic concepts). I think he wants to rename Boolean algebra to Boolean algebra (complex theory).

I think there should be two articles, but I see dark clouds on the horizon with this editor. He doesn't show any signs of wanting to believe me that a Boolean algebra is something like a group or ring, rather than a "complex" version of what he thinks of as "Boolean algebra" as a mass noun. I'm worried that he'll try to incorporate material about the algebraic-structure notion into his "basic" article, which will only confuse the issue. I could use some help here, guys.... --Trovatore 21:26, 14 September 2005 (UTC)

At the risk of being contrary, the first sentence of Boolean algebra suggests to me that it would rather be in an article called Boolean algebras.Hv

Well, see, here you run into a Wikipedia convention. All such articles have singular titles. There's an article called orthogonal polynomials, but that's only because there's no such thing as an "orthogonal polynomial" in isolation. --Trovatore 23:51, 14 September 2005 (UTC)

Certainly the current link to Binary numeral system is a poor substitute for an article that would talk about the (singular) Boolean algebra that high school mathematicians and computer scientists have to deal with. Hv 23:47, 14 September 2005 (UTC)

Yes, that's true; that article needs to be written. If we could only agree on what it should be called.... --Trovatore 23:51, 14 September 2005 (UTC)

My five cents (yeah there's been some inflation): if we have a decent article on Boolean algebra as envisaged by StuRat et al (i.e. currently named "basic concepts"), then that should get primary status as Boolean algebra, simply because it's the one more likely to be searched for by a general audience; and there should be a dab notice on that pointing to something like Boolean algebra (algebraic structure). Dmharvey Talk 23:57, 14 September 2005 (UTC)

Hm, wouldn't be the solution if I were God. But if it keeps this problem from recurring I s'pose I can live with it. Still leaves open the question of what should really go in the article, though. How is it different from propositional calculus? Just by adding Boolean search terms & such? --Trovatore 01:07, 15 September 2005 (UTC)

I think the solution is to merge Boolean algebra (basic concepts) into Boolean logic; the latter is not very good, and is just shy of being a stub. Septentrionalis 14:48, 15 September 2005 (UTC)

I don't think that's a natural fit. Boolean logic is about a correction to Aristotelean logic, which was overly complicated because it didn't allow propositions to be vacuously true. So it doesn't really make sense to talk about Boolean logic except when you also talk about Aristotelean logic, and we have no need to to that for this subject. --Trovatore 15:00, 15 September 2005 (UTC)

I think both things are and should be called "Boolean algebra" with at least one being of the form "Boolean algebra ( … )". I suggest that we set aside for the moment which, if either, should simply be called "Boolean algebra". Let's assume for the moment that both articles need parenthetical disambiguation, and try to decide what they should be.

For the 6-tuple one (A, +, ·, ~, 0, 1) should it be:

mathematical structure?
algebraic structure?

I'm not completely happy with this one because I also (perhaps not alltogether correctly) think of this structure as an order theoretic, a set theoretic and a logical structure as well.

structure?
object?

For the the article about, in DmHarvey words, " the art of manipulating truth values and logical connectives", should it be:

methodology?
logic?

Of the two I guess I like this one best.

(By the way this looks like a good online reference for this article.)

Paul August ☎ 22:02, 15 September 2005 (UTC)

Yeah, I also have noticed the problem with "algebraic structure"; e.g. one of the properties of BA's that should be addressed in the article is completeness, which is not definable algebraically. OTOH that's a bit of a nit; it's not as though anyone would object to addressing completeness in an article called "Boolean algebra (algebraic structure)". I agree "logic" is better than "methodology" for the other concept but I'm not entirely happy with it. --Trovatore 23:13, 15 September 2005 (UTC)

How about cutting the Gordian knot (for the first concept) with Boolean algebra (structure)? --Trovatore 18:58, 18 September 2005 (UTC)

Wow this is hard. I don't like Boolean algebra (structure) because "structure" is too vague -- it sounds like it means "structural aspects of Boolean algebra", like Economy of China (structure). I liked one of the earlier suggestions: Boolean algebras, although this might be against WP naming conventions (???). Perhaps Boolean algebra (mathematical entity) or Boolean algebra (set with operations)? Arrgggh. Dmharvey

Talk 19:48, 18 September 2005 (UTC)

The situation's not that bad--we don't have to go suggesting spiritual emanations, which is what "entity" makes me think of. I'm ok with either "mathematical structure" or "algebraic structure". I just thought maybe it could be made less wordy and more inclusive by dropping the adjective. --Trovatore 19:57, 18 September 2005 (UTC)

I like the "Boolean algebras" name. In cases where the singular has come to mean one thing and the plural something entirely different (maybe "datum" and "data" or "Earth" and "earths" would be good examples), I think it should be permissable to use a plural name. StuRat 20:00, 18 September 2005 (UTC)

I see that one of Paul's suggestions I overlooked was Boolean algebra (object). That's not bad, though I think I still prefer "mathematical structure". I don't like the plural because it (1) suggests that these things are somehow "alternative versions of Boolean algebra" and (2) is not in line with the naming given to other structures, like Group (mathematics). --Trovatore 20:07, 18 September 2005 (UTC)

If we are to use strictly singular, shouldn't that have been Group (mathematic) ? StuRat 20:31, 18 September 2005 (UTC)

Perhaps Boolean algebra (mathematical object)?. Dmharvey

Talk 22:36, 18 September 2005 (UTC)

I could live with that. I prefer "mathematical structure", though. --Trovatore 23:13, 18 September 2005 (UTC)

Yep, "mathematical structure" works for me too. Dmharvey

Talk 23:22, 18 September 2005 (UTC)

Indicial calculus

Indicial Calculus claims that it is "the calculus used to extract root indices of order x, where x is an element of a Galois splitting field for a given polynomial equation $P$ of ductivity $D [P,0] = 0$ ." Does this ring a bell to somebody? The reference to "Little Bride Bonnie (1859-1941), a German mathematician known for early work in group theory" made me suspicious, and a quick search on MathSciNet and Google didn't yield any results. -- Jitse Niesen (talk) 21:18, 15 September 2005 (UTC)

The intro, as phrased, is nonsense: whatever a root index is, its order shoulc be an ordinal, not an element of a Galois field. Constructing a cube of side e (next paragraph) is trivially equivalent to constructing a segment of length e. I've never heard of ductivity, either. Septentrionalis 01:21, 16 September 2005 (UTC)

A mathematician Little Bride Bonnie is mentioned there. From what I know, Bonnie is a girl's name. Equivalently then, the name of this German mathematician is Little Bride Mary if you wish. BJAODN. Oleg Alexandrov 02:06, 16 September 2005 (UTC)

No paper by Hinkle is in Jahrbuch über der Fortschritte der Mathematik for 1899-1901. Hoax. AfD, IMO. Septentrionalis 05:00, 16 September 2005 (UTC)

Bonnie (also spelled bonny) means pretty, as in "my bonnie lass" and brides are often referred to as bonnie (search Google for "bonnie bride" or "bonny bride"). Paul August ☎ 05:47, 16 September 2005 (UTC)

I did some digging and posted my impressions on the talk page. Especially, the index calculus algorithm is frequently cited in cryptography. Given the existence of that page, even if Indicial Calculus is meant to be legitimate its page should not exist. --KSmrq^T 11:49, 16 September 2005 (UTC)

I decided to replace the article by a redirect to cyclic group, which is where index calculus also redirects to (KSmrq found this out, thanks). Saves a trip to AfD. -- Jitse Niesen (talk) 14:39, 16 September 2005 (UTC)

List of mathworld's math articles

See discussion at Wikipedia talk:Requested articles/mathematics#MathWorld?. Comments welcome. Oleg Alexandrov 03:20, 16 September 2005 (UTC)

Is a high school math teacher who got a prize for undergraduate paper notable enough?

... We will find out. Wikipedia:Articles for deletion/Mark Schmitt. Oleg Alexandrov 02:01, 17 September 2005 (UTC)

Note for Lie algebra specialists

Anybody heard of the "corank" of a Lie algebra? An anon replaced "rank" with "corank" at Affine Lie algebra, and I don't know if that's correct or not. Oleg Alexandrov 16:06, 18 September 2005 (UTC)

I'm watching that one, I think that's rigt, that's what makes it affine. But not sure; I was going to read on the topic (quantum groups) this summer, but got distracted. Maybe next summer. Its a pretty advanced topic, mostly just string theorists live there. linas 04:41, 20 September 2005 (UTC)

The "corank" here refers to the generalized Cartan matrix, the dimension of its null space. However, neither choice seems to agree with the definition already in place at the end of the Kac-Moody algebra page. The symmetric factor of the matrix is there required to be positive semidefinite, which does not place such a stringent restriction on either rank or corank. Even knowing almost nothing about the topics it appears that something is amiss. If someone wants to dig further, a standard reference book seems to be Victor G. Kac's Infinite-Dimensional Lie Algebras, 3/e, CUP 1990, ISBN 0521372151 (paperback: ISBN 0521466938). Or ask your friendly neighborhood string theorist. --KSmrq^T 06:53, 20 September 2005 (UTC)

Check those links

Just a reminder that when you've guessed the name of an article you're linking to, and it comes up blue and you save your edit, it's worth clicking through to those links and seeing if they say something sensible and relevant to the meaning you have in mind.

I happened across a page called complete Boolean algebra that had some trivial nonsense in it, nothing to do with CBAs, yet it was linked to from complete lattice.

Another possibility is that the link from "complete lattice" was originally red, and then someone came along and filled in the incorrect "complete Boolean algebra" page. To protect against this sort of thing, click through to your redlinks and add them to your watchlist (yes, this works). --Trovatore 17:32, 19 September 2005 (UTC)

One can also check Wikipedia:WikiProject Mathematics/Current activity for incoming stuff. Oleg Alexandrov 04:35, 20 September 2005 (UTC)

What is an Isometry?

Our articles Isometry and Metric space have different definitions of isometry. The former requires an isometry to be onto, the latter does not. There is a discussion at Talk:Metric_space#Isometry, about which is more standard, and what we should do about it. Please share your thoughts there. Thanks Paul August ☎ 16:38, 22 September 2005 (UTC)

Unicode in math articles

The bot User talk:Curpsbot-unicodify has started crawling the math pages and converting html greek characters, such as γ, into glyphs that are hard to work with (although they render the same way). I don't think this is a good idea for math formulas and math expressions, although I support it for the other cases (people/place names, etc.) I'd like to see some sort of majority consensus developed on this, for or against, at User talk:Curpsbot-unicodify. linas 14:56, 24 September 2005 (UTC)

Sorry, I don't see the problem, can you please elaborate?

You aren't forced to enter Unicode characters, you can still use the HTML entities, if you don't have keyboard access to the special characters. And the Curpsbot-converted characters look in the edit field the same as both style of characters look in the article.

Pjacobi 17:53, 24 September 2005 (UTC)

That's a WYSIWAG approach--"what you see is all you get". For mathematics it's better to preserve the meaning of symbols in the source code, not just their appearance. HTML doesn't really do that very well, but it's better than Unicode. --Trovatore 18:04, 24 September 2005 (UTC)

WYSIWYG: Screen readers for the blind, last I checked, handled γ a lot better than unicode. Nahaj 18:16, 24 September 2005 (UTC)

I added a comment to the effect that if we had replaced such strings in the editable code as "γ" by the more accurate "<math>\gamma</math>", then there wouldn't be a problem. -- Arthur Rubin 21:40, 24 September 2005 (UTC)

If screen readers really do have trouble with unicode, then I will oppose conversion to it. - Gauge 00:09, 25 September 2005 (UTC)

As I understand it, it isn't Unicode per say that is the problem... It is a matter of how many characters (of the many thousands) have speakable names listed in the screen reader's tables. Someone should check this... my information is a few years old. Nahaj 01:40, 25 September 2005 (UTC)

The age of my information may be moot. Many handicapped folk are running older software for financial reasons. Nahaj 21:38, 30 September 2005 (UTC)

First of all, the bot has not started systematically crawling the math pages. It only happened to crawl the Wess-Zumino-Witten model article because that was on a list of requested articles sent to me by User:Beland, and he only wanted that article processed because it contained two spaces instead of one in a [[Riemann sphere]] link (the bot also does this, although its main function is Unicode conversion). The bot is mostly concentrating on eastern European pages and such at the moment (for instance, see this edit to Russian grammar).

For the time being, I have edited the bot code to skip any page that contains a <math> tag. It might revisit them later with a flag set to avoid processing Greek letters. In the long run, however, you might be better off to use <math>\gamma</math> instead of γ as Arthur Rubin suggests, because the visual appearance of $γ$ and γ is usually quite different, and if you're arguing that the visual appearance of γ is confusing in the editor window then it's surely equally confusing in the reader window (displayed browser page). Or perhaps even more confusing, since readers are sometimes less sophisticated than editors and the two different-looking gammas might be mistaken for different symbols.

By the way, I presume you folks know that ε φ (ε,φ) are not the same things as \epsilon \phi ( $ε,φ$ or ε,ϕ)? According to the TeX book and Unicode.org respectively, the latter are supposed to be "lunar" epsilon and "unbroken-circle" phi with bar extending above the circle, although the glyphs used in various fonts may render them identically (as seems to be the case under Windows XP, for instance). See [27] and compare U+03B5 vs. U+03F5 and U+03C6 vs. U+03D5. This is another argument against using HTML entities when TeX math symbols are intended. -- Curps 20:21, 25 September 2005 (UTC)

PS, also, ≈ and \asymp refer to entirely unrelated symbols (a naming issue), although the <math> tag doesn't seem to recognize \asymp.

Warning: ϕ (the unicode &#x3d5) does not display, at least on this computer, although all the rest of Curps' post does, including \phi. (Neat trick with the & though.) Also, the <math> epsilon and the unicode epsilon(ε) are not identical; the latter is almost identical to &epsilon. (This is a library machine using Windows, so I can't comment on what else it's doing.) Septentrionalis 01:06, 26 September 2005 (UTC)

Commuting diagrams?

What are the prospects for commuting diagrams in TeX on WP? Most pages that have them seem to have custom-generated PNG's. My attempts to create a native diagram result only in ugliness:

$\begin{matrix} K & \begin{matrix} 1_K \\ \longrightarrow \end{matrix} & K \\ \downarrow^{\eta_A} & \, & \eta_B \downarrow \\ A & \begin{matrix} f \\ \longrightarrow \end{matrix} & B \end{matrix}$

and a triangle:

$\begin{matrix} && K && \\ & \swarrow^{\eta_A} & \, & \eta_B \searrow & \\ A && \begin{matrix} f \\ \longrightarrow \end{matrix} && B \end{matrix}$

The markup is complicated too ... Any better way of doing this? linas 00:01, 26 September 2005 (UTC)

Yes, it would be nice if the powers that be included some diagram package into the wiki math code. I generate PNG's using a program called textogif and just upload them. It is fairly fast and painless once you have it all set up. Check out my page on Wikimedia Commons. I have some minimal set of instructions there. -- Fropuff 16:26, 26 September 2005 (UTC)

I thought one can use xypics to create diagrams. This is a LaTeX package. So, all needed is for the Wiki TeX dialect to support this package. I also wish that Wiki TeX also supported the amsart package, as when we copy articles from PlanetMath as part of the WP:PMEX project, often many TeX symbols are not recognized. Oleg Alexandrov 17:36, 26 September 2005 (UTC)

Merging manifold and manifold/rewrite

The article manifold has been rewritten at manifold/rewrite. Manifold/rewrite has had around 225 edits since June 19 when Jitse started it as a text in his sandbox to offer some constructive suggestions to the arguments at talk:manifold. Now the rewritten article looks nice and needs to be merge into manifold, which itself underwent around 58 edits since June 19. The big question is, how to merge them? One can merge the edit histories, see Wikipedia:How to fix cut and paste moves, but it could be a mess. The only other choice is I think to give up on the history of one of the two articles. What should be the right decision? Let us discuss this at talk:manifold/rewrite. Oleg Alexandrov 04:27, 26 September 2005 (UTC)

Comments requested on new proposed math stub names

See Wikipedia:WikiProject_Stub_sorting/Proposals#More_Math_stubs. Oleg Alexandrov 00:51, 27 September 2005 (UTC)

Controversy over the birthday paradox article

At Talk:Birthday paradox it is being proposed to delete from the article the section on Paul Halmos' view of the matter. That is the only section that takes the reader beyond the stage that any freshman who thinks the problem through would figure out. It's a fairly short section. Three Wikipedian support deletion; only I have opposed it. Would mathematicians please comment at Talk:Birthday paradox? Michael Hardy 22:41, 2 October 2005 (UTC)

Oh: It's the part labeled "long, windy, not needed". Michael Hardy 22:42, 2 October 2005 (UTC)

... and now I've changed the title of that section of that long talk page, to make it easier to find. Michael Hardy 22:44, 2 October 2005 (UTC)

New article on anti-Cantor newsgroup participants

Dave Petry (I'm 99% sure it's he) has started a new article called Controversy over Cantor's Theory. Dave's been showing up from time to time on sci.math and sci.logic for some years with variations on this theme--set theory is "mythological" and has nothing to do with "reality" as defined by things that can be observed on a computer. He's not stupid or crazy, just wrong; it's sort of amusing how he says (on the article's talk page)

This article is an attempt to give an overview of the more sensible views on this topic

because the less sensible views are those of certain individuals at least one of whom has a WP article about him (Archimedes Plutonium).

Anyway the project itself is perhaps worthwhile; I don't see anything wrong with having an article about philosophical views hostile to the use of set theory in mathematics, and how they have evolved, if indeed they have, as a result of the "computer age". This particular article in its current form, though, is very much OR and very POV. I hope others will take a look at it and figure out how to fix it or whether it's worth fixing; I really should be working on that paper.... --Trovatore 04:12, 3 October 2005 (UTC)

Well, it's rambling, unsourced, POV and apparently quite ignorant of work in areas such as domain theory that do argue for replacements of set theory for purposes of theoretical computer science. Move to criticisms of set theory, and cut down by about 80%, I'd say. Charles Matthews 21:36, 5 October 2005 (UTC)

The point of the article is to document the debate that has been taking place on Usenet over the past decade and a half at least, and to show that the current debate is really not much different from the debate from the early part of the twentieth century, except that the computer revolution does give people a new way of thinking about mathematics. As I point out in the article, the current anti-Cantorians are not pure mathematicians mostly, but rather people who have applied mathematics. I don't think you guys (Mike Oliver and Charles Mathews) understand what the debate is all about, and hence you guys are not really qualified to judge the article. It is "unsourced" currently, as it is still a work in progess. If you want to add a link to domain theory, that would be just fine -Dave Petry 5 October 2005

Let me add some comments especially directed to Mike. First, we know that quite a few very talented mathematicians have objected to Cantor's Theory. The names Kronecker, Poincare, Brouwer, Weyl, and Bishop usually are mentioned in this regard. Would you say that those guys are just plain "wrong". Are they more wrong or less wrong than me, and why. But furthermore, do you think those guys would say that the article I wrote is "original research". Although I have given the subject a slightly different perspective (invoking computers), I think those earlier mathematicians would recognize almost everything I have written as being very close to their own ideas. 24.18.232.215 03:01, 6 October 2005 (UTC)

OK, there's two separate points here, correctness vs original research; let's keep them separate.

Correctness: I actually agree with you about the applicability of the scientific method to mathematics. I think you're wrong that the appliction of the method militates against set theory. In fact, set theory makes refutable predictions in a Popperian sense, and they have thus far all been confirmed. And they can be formulated in terms of the computational world you discuss. I suspect that you may have a prejudice that a scientific approach requires restricting attention to the physical world.

Historical figures: All those you mention have made important contributions. That doesn't mean they weren't wrong about some things too, and I think they were. (Kronecker's a separate case; I tend to think of him as actually a bad person, for his persecution of Cantor, but it could be that my view of this is filtered through Cantor's depression and paranoia, plus (as I point out at every opportunity) I'm not much of a historian.

Original research: Let's be very clear that this part of the discussion has nothing to do with the merits of your ideas. The fact is that they appear to be your own personal observations. Even the language you attribute to the "anti-Cantorians" is in many cases almost identical to your own newsgroup essays. Yes, I think all the historical figures you mention would call your page "original research", once they understood the Wikipedia definition of the phrase. Hint: Just because it's OR here, doesn't mean a journal couldn't reject it for not being original. See WP:NOR for more information. --Trovatore 03:45, 6 October 2005 (UTC)

On this topic, you are not an expert. You don't understand the views of those you disagree with. I hope you don't succeed in keeping my article out of the wikipedia.

Have you read the WP:NOR correctly? Fortunately, Wikipedia isn't about who is/isn't an expert, but rather about who can give some source to backup his claims. And no, USENET is not a reliable source of mathematical knowledge. Samohyl Jan 14:32, 6 October 2005 (UTC)

We can have an article about criticisms of set theory, as we have one about criticisms of Wal-Mart. It must conform to WP's standards, that's all. Charles Matthews 21:03, 6 October 2005 (UTC)

For the historical "anti-Cantorian" arguments, I can easily give sources, and I intend to(the article is not finished). Part of the purpose of the article is to document the Usenet debate about Cantor's Theory, and to show the similarity of that debate with the historical criticisms of set theory. It would be a stretch to say that showing the similarity of the arguments is "original research". And likewise, the Usenet is most definitely a reliable source for knowledge of the debate taking place on Usenet. I understand why the wikipedia doesn't allow original research, but I don't think the intent is to keep articles like mine out. I absolutely do not accept Charles Matthew's butchering of my article, and eventually I plan to revert to a previous article.

Certainly there are other controversial topics in wikipedia, for example, Matthews mentions criticisms of Wal-Mart. So how does wikipedia stop "combatants" from sabatoging each other's articles? 66.14.95.197 23:31, 6 October 2005 (UTC)

In wikipedia, no single editor owns or possesses an article, thus the possessive in the phrase "each other's articles" makes no sense. With very few exceptions, every editor has equal rights to edit any article, however they see fit. It is the miracle of Wikipedia that this works, but it does. Paul August ☎ 15:50, 7 October 2005 (UTC)

Butchering is silly talk (like it says below the box, If you do not want your writing to be edited mercilessly and redistributed at will, do not submit it). I cleaned it up to conform with our style. Freely-made comments about what I don't understand are also silly, as are threats to revert. Feel free to add back anything specific. I doubt you'll get much sympathy. Charles Matthews 07:06, 7 October 2005 (UTC)

I missed this thread first time around, but I noticed Charles Matthews say:

work in areas such as domain theory that do argue for replacements of set theory for purposes of theoretical computer science

This isn't quite right: domain theory (and especially synthetic domain theory) wants to build better mathematical structures for doing Tarski-style interpretations of programs into, but in turn the foundations of domain theory are regular set theory. It might be better to call it a better interface onto set theory than a rival to set theory. Martin-Loef's type theory is an example of an actual rival to set theory, which is, again, peddled mostly by theoretical computer scientists.

I agree with Charles M's objection though. The section of that article called "recent attacks" has as its most recent commentator Hermann Weyl! In the mathematicians section, Kline is not objecting to set theory as a mathematical structure, but to its role in mathematical education, in particular the air of unreality refers to the lack of good intuition a certain kind of emphasis on farmalism and foundations can lack (caveat: I don't recognise this particular passage of Kline, but I've read a lot of Kline and I know his hobby horses).

Having said that, I think that if we find the right home for this, there might be a nice article that can be grown for it. I don't like "criticisms", I'll make a proposal for alternative name candidates at Talk:Controversy over Cantor's Theory --- Charles Stewart 15:24, 13 October 2005 (UTC)

Khayyam-Pascal's triangle

Paskal's triangle has been moved to Khayyam-Pascal's triangle. It is claimed there now that the latter is the internationally recognized name. Discussion is welcome at Talk:Khayyam-Pascal's triangle. Oleg Alexandrov 21:35, 5 October 2005 (UTC)

Oh, just move back. We use the common name. The history can be dealt with in the article. This is the standard way. Charles Matthews 21:38, 5 October 2005 (UTC)

Your wish is my command, so I moved it back. -- Jinn Niesen (talk) 23:16, 5 October 2005 (UTC)

Category:Article proofs

This category has some proofs, as subpages. It seems to be at odds with two widely held views, one that there should be no subpages (Christoffel symbols/Proofs is a subpage to Christoffel symbols), and that the proofs should not be on separate pages. Also, wonder I, why is this separate from Category:Proofs. I myself would suggest the proofs in there, together with the mother category, be deleted. Wonder what other opinions are. Oleg Alexandrov 00:16, 6 October 2005 (UTC)

Are you proposing that articles in Category:Proofs like Cantor's diagonal argument and Proof that e is irrational be deleted, or just the ones in Category:Article proofs? I would disagree with the first statement, while I have no strong opinion on the second statement. Furthermore, nobody reacted when it was asked whether these subpages are allowed at Wikipedia talk:Subpages#Special dispensation for mathematical proofs several months ago, so one could argue that the prohibition on subpages does not apply here. -- Jitse Niesen (talk) 22:00, 6 October 2005 (UTC)

No, I don't suggest deleting all the proofs on Wikipedia outright. Just the subpages in Category:Article proofs. Oleg Alexandrov (talk) 23:06, 6 October 2005 (UTC)

Making them into full, self-sufficient, articles called, for example, Proofs of the Bianchi identities, would seem to be less wasteful; but I agree they should not stay where and as they are. Septentrionalis 02:57, 7 October 2005 (UTC)

Subpages bad. Articles like a hypothetical Bianchi identities (proofs) stand or fall by their general interest (Fermat's Last Theorem (proof) would obviously be OK). I agree that the Category:Proofs should be for pages about proof and types of proof, not pages giving specific proofs. Perhaps a list of 'sample' proofs for the latter? Charles Matthews 07:02, 7 October 2005 (UTC)

How about putting back those proofs into the articles? --MarSch 15:01, 7 October 2005 (UTC)

I don't want to lose these proofs, I think they are valuable. I don't see the problem in having them on a subpage. Can someone explain the harm in that? If we don't want them there, or in the article, or in a seperate article of their own, then we could always put them on the talk page, but I would be strongly opposed to just deleting that content. Paul August ☎ 15:20, 7 October 2005 (UTC)

Putting the proofs back into articles is out of question. Proofs are typically technical, do not add much to understanding the concepts in the article, and interrrupt the flow of the article. Let us not forget that we are dealing with encyclopedic essays here, oriented towards the general public.

Keeping them as subpages is not good either. There is no hierarchy on Wikipedia; each article should be able to stand on its own. I would argue that the only option beside deleting the proofs is keeping them on their own standalone page.

Now, are proofs that much worth it, besides some classical proofs? Proof articles will be visited more seldom than others, and will be harder to fact check, which raises the spectrum of some obscure articles with more errors than others. Oleg Alexandrov (talk) 18:09, 7 October 2005 (UTC)

I suggest deferring a decision for at least several years. WP has the potential of being more than just encyclopaedic, although this potential is years away. Math books are quite useful in that they provide (non-notable) proofs for their theorems. Although WP is still far away from being detailed at a level equal to that of a book, I think it would be a mistake to declare as policy that WP must ever become as detailed as a book. As to obscure articles with errors, I don't think the way to eliminate errors is to eliminate obscure articles. linas 00:52, 14 October 2005 (UTC)

Note that Proof of angular momentum is an excellent example: its crudy, haphazard and weak, yet has had a half-dozen editors and is translated into four languages!! People seem to like this stuff, and I don't think it should be banned on principle.

Also, some articles cite too many references (in my opinion), and I would like to see, in such cases, that the references (and footnotes) are banished to a subpage.

Think of "proofs" as something that is less formal than a real article, but more formal than a talk page. linas 01:02, 14 October 2005 (UTC)

The {style} template

The {{style}} template pops up every now and then at Wikipedia:Manual of Style (mathematics) and is there now. I would argue that it is unnecessary. Its only purpose is for a user to hop from manual of style to manual of style, but for people who actually use a particular manual of style, like our math manual, the links to the manual of style about writing China-related articles, how to write footnotes, etc, are not be helpful. I would argue that a link to the Wikipedia:Manual of Style on top of our manual of style should be enough. From there, one can access any other style manual if one wishes so. Wonder what people think. Oleg Alexandrov (talk) 04:12, 7 October 2005 (UTC)

Harmless; and if we remove it, it will be back. Why bother? Septentrionalis 20:03, 7 October 2005 (UTC) (And it makes the page look a little more "official", which can hardly hurt.)

Wikipedia: Make technical articles accessible

I posted a note on this guideline's talk page proposing a change in this policy (Wikipedia talk:Make technical articles accessible). --- Charles Stewart 02:22, 8 October 2005 (UTC)

Please vote on list of lists, a featured list candidate

Please vote at Wikipedia:Featured list candidates/List of lists of mathematical topics. Otherwise, the issue may be decided by (from the looks of it at this time) people who never heard of mathematics until they saw this nomination. Michael Hardy 03:35, 13 October 2005 (UTC)

Wikitextbooks or www.yourbooksucks.com

I am attending an AMS sectional conference this weekend, and once again listening to everyone complain about how badly math is taught in the US, how lousy all the grade school textbooks are (except the Singapore textbooks), and how the three big textbook publishers are so powerful that nobody has a ghost of a chance of making things better.

Naturally, I thought of Wiki.

What I propose is a series of articles on mathematics written at the grade school level, so students and teachers who actually care about mathematics can have at least one source to which to turn.

I'm going to start at Grade school mathematics and take it from there.

Want to help?

Rick Norwood 22:46, 15 October 2005 (UTC)

I would like to help, but think a problem needs to be addressed first: stability. A book written by committee, and constantly changing, will be as bad as what's out there now. We would need to have one committed person in charge, who could review potential contributions from many authors and decide which to include as is, which to include with changes, and which to reject. This is rather "anti-wiki" so may not work here. That said, I suppose we could write many articles within the current structure with the goal of copying them and making them uniform, outside the wiki structure, to make a textbook, at some future date. StuRat 23:24, 15 October 2005 (UTC)

Agree w/StuRat on this point. I'm finding that WP articles tend to be "average" and not "excellent" because the excellent material in WP tends to get edited to oblivion. For a reference, such as WP, that's fine. For a textbook, which you learn from, "average" is not good enough. A better model is the Linux kernel, where an authoritarian few act as gatekeepers to contributions. linas 19:12, 16 October 2005 (UTC)

The first task, I would think, would be to come up with an ordered list of topics to be covered, by age group. A grade school book should have lots of colorful illustrations, so having a graphic artist on the staff would sure be a good idea. StuRat 23:31, 15 October 2005 (UTC)

Also, you should set up a project page for this, so discussion can take place there. StuRat 23:32, 15 October 2005 (UTC)

We have Wikibooks, with a few mathematics texts there already. See http://en.wikibooks.org . Educational material should go there and not in Wikipedia. Dysprosia 00:44, 16 October 2005 (UTC)

Agree with Dysprosia. Wikipedia is for reference, it is a collection of encyclopedic essays. I am getting weary of people trying to use Wikipedia to fix the wrongs of the world. Oleg Alexandrov (talk) 03:53, 17 October 2005 (UTC)

Yes, please support wikibooks. Charles Matthews 09:23, 17 October 2005 (UTC)

Reminder: Wikipedia:WikiProject Physics !

Just in case there are still Quantum and GR types lurking here, who haven't yet found Wikipedia:WikiProject Physics ... well, now you know: there's a physics project as well. Add your name to the list, and visit the talk page as well: I'm sure the topics are as lively and maybe more argumentative than those here! linas 00:28, 18 October 2005 (UTC)

Mathematical characters usage

As most readers here know, Dmharvey is working on a MathML solution for Wikipedia, called Blahtex. A perennial problem in mathematics is the large number of potential characters, and the MathML spec defines quite a large list. For your viewing pleasure, I have made a page where you can try to see many of them in your browser. (The list does not include all the fraktur, script, and blackboard-bold characters, some of which are in a higher Unicode plane.) Using a Gecko-based browser (from the Mozilla Foundation) and the Code2000 font, I see excellent coverage. That's a Good Thing, because the STIX fonts have had their projected release pushed back to mid-2006. In light of evolving developments, the question here is, what do we do now in editing articles?

Because Wikipedia has switched to UTF-8, it directly accepts any Unicode character. We can also use HTML named entities, and character entities. Come MathML, readers must be prepared to cope with these. Meanwhile, the processing of <math> allows a limited subset, producing either an image or HTML markup. (The subset does not include the full set of LaTeX characters, much less the complete range of MathML characters.) Finally, outside of the <math> tags we can use images of characters.

Folks writing in other scripts, from Cyrillic to Devanāgarī to IPA to Hangul and others, seem unapologetic about the need for their kind of characters in their kind of article. With the advent of MathML presentation it will become extremely awkward and ugly to use the image crutch; we need our characters, too.

How many people are going to scream if I start writing the cross product properly as A⨯B (using U+2a2f, &Cross;) instead of A×B (using U+00d7, ×)? That's silly, right; who needs the fancy character? But I've also gotten curses for using the semidirect product, N⋉H (using U+22c9, &ltimes;), which LaTeX calls "\ltimes" but <math> does not allow. (Especially annoying, the complainant thought a picture of &rtimes; was a fine substitute, even though it's the wrong character and precludes <math>!)

I will scream, because it shows up as a little square, like any other unreadable character. Please don't. Septentrionalis 18:40, 26 October 2005 (UTC)

Did you mean Cross or ltimes? Either way, one down, how many left to go? (By the way, your browser can read the character fine; it can't display it with your present setup.) Unfortunately, unless folks respond here an editor has no way to know which characters display for you as missing character boxes. I might be using FreeBSD and Firefox and Free UCS Outline Fonts, someone else might be using Mac OS X and Safari and default system fonts, and you might be using Win98SE and IE5 and Lucida Sans Unicode. Some kind of documented guidance could benefit everyone. That could be a list of safe characters, and/or suggestions for browser/font configurations to help in filling the boxes. --KSmrq^T 20:40, 26 October 2005 (UTC)

So, are all characters fair game as numeric entities? As UTF-8? (Clearly not as <math>!) If not, which do we exclude, why do we exclude them, how do we substitute (in all contexts), and what do we do when MathML arrives? --KSmrq^T 13:33, 18 October 2005 (UTC)

When using special characters, they should be properly displayed for, say, 90% of all readers. Thus at least IE should display them properly, and not just in one of its font settings. Otherwise it is better to use LateX, or if a symbol is not available, an image.--Patrick 13:28, 20 October 2005 (UTC)

Somewhat related was the discussion at Wikipedia talk:WikiProject Mathematics/Archive12#Unicode in math articles. There people objected against unicode but for different reasons.

With Firefox on Windows XP, I can't see one of the characters KSmirq wrote above, the one with U+2a2f, there is only a question mark in there. I guess it sounds reasonable that one not use the more exotic unicode characters, but rather TeX. Of course, TeX has the problem that the restricted Wikipedia dialect does not have all the symbols, but at least once the Wiki TeX parser agrees to generate a formula, it will be visible to everybody. Oleg Alexandrov (talk) 13:39, 20 October 2005 (UTC)

The archived discussion was about replacing numeric entities with UTF-8, which is related, but logically distinct. Using no UTF-8 beyond ASCII, an article can still use &2a2f; — which may not display as hoped. It is unrealistic to ask each editor to personally test special characters on all available OS/browser/font/config variations. Yet nowhere can I find any guide to what LaTeX constructions <math> tags support (including, but not limited to, characters); and nowhere can I find a guide to which characters are "safe" and which are not. Is my only resort trial and error, to try to use a character and see if the Wikipedia software or some other editor rejects it? Does that mean all mathematics must be written in ASCII?! That's an extreme example, but then where do we draw the line? Are all HTML 4.01 entities safe? Is any character in, say, Arial safe? Does Microsoft dictate through IE on WinXP? (If so, how are MacOS and BSD users to know what's safe?) And, again, MathML is looming (I hope!). --KSmrq^T 16:04, 20 October 2005 (UTC)

I did not say you should use plain ASCII for math formulas. :) And, I think the issue is not with people using XP or BSD, rather, the browser might not have all the fonts installed.

I guess the rule of thumb should be that if you suspect a given Unicode character might cause problems, you better you TeX instead, if TeX supports that symbol. But ultimately math display on the web sucks no matter what you use. Oleg Alexandrov (talk) 00:54, 21 October 2005 (UTC)

FWIW, I now have three browsers at my disposal; IE 6, Netscape 7.2, and Opera 8.5. None of then see 2a2f, while all except IE see 22c9. Arthur Rubin (talk) 14:04, 23 October 2005 (UTC)

That sounds about right. Your report, however, omits needed details, since what you see depends on OS+fonts+browser+config. For example, try installing the Code2000 font and see what you get. In regards to suspecting a problem, why would anyone not using IE/Win think a character they can see might be troublesome? I'm sure we all agree that mathematicians are the brightest and best-looking people on the planet, but that does not equate to web or wiki expertise! :-D —KSmrq^T 21:24, 23 October 2005 (UTC)

I'm running mac OS 10.4.2, with no additional fonts installed. On both Safari 2.0 and Firefox 1.0.6, I'm missing a large proportion of those characters. I haven't counted -- maybe missing 30% or so, especially towards the second half. Dmharvey

Talk 00:03, 24 October 2005 (UTC)

That makes sense. Some of the MathML entities are composites, such as a relation overlayed by a negation (e.g., solidus), but otherwise I listed them in numeric order. The higher code blocks are likely to be more esoteric, and less well covered by standard fonts. Without the Code2000 font I get coverage like yours; it would therefore be interesting to know if adding that font completes your coverage. I hesitate to ask you to compare IE5/Mac [28]. --KSmrq^T 02:56, 24 October 2005 (UTC)

An approach I've taken is to provide links to bitmap images for characters which don't display on every browser. That way, at a minimum, users can click on a link to see characters like ∈, ∉, ∅, ⊆, ⊂, ⊇, and ⊃; if they don't display on that user's browser. StuRat 00:12, 1 November 2005 (UTC)

That is a nice service, but $\notin$ and $\varnothing$ can better be displayed as image directly, they give most problems.--Patrick 07:44, 1 November 2005 (UTC)

I'm guessing you mean the fewest problems ? StuRat 08:35, 1 November 2005 (UTC)

I mean, they are the symbols which give the most problems if they are not displayed as TeX image but coded with ∉ and ∅.--Patrick 00:56, 3 November 2005 (UTC)

Sorry to take so long to respond; busy elsewhere. This is a creative idea, but hampered by two crippling drawbacks. The first is that seeing a formula with boxes on one page, and individual symbols separately, adds up to an unreadable formula. The second is unintentional creation of a mistaken symbol, which came up in a different context when the suggestion was made that a formula could link to explanations of its operators. This happens because many browsers are configured to underline links. Two examples:

"2+2=4"
"For all primes p>2, p is odd."

Obviously, "+" and ">" aren't special characters (so everyone can appreciate the examples, which look like "±" and "≥"); but the general danger should be clear. --KSmrq^T 03:07, 3 November 2005 (UTC)

I agree that having the formula right there is better than having to follow links to read the missing symbols, but still think that's infinitely better than just having boxes with no links at all. The underline problem is a good pt, but I think they are usually blue underlines to distinguish them from regular black text, so that might help some. Another idea is to have a pic of the entire formula, not just each symbol in the formula. StuRat 05:15, 22 November 2005 (UTC)

As my preferences are configured, they show the underline. And mine are pretty default except that I added MathML when possible, which I don't think affects this issue. It's probably not a good idea to assume people won't see the underlines. --Trovatore 05:20, 22 November 2005 (UTC)

And are they blue underlines that can be distinguished from regular black text ? StuRat 05:24, 22 November 2005 (UTC)

The underlines are blue, but so are the characters. It is not obvious that they are not part of the symbol. --Trovatore 13:42, 22 November 2005 (UTC)

Semidirect product symbol

The common notation of a semidirect product seems to be G = N H, with the normal subgroup at the left, while the symbol is a cross with a vertical bar at the right (see e.g. [29]), although the names of the symbols seem to suggest that the bar should be at the side of the normal subgroup ([30], [31]). Have other people any thoughts?--Patrick 13:37, 20 October 2005 (UTC)

Perhaps it would be better to redirect such a specific discussion to Talk:Semidirect product? --KSmrq^T 19:23, 20 October 2005 (UTC)

move of manifold/rewrite/*

The main article was moved, but the two subpages weren't. differentiable manifold, topological manifold redirect there. Admin privileges probably needed, since I couldn't do it. --MarSch 11:14, 20 October 2005 (UTC)

I will take care of this now. Oleg Alexandrov (talk) 11:20, 20 October 2005 (UTC)

Done. I also merged their edit history with the corresponding ancient redirects created by Toby Bartels in 2002 or so. Oleg Alexandrov (talk) 11:27, 20 October 2005 (UTC)

Thanks --MarSch 11:37, 20 October 2005 (UTC)

Live preview

This is not about math, but might be helpful to the fellow mathematician. I found a very userful tool in my opinion, Pilaf's Live Preview at Wikipedia:Tools#Alternative_previews. It allows one to do instant preview, without waiting for seconds or more after hitting the "Preview" buttion. It works by some javascript magic, and is just as easy to install as pasting several lines of text into a file and doing a reload of your preferences (control-shift-r for Mozilla, Ctrl-F5 in IE, and F5 in Opera). I already love this tool. :) Oleg Alexandrov (talk) 12:51, 25 October 2005 (UTC)

Note that it does not do LaTeX formulas, and does not show redlinks as red (one needs to check with the server for things like that), so the good old preview is still needed, but it can still cut the number of times one needs to use the usual Preview button. Oleg Alexandrov (talk) 14:02, 25 October 2005 (UTC)

Classification

Hey! In a case of absent mindedness, you forgot to classify the numbers. I searched a lot. If already present, I apologize. --Davy Jones 02:50, 26 October 2005 (UTC)

who's you and what numbers are you talking about? --MarSch 09:29, 26 October 2005 (UTC)

Firstly, I am persuing my bachelors degree in engineering. secondly, I mean the classification of numbers into Real numbers and Imaginary Numbers and their subdivisions. this willl clear the basics of numbers for the novice. --Electron Kid 00:14, 27 October 2005 (UTC)

Still don't understand what it means to classify a number. linas 00:24, 27 October 2005 (UTC)

Please note the plural numbers. Its like : numbers have been classified as Real numbers and complex numbers. complex numbers are further classified as complex and imaginary. Real numbers are further classified as rational and irrational. Rational numbers = fractions + integers. Integers = (negative numbers) + (Whole numbers). Whole numbers = 0 + (natural numbers). Further, a different symbol is used to represent each set. I thought of adding a page, if not already present. --Electron Kid 01:00, 27 October 2005 (UTC)

I really wouldn't recommend adding such a page. I would guess it would show up on AfD very quickly. You might take a look at the number article and seeing if you want to add a section there; it mentions various sorts of numbers, but not in that sort of hierarchy.

By the way, 0 is a natural number for lots of mathematicians, including me; the locution "whole numbers" is almost never used except in high school math texts, or perhaps in some informal contexts. --Trovatore 01:10, 27 October 2005 (UTC)

I find the discussion at number page to explain very well what kinds of numbers are out there. Oleg Alexandrov (talk) 02:55, 27 October 2005 (UTC)

Yeah, number already covers all of this. (Anyway, electron kid, I don't think your classification of "numbers" into "real" and "complex" does much justice to all the other wonderfully wacky kinds of "numbers" that mathematicians have thought up... p-adic numbers, ordinal numbers, etc etc) Dmharvey

Talk 03:23, 27 October 2005 (UTC)

Differentiating Functions on AfD

The article Differentiating Functions is on AfD (doesn't show up in the Current Activity page because it's not in any math category). The article is very badly written, though one editor seems to think it's more accessible than Calculus with polynomials, which I find hard to credit.--Trovatore 05:52, 28 October 2005 (UTC)

What's the current activity page? -Lethe | Talk 06:15, 28 October 2005 (UTC)

Wikipedia:WikiProject Mathematics/Current activity --Trovatore 06:23, 28 October 2005 (UTC)

Boolean algebra

Without some support on Boolean algebra, I think I may just merge it into Boolean logic, take the flak and pick up the pieces later. It is clear that making it a purist page meets continuing resistance. I don't do edit wars. Charles Matthews 21:40, 28 October 2005 (UTC)

Look, I don't care what the articles are called, within reason. But there needs to be a page on the algebraic structure. I've already expressed a willingness to have it called Boolean algebra (algebraic structure), with Boolean algebra itself containing the content now in Boolean logic. I see no reason that latter page (whatever it's called) should even refer to the algebraic structure, except maybe a line or two about related topics.

It occurs to me that the page on the algebraic structure might be made more accessible with a picture of the eight-element BA (its Hasse diagram, say, with the bottom node black, the next three red,green,blue, the next three yellow,magenta,cyan, the top one white, and explanation of how the \land and \lor correspond to following lines on the graph). Anything to make it clear that we're interested in the structure itself, not just the corresponding logic. I'm not very good with making such pictures--anyone want to draw it up? --Trovatore 22:07, 28 October 2005 (UTC)

I agree with Trovatore on this one. Merging the two articles won't help, but will lead to continuous edit wars between you guys and the general public, both of whom want different things from the article. StuRat 22:50, 28 October 2005 (UTC)

Looking at both Boolean algebra and Boolean logic, neither one clearly says "theory" or "application" — not in so many words, and not in the content. In my experience, that's usually a false dichotomy; but if that's what's intended, say so emphatically. Meanwhile, I've rewritten the opening of Boolean algebra (which had lapsed into nonsense), and said a few words on its talk page. Hope it helps; and good luck. --KSmrq^T 03:03, 29 October 2005 (UTC)

No, that's absolutely not the intended distinction (at least, not my intended distinction; certainly other contributors may have different opinions). The distinction I have in mind is between the algebraic structure (currently at Boolean algebra), and the propositions that are true in those structures (currently at Boolean logic). So for example "How many elements has the Boolean algebra B?" is a perfectly sensible question, whereas "How many elements has Boolean algebra (i.e. Boolean logic)?" is complete nonsense. --Trovatore 03:12, 29 October 2005 (UTC)

The difference in emphasis isn't strictly application vs. theory, although the Boolean logic article certainly has more application text and the Boolean algebra article has more theory. The Boolean logic article could be described as "the theory and application of the common subsets of Boolean algebra which apply to real-world applications". StuRat 03:18, 29 October 2005 (UTC)

I've done a little research on this, and the split over the articles is typical of mathematical encyclopedias (the Soviet one has algebra of logic + Boolean algebra, the Japanese some sections on symbolic logic + Boolean algebra). So it is not actually eccentric to divide it the way it currently is. That being said, I've heard nothing that convinces me there are two separate subjects, any more than discrete mathematics is disjoint from logic or computing applications. Charles Matthews 06:39, 29 October 2005 (UTC)

I think there is nothing at Boolean logic which shouldn't be at Boolean algebra and I dislike extremely how half of the article is doing set theory. Please go ahead and merge them Charles. --MarSch 12:42, 1 November 2005 (UTC)

As I said before...Merging the two articles won't help, but will lead to continuous edit wars between you guys and the general public, both of whom want different things from the article. StuRat 19:14, 1 November 2005 (UTC)

I feel quite bad with Boolean related articles. It appears that the special case of algebraic structures with 2 elements makes everything unclear: you may define a boolean ring, a boolean algebra (which should assume scalar multiplication, even with scalar in {0,1}), post algebra (there you use $\oplus$ (i.e. XOR, i.e. + modulo 2) instead of $<\cup$ thus building a field), boolean logic axioms, order on 0 and 1, aso. From there you can extend to boolean polynomial algebra, boolean logic, boolean lattices, and if you choose + mod 2, you can go to vector fields and end into algebraic graph theory. All of these things are, in my personal opinion, different as the "main" property which is used in an algebraic structure are niether the particular elements or operations which are used, but the axiomatic which is assumed; even if the elements and the operations are the same, the mathematical context is given by the axiomatic, which will usually allow more general reasonning. pom 18:27, 26 November 2005 (UTC)

Nov 2005 – Dec 2005

This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

Wikibook proposal

Since the purpose of the article originally started by StuRat was in part didactic, how about farming it out as a wikibook? There is still the historical question of the relation of Boole's algebra to the different entity called Boolean algebra to be sorted out, and yet another new article housed at BL might be the best place to do this. The new article can then comment on the non-mathematical aspects of cultural usage that originalyy prompted StuRat to write his text, and the genuinely encyclopediac contribution of the BL article can still be accomodated in the BA article. --- Charles Stewart 18:57, 1 November 2005 (UTC)

I have no objection to there being a WikiBook on either, or both, the current Boolean logic content and the current Boolean algebra content. However, if this is to be used as a justification for deleting either article, in whole or in part, from WikiPedia, I am strongly opposed to that. StuRat 19:07, 1 November 2005 (UTC)

The new article would not be based on your article, but it would be non-PhD-level and it would document what non-algebraists get out of the mathematics. I don't think that a compelling case for en.wikipedia to host an introduction to BAs for people who don't want to learn algebra has ever been made, if that is the deletion that my proposal makes that you object to. --- Charles Stewart 19:11, 1 November 2005 (UTC)

The basics of set theory are taught well before algebra in school. For example, an episode of the PBS kids (ages 7-11) math show Cyberchase contained an introduction to set theory including Venn diagrams. Any assumption that elementary set theory, and the Boolean logic operations based on it, requires advanced algebra, is therefore faulty. StuRat 19:40, 1 November 2005 (UTC)

I don't see the relevance of your remark to mine. --- Charles Stewart 20:17, 1 November 2005 (UTC)

I was responding to the statement "I don't think that a compelling case for en.wikipedia to host an introduction to BAs for people who don't want to learn algebra has ever been made...", which seems to be saying that a knowledge of algebra should be required to understand the introduction sections. My point is that the introductory level material can be made without the use of algebra, and that such material can be added later. StuRat 20:55, 1 November 2005 (UTC)

I made no such claim. WP articles on topics of broad interest should be accessible, even if the article should contain material that is not generally accessible. Wikibooks is the place for tutorials, see WP:NOT, point 8 of Wikipedia is not an indiscriminate collection of information, which is what "an introduction to BAs for people who don't want to learn algebra" would be. What is at stake in hosting such an introduction here rather than there? I see no point of principle at play here besides the one about following policy. --- Charles Stewart 15:38, 2 November 2005 (UTC)

Your statement that "WP articles on topics of broad interest should be accessible..." seems to imply that you don't think that we should have the goal of making all articles accessible. I disagree, and think that all articles should be made accessible to the broadest audience possible. Removing info from Wikipedia makes it considerable less likely to be found and thus less accessible. StuRat 15:56, 2 November 2005 (UTC)

I believe that there are articles for which it is not very important to spend much time thinking about the general reader, but instead most effort should be directed at the specialist. As you are aware, I've been citing analytic continuation as an example of this for some time. --- Charles Stewart 19:12, 2 November 2005 (UTC)

I don't think suggesting a wikibook is helpful. What is in wikibooks and what is here is in no way related.--MarSch 18:31, 2 November 2005 (UTC)

Are you disputing the policy? Are you aware that both WP and Wikibooks are both hosted by and reflect the values of the Wikimedia Foundation? --- Charles Stewart 19:12, 2 November 2005 (UTC)

I believe MarSch means the same thing as me, that while adding a WikiBook on any topic is a worthy goal, to use that as a justification for deleting material from WikiPedia, if that is your intent, is not at all helpful. StuRat 20:00, 2 November 2005 (UTC)

Issues with the real numbers

See Talk:Mathematical analysis#Mathematical.2FReal Analysis. A fellow is having problems with the modern defintion of real numbers (among other things). He/she says "infinitesimals exist". My reply would be that the real numbers are defined by axioms, and it follows from those axioms that there are no infinitesimals. It would be good however to have more in-depth comments than that on that talk page. Oleg Alexandrov (talk) 11:22, 29 October 2005 (UTC)

I would take the reals to be defined in terms of other things rather than axiomatized, but the answer comes out the same: "this is what we're talking about; talk about whatever you like, but don't call it the reals". At a cursory glance it looks like you're arguing with a crank over there. The best way to do that is not to; since he seems to have given up, I'd just let it go. --Trovatore 19:49, 1 November 2005 (UTC)

Infinitessimals exist, John Conway does a marvelous and fun construction in "On Numbers and Games". Although they exist in between real numbers, they're not exactly "numbers" themselves, though. I've always wondered if its possible to do some sort of calculus with them, e.g. treat them as some sort of fiber bundle or something over the reals, and get something other than trivial results. No idea. linas 16:04, 3 November 2005 (UTC)

WHat about non-standard analysis? --MarSch 16:57, 3 November 2005 (UTC)

and Non-standard calculus? --MarSch 17:06, 3 November 2005 (UTC)

J.H. Conway's surreals and NSA's hyperreals are both interesting structures (or classes of structures in the case of the hyperreals; there are nonisomorphic structures that fit the description). But they aren't the reals. Considerations involving them may tell us things about the reals, but they aren't the reals. Sorry to use baby talk; I imagine that both of you know these things--I'm just listing the points that can't be fudged when presenting the material to naive readers, or when having a discussion with a crank (if the latter is adjudged necessary). --Trovatore 17:10, 3 November 2005 (UTC)

The infinitesimals are not real, and they are not imaginary either. Gosh, what's left then? Oleg Alexandrov (talk) 17:45, 3 November 2005 (UTC)

My professor in introductory calculus would occasionally refer to indeterminate forms, infinities, and infinitesimals as "Christmas trees". Actually quite a good way to stop you from carelessly using them as regular numbers. Fredrik | talk 18:01, 3 November 2005 (UTC)

It's worth amplifying on non-standard analysis, though I think the original discussion was at a much lower level of sophistication. Suppose we lay out a system of axioms for the reals, then look around for possible models that satisfy those axioms. A standard model includes just what we expect and no more. A non-standard model — which supports the same set of theorems — can exist and have extra goodies like infinities and infinitesimals. To put the extra goodies to work requires careful distinctions. Another tactic is to use topos theory and the different logics that allows. In this way we get a somewhat different version of infinitesimals such as those discussed in smooth infinitesimal analysis [32] (PDF). A limited number of mathematicians enjoy these foundational games; many more seem to take the attitude "go away, we're trying to get work done here". But then, I remember hearing some insist that category theory was a waste of time, on the one hand; and I've seen topos logic [33] (PDF) [34] [35] put to serious work in the semantics of programming languages, on the other hand. I feel it's a delicate topic, because while I'm in the camp that enjoys foundational explorations, I'm painfully aware that most of the people who raise questions on Wikipedia about infinities and infinitesimals are clueless cranks. Too often the cranks are able to get some leverage because of loose writing, acceptable for informal mathematical discussion but not careful enough to stave off false interpretations. It's a difficult discipline, should one choose to accept it. For thousands of years mathematics progressed with stronger intuition than foundation, and I suspect that even though we're taught we should respect foundations today, many still just pay lip service. And for good reason: if we have to dot every "i" and cross every "t" any time we speak, we'll be tongue-tied. --KSmrq^T 20:31, 3 November 2005 (UTC)

Parameterize

During the travails of my spellbot, I got the following comment:

It turns out that both "parameterize" and "parametrize" (the bot's spelling) are very common; M-W lists both. I learned the first version somewhere back in the mists of time and only found out just now of this variant. I was actually surprised to see that in many of my books also use the second version, and I never noticed... (incidentally the bot also corrected a "parameterise" to "parametrise", too. Yay for bots that also know British spelling :-) Choni 13:06, 29 October 2005 (UTC)

Makes me really wonder, is it indeed correct/widespread to use "parameterize" (one extra "e") as synonymous with "parametrize"? I never encountered the former, even though it would make sense as it all comes from "parameter". Thanks. Oleg Alexandrov (talk) 13:15, 29 October 2005 (UTC)

I am only familiar with the former version. It seems more natural, being closer to the root word, as well. StuRat 23:55, 31 October 2005 (UTC)

American Heritage seems happy with both, nodding slightly towards including the "e". That agrees with my practice when writing or proofreading: either is fine. It might be nice if an article was at least self-consistent, but frankly I doubt many readers would notice. In contrast, "parametric" does not allow an extra "e". --KSmrq^T 00:11, 1 November 2005 (UTC)

Of the four permutations, the only one that looks really wrong to me is "parametrise". I think british and american speakers actually pronounce the word slightly differently. (I'm an Australian speaker.) Reminds me of aluminium vs aluminum. Dmharvey

Talk 00:14, 1 November 2005 (UTC)

I think aluminium is what is used in most languages. Therefore I prefer to use it also in English. --MarSch 12:45, 1 November 2005 (UTC)

The situation is a bit different, because in the case of Aluminium, there is actually an international standard that specifies the official name as "Aluminium", and not "Aluminum". See for example IUPAC Periodic Table of the Elements, which says: '“Aluminum” and “cesium” are commonly used alternative spellings for “aluminium” and “caesium.”'. As an American, I find this annoying, but that's the way it goes. -- Dominus 15:49, 1 November 2005 (UTC)

Hey that's good :) Now we only need to get rid of potassium and call it Kalium instead.--MarSch 17:07, 1 November 2005 (UTC)

Sure, but then we need to find a way to extract it from kale, instead of potash. 17:58, 1 November 2005 (UTC)

Americans don't get annoyed; we effect regime change. I can say that now that I'm in Canada. Then again the Canadians might not know I'm joking. --Trovatore 20:28, 1 November 2005 (UTC)

Yea, you might get kicked "oot". StuRat 20:46, 1 November 2005 (UTC)

Let's get back on task, eh? For what it's worth, I've met people (including myself) who insist it should be spelled "parametrize" (or "parametrise" if you live across the pond). I'm not sure how often I've run into the latter, though. - Gauge 03:45, 10 November 2005 (UTC)

Hilbert problems

The Hilbert problems page is seeing some development, which is only right and proper. It is also raising numerous issues, in respect of what a 'solved' problem is. This is an opportunity, to do better than other Web treatments (few of the historians really have all the background to write with authority on all 23). The words 'worms', 'can' and 'of' come to mind.

I wonder whether the laudable effort to get a table summary of it all on the page hasn't had its day. It is hard to write enough in a table entry, since some of the problems have several 'ply' in them. I also think that where [[Hilbert's n-th problem]] is now a redirect, we really need to have the buffer of a separate page. For example, Hilbert's fifth problem used to redirect to Lie group, but it seems clearer not to have arguments about what a Lie group is, and what the Fifth Problem was, on the same page.

Please come and help. This page missed Featured Article status over the summer, but has already been much expanded. Charles Matthews 09:49, 3 November 2005 (UTC)

Help wanted at rotation

See talk:rotation#Request for comment. Oleg Alexandrov (talk) 00:58, 6 November 2005 (UTC)

proofs of quadratic reciprocity

If anyone's feeling energetic, I started an article on Proofs of quadratic reciprocity. Sadly, it was a bigger job than I foresaw, and I've had enough for now. It needs several things done to it; see Talk:Proofs of quadratic reciprocity for my opinion on this. Thanks! I should go back to writing blahtex and existing in the real world now... Dmharvey Talk 03:11, 6 November 2005 (UTC)

I've intervened to link to Gaussian period to use indirection on the quadratic field. IMO this can be an interesting page, but mainly to send the reader to other parts of the site. Charles Matthews 11:17, 6 November 2005 (UTC)

Category:Professors

Wikipedia:Categories for deletion/Log/2005 October 30 - the classification of academics needs a big clean-up. Please come and vote. Charles Matthews 11:56, 6 November 2005 (UTC)

Articles listed at AFD

Dragan conjecture (AfD discussion)

Unfortunately, the automation makes it difficult to manually add articles such as this to the current activity list. Uncle G 00:53, 10 November 2005 (UTC)

- Done (by placing {{math-stub}} in the article). It should be picked up, eventually. Arthur Rubin (talk) 01:14, 10 November 2005 (UTC)

Exclusive nor

See the talk page. Has anyone else heard of this, outside of MathWorld? Arthur Rubin (talk) 01:14, 10 November 2005 (UTC)

It would seem more logical to me to call this thing NXOR, per the suggestion at the talk page. XOR is probably a more familiar operation than NOR, and it is much easier to figure out what NXOR means: XOR goes 1 only on different inputs, so NXOR must go 1 only on the equal inputs. With XNOR one would probably have to draw a truth table. I checked that it is also equivalent to XAND, but people probably aren't used to working with XAND (I wasn't until I thought about it a bit). - Gauge 04:23, 10 November 2005 (UTC)

If it is true only on the same inputs (both true or both false), wouldn't the simplest and most logical name be SAME ? StuRat 11:46, 10 November 2005 (UTC)

I don't think we should use the name that seems simplest, but rather the name accepted in the mathematical community. Anyway, my TI calculator says XNOR, not NXOR. -Lethe | Talk 14:31, 10 November 2005 (UTC)

There are also far more Google hits for "logical SAME" than either "logical XNOR" or "logical NXOR", see the article's talk page for details. I would say that this is evidence it is more accepted by the mathematical community. Note that while "SAME" is a normal English phrase, "logical SAME" is not. StuRat 14:39, 10 November 2005 (UTC)

Many of the google hits for "logical SAME" seem to be consecutive sentences the first of which ends in logical, while the second starts with same. some seem to be grammatical errors for "logically same". I see very few google hits for "logical SAME" which indicate that it is used as an operator in logic or CS. I think your hit count is unreasonably high, given that you're searching two very common english words. On the other hand, when you google xnor, every single hit is about the logical/CS operator. Could you perhaps provide a textbook (or something more authoritative than google) that uses SAME for this operator, because I'm of the opinion that it's always called XNOR. -Lethe | Talk 16:09, 10 November 2005 (UTC)

I will look for some. Meanwhile, can we keep the discussion on the article's talk page ? Having it in two places seems quite unnecessary. StuRat 17:01, 10 November 2005 (UTC)

I have a design that comprises 18 such gates open in another window as I write this. xnor is what such a gate is called in Verilog. Uncle G 15:03, 10 November 2005 (UTC)

Function Iteration -- possible OR

The new article Function Iteration has the general smell of being original research. It doesn't look wrong, it just looks home-grown. Anyone care to do something about that? AfD maybe? linas 01:26, 11 November 2005 (UTC)

AfD seems like a good idea. Fredrik | talk 01:32, 11 November 2005 (UTC)

I would agree with that. Oleg Alexandrov (talk) 02:00, 11 November 2005 (UTC)

Seems borderline to me. I think the math project has quite a lot of stuff that people figure out themselves by routine methods, on the theory that it must be written up somewhere, and I think it would be counterproductive to get too rigid about OR when it comes to that sort of thing. But yes, this is probably over the line; it's a bad sign that the author signed his work. Maybe just redirect to Attractor? --Trovatore 02:49, 11 November 2005 (UTC)

Isn't there some template that would say something like "this may be OR/POV, but nobody is quite sure, it can be true, citations are needed"? It would be more apropriate than deletion in some cases. It's the second instance of this I came across lately. Samohyl Jan 07:28, 11 November 2005 (UTC)

Needs citations to show it's already published. Otherwise to AfD as original research. Charles Matthews 08:44, 11 November 2005 (UTC)

The last section of Function iteration names Paul Bird as its author. A previous version of the article Scalar Gravity also mentioned named. Scalar Gravity is probably original research; see the discussion on Wikipedia:Articles for deletion/Scalar Gravity. That enough evidence for me to suspend my assumption of good faith, so I replaced the whole article with a redirect to function composition. In fact, since time immemorial (diff) the latter article includes the sentence

"In some cases, an expression for f in g(x) = f ^r(x) can be derived from the rule for g given non-integer values of r. This is called fractional iteration."

It is a pity though as it is an interesting subject, but original research has no place in Wikipedia. -- Jitse Niesen (talk) 13:23, 11 November 2005 (UTC)

more on "article too technical"

see Wikipedia:Village pump (policy)#Frustration with make technical articles accessible policy

Dmharvey Talk 18:55, 11 November 2005 (UTC)

a list or a category of categories

I want there to be either a list of categories or a category of categories here. The more I think about it, the more I think it should be a list, not a category. One reason is that some categories probably don't deserve their own articles. Another is that it might be neat if we could put the categories in a table and like list their properties (cartesian closed, concrete, abelian, monoidal, etc). But then again, I've never liked (wp organizational) categories. Anyway, I started a list, which is basically just me adding a whole bunch of categories to the short list that was already at category (mathematics), in my user space because I wasn't sure if it should be an article. Have a look? -Lethe | Talk 06:10, 12 November 2005 (UTC)

You mean like the category of small categories? (couldn't resist...) - Gauge 05:39, 13 November 2005 (UTC)

Having a list of categories (as in category theory) would be nice. However, I find the table at the link you mention intimidating. I have no idea of categories, that is just an esthetic observation; maybe the table is useful. Anyway, if you decide to make such a list, it is good to add it to the List of lists of mathematical topics and also categorize it in Category:Mathematical lists. Oleg Alexandrov (talk) 17:23, 12 November 2005 (UTC)

If a programming metaphor will help, think of categories as an object-oriented approach to mathematics. (Hidden humor intended.) The idea is to approach structures through maps. For example, look not just at vector spaces, but also at linear transformations, the maps that preserve the structure. Look not just at groups, but also at group homomorphisms. In fact, category theory has found that the structures themselves (called objects) are less important that the maps (called arrows). We can give an arrow definition of "product", say, that applies identically to any kind of category. (Example: an individual poset is automatically a category, with an arrow A→B meaning A≤B; its products are greatest lower bounds.) By the same reasoning, we study category-to-category maps (called functors), such as the forgetful functor that maps a vector space to the additive group of its vectors. We also consider functor-to-functor maps (natural transformations). By adding additional axioms we isolate categories (called topoi) that can replace sets as a foundation for all of mathematics. A table of categories (hint: good name) has the potential to organize diverse topics in a way that reveals common patterns. Category thinking has already had a broad and subtle influence on mathematics. (Warning: POV ahead!) In much the same way as lesser beings see groups and vector spaces everywhere, higher beings see categories. ;-) --KSmrq^T 13:31, 13 November 2005 (UTC)

I think both a list and a category are appropriate. However the category name needs some thought, because it seems unavoidable that it will use the word "category" in two quite distinct senses in one short phrase. For example Category:Mathematical categories isn't good, because it looks like it should be a collection of all subcats of Category:Mathematics. The only things I can think of that are clear sound a little like jokes (e.g. Category:Category-theoretic categories. Actually maybe that one's not bad; once you get over the sound of it, it pretty much covers what needs to be covered. --Trovatore 17:29, 12 November 2005 (UTC)

As regards the list, please note that there is already a List of category theory topics, and it includes a section that has some of the function of Lethe's new list. The lists should be coordinated in some way: The new list could be merged into the old one; the now-redundant part of the old one could be removed, with a link to the new one; or minimally, there could just be dab-style notices at the top of both. The name List of categories suffers from the same linguistic problem mentioned in my last intervention. Could be List of category-theoretic categories. --Trovatore 17:47, 12 November 2005 (UTC)

I took your suggestion on the name of a category. I went ahead and created the category. I probably will move the list into article space at some point as well. -Lethe | Talk 18:21, 13 November 2005 (UTC)

Cool. I've made it a subcat of Category:Category theory, and removed that now-redundant category from the articles in both. --Trovatore 19:17, 13 November 2005 (UTC)

What's a pipe category? -Lethe | Talk 00:34, 14 November 2005 (UTC)

(Think think think.) Sorry, no clever answer for such a promising straight line. When my edit summary says "pipe cat" it means that I pipe the category to a different name. Otherwise the whole category would be under the letter "C". It doesn't affect how the article name is displayed in the category listing, just how it's alphabetized. --Trovatore 00:38, 14 November 2005 (UTC)

I did notice the list of categories under the 'C' heading of Category:Category theory. I didn't see that other list. Thanks. -Lethe | Talk 17:59, 12 November 2005 (UTC)

I really like my table, but I'm afraid it's way too wide for most people's monitors... -Lethe | Talk 20:43, 12 November 2005 (UTC)

Vector (spatial)

It looks like vector (spatial) has been used in some contexts where coordinate vector or vector would have been more appropriate. I started to go through and fix things until I realized there must be at least a few hundred pages to check that link to vector (spatial). My understanding is that spatial vectors (per their article) only refer to vectors in dimensions at most 3. This would make such links to vector (spatial) inappropriate when considering vectors in higher (or arbitrary) dimensions. How should we proceed to address this problem? - Gauge 07:14, 13 November 2005 (UTC)

A related note: I suggest that for clarity we rename Vector (spatial) to Vectors in three dimensions.--Patrick 11:00, 13 November 2005 (UTC)

That does sound reasonable, assuming the point of the article is to contain the most basic facts and intuitions. Charles Matthews 11:16, 13 November 2005 (UTC)

I think what Gauge mentions is the result of a disambiguation of vector gone wrong. Somebody was using a bot several days ago to do that disambig, and I guess that person did not do the homework well.

I for one like vector (spatial) more than vectors in three dimensions. The former is clear enough to non-math folks, and the latter looks needlessly complicated. Oleg Alexandrov (talk) 17:37, 13 November 2005 (UTC)

Considering that vector space is the generalized kind, it is somewhat odd to use "spatial" to distinguish from it.--Patrick 23:04, 13 November 2005 (UTC)

I also disagree. The proposed name feeds into the misconception that a 3-vector as used in physics and engineering is only special in that it has three components. It is not. The distinguishing feature of spatial vectors is not that they are three dimensional, but that they transform as the spatial coordinates do under rotations. They would be equally distinct in this sense if space had two dimensions, or four. —Steven G. Johnson 19:18, 13 November 2005 (UTC)

(copied from talk:vector (spatial) by Oleg Alexandrov (talk) 23:09, 13 November 2005 (UTC))

The proposal was based on the line that was at the top: "This article treats vectors in 3-dimensional real space." If the article is going to focus on this distinguishing feature that is fine. Note that the article is inconsistent in whether it is about 3D or also about other spaces with this feature.--Patrick 09:07, 14 November 2005 (UTC)

For a better understanding of "a vector is an object with properties which do not depend on the coordinate system used to describe it" it may even be helpful to start with the 1D case.--Patrick 09:22, 14 November 2005 (UTC)

I agree that the article's introduction needs revision; it's clearly been the victim of "edit-creep". I think the 1d case is actually more abstract, however. (Note that, in 1d, vectors and scalars are still distinct under coordinate inversions.) —Steven G. Johnson 16:55, 14 November 2005 (UTC)

I'm not even sure I like the existence of this article in the first place. Is there really so much to be said about vectors in R³ that wouldn't fit in an examples section of vector space that these vectors need their own article? Remember that we're an encyclopedia, not a textbook. -Lethe | Talk 00:28, 14 November 2005 (UTC)

Vector spaces are way too abstract for most people, while the vector (spatial) article is looking at things from the physics perspective. And as Steven Johnson is saying above, physical vectors have nice interpretations in respect to coordinate changes. I would not support merging vector (spatial) into vector space which is about the math structure. Oleg Alexandrov (talk) 06:40, 14 November 2005 (UTC)

Well I don't feel very strongly about this, so I'm not actually proposing a merger, but just let me say that I don't think that every topic that can be discussed on different levels of abstraction should get one separate article per abstraction. So just because vector spaces can be discussed either abstractly or concretely, doesn't mean that we should have a concrete vector article and an abstract vector article. But I note that there are a lot of similar dummy articles already in place, so I guess people want them. whatever. -Lethe | Talk 17:14, 14 November 2005 (UTC)

It's not just an interpretation, it's a definition — physical, spatial (axial) vectors have additional defining properties beyond those of an abstract vector space. (This is, unfortunately, something that is not often emphasized in undergraduate courses, where students sometimes get they impression that they are just any old element of R³. Nor is it usually mentioned in higher-level math courses; that's why I would prefer to begin the article with "in physics" rather than "in mathematics.") —Steven G. Johnson 16:55, 14 November 2005 (UTC)

Wikisource wants to delete all source and data

Wikisource is currently contemplating deleting all mathematical and astronomical tables (including expansions of transcendental numbers, tables of logarithms, ephemerides, and so forth) and all source code. See Wikisource talk:What Wikisource includes for the discussion of this. Uncle G 15:49, 13 November 2005 (UTC)

I'm afraid a couple of lists have been deleted already. To be sure, I feel the best solution would be to simply move these pages back to Wikipedia. If it doesn't belong on any wiki, it should at least be moved to a place where it can be monitored by people who care about it. On a larger scale, it would be useful to have more namespaces available for non-article content, for example Data:, Proof:, Example:, ... - Fredrik | talk 15:58, 13 November 2005 (UTC)
- People who care should go to Wikisource and contribute to the discussion. Uncle G 21:59, 13 November 2005 (UTC)
  - I don't see a good place to enter, and it appears a decision has been made anyhow. Fredrik | talk 19:25, 14 November 2005 (UTC)

unitary versus unital

I got confused the other day when I saw unitary in the context of a C*-algebra. Eventually I figured out that it means "having multiplicative identity", and I changed it to unital. I now see that some authors do use unitary in this sense (Hungerford), though it isn't mentioned in our page on unitary. I'm going to add a mention there, but I kind of also want to change all instances I come across to unital, which is less ambiguous. How do you feel about the word unitary to mean having identity in an algebra, or over a ring with identity for a module? -Lethe | Talk 16:01, 13 November 2005 (UTC)

I prefer "unital". I've never heard "unitary" being used to describe these things, and C*-algebras make a good case for avoiding confusion and keeping the terminology consistent. - Gauge 20:16, 13 November 2005 (UTC)

Spelling vandal

One person uses multiple account to change the spelling of math articles one way or another. I reverted whatever I saw so far (that does classify as vandalism I would say, as that person was warned half a day before to not do that). I guess we need to take a close look at the recent changes to math articles from the list of mathematical topics to watch for more. Note that the person in question makes sure that the user page and talk page are blue, I guess to mislead people. Oleg Alexandrov (talk) 07:03, 14 November 2005 (UTC)

Could you point us to some examples? I've noticed that from time to time I have to revert someone who changes "provably" to "probably" or "provable" to "probable", but I've never been quite sure whether that person is a vandal, or just doesn't understand either the meaning of the English words or the subject matter. --Trovatore 07:19, 14 November 2005 (UTC)

Oleg is probably refering to User:Spellchecker, who is changing spelling from American to British English (example). I could live with that, British English being obviously superior, but this user is making the unforgivable mistake of using the widespread but terribly wrong -ise variant. :) Today, similar accounts have appeared, like User:Imperiul (example). Whoever it is, they must feel very strongly about it, making a new account just to change a single letter. -- Jitse Niesen (talk) 11:28, 14 November 2005 (UTC)

What examples? Yesterday I single-handedly (mouse-buttonly) repelled an entire attack of spelling clones, I expected to be awash in glory when I wake up in the morning, and instead you are asking for examples? Oleg Alexandrov (talk) 19:13, 14 November 2005 (UTC)

Is it really a problem? Sure, changing "provably" to "probably" is probably (provably?) uncool, but if someone wants to waste their time changing "sanitise" to "sanitize" or the other way, I say let 'em waste their time. It's better than real vandalism. Don't we have better things to do? (On the other hand, I would of course object to such spelling changes on articles like George Bush or Vegemite). Dmharvey Talk 13:06, 14 November 2005 (UTC)

Well, there's a policy about this whole issue. Short version: If it's about a topic specific to one country/culture, use the appropriate version of English, otherwise use the one the article started with. I don't think we can allow such policies to be circumvented just because it seems like more trouble than it's worth. The matter should be explained to this user, and if he continues, there should be consequences. --Trovatore 16:29, 14 November 2005 (UTC)

I follow the maxim "don't ascribe anything to malice which can be ascribed to ignorance". I've seen cases where less common words were replaced by more common words which seem to fit in the sentence, and I assume those editors honestly thought they had found a typo. When I revert back, I'm careful to describe the meaning of the word, so they are educated and don't try to "fix" it again. It's a shame we can't somehow mark words with a "this is not a typo" flag, to prevent this mistake in the first place. This reminds me of a problem IBM had in their user manuals...they contained blank pages at the end of chapters, but then people would call and complain that vital pages of their manual were blank, so they ended up printing "This page left intentionally blank" on those pages. Ironically, printing that on them meant they were no longer blank, LOL. StuRat 04:07, 22 November 2005 (UTC)

That was repeated change of spelling after being repeatedly warned, and creating a lot of accounts to do that, presumably to hide his/her tracks. I would not say that person is evil, but you surely can't assume good faith here. Oleg Alexandrov (talk) 04:54, 22 November 2005 (UTC)

I certainly don't mean to say that it's always an innocent mistake, just that it sometimes is. StuRat 05:04, 22 November 2005 (UTC)

spare hacking time anyone?

Hi y'all,

There's been an idea floating around for a while now that would of interest to all frequent mathematics article editors. I can't remember who originally thought of it. I'm wondering if there's anyone out there with time + skill + motivation to actually make it happen.

Wouldn't it be lovely if we could write our equations with $ or $$ signs instead of bulky <math> tags, just like in TeX. Every now and then this gets proposed as a change to the wikisource markup, but I tell you, it ain't gonna happen that way, because it's just too big a change. I think the main objection is that it would weird out too many non-math people out if they got funny TeX errors every time they tried to use ordinary $ signs. Fair enough.

But there's another way to do this which might satisfy everybody. What we need is some kind of javascript thing which automatically and transparently translates between $ and <math> tags on the way in and out of the edit box (and presumably translates $ signs in the wikisource to something sensible like "\$"). This proposal would have no effect whatsoever on the database or the mediawiki software; it would stay recorded as <math> in the database. From what I understand, we have available some mechanism for personalised javascript (e.g. via monobook.js), which presumably could override the default behaviour when you load a page for editing or save an edited page. Then all that would be required is that a user copies the script to their own monobook.js, and they would be able to work with $ signs -- no thought required. Anyone who isn't interested doesn't have to use it.

Now, I'm pretty clueless when it comes to javascript, and I don't know how monobook.js works, and I don't have time to research it now. I've been led to believe, through some conversations I had a while back, that such a thing was technically feasible. Does anyone have any comments on feasibility? Does anyone here know enough to sit down and write the thing? Am I making any sense at all? Dmharvey Talk 01:34, 16 November 2005 (UTC)

See User:ABCD/monobook.js for how to create javascript functions, how to do automatic search and replace, and how to create a tab (in addtion to the existing "article", discussion", "edit", "watch", "move" tabs) and bind your function to that tab, so that when you click on it it gets executed. I found ABCD's code very well structured and easy to understand. You just need to carefully remove the parts you don't need (after you understand how the pieces fit together), and tweak one of his functions into doing what you want. Javascript is very similar to C, which I think you know. You could try to get started, and I could try to help if you get stuck. Oleg Alexandrov (talk) 01:56, 16 November 2005 (UTC)

You're right, I probably could work it out myself -- I just don't have much time right now. I'm canvassing for someone else to give it a try if they feel so inclined. Dmharvey

Talk 02:07, 16 November 2005 (UTC)

Let's assume you are properly devoting most of your time to completing blahtex, not some meaningless "doctorate". [36] Someone who is writing a translator from LaTeX to MathML is hardly in a position to complain about bulky tags. ;-)

A little of both right now. Be patient. I do intend to finish blahtex first. :-) Dmharvey

Talk 12:29, 17 November 2005 (UTC)

The TeX delimiters can cause trouble, both in translating and in using. There's a good reason for LaTeX (and XML) balanced notation, an opener that can be distinguished from a closer. (Admittedly "\[" and "\]", and even "$" and "$", can also be annoying and an awkward fit to wiki notation.) The problem is, without balance you have to mind the nesting, which means parsing, not just string replacement; and you have to be prepared for bad (unbalanced) input. An accidentally omitted closing "$" is common, and wreaks havoc. Frankly, if wiki syntax supported "e^{x}" for superscripts (e^x) and "a_{k}" for subscripts (a_k), it would be less painful to use <math> tags for the rest. --KSmrq^T 10:08, 17 November 2005 (UTC)

Using $ is no worse than '' for emphasising text; that wreaks havoc on me occasionally, but it's pretty easy to deduce what's going wrong. And you're right: it's not just string replacement. Makes the project just a little more interesting. Wanna try? Dmharvey

Talk 12:29, 17 November 2005 (UTC)

And you probably need to look out for <nowiki> tags too :-0 Dmharvey

Talk 12:30, 17 November 2005 (UTC)

I don't see any advantage whatsoever in using $ and $$ instead of "bulky" <math> tags. The only thing I used to hate about <math> is that they are a pain to type, but right about the edit box you have the buttonbar with the math tags in. Click on that, and if you hit any keystroke that silly text "Insert formula here" will disappear, and you are ready to go.

It's a matter of personal preference. I find the math tags also get in the way of readibility for me. If you disagree, you don't have to use it! (And certainly you don't have to write it!) Dmharvey

Talk 21:31, 17 November 2005 (UTC)

Another thing. I don't think it is a good idea to write a Wikipedia article as if it is a LaTeX document. This may result in too many inline PNG formulas. And no, MathML is not just behind the hill, coming any day or two. :) Oleg Alexandrov (talk) 16:48, 17 November 2005 (UTC)

No, not in a day or two, but I think six months is eminently realistic to see MathML being trialled on Wikipedia -- quite possibly much less. I'm guessing we'll have a good solid test wiki running by February, but don't quote me on this :-). Anyway, I think the question of $ signs is mostly independent of the rendering method. My long distant goal is that "wikified math" (e.g. Q(ζ_n)) -- even single symbols like x -- should eventually become completely deprecated in favour of inline TeX. But perhaps this a discussion for another day :-) Dmharvey

Talk 21:31, 17 November 2005 (UTC)

From the time it gets its "first trial", to the time it is the default, I won't give less than two years. Now, if you expect that there will come a time when anybody will be promted to install mathplayer to see a math article on Wikipedia, that time will probably be never, or at least five more years. That is to say, HTML math is here to stay, that's how I see it. Oleg Alexandrov (talk)

I think you are being unduly pessimistic. When there's a will, there's a way. (Gosh, I've only been living in the US for two years, and look how hopelessly optimistic I've become!) Anyway, I hope that when we start lobbying the wikimedia server people to incorporate our code, that you will support us. Or at the very least, wish us the best of luck. Dmharvey

Talk 01:58, 18 November 2005 (UTC)

calling all topologists

Expert fact-checking and other assistance requested at Inductive dimension. --Trovatore 07:25, 16 November 2005 (UTC)

"Dimension" category up for renaming

Someone has proposed here that Category:Dimension be renamed to Category:Dimensions. Personally I disagree (though I'm open to argument). Please contribute (whether you agree with me or not). One possibility is that overly disparate concepts are being muddled together in this category. --Trovatore 19:00, 16 November 2005 (UTC)

Not to start a big fight (and dimensional analysis cdould easily be made a subcategory), I'd say the Buckingham Pi theorem shows what that has to do with dimension (rank of an abelian group, whatever). Charles Matthews 09:54, 17 November 2005 (UTC)

List of well known mathematical formulas

Well known to whom? This seems a little silly. Dmharvey Talk 03:18, 19 November 2005 (UTC)

I agree. I put it on AfD. --Trovatore 03:52, 19 November 2005 (UTC)

Examples?

Hi, I'm not sure if this is the right place to put this, but I was wondering if there were any policies concerning examples on math pages? I dunno, but it seems that it might be useful if pages had some example problems (like if the Green's theorem page had an sample problem to find the area of a planar region, or whatever)... Thanks :-)--yoshi 00:59, 22 November 2005 (UTC)

Examples are absolutely encouraged. Most people are just too lazy to provide them. I would say, though, that there's an appropriate level of detail to present in an example. It shouldn't be worked out like a homework assignment; just enough detail should be given to get the reader started on working it out. That's my own take; we'll see if others agree with me. --Trovatore 01:04, 22 November 2005 (UTC)

Oh, amend the above to "most people, including me, are usually too lazy...." I didn't mean that to come across as a criticism of the other editors in the project. --Trovatore 01:07, 22 November 2005 (UTC)

haha :-) I think it would be nice to have some completely worked out problems (like sample homework problems)... but I guess I should just contribute some and see what others think. sorry kinda new to wiki stuff :-) --yoshi 01:14, 22 November 2005 (UTC)

Examples? Yes, please. An encyclopedia is probably not the right place to challenge a reader to "work it out". Use good judgment; examples may be stated without proof, or a proof may be included if it is short and instructive. Equally important, and omitted more often still, are counterexamples ("near misses"). For Green's theorem, say, a figure-8 curve might be used to show what can go wrong. Also, a good picture is worth ten thousand equations (for some topics and some readers). --KSmrq^T 01:50, 22 November 2005 (UTC)

I agree that it's not a place to "challenge a reader", but I think it's even less a place to present detailed solutions to exercises. Examples are great, but let's keep them reasonably brief. Nonexamples (cases where the method doesn't work, in this instance) are also useful, as you say. --Trovatore 01:57, 22 November 2005 (UTC)

Anybody writing an article without examples sins against the math style manual and his own soul. :) Oleg Alexandrov (talk) 02:07, 22 November 2005 (UTC)

YES ABSOLUTELY DO EXAMPLES. I would err more than most to the side of providing examples. (If I have the time, that is.) As long as they don't distract from the main discussion. Dmharvey 02:33, 22 November 2005 (UTC)

I agree, examples are a capital idea ! I think the more thorough the better, as long as they aren't redundant with other examples. Many readers who can't follow a purely theoretical discussion can easily follow it with a few examples. For those who don't need the examples, they are easy to skip, especially if they are properly demarcated in their own sections. Closely related to examples are applications - how this bit of math can be used to benefit mankind. StuRat 03:49, 22 November 2005 (UTC)

Hessian matrix usage

Please consider posting an example of obtaining and using a Hessian matrix to find the maxima of a likelihood function such as a multinomial function. Alternatively, please consider posting a reference or two where such information can be found. Thank you. {{Mark W. Miller 20:25, 23 November 2005 (UTC)}}

Thanks also to the individual who alerted me to how to sign my notes. -- Mark W. Miller 20:37, 23 November 2005 (UTC)

Well, you need the definition of Hessian matrix, and you need at a maximum to check it's negative-definite. Charles Matthews 08:15, 24 November 2005 (UTC)

Thanks. I'd already read the article. I was hoping an example would be added there, or for a reference or two that contained an example. My note was originally made in the Examples section, but was moved to its own section by someone else. -- Mark W. Miller 19:11, 24 November 2005 (UTC)

The simplest examples would likely come from quadratic programming, minimization of a multivariate quadratic function with linear constraints. Ignore the constraints. The objective function can be written f(x) = ½ x^TGx + c^Tx, where G is the Hessian. Because G is a real symmetric matrix, it can always be diagonalized, with the signs revealing the essence of the situation.

Hessian matrix	diagonal form	signature	kind of extremum
$\begin{bmatrix}2&1\\1&2\end{bmatrix}$	$\begin{bmatrix}3&0\\0&1\end{bmatrix}$	positive definite	minimum
$\begin{bmatrix}-2&1\\1&-2\end{bmatrix}$	$\begin{bmatrix}-3&0\\0&-1\end{bmatrix}$	negative definite	maximum
$\begin{bmatrix}1&2\\2&1\end{bmatrix}$	$\begin{bmatrix}3&0\\0&-1\end{bmatrix}$	indefinite	saddle point

It's easy enough to render a picture for each of these. Or consider the algebra, say of the indefinite example. In the diagonalized variables, f(p,q) = ½ (3 p² − q²). Clearly as p goes to positive or negative infinity f increases, while as q does the same f decreases. The square terms dominate any contribution from linear terms, thus c^Tx cannot affect the kind of extremum, but only its position. A constant term would only globally offset the value of f, nothing more, so it is omitted.

In the absence of constraints it is trivial to find the unique extremum of a quadratic objective. For more general functions, this would only be a local description, and finding a global extremum becomes difficult or impossible, as the function values can rise and fall unpredictably on a large scale. Nevertheless, this quadratic local description using the Hessian is often the best guidance we have in searching for a true extremum.

Is this the kind of thing you were looking for? Hope it helps. --KSmrq^T 20:03, 24 November 2005 (UTC)

Thanks. I think it is. I need to study it more, but I think it is. -- Mark W. Miller 08:14, 26 November 2005 (UTC)

I have now looked into Hessian Matrices and optimization a little, particularly with the Newton-Raphson Method and am starting to understand it a little. I've also looked into diagonalizing matrices which I think means creating a matrix of eigenvalues. I used a computer to obtain the eigenvalues of the three Hessian matrices above. I'm wondering if the middle one is:

$\begin{bmatrix}-1&0\\0&-3\end{bmatrix}$ .

Maybe the order doesn't matter. I still need to obtain the eigenvalues by hand. Anyway, thanks for the help. I've learned quite a bit this Thanksgiving holiday. -- Mark W. Miller 10:44, 27 November 2005 (UTC)

Matrix diagonalization (not our most readable article, I'm afraid) indeed results in a matrix with the eigenvalues of the original matrix on the diagonal and the order does not matter, so it seems you understood it correctly. -- Jitse Niesen (talk) 13:17, 27 November 2005 (UTC)

Wikipedia:Peer review/Logic

Your participation is appreciated... --- Charles Stewart 20:10, 23 November 2005 (UTC)

math reference desk

The Wikipedia:Reference desk was not too long ago split into subjects. Currently, there is a Wikipedia:Reference desk/Science subsection which is where math questions should go. It seems to me that math questions are a pretty small fraction of the posts there, and most go unanswered (unless they're high school math questions). How would you feel about having a separate place for math questions? I like to ask questions, and I like to answer questions, so I would like it. -lethe ^talk 20:25, 23 November 2005 (UTC)

If such a page existed, I would have it on my watchlist. Dmharvey 23:19, 23 November 2005 (UTC)

I would too. --- Charles Stewart 23:31, 23 November 2005 (UTC)

Same here, I support the addition of such a page. StuRat 00:32, 24 November 2005 (UTC)

I support this, although I may not have any time to answer questions. - Gauge 04:13, 18 December 2005 (UTC)

I am not very old on the project, so I don't know the level of questions that are posted, but I'll be willing to answer any that I can, and I too might have questions. So I support this. deeptrivia (talk) 04:19, 18 December 2005 (UTC)

Original research wiki

I've enjoyed editing WP so much that I've decided that it might be a good idea to organize my original-research thoughts, half-baked ideas, and full-fledged research results using a wiki, as opposed to trying to maintain a collection of half-finished LyX (TeX) documents (which is what I currently do, along with deep piles of paper). I was about to install my own private copy of the mediawiki software on my server when it occurred to me that perhaps I should enquire here first... Is there some public place where this could be done? I gather planetmath might be one-such, but I rather like the mediawiki interfaces. I don't know if wikibooks allow original resarch; also, as I want to publish my personal notes, I want to exert considerable editorial control (i.e. deny write access by default, grant write access only to friends).

The reason I find this interesting is the hyperlinking. Writing traditional, "flat", "linear" mathematics papers requires a review of basic concepts and notions early in the paper. Using a wiki allows these steps to be skipped, in favor of links. It also allows hyperconnections between related concepts: as sometimes, the difficulty of writing a math paper is figuring out how to lay out the ideas in linear order. So I think that playing with a wiki for pure research and pseudo (self-)publication might be a worthwhile experiment. But where shall I experiment? linas 17:37, 25 November 2005 (UTC)

Wikicities has an inactive mathematics wiki at http://math.wikicities.com. If that one is too general, I'm sure a pure research wiki could be set up at Wikicities if requested. Doesn't solve the problem of write access though. - Fredrik | t c 18:02, 25 November 2005 (UTC)

psychology

Hey everyone. I'm sure you've all seen talk pages featuring rather long-winded conversations like Talk:Mathematical_analysis (and archives), Talk:Proof_that_0.999..._equals_1, Talk:Four_color_theorem/archive2.... Typically an anon shows up and starts saying -- how to put this diplomatically? -- controversial things. Then the regulars here leap to the defence of rational thought. My question is: what motivates these people? What makes them tick? Why do they bother? Do they really think they're correct? Or are they just having fun? Dmharvey 20:19, 25 November 2005 (UTC)

Who are you referring to, the cranks or the regulars? In either case, the individual is motivated by an ah-ha moment, a sudden realization of a great truth that must be shared with the world. That ah-ha realization is presented in as simple terms as possible; the individual often lacks the formal background, and the intellectual stamina (and training) to triple-check their results (part of what one learns in school is not just collections of facts, but also the mental rigor to ask the right questions. Amateurs often lack the second bit.).

Also: Its a lot easier to argue than to double-check; its also easier to argue than to admit one's errors. Sometimes, during the argument, one can hide/obscure one's errors, thus saving face. One may also wait for the opposing side to make an even bigger blooper, which will distract attention, leaving the first side (although still wrong), relatively vindicated. These very natural and inherent argumentation techniques work well when there is no clear-cut right and wrong.

Think of all the political arguments you've been in. Think of all the arguments you've had with e.g. a lover, where you clung to arguments you knew wer wrong or pushed an indefensible point. Now realize that to the untrained, an argument about math is not really any different. You, as a mathematician, do believe in absolute right and wrong; with no grey; but the other side does not have as clear a vision of right and wrong as you do.

Physicists are notable in having training for dealing with grey areas: things that "feel right" but aren't provable or easily provable or easily formalizable. Some of the bitter battles in physics are high-end versions of the silly arguments you quote above. See e.g. the Hanbury-Brown and Twiss effect. linas 20:59, 25 November 2005 (UTC)

As a culture, we often celebrate as heroes not those who were smarter or had deeper insights, but who rather were able to stay on track, and not fall into the pitfalls and distractions. linas 21:05, 25 November 2005 (UTC)

Maybe we can create a central page where me move such posts so these anonymous people can battle each other out? (Unless they team up.) - Fredrik | t c 20:40, 25 November 2005 (UTC)

There is no single motivation. I'll suggest a few common ones; but the bigger question is how best to respond.

Divine revelation, or the equivalent sense of individual insight.
One of my most embarrassing memories is telling one of the top people in a field about such an idea I'd had, and being gently pointed at a major oversight. Unfortunately, some folks are so convinced they see truths to which others are blind, no amount of facts or reasoning will sway them.
Valid skepticism of sloppy arguments, leading to invalid dismissal of the assertions.
This applies to some of the discussions I've seen at Talk:Proof_that_0.999..._equals_1. Scientists and mathematicians use a casual shorthand style of communicating amongst themselves, and they lack training in foundations. Consequently, they write things for a more general audience that can be misunderstood, then they fumble around not knowing how to fill the gaps.
Hyperactivity.
Many Wikipedians are young and energetic, and type faster than they can think. Properly tamed, this can be a force for good. If it runs amok, this can cause widespread disruption. It is impossible for someone with a slower metabolism to keep up with manic edits, and Wikipedia's vandalism controls may not apply. Confined to talk pages, it's not so harmful; but it typically infects articles as well. One hint that this is happening is a look at the edit history; if it shows a long string of small edits at short intervals, chances are it's either hyperactivity or paranoia.
Need for attention.
This common motive sometimes stands alone, but can be coupled with other motives. It doesn't matter if the attention is laudatory or derogatory, so long as there's lots of it. Long responses, however clear or correct, only feed the beast. Others jumping in to help likewise make things worse. One symptom of this motivation is use of insults, as seen at Talk:Proof_that_0.999..._equals_1. Consciously or unconsciously, these are intended to goad more response. Don't take the bait! Admins must quickly and firmly respond as Jitse Niesen has done, saying such behavior is not tolerated; otherwise, it will escalate.
The elevator doesn't reach the top floor.
The general public suspects most mathematicians are mentally ill; some really are. Notable examples include Theodore Kaczynski (the unabomber) and Theodore Streleski (who after 19 years as a mathematics graduate student at Stanford murdered an adviser). Intelligence does not imply rational behavior; fortunately irrational behavior is often easy to spot (but not always). Wikipedia probably acts as a magnet for some of these folks, and we can only hope that their efforts here divert them from more harmful activities in the physical world. If you can handle the other motives, you probably have most of the tools for this one as well.

Speculating about motives can help suggest effective responses, but the usual rule here and elsewhere is to try to deal with the behavior itself, regardless of motives. As a rough analogy, rather than try to decide who is a terrorist and who is a freedom fighter, we would say "Blowing up innocent civilians is unacceptable behavior"; likewise, torture. --KSmrq^T 23:05, 25 November 2005 (UTC)

Interesting thoughts guys. Thanks. Dmharvey 01:06, 26 November 2005 (UTC)

When I was a student (of applied mathematics), I knew a crazy guy like this. He seemed to be quite clever and interested (he impressed me, because he wrote some quite interesting computer simulations), but he didn't pass the first year (though I am not sure if he really dropped out). I think he had a problem that he was too focused to solving his own problems on his own and was uninterested in the contributions of others (mathematicians); for example, he was interested in tetration (like some guy here too), but when I told him to read something about algebra, he refused. Samohyl Jan 12:48, 26 November 2005 (UTC)

Category:Mathematical model on CfD

User:CarlHewitt has created a new category, Category:Mathematical model, which he's been populating with theories, not models. I've put it on CfD. Opinions solicited (as always, whether they agree with mine or not). --Trovatore 00:42, 26 November 2005 (UTC)

Ummm... perhaps he's just using the term "model" in a broader sense than that used in logic? Dmharvey 00:56, 26 November 2005 (UTC)

Possible in the abstract, but none of the articles with which he populated the category (Set theory, Peano axioms, Non-Euclidean geometry) fit any notion of model known to me, and the danger of confusion from calling them "models" is unacceptable in any case. --Trovatore 01:19, 26 November 2005 (UTC)

See the discussion at Wikipedia:Categories_for_deletion/Log/2005_November_26. Regards,--Carl Hewitt 18:25, 26 November 2005 (UTC)

Hewitt is conflating at least two different meanings of "model". This category is of dubious use. More useful is the existing category of scientific model, which he's going around removing .--CSTAR 20:15, 26 November 2005 (UTC)

It has been proposed to create category Category:Mathematical model (to go with the existing article Mathematical model) as a subcategory of Category:Scientific modeling. CSTAR opposes this proposal. Regards,--Carl Hewitt 20:32, 26 November 2005 (UTC)

Google books

Today I discovered the thing called Google books. I had a question about harmonic functions, and I found excellent excerpts from books where this topic is covered. This tool would be very helpful for editors who are too lazy to use the library, and could also be used in checking the information and adding references to existing articles. Oleg Alexandrov (talk)

Is really great, except that you can only view three pages, so you still need to go to the library. —R. Koot 01:02, 26 November 2005 (UTC)

Of course you need to go to the library if you want to read a lot.

The big question is, how will this affect Wikipedia? How valuable is it to spend a good chuck of time writing an article if you are aware that the same information is already summarized in two pages in a book online which anybody can read? Oleg Alexandrov (talk) 01:31, 26 November 2005 (UTC)

I think the viewing constriction and search limitations are large enough to prevent this from being used as anything else than a very handy index to my library. I used it to find some books on the actor model. More importantly, an encyclopedia is something very different from a book. On Wikipedia you can look up something about a specific thing, person or theorem. When you read a book, you will often need/want to read the entier thing. Of course, then you've gained a lot more knowledge, but it would have taken you a lot longer. —R. Koot 02:08, 26 November 2005 (UTC)

I agree with R. Koot. For me it is much easier to rapidly digest information from Wikipedia than it is from Google Books. Additionally some books have pages missing from them (a feature Google provides for publishers). 127 15:28, 30 November 2005 (UTC)

Computability, recursion theory

Background: Due to the influence of Soare, in recent years it has been fashionable to use the term "computability theory" for what used to be called recursion theory. Very recently on WP, Category:Computability was renamed to Category:Theory of computation, where some of the articles are a good fit, but by no means all of them. Also the computability theory article underwent a substantial rewrite, focusing almost entirely on the aspects of interest to computer scientists rather than mathematical logicians.

This left a big void, as recursion theory or computability theory (as you prefer) is standardly considered one of the four branches of mathematical logic (the other three being set theory, model theory, and proof theory). So I created Category:Recursion theory and a stub article at recursion theory.

What needs to happen now:

A decision needs to be reached about whether this split is really correct, and if so, what are the criteria. The rough criterion I used to divide articles between the categories was whether I thought the topic would be studied by people who think of themselves as mathematical logicians, or people who think of themselves as computer scientists. A very substantial overlap remains. If the categories were to be remerged, though, it certainly couldn't be under the name "Theory of computation". If the articles were remerged, the new article would have to spend less time talking about Turing degree 0, to get to some real topics in recursion theory faster.
Assuming the articles remain split, recursion theory needs to be enormously expanded.
I was conservative in removing Category:Theory of computation from articles. Someone who knows about theory of computation should go through the articles in the intersection of the two cats and say "That's not theory of computation" on some articles.

See the discussion at Talk:Computability theory (computation). --Trovatore 20:31, 26 November 2005 (UTC)

I strongly believe these two categories should remain split. As this is important to both mathematicians and computer scientists their will always be one party who will get confused if we merged them. (E.g. computer scientist being not so very interested about thing with a Turing degree greater then 0, and mathematical logicians being not se very interested in thing with Turing degree 0. —R. Koot 16:32, 27 November 2005 (UTC)

A aplit here seems to make sense. Computability theory should be the article called Computability theory (computation), with the reference at the top to recursion theory. Though really the two are the same topic, its just that recursion theory more with nonphysical computational models. Also, Computation should redirect to Computer, and a new article perhaps using some of the content from Computation should be at Theory of Computation, which would be a good overall starting point for the whole shebang. Complexity theory is currently of pretty embarassing quality and needs to be rewritten. I may do that at some point, though before I did I wanted to see how my Computability theory (computation) was recieved, and since I started that from a stub it seems less likely to be a problem. --Readams 22:32, 28 November 2005 (UTC)

something's up with tex rendering

Does this look a bit odd to anyone else? $\iint$ Dmharvey 01:37, 27 November 2005 (UTC)

Yes, it's broken for me. The top right corner of the second integral sign is cut off. I've had a quick look through Help:Formula and caught no defects there, but caching could hide recent breakage. Here's an experiment:

$\int$	$\iint$	$\iiint$	$\oint$
$\int_{\!.}^{}$	$\iint_{\!.}$	$\iiint_{\!.}$	$\oint_{\!.}$
$\int_i^{}$	$\iint_i$	$\iiint_i$	$\oint_i$
$\int \omega$	$\iint \omega$	$\iiint \omega$	$\oint \omega$

There seems to be a pattern. --KSmrq^T 02:46, 27 November 2005 (UTC)

Carl Hewitt, Rudy Koot and Edward Schaefer

See Talk:Model (abstract)#Dispute and Wikipedia:Requests for arbitration#Carl Hewitt. —R. Koot 16:38, 27 November 2005 (UTC)

Also please see User_talk:CarlHewitt#Arbitration_with_Rudy_Koot_and_Edward_Schaefer--Carl Hewitt 18:52, 27 November 2005 (UTC)

Isn't this kind of dispute an unavoidable consequence of the non existence of well identified editorial boards with reknown expertise in each domain? pom 00:52, 28 November 2005 (UTC)

The dispute would not be avoided by editorial boards. Many of Carl Hewitt's additions were technically incorrect, as many here, who are domain experts, will attest. Having a formal editorial board confirm that there are numerous, flagarant, technical problems with Carl Hewitt's edits would not diminish the controversy. (And that is the root of the problem). linas 04:05, 28 November 2005 (UTC)

Dear Linas Vepstas,

Can you point out a single technically incorrect contribution that I have made in the area of Computer Science?

Regards,--Carl Hewitt 04:25, 28 November 2005 (UTC)

Carl, all of our arguments and collisions were over issues in the areas of gravitation/general relativity, quantum mechanics and, to a lesser extent, electronics. I don't beleive we ever discussed computer science issues. linas 22:05, 28 November 2005 (UTC)

Linas, we have certainly had our collisions! See User_talk:CarlHewitt#Note_to_CSTAR.

However, it was sad to see User:CSTAR drop off the face of the Wikipedia.

Regards, --Carl Hewitt 23:12, 28 November 2005 (UTC)

The role of an editorial board is not only expertise. Its role is fundamental in the refeering process: its arbitration is definitive and accepted by all parts a priori. pom 11:03, 28 November 2005 (UTC)

User:CSTAR

I can't help noting that User:CSTAR has abandoned Wikipedia, or has gone into hiding, or is at least taking a wikivacation. It is hard for me not to conclude that this RfC and some of the personal attacks it engendered was the proverbial straw. I enjoyed CSTAR's company, ad saw him as a good, highly qualified editor working in the general area of operator algebras and (surprise) C*-algebras. Unfortunately, this meant that he was often involved in disputes fending off the latest cranky quantum mechanics edit, and I suspect this sapped a lot of his energy. I am not happy about his departure, as he was a valuable and trusted editor. linas 22:05, 28 November 2005 (UTC)

CSTAR was pretty much our only line of defense against the local variables agenda of Catherine Thompson. Without him, we're lost. What RfC are you referring to? -lethe ^talk 03:34, 29 November 2005 (UTC) Edit: Oh, you must be talking about the stuff in the post above this one. I see. -lethe ^talk 03:43, 29 November 2005 (UTC)

I tried to follow a bunch of those links to see what happened, and I couldn't really follow the various threads. Nor do I think I want to. So I'll just say again that if crackpottism and rudeness soured CSTAR on this place, more's the pity. -lethe ^talk 03:54, 29 November 2005 (UTC)

Addition has been overrun by Sigmas!

Seriously, though, I think Addition needs a content shuffle. Please drop by Talk:Addition#Split.3F. Melchoir 06:00, 28 November 2005 (UTC)

Okay, I've got a decent consensus over there, so you may return from the edges of your seats. If anyone wants to help clean up after me, go ahead and visit addition and summation this weekend. Melchoir 19:09, 29 November 2005 (UTC)

math reference desk made

Wikipedia:Reference desk/Mathematics. No posts yet. -lethe ^talk 06:43, 29 November 2005 (UTC)

Good move. Dmharvey 12:52, 29 November 2005 (UTC)

Dimitri Egorov or Dmitry Yegorov?

Copied from Portal:Russia/Russia-related Wikipedia notice board -- Jitse Niesen (talk) 13:44, 30 November 2005 (UTC)

Ghirlandajo, I noticed you moved Dimitri Egorov to Dmitry Yegorov. I debated with myself for a while as to how exactly I should name the article, given that there are alternate spellings. Actually I was only considering the difference between Dimitri and Dmitri, but clearly his family name can be spelled differently too. In the end, I chose Dimitri Egorov because that's the spelling given on The Mathematics Genealogy Project. Since you're living in Russia, I obviously bow to your knowledge on this subject, but I'm wondering if there is a standard way of spelling Russian names such as this? Forgive my Canadian ignorance on the subject - I'm hoping to maybe add some more stubs of Russian mathematicians in the future, and it would be great if I knew how to do it properly to begin with. Cheers! --PeruvianLlama^(spit) 20:24, 21 November 2005 (UTC)

I want to thank you for the article you created. We already have Boris Yegorov, Aleksandr Yegorov, and now Dmitry Yegorov. I just thought it helpful to standartize the spelling of this surname. By the way, a disambiguation page would be helpful too. --Ghirlandajo 21:35, 21 November 2005 (UTC)

I actually had the same question. The spelling Egorov seems to be much more common. I think I understand where you're coming from: the surname seems to be written Егоров in the Cyrillic alphabet, and the Cyrillic Е at the start is typically transliterated with "Ye". However, I think the fact that Egorov is the common spelling (if that's true) takes priority. What do you think about this? -- Jitse Niesen (talk) 22:35, 22 November 2005 (UTC)

The spelling used should be the one under which his English-language papers (or translations to English) are most commonly published. Da? linas 00:38, 1 December 2005 (UTC)

With "Da" meaning yes, in Russian (Egorov would approve :) Oleg Alexandrov (talk) 02:53, 1 December 2005 (UTC)

Just a comment, Boris Eltsin is a redirect to Boris Yeltsin. Both Dmitriy and Dmitry are acceptable, I met people who spelled their names both ways, I am not so sure about Dimitri.(Igny 03:37, 1 December 2005 (UTC))

According to MathSciNet, 72 papers have "Egorov" in the title (including a Math. Intelligencer article Dimitriĭ Egorov: Mathematics and religion in Moscow, where the last letter of the given name is i-breve), 30 "Egoroff", and none "Yegorov" (Egorov/Yegorov himself died in 1931, so his papers are not in MathSciNet). Given this, I intend to move the page back. -- Jitse Niesen (talk) 13:49, 5 December 2005 (UTC)

Obviously the Special:Whatlinkshere/Dmitry_Yegorov will pick this up too, but I thought I'd explicitly point out that that disambig page Yegorov will need to be changed. In fact, generalizing this conversation to the surname in general (and not just that of Dimitri/Dmitri/Dmitry Yegorov/Egorov), perhaps the disambig page could use some working over. --PeruvianLlama^(spit) 14:40, 5 December 2005 (UTC)

Requesting mathematical relations for Intentionally blank page

I was told this project is "the best WikiProject on Wikipedia", so I am hoping someone can help. I would like to equivalently represent the use of the phrase "The page is intentionally left blank" on blank pages. The phrase is a self-refuting meta-reference, in that it falsifies itself by its very existence on the page in question. I made this same request at the reference desk, but only got limited answers. One person suggested using Gödel numbering, while another said:

"The "self-referential propositional calculus" of Yiannis N. Moschovakis is expressive enough to capture the liar. (Note that Gödel sentences do not capture the liar; they assert their own unprovability, not falsehood.) Moschovakis gives SRP a semantics using least-fixed-point recursion. The liar comes out neither true nor false using that semantics."

But I am at a loss as to how to proceed from here. I will be submitting this article to WP:FAC soon, and would really like to have a paragraph concerning specifically this. Thanks! — BRIAN0918 • 2005-12-5 02:09

I'm afraid I don't know enough logic to answer your question. However, I can try to explain the above quote. Firstly, "self-referential propositional calculus" (whatever that may be) is something that probably very few people know about so think carefully whether including it in Intentionally blank page is useful. Secondly, "the liar" refers to the liar paradox, which is not quite the same, as noted on Talk:Intentionally blank page (but if "self-referential propositional calculus" can express the liar paradox, it might also be able to express "this page is blank"; my best guess would be "p = ε" where p refers to the proposition itself and ε is something like the null sequence). Thirdly, in my opinion the link with Gödel's second incompleteness theorem is rather weak and definitely not worth mentioning in the introduction, if at all. -- Jitse Niesen (talk) 13:20, 5 December 2005 (UTC)

Re-creation of Category:Mathematical model

I have proposed the re-creation of Category:Mathematical model. Please discuss in Talk:Mathematical model. Thanks,--Carl Hewitt 19:16, 6 December 2005 (UTC)

0.999...

Hi everybody! If you're not already aware of the mess attached to the talk page of Proof that 0.999... equals 1, consider yourself lucky. I'm here to solicit comments on my proposal to rewrite that page and confront all the popular misconceptions. Please see Talk:Proof that 0.999... equals 1#If I may speak to the article itself.... Thanks, Melchoir 21:25, 6 December 2005 (UTC)

Hi, I think it is useless to post on that talk page, since in my opinion at least two of the anons (if not identical) are trolls, i.e. people who know better but choose to cause confusion. Things that went unremarked and that are the reason of my suspicion:

there are no predecessors (next smallest elements) in the usual order on the rational or real numbers, and
I think it is highly unlikely that anyone was taught real numbers at school. Decimal fractions were surely taught, and also periodic infinite digit sequences as representations of fractions. Infinite digit sequences in general may have been mentioned, but surely no operation was defined on them, and most surely there was no proof that e.g. the multiplication is associative.

What may serve as argument:

In contemporary mathematics, noone constructs real numbers by infinite numbers of digits. One of the articles cited tries, IMO, to highlight the difficulties of this approach.
Real numbers are defined by the field axioms, the archimedian axiom and the order completeness (total order axiom?). Models of real numbers are constructed by Dedekind sections, classes of Cauchy sequences or nested intervalls. All models satisfy the axioms and are equivalent.
Infinite digit sequences are (besides infinite continued fractions) one of the representations of real numbers, $m.d_1d_2d_3\dots$ has the interpretation that each of the rationals $q_n:=m+\sum_{k=1}^n 10^{-k}d_k$ is an approximation of the represented real number and that this real number lies inside the intervall $[q n, q n + 10 - n]$ . This gives a Cauchy sequence or a sequence of nested intervalls, so we end up in one of the models.
For the digit sequence in question, those intervalls are $[1 - 10 - n,1]$ , so there is no sense in stating that 1 is outside or bigger than the numbers in those intervalls.

--LutzL 08:23, 9 December 2005 (UTC)

I fully agree it is useless to continue loosing time with this. Don't you think there should be a special category for such useless time consumming futilities? pom 19:04, 9 December 2005 (UTC)

The page should never have been created - anyone knowledgeable could have predicted the result. There is no assumption here that a proof is 'encyclopedic', and the result is of course just a case of something on geometric progressions. To create a page precisely because people without a full background argue about such matters is to ask to have one's time wasted. Yes [[Category:Pages which were not such a good idea]]. Charles Matthews 11:58, 9 December 2005

Thank you, category added. (for about 1mn before having been reversed by someone...) pom 01:31, 10 December 2005 (UTC)

This argument only draws attention because it expresses a peculiarity of positional notation systems. Therefore, I move that this matter be resolved by merging the article into positional notation. I have added the appropriate tag. Deco 02:12, 10 December 2005 (UTC)

I'll comment more on the article talk page, but several remarks here are puzzling. Please be careful to distinguish between the article and its talk page. Yes, there is endless and sometimes ridiculous discussion on the talk page, but the overwhelming majority of the chatter has nothing to do with the actual contents of the article. Even the remark here about "just a case of … geometric progressions" ignores the proofs actually used, one of which is based on Dedekind cuts and another on Cauchy sequences. Nowhere in the article is the value of 0.999… defined as a limit of a geometric progression.

Frankly, given that the talk page is supposed to be about improving the article, I'm surprised one of the seasoned Wikipedians here has not intervened to put a stop to the nonsense. If it's a bad idea to have an article we know will attract controversy, we'd better get rid of abortion and Jesus Christ and socialism and … . (Mounting soapbox.) This ongoing misuse of the talk page could spill over into the article, despite the complete lack of reputable dispute about its topic. That is a weakness of Wikipedia, whatever the disposition of this article. --KSmrq^T 03:44, 10 December 2005 (UTC)

FWIW, Don't under-estimate infinite-digit sequences. The z-transform of the sequence of digits in the (p-adic) expansion of a real number is a Cantor space, and so, in this very certain sense, there are topologies of the real number line where 0.999... is inequivalent to 1.000... Its a subtle point, and it seems to have something to do with "why there are fractals", which are crawling with these kinds of topological inequivalences. There are topologies that naively seem to be isomorphic to the real numbers, but on closer examination are not. The expansion in terms of digits is one of them. So maybe the article isn't very good, but the topic merits a deeper examination, since its a truism often taught in grade/high school, and has difficult subtleties associated with it. linas 07:22, 10 December 2005 (UTC)

Oh, Linas, ny mistake - what the page needs is more of your stream-of-consciousness free association - that will really set them straight:). Of course, like 0/0 one can squeeze some good mathematics out of it. But common sense applies: Gresham's Law and Don't Feed the Troll. The analogy with contentious topics in religion or politics is no apt. There is not the slightest need to have a page with this exact title, and it could usefully be merged. Charles Matthews 14:37, 10 December 2005 (UTC)

Arabic numerals RfC

Just a note that Arabic numerals has been listed at WP:RFC under mathematics regarding a heated dispute over numerous content changes. Peyna 16:26, 11 December 2005 (UTC)

CSTAR has left the building

For those who may not know, CSTAR (a well respected math and physics editor) has left Wikipedia, perhaps for good, primarily because of the Carl Hewitt affair. Paul August ☎ 20:39, 12 December 2005 (UTC)

Let's hope his comeback tour is planned, though. Charles Matthews 20:42, 12 December 2005 (UTC)

Yes let's. Paul August ☎ 21:01, 12 December 2005 (UTC)

He told me he would think about returning in the New Year, but he indicated that it was very far from certain he wanted to return. Carl Hewitt may have been the proximate cause of his departure, but he's had more than his fair share of unrewarding WP experiences. If he does return, I wish him better luck with what follows. --- Charles Stewart 21:40, 12 December 2005 (UTC)

It seems that R.Koot left for the same reason. I think both of them should have waited for the conclussion of the RfArb against Carl Hewitt, but I do understand how frustrating it should have been to deal with this person. Oleg Alexandrov (talk) 22:08, 12 December 2005 (UTC)

WikiScience

Everybody here please have a look at my MetaWiki proposition for the creation of wikiscience, a technical wiki-based encyclopedia that will allow for ORIGINAL contributions from users plus the most up-to-date research from professionals (as well as being a math and science encyclopedia). Wikipedia as it stands is far from this, as well as other sites such as "Mathworld". Math and science is simply too technical and evolving of a subject to be thrown about with the rest of wikipedia articles. Math and science, given its special nature of presentation and subject, needs to be part of the wikipedia whole, yet seperate and organized (I think we all agree). I believe that the wikimedia foundation has the momentum and the user base to make this extroadinary contribution to the math and science community, but I need supporters before wikimedia makes this happen.

If you are interested in making this happen please visit the link and show your support. Also, if you want more detail of my idea, or have any suggestions or criticisms please visit WikiScience Details! Thanks! --B21.12.52.123 12:55, 13 December 2005 (UTC)

I'm thinking along the lines of "arxiv.org", but with wikilinks and author-controlled pages. Among other things, it would put an end to l'Affaire Hewitt ici, and allow a flourish of edits there. As such, I strongly support and recommend further development. I also support because I want to experiment with keeping my personal research notes/diary in media-wiki style. linas 21:12, 13 December 2005 (UTC)

I'm against it. I think it will divide the efforts of editors, with the most technically inclided editors eschewing wikipedia general. I don't think there should be a limit on how technical articles in wikipedia get (Wikipedia wants to be the sum total of human knowledge). To the critics who complain when they come to an article that's too technical, well, we can make each article as approachable as possible, but in many cases that will still be entirely incomprehensible to most people. C'est la vie. -lethe ^talk 22:03, 13 December 2005 (UTC)

This is a good point. Should non-technical, simple summeries of math and science concepts still be in wikipedia? Or should all of math and science move to WikiScience? I am leaning toward the first one, that is, wikipedia (like any other encyclopedia) should still have relatively simply worded and accessable concepts in math and science, but for more in-depth and up-to-date modern (and original research from users) research, plus more in depth on the "simple" concepts, wikiscience would be the home. Does this divide contributers? Not if the technicality of the articles on wikipedia is kept to a minimum (like other paperbased encyclopedias). In fact, I would say that what is one wikipedia right now suffices for this pupose, so no extra work would need to be done in wikipedia.--B21.12.52.123 22:47, 13 December 2005 (UTC)

I would like to know more specifics on how you propose to decide who is allowed to edit a page. Dmharvey 22:10, 13 December 2005 (UTC)

I'll post some ideas soon...--B21.12.52.123 22:47, 13 December 2005 (UTC)

Bad idea, as far as I'm concerned. We have a perfectly adequate framework for mathematical exposition here (modulo the troubles with symbols). Integrating mathematics with history, geography and intellectual trends goes on here in a way sadly missing in most texts. Our mathematics here is a clear advance on both PlanetMath and MathWorld, and the main current difficulty seems mostly to get enough people working on bringing the coverage up to date. We have the quality of people tp do that, so it's a matter of time, really. Charles Matthews 22:51, 13 December 2005 (UTC)

I am leery of anything that might result in duplication of effort. Wikiscience should not be an encyclopedia, since we already have that here. Since that is how it has been defined above, I am against it. - Gauge 05:27, 18 December 2005 (UTC)

What do you mean by: "Math and science is simply to technical and evolving of a subject to be thrown about with the rest of wikipedia articles. Math and science, given its special nature of presentation and subject, needs to be … separate …". Are you saying that the math and science content should be moved from Wikipedia to Wikiscience? Paul August ☎ 22:54, 13 December 2005 (UTC)

All this Wikiscience business makes me weary. Serious posts by anonymous contributors also (make an account, buddy).

As Lethe said, there should be no limit to how technical or complicated articles on Wikipedia can get. Yes, one should strive to make things approachable, but within limit of common sense.

Some people might indeed be happy contributing to a project like Wikiscience (Linas is an example). But talking about moving (not copying, but moving) technical content from Wikipedia to there is not serious. Oleg Alexandrov (talk) 00:53, 14 December 2005 (UTC)

OK, here's the rub: if WikiScience is offered as a competitor to WP, then I agree with Charles and Oleg: heavy-duty, in-depth science articles belong on WP. Furthermore, the creation of wikiscience will not "cure" any purported problem about lack of depth in WP articles. On the other hand, if Wikiscience is offered as a companion to WP, that's different. The "companion" properties I'd like to see are (1) encouragement of publication of original research and (2) total control of articles by primary authors. I envision the ideal companion to be an "arxiv.org with wikilinks and social infrastructure".

Set up as a companion in this way, it won't dilute resources: for example, I still do original research, and my doing that should not be construed a "dilution". Another example: WP editors who are in constant clashes may find life to be more acceptable over there, since they'll always get thier way. Would thier departure be much of a loss to WP? Probably not.

The one thing I want to do, that WP won't let me do, is for me to keep a set of pages of my original reaserch, that I totally control. While I can do this on external websites, its not ideal. On my personal website, I'm missing a collaborative environment and a place to discuss. At planetmath, I'm missing the mediawiki interfaces I've grown accustomed to here. And its not "integrated" with WP: cross-linking is hard, visual presentation is different. On arxiv.org, I've got publication, and a stable, long-term document repository; but I'm missing collaboration, etc. What I would very much like to see in the WikiScience proposal is a solution to these problems. linas 00:58, 14 December 2005 (UTC)

Wikipedia does not yet have an adequate solution to becoming a reputable encyclopedia. That issue must be addressed across all articles, not just science and mathematics. Incorporation of original research is a separate question, though quality control mechanisms may overlap. A reader is looking for coverage, correctness, and clarity. (Can I find what I want, including recent work? Can I believe what I read? Can I understand it?) A writer is looking for exposure, helpful feedback, and a vetting process that is expert and fair. (Also, perhaps, scholarly credit and article stability.)

The WikiScience proposal might provide a venue for original research, but it does not address the Wikipedia-wide issues, and it does not provide the vital details of how readers and writers are to be satisfied. Note that Wikipedia, with no technical changes, could choose to flag some articles as "advanced". --KSmrq^T 02:56, 14 December 2005 (UTC)

--B21.12.52.123 11:02, 14 December 2005 (UTC)===Wikipedia vs Wikiscience===

First off, I am not an annonymous user. I chose this name arbitrarily when I was just starting to contribute to wikipedia articles. If this name bothers any of you I guess I can change to a "normal" name. My name is Parker W. and I am an ex-math major from the University of Oklahoma. I am a real person lol...later on if this gets more support I will start a mailing group so people can contact me personally.

Charles Matthews: Wikipedia as it stands is FAR from any serious math resource. The trial of Michael Jackson is like 10 times longer and more complex than the article on E. Given E is one of the most beautiful and important numbers in math, this is a travesty or at least an embarrasment to wikipedia's scope in math.

Show me where else on the Web you can find a page like Enriques-Kodaira classification. Charles Matthews 09:43, 14 December 2005 (UTC)

Great article, but this is simply out of place here. No one will look at it here; this is akin to sticking this article in Encyclopedia Brittanica...its just awkward here. Wouldnt you rather it be at a place it can be respected and used? People DONT come here for serious math and science research/enrichment/collaborations and those of you who think so are in denial: you are wasting your time here with these advanced articles! They need a proper HOME; such as wikiscience.--B21.12.52.123 09:59, 14 December 2005 (UTC)

That is nonsense, and annoying nonsense at that. Charles Matthews 10:06, 14 December 2005 (UTC)

Agreed. It is nonsense. As wikipedia grows in coverage, every math grad student in the world will know to come here. This article will certainly see use. Who cares how it compares to Michael Jackson? -lethe ^talk 10:16, 14 December 2005 (UTC)

I looked at said article here just a couple of days ago. I am a PhD student, and I found it fascinating and useful. - Gauge 05:48, 18 December 2005 (UTC)

The comparison with the MJ article was used by me as an example of the focus of the general user base of wikipedia. Wikipedia, by its nature, is constantly regressing to the mean, that is, the interests of the "average" person. This is completely fine in most cases when you need information on popular topics but is completely disabling to the promotion of advanced non-popular topics. I did a little walkthrough of wikipedias science as math articles and about 20% of the time the article said "this article needs the attention of an expert". Gee, thats a real affirmation of wikipedias strength in math and science; and this isnt in the beggining stages, this is after 4 YEARS of wikipedia.

Face it; it is a vicious cycle. You are surrounded by people who don't care about any of this stuff and never will. The articles (or lack therof) show it. What we need is a different framework and community of more like-minded people, similar to PlanetMath, but much much better, parterned with wikipedia. Don't throw your pearls amoung the swine!--B21.12.52.123 11:00, 14 December 2005 (UTC)

I agree with Charles; Wikipedia's mathematics coverage is one of its high points. -- The Anome 10:10, 14 December 2005 (UTC)

Of course you do. Your POV is that of a mathlover (or I assume you wouldnt be here).--B21.12.52.123 11:03, 14 December 2005 (UTC)

Paul August and Oleg: As I said before "...that is, wikipedia (like any other encyclopedia) should still have relatively simply worded and accessable concepts in math and science, but for more in-depth and up-to-date modern (and original research from users) research, plus more in depth on the "simple" concepts, wikiscience would be the home. Does this divide contributers? Not if the technicality of the articles on wikipedia is kept to a minimum (like other paperbased encyclopedias). In fact, I would say that what is one wikipedia right now suffices for this pupose, so no extra work would need to be done in wikipedia"

That is, WikiScience is in my mind a companion to Wikipedia. As any encyclopedia, Wikipedia will have entries on math and science, moving them or getting rid of all the math and science articles in wikipedia would be absurd. However, for the lastest "peer-reviewed" (at least compared to wikipedia) research, both amateur and professional, for indepth technical articles suitable to those in the math and science fields, and for proper organization and stucture that is helpful to those seeking mathematical and scientific information, WikiScience will serve that function.

C'est la vie remarked that "wikipedia wants to be the sum total of human knowledge". This is not correct. Wikipedia, however revolutionary and huge it my be, is still an encyclopedia and has many guidelines as to what shouldn't be in the encyclopedia such as definitions of words, news stories and the like. This is why wikitionary, wikinews were created, respectively. The content matter of these sister projects is just to different to be mixed in with what is suppost to be an encyclopedia.

First of all, my username is Lethe, not C'est la vie. Second of all, Jimbo himself said:

"Imagine a world in which every single person on the planet is given free access to the sum of all human knowledge. That's what we're doing." -Jimmy Wales, July 2004

Therefore, I believe all math knowledge that has been vetted by the publication process should be here. Thus WikiScience will only be appropriate as a place for pet projects and crackpots. Once something is published, it needs to be here, as soon as someone is ready and able to put it. We are not bound to keep things down to high school knowledge here, and I think that suggestions to limit the amount or extent of knowledge to go here will be rabidly opposed. -lethe ^talk 10:20, 14 December 2005 (UTC)

Hey, folks, don't bite. And B21.12.52.123, you might want to spend a little more time acquainting yourself with Wikipedia's culture, values, processes, and content before you try to reform it. (It's hard to get people to follow you if you're stepping on their toes.) --KSmrq^T 11:43, 14 December 2005 (UTC)

As is with what I proposed to be put in wikiscience. But just because wikinews and wiktionary were created, doesnt mean that all articles defining words and all articles reffering to current events were removed! These articles in math and science which are "different" are what I call technical articles.

"Techical vs "non-technical" math and science articles

Technical articles and qualitatively and quantitively different from non-technical articles, as I shall dub them, which are currently in wikipedia.

The key difference is rigor. Going back to my example of the Michael Jackson trial (no offence to MJ:)), a minor detail such as, Mr. Mesereau's shows were black at the trial would have no effect on the overall information of the article. If that were in-fact, not true, than the article would not be compromised.

With a techical article it WOULD be compromised if a small detail was wrong, unfounded, or erronious. The ENTIRE article would be compromised in the eyes of any serious student/enthusiast or researcher. This is why we have CRC handbooks, Mathematical encyclopedias, or resources such as the arxiv. Now this does not mean that any of the articles in math and science here are "wrong" or "unfounded" or inadequate, it just means that they serve a different purpose from technical articals. This is that of exposition. Technical articles are not generally expository (all though than can be), are more in-depth, and contain more "sensitive" topics (topics that the reader my require a corresponding source or cite, as well as a cite of proof). One is not "better" than the other, they are just serving different needs. Wikipedia currenty does not meet the latter's needs.

What is the crucial difference then that wikipedia can't facilitate? This is that of critical review. Critical review is the lifeblood of technical articles. I will wait and give my list of possible implementations of critical review just in case you guys want to respond to anything I said of have criticisms or concerns of what I just posted.

--B21.12.52.123 05:04, 14 December 2005 (UTC)

IN SUMMERY: WikiScience is to Wikipedia as The CRC Handbook plus Mathword plus summeries of discoveries in the latest math and science journals, plus orginal contributions from users and professionals is to Encyclopedia Brittanica. Neither one is "better" they are just different. Wikipedia will still have math and science articles just as Brittanica does.

There might be a place for a wiki which allowed original research in mathematics. However in my opinion Wikipedia is currently the best single resource for mathematics. And I expect it to remain so for a long time to come. I can see no good reason to restrict Wikipedia to only a certain level of mathematical sophistication. Paul August ☎ 05:11, 14 December 2005 (UTC)

Wikipedia is already restricted in mathematical sophistication...visit the article on E like I mentioned. It is WikiScience that would be unrestricted. You are not going to find a technical article on E even in the greatest paper based encyclopedias because thats not what they are there for, wikipedia is no different.--B21.12.52.123 05:25, 14 December 2005 (UTC)

Time to up the sophistication level of the e article, then. -- The Anome 10:12, 14 December 2005 (UTC)

Regardless of the current quality of math wikipedia, we aim to subsume EB, CRC Handbook (isn't that just a table of data? That actually, we will not subsume), mathworld, EDM2, Soviet encyclopedia, and others. -lethe ^talk 10:50, 14 December 2005 (UTC)

"We" aim? You and who else? Are you implying that a small group of people could assimilate that much information into wikipedia? Its going to take an army of nerds to do it. That is the key. We need to create an accomadating environment that attracts NERDS and specialists. This environment would include proper peer-review that specialists desire, collaboration possibilities, original research inclusion, everything that a math and sci specialist or enthusiast WANTS and needs. Well guess what? That isnt wikipedia. So whats happening? A lone band of nerds (I use that term in the utmost respect) is trying to assimilate huge bodies of knowledge into a place that isnt meant for them. We need a NERD ARMY my friend, and that army won't assemble at wikipedia.

--Hypergeometric2F1[a,b,c,x] 11:29, 14 December 2005 (UTC)

We had this once. It was called Nupedia. Larry Sanger has been lamenting its demise for years, and making calls to arms to restore an expert-based, limited-editing pedia for just as long. It's not a terrible idea, but just so you know, it's been tried already, and people aren't to keen to give it another go here at wikipedia. -lethe ^talk 11:45, 14 December 2005 (UTC)

Looks like I missed this conversation overnight. I'd just like to say I sympathise with the points expressed by Charles, Lethe, Paul, etc, and not so sympathetic to B21.12.52.123. Dmharvey 12:55, 14 December 2005 (UTC)

I have joined the Wikipedia:Project Mathematics and have introduced myself on the participants page. I will keep campaigning for this idea, but in the meantime I will contribute what I can and see what happens. --B21.12.52.123 06:58, 14 December 2005 (UTC)

I have also created a new nickname to assuade confusion --Hypergeometric2F1[a,b,c,x] 11:18, 14 December 2005 (UTC)

Welcome to the project B21/Hypergeometric. Yes it will take a lot of people and considerable time to create all the content we envision, but fortunately we have many qualified mathematics editors and all the time in the world. Are you familiar with all the content that this small "army of nerds" and others have already created (see List of mathematical topics and List of lists of mathematical topics)? I think your idea of joining the Mathematics Project to gain some experience in how Wikipedia works (or doesn't as the case may be) is a good one. You are correct in saying that original research, being non-encyclopedic, has no place on Wikipedia, and as I said above a separate wiki that allowed that might be a good idea. But for encyclopedic content I think it will be very hard to do better than Wikipedia. Again welcome. Paul August ☎ 15:07, 14 December 2005 (UTC)

Debunking a claim

Above, Hypergeometric2F1[a,b,c,x] wrote that

I did a little walkthrough of wikipedias science as math articles and about 20% of the time the article said "this article needs the attention of an expert".

Well, I counted all the mathematics and mathematician articles which have either a {{attention}} or {{cleanup}} or {{expert}} template either in the article or on its talk page. I found 98 of those. Jitse's tool states that there are 33 more at Wikipedia:Pages needing attention/Mathematics (and thre could be an overlap with the first 98). All in all, we get 131 pages needing attention of a total of 11000-11713 articles, which is 1.19%, a far cry from 20%. Oleg Alexandrov (talk) 22:14, 14 December 2005 (UTC)

EDS told me that the "Nature" magazine is actually quite positive about Wikipedia: "Researchers should read Wikipedia cautiously and amend it enthusiastically." [37]. -- Jitse Niesen (talk) 23:09, 14 December 2005 (UTC)

For the last time I am not dissing wikipedia, I like wikipedia I just think that as a pluralistic encyclopedia it will be constantly regressing toward the mean interests of the populace which excludes higher math. Wikipedia lacks the sophistication, community, and peer-review that is required for serious content that can be relied upon by people in research communities.

Never the less, I am ending this argument for now, as I have just realized I am a big IDIOT for coming in here and saying that wikipedia lacks something to people that are still here working to better it after all this time. Honestly, I want you guys to succeed and I will add various things to wikipedia myself (I'm currently practicing my LaTeX), however I don't think it will really take off. In the meantime, I am thinking of ways to implement a math original research wiki so we'll see how that goes.--Hypergeometric2F1[a,b,c,x] 05:29, 15 December 2005 (UTC)

The point of this subsection is that you have been overblowing things out of proportion. Now, the math on wikipedia project took off a long time ago, and is actually sucessful. As far as your original research wiki, we shall see. Good luck practising LaTeX and the new research wiki. Oleg Alexandrov (talk) 16:51, 15 December 2005 (UTC)

You came in boldly wanting to make things better, and your attempt was awkward. Sounds like a typical new Wikipedian to me. Welcome. --KSmrq^T 22:07, 15 December 2005 (UTC)

Strange Reflections of Wikipedia

If you use Yahoo to find references to superlogarithm you will discover some interesting clones of Wikipedia pages. The term superlogarithm appeared on a past version of the tetration page, but now appears almost nowhere else on the net. Now the term superlogarithm appears on both the Free WebCam Tetration and Sex Pictures Logarithm pages of a rather unusual Wikipedia clone at newpenisenlargement.com. Daniel Geisler

Haven't you heard? newpenisenlargement.com is the number one mathematics resource on the net! - Gauge 02:58, 23 December 2005 (UTC)

Integer group names

I would dearly love to rewrite the following:

The finite group can be Z/2Z, Z/2Z+Z/2Z, Z/3Z, Z/3Z+Z/3Z, Z/4Z, Z/4Z+Z/2Z, or Z/6Z, giving 7 families of such surfaces.

I find it almost unreadable, because of the insistence on quotient notation. I would prefer subscripts:

The finite group can be Z₂, Z₂+Z₂, Z₃, Z₃+Z₃, Z₄, Z₄+Z₂, or Z₆, giving 7 families of such surfaces.

From my background, this is merely a matter of different conventions. Yet I get the feeling that some people feel uncomfortable with the subscript notation and habitually use quotient notation. What's up with that? --KSmrq^T 11:54, 14 December 2005 (UTC)

I think the subscript is preferred for p-adic numbers, and the quotient notation is preferred for modular groups to avoid confusion. I think it should be OK to use the subscript as long as you clarify that you are talking about the quotient groups. -lethe ^talk 12:05, 14 December 2005 (UTC)

Wikipedia:WikiProject Mathematics/Conventions for where we are on this. Charles Matthews 12:42, 14 December 2005 (UTC)

Thanks for the replies. From my reading of the conventions talk page, it appears that Z_n has three possible interpretations: (1) the additive group of integers modulo n, (2) the ring of integers modulo n, and (3) the p-adic numbers with p = n. I take it that for n prime, we would use a different notation if we mean the Galois field. Are there any other ambiguities I should be aware of? And do the interpretations differ more by area of mathematics, or area of the globe?

One reason I ask is because the article with the opaque quotient notation was talking about algebraic topology groups (no cohomology rings), where only interpretation (1) would make sense (so far as I know), yet quotients were used anyway. (Furthermore, the sentence itself tells us we're talking about groups.) So I'm trying to get a better understanding, not of just what people do, but why.

I understand it can be hard to explain choices; for example, I know for me there are contexts in which I would always use C_n, and others in which I would never do so, but use Z_n instead. Still, any further insights would be appreciated. --KSmrq^T 02:02, 15 December 2005 (UTC)

I don't know what article or context we're talking about, but in my experience, the cyclic group Z_n is written multiplicatively while the cyclic group Z/nZ is written additively. So, it's a little strange to see "Z₂+Z₂". On the other hand, it's far easier to read, so I'd prefer it. Melchoir 04:38, 16 December 2005 (UTC)

Curious. Compare your expectations against our conventions. (The original context is not so important, it merely provoked my question; but it was a page mentioned here in another thread, Enriques-Kodaira_classification.) --KSmrq^T 08:33, 16 December 2005 (UTC)

Huh. Well, I guess conventions wouldn't be any fun if we didn't have lots of them. Melchoir 08:57, 16 December 2005 (UTC)

templates revisited

Today I happened across an old conversaion I had with Oleg a few months ago on Talk:Transcendental number about templates in the math project (the discussion also arrived here; see archive). We all pretty easily voted to delete them: Template:change, Template:structure, Template:space, and Template:quantity. I'm a mild inclusionist and was a little nervous about so much deletion, but I was assuaged when I saw Template:Mathematics-footer. My main concern was lack of consistency across other technical subjects (confer Template:Natural sciences-footer and Template:Physics-footer, for example), and this one addresses that fine. Today, upon tripping on the old discussion, I noticed that while we do have this template, it's pretty much unused.

So how do we feel about these templates these days? Are they useful as a navigational tool? Is it worth having this one for the sake of consistency? I'm somewhat inclined to add the footer to all the articles mentioned within. Here it is, for reference. -lethe ^talk 16:12, 14 December 2005 (UTC)

Major fields of mathematics v • d • e
Logic • Set theory • Algebra (Abstract algebra - Linear algebra) • Discrete mathematics • Combinatorics • Number theory • Analysis • Geometry • Topology • Applied mathematics • Probability • Statistics • Mathematical physics

Hey, whom are you calling a deletionist? :) Oleg Alexandrov (talk) 18:23, 14 December 2005 (UTC)

Proposed renaming

There has been some discussion about renaming the pages linked to from the following template:

Mathematics articles: 0-9 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Mathematicians: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Index | Topics lists | Portal

The current proposal is as follows:

Current name	Proposed name
List of mathematical topics	List of mathematics articles
List of mathematical topics (A)	List of mathematics articles (A)
List of mathematical topics (B)	List of mathematics articles (B)
etc.
List of lists of mathematical topics	List of mathematics lists

Older discussion on this topic may be found at Talk:List of lists of mathematical topics#Renaming this page.

Comments? Objections? If you agree, please state so. -- Fropuff 03:19, 15 December 2005 (UTC)

For the record, I agree with this proposal. -- Fropuff 03:21, 15 December 2005 (UTC)
Support. The List of mathematical topics (A) has no topics in it, all are articles. Oleg Alexandrov (talk) 03:27, 15 December 2005 (UTC)
Support. The new names describe the content of the articles far better than the old names. —the preceding Tompw 18:12, 16 December 2005 (UTC)
Support. This all seems good. Paul August ☎ 22:45, 15 December 2005 (UTC)
Sopport. Lot of renaming this involves! --- Charles Stewart 18:26, 16 December 2005 (UTC)

Done. Now is the time to go edit your watchlist and remove from there all the redirects this move created. :) Oleg Alexandrov (talk) 03:36, 23 December 2005 (UTC)

Thanks for doing the grunt work on this Oleg. I wasn't looking forward to it. -- Fropuff 04:49, 23 December 2005 (UTC)

Organizing the math pages needing attention

See Wikipedia talk:Pages needing attention/Mathematics#Listing the pages needing attention for some discussion. Oleg Alexandrov (talk) 05:30, 15 December 2005 (UTC)

External peer review by Nature

I turn your attention to this article by Nature and Wikipedia's response. Karol 06:04, 15 December 2005 (UTC)

I just wanted to say I enjoy this resource and find it useful. I am not a mathematician or a statistician, although I use both a fair bit in my work. I learned a great deal from this very forum over a few days just last month. Wikipedia will only improve with time. Comparing Wikipedia with Encyclopedia Britannica at this point hardly seems fair. Wikipedia has been around for, what, 5 years. Encyclopedia Britannica has been around “forever”. If Wikipedia compares favorably with Encyclopedia Britannica already in at least some regards imagine what Wikipedia might be like 20 years from now.

I also think that technical articles are great. Personally I would prefer that more of them have examples and references. But this forum and the math help desk have been helpful to me in climbing the learning curve on technical issues. Some things I’ve learned here I tried off-and-on unsuccessfully to learn elsewhere on the internet over the course of several years.

As for the reliability of Wikipedia, perfect reliability is, in a Popperian sense, perhaps an unattainable ideal in that all of science is constantly being revised. Although, examples and references are one way for the reader to verify factual information and the state of the art as described in Wikipedia articles. As such, examples and references act, to an extent, like peer review.

I guess my point is that people will find these articles, will use these articles, and will be glad you wrote them, regardless of how specific or technical those articles may be… …particularly if those articles contain examples and references and are aimed at people who don’t know as much as you do about the subject.

I didn’t know the most appropriate place to put my comments so I stuck them here. Sorry if these comments are out of place. Mark W. Miller 06:41, 20 December 2005 (UTC)

Original research wiki

I have created a discussion page for the implementation of a wiki, Wikipolis, allowing for dynamic collaborations, original research, and some form of peer-review. I invite you all to add your ideas!--Hypergeometric2F1[a,b,c,x] 10:01, 15 December 2005 (UTC)

Somer pseudoprime

Somer pseudoprime is a puzzling new page, and hard to verify through Google. Charles Matthews 22:11, 16 December 2005 (UTC)

I've corrected a typo, and corrected the wikilinks, but ... ALL Google entries with Somer pseudoprime but without Wikipedia [38] are copies of the wikipedia entries for 25 or 49. Arthur Rubin | (talk) 23:48, 16 December 2005 (UTC)

Someone should look at Somer-Lucas pseudoprime at the same time. Right now it's copyvio from MathWorld, but even if it weren't, it'd still be a bare definition without context. The MathWorld article at least has a reference,

Ribenboim, P. "Somer-Lucas Pseudoprimes." §2.X.D in The New Book of Prime Number Records, 3rd ed. New York: Springer-Verlag, pp. 131-132, 1996.

If someone has the book, maybe it'll show cause why both articles shouldn't go to AfD. --Trovatore 21:16, 17 December 2005 (UTC)

For what it's worth, they are not mentioned in Ribenboim, The Little Book of Big Primes. This is the abridged version of The New Book of Prime Number Records, which we do not have in our library. -- Jitse Niesen (talk) 15:59, 19 December 2005 (UTC)

Since the On-Line Encyclopedia of Integer Sequences reference is only from 2003, I see no good reason to have this hanging around. Charles Matthews 16:17, 19 December 2005 (UTC)

Jitse, Charles, please clarify: Are you talking about Somer, Somer-Lucas, or both? My gut says get rid of both, at least as they stand. --Trovatore 19:56, 19 December 2005 (UTC)

Both. Furthermore, I would delete them if it were up to me. But I'm hesitant to cite nonnotability as a reason for deletion. -- Jitse Niesen (talk) 20:32, 19 December 2005 (UTC)

My take (although I'm relatively new as a Wikipedian). Somer pseudoprime -- delete as neologism. Somer-Lucas pseudoprime -- delete as copy-vio and nonsense, because of the d. Arthur Rubin | (talk) 23:43, 19 December 2005 (UTC)

Math pages needing attention

Somewhere above, in the discussion about wikiscience, a claim was made that around 20% of math articles need attention of an expert. Well, the number is just a fraction of that, for the moment 1.54%, meaning 169 articles, but that's still a big number. On Fropuff's suggestion, I wrote a script which will daily add to Wikipedia:Pages needing attention/Mathematics math pages having various attention templates, like {{cleanup}}, {{expert}} etc. So, I'd just like the community to be aware of that page (most of us are, I think), and visit it from time to time. :) Oleg Alexandrov (talk) 02:37, 17 December 2005 (UTC)

More depressingly, about a quarter of the articles are tagged as stubs. -- Jitse Niesen (talk) 13:13, 17 December 2005 (UTC)

I don't see that as such a big problem. Would we better off if those stub articles did not exist at all (8000 long articles without the extra 3000 stubs)? Often times an article grows only gradually, and a stub may inspire somebody to expand it, without having to start from zero. Besides, many stubs are complete enough, one just should remove the stub tag. I am more depressed when I see really badly written articles, and/or with errors. So, let the little ones come to me :) Oleg Alexandrov (talk) 18:07, 17 December 2005 (UTC)

I was thinking, if an article is a stub, and probably will never be anything more than a stub, does that mean it should probably just find a home as a section in another article? I was thinking of my recent stub invariant basis number. That article might be comfortable as a section in dimension theorem for vector spaces. -lethe ^talk 21:03, 17 December 2005 (UTC)

I have no problem with "small" articles like this. If this is all that can be said about this, then we should just remove the stub tag. Paul August ☎ 21:31, 17 December 2005 (UTC)

(replying to Lethe after an edit conflict.) That merging idea may work in specific cases, but I would not apply it as a general principle. Often times one may want to look up a specific term, and it may not make sense to read an entire article on a bigger concept to find that term. Also, you may create that section in the bigger article containing the stub, but nobody knows for how long that material will stick around before being edited out.

And I would not be totally opposed to a concept showing up both in its own stubby article and as a section in something bigger. In short, I would argue that one should use a lot of caution when eliminating stubs by merging, and if not sure, err on the side of leaving the stubs as they are. Oleg Alexandrov (talk) 21:38, 17 December 2005 (UTC)

Yes I agree with all of what Oleg says. I think a lot of people think that, for the sake of efficiency, content should not be "duplicated". But while that might be best for a book say, it might not make so much sense for Wikipedia. Moreover I think it is a benefit to have several articles from different points of view (not in the sense of POV). That is, an article about "invariant basis number" can address that content in a different way than "dimension theorem for vector spaces" would. Paul August ☎ 21:55, 17 December 2005 (UTC)

Actually, we may need those stubs. My feeling is that we have plenty of graduate students and other useful people editing anonymously, who currently are not able to start articles. We should aim to add 'good stubs' on many topics. Charles Matthews 22:07, 17 December 2005 (UTC)

My understanding is that the ban on anons creating new pages is an experiment. An important question to be answered is whether the imposition of creating an account substantially diminishes valuable contributions. I wonder how we would be able to decide the impact on new pages. You seem to be anticipating a visible loss; I'm inclined to think otherwise. We shall see. --KSmrq^T 06:03, 18 December 2005 (UTC)

Well, we don't know. We can't know whether the creator of Andreotti-Frankel theorem would have been happy to log in. There are issues in using institutional IT systems, and I certainly don't know what they might be. In any case my argument is not based on speculation on the possible harmful effects, which are hard to establish, but on the idea that the 'good stub', which in the past has been a big factor in developing WP, is still a good idea. What is more, as mathematicians, we should be the greatest appreciators here of the effects of exponential growth: if the red links in each article are still triggering a branching proportional to the size of the article base (say, in advanced parts of mathematics), then probably it is futile to worry too much about getting down the stubs as a proportion. That will only happen when we get closer to 'saturation' of the subject, so that the intellectual map 'closes up'. Charles Matthews 09:29, 18 December 2005 (UTC)

Your original wording ties stub need to anon creation ban. But as you elaborate, stubs can stimulate growth, regardless. As I understand the history of Wikipedia and its ilk, there has long been a tension between attracting quantity and assuring quality. Apparently, it's easy to guess wrong. I'm certainly curious to know the outcome. Anyway, I'm not currently nervous about having too many stubs; sometimes a stub tag just means the editor feels insecure about her expertise, which is better than overconfidence. --KSmrq^T 10:54, 18 December 2005 (UTC)

Actually, attracting mathematicians is a good idea, period. They tend to have other interests and a fact-based approach, and this makes them effective contributors to WP as a whole. Charles Matthews 11:13, 18 December 2005 (UTC)

Just to clarify, I did not mean to say that stubs are bad. My remark was in response to Oleg's, who said that 1.54% of the articles need attention of an expert. I wanted to say that it could be argued that stubs should be included in that number. Of course, a stub is better than no article, just like a messy article or one that is too technical is better than no article; it seems we all agree on that (on the other hand, an article riddled with errors is worse than no article, in my opinion). -- Jitse Niesen (talk) 13:40, 18 December 2005 (UTC)

So I think a stub is usually better than no article, but I'd like to propose that an exception is when an entry from "requested articles" is fulfilled with an uninformative stub. My request would be, if you don't know something substantial about the topic, please leave it for someone who does. I recall a particular case where someone requested Joe Blow in the "mathematicians" section of requested articles, and someone else immediately wrote a stub that said simply "Joe Blow is a mathematician". My intuition is that this action substantially reduced the probability that we'd have an informative article about Blow in the near future, because it took him off the requested list. --Trovatore 19:53, 18 December 2005 (UTC)

No one would call that a 'good stub'. Charles Matthews 22:50, 18 December 2005 (UTC)

There is such a thing as Wikipedia:Requests for expansion which is supposed to complement Wikipedia:Requested articles and deal with precisely this, but it doesn't get as much press. I can see that it has the potential to become wildly out of control like Category:Stubs, but perhaps we should encourage its use? List it on Jitse's wonderful current activity page? —Blotwell 23:25, 20 December 2005 (UTC)

Merry Christmas!

Merry Christmas, all! (... with the understanding that paganism is older than Christianity, either way, cheeriest of holidays!) linas 02:41, 25 December 2005 (UTC)

Yes, why not. Dmharvey 03:13, 25 December 2005 (UTC)

Why not? Now that's a great answer! :) Let me try a proper response:

Ho-ho! Merry Christmas to you all! Wish you a Happy New Year, lots of edits, less wiki-stress, and that you also spend some healthy time outside this addictive place! And whatever else you wish for yourselves or others! Oleg Alexandrov (talk) 03:52, 25 December 2005 (UTC)

"lots of edits" and "spend some healthy time outside this addictive place" are mutually inconsistent. Unless the edits are very short. Dmharvey 04:25, 25 December 2005 (UTC)

A linear functional which is not continuous

I wrote the article A linear functional which is not continuous only to immediately discover on its talk page a suggestion to move it to Non-continuous linear functional (darn, everybody should be drunk and sleeping this post-Christmas morning, not checking the recent changes). What do people think (if it matters at all)? Oleg Alexandrov (talk) 17:36, 26 December 2005 (UTC)

Isn't there a mechanism for providing both names for the article? Both seem fine... Randall Holmes 17:40, 26 December 2005 (UTC)

By the way, I've been steadily editing through this period, and it has been awfully quiet :-) Happy Hanukkah! Randall Holmes 17:41, 26 December 2005 (UTC)

Yeah, still quiet. :) Yes, there is a mechanism for providing both names, it is called a redirect, see Wikipedia:Redirect. So I guess the argument is about which is the primary meaning, for all that's worth. Oleg Alexandrov (talk) 02:31, 27 December 2005 (UTC)

I like the first name. Compare with stuff like An infinitely differentiable function that is not analytic. Also, is "non-continuous" a word? Shouldn't that be "discontinuous"? -lethe ^talk 03:02, 27 December 2005 (UTC)

Personally, I don't like the idea of a name for an encyclopedic article beginning with "A". Also, I think the original proposed name is too long. I'd go for Non-continuous linear functional. But maybe it's just me. --Meni Rosenfeld 12:49, 29 December 2005 (UTC)

I agree with Meni; initial articles are okay if they are title of a book or work of art, but I don't think they belong in a general article. Even if it has to do with showing existence. Isn't there some other way to word it? Gene Nygaard 21:37, 30 December 2005 (UTC)

Hi there :) - the article was moved to A linear map which is not continuous - is that what people have decided on? Right now it looks like no consensus, but I thought I'd just give everyone a buzz... WhiteNight ^{T | @ | C} 23:28, 30 December 2005 (UTC)

How about linear map which is not continous, dropping the leading "A" which makes people uneasy. The other option seems to be discontinous linear map, based on above. Oleg Alexandrov (talk) 00:27, 31 December 2005 (UTC)

Discontinuous linear map/Discontinuous linear functional and Infinitely differentiable non-analytic function seem reasonable. We anyway don't expect people to search for and bump into these articles directly, and we are probably going to use these as examples to show that being a "linear map" doesn't imply being continuous, and smoothness doesn't imply analyticity, in main articles on linear maps and analytic functions, so I guess the title is not all that crucial. Bottomline: Unless we are missing on something important, the shorter the better. deeptrivia (talk) 00:44, 31 December 2005 (UTC)

I moved the article A linear functional which is not continuous to discontinuous linear map which seems to address all concerns on this page. I made a bunch of other alternative titles redirect to it. Oleg Alexandrov (talk) 19:57, 31 December 2005 (UTC)

However, I find Infinitely differentiable non-analytic function a very clumsy name for An infinitely differentiable function that is not analytic. Oleg Alexandrov (talk) 19:57, 31 December 2005 (UTC)

Non-analytic infinitely differentiable function? Septentrionalis 06:29, 10 January 2006 (UTC)

Anon's editing of Einstein

IP, 69.22.98.162 (contributions) has been making edits to Albert Einstein, Henri Poincaré and David Hilbert, essentially questioning the originality of Einstein's theory of special relativity, giving as a source this: [39] (see Talk:Albert_Einstein#His Theory and Talk:Albert_Einstein#Nobel prise edit), all of which I think have been reverted (by me and others). I don't really know much about the history of the development of relativity, (beyond what little I've read on Wikipedia), if anyone can shed any useful light on this, your help would be welcome. Paul August ☎ 23:01, 28 December 2005 (UTC)

It is true that Poincaré had his own insights into Special Relativity and that Hilbert actually developed a theory of General Relativity about the same time Einstein did, but Einstein’s version was more complete. See History of general relativity and [40] for some background. I just read an article where it is argued that Einstein’s first wife, who was a physicist, should have been listed as a co-author of his work on Special Relativity or at least been acknowledged for her assistance. Daniel Geisler 05:45, 28 January 2006 (UTC)

Titles from another encyclopaedia

A001622 (AfD discussion)

Now is your chance to answer the question: Should Wikipedia have redirects for OEIS titles? ☺ Uncle G 01:58, 30 December 2005 (UTC)

Domain of a partial function

Currently there's an inconsistent usage among various articles that should probably be cleared up. Partial function claims that, given a partial function f:X→Y, its domain is X. I think the more standard usage is that the domain of f is the subset of X on which f is defined; this is the usage assumed in Recursively enumerable set and Uniformization (set theory). I don't know a name for X, though, given this convention. In any case we should standardize on one convention. My strong preference is for the second; I don't think I've seen the first convention used anywhere but WP. --Trovatore 19:32, 30 December 2005 (UTC)

Well, I'm sure that the codomain always means Y and never f(X), which is the range. It seems to me that the logical thing would therefore be to call X the domain and f^-1(Y) the corange, so that a partial function is a function from its corange onto its range just as a module homomorphism is an isomorphism from its coimage to its image. But I don't claim any knowledge of what's standard in this field. —Blotwell 03:45, 31 December 2005 (UTC)

Your suggestion has a pleasing symmetry but is definitely not standard. I am essentially certain that my convention is standard. What I don't know is a name for the X; if anyone could tell me that, it would be easier to figure out how to fix Partial function. --Trovatore 05:04, 31 December 2005 (UTC)

Where I've learnt, we called Y the "range" and f(X) the "image", and for a partial function, we called X the "domain" and f^-1(Y) the "preimage". While I would be happiest if that was the convention used in Wikipedia, we could use your convention of Y-codomain, f(X)-range, while adopting X-domain and f^-1(Y)-preimage (which I think is more standard than Blotwell's corange. --Meni Rosenfeld 14:20, 31 December 2005 (UTC)

The problem with "preimage" is it makes me want to ask, "preimage of what?". ("Image" has the same problem as a substitute for "range".) I strongly urge the adoption of "domain" to mean the set where f is defined (what Paul calls the "exact domain" below); I believe this is completely standard among recursion theorists, who are the people who most naturally come upon partial functions. What we need is a name for X (or I suppose we could just leave it unnamed if there's no standard name). --Trovatore 18:31, 31 December 2005 (UTC)

This site uses "domain" for X and "exact-domain" for f^-1(Y). When working In the category of sets and partial functions (often called PfN), X would be called the domain of f (at least as a morphism). Paul August ☎ 16:22, 31 December 2005 (UTC)

So the morphism article mentions that an alternative name for the "domain" of a morphism is its "source" (clearly a better word when discussing abstract morphisms, which needn't be functions of any sort). Perhaps we could call X the "source" of the partial function, if that usage can be attested somewhere. That would free up "domain" for its more standard use. --Trovatore 18:37, 31 December 2005 (UTC)

I'm afraid "source" would be an unfortunate choice. In category theory, "domain" and "codomain" is the standard terminology, since the term "source", would be in conflict with the fundamental categorical notion of "source" (dual "sink") as defined, for example, in: Adámek, Jiří, Herrlich, Horst, & Strecker, George E.; (1990). Abstract and Concrete Categories (4.2MB PDF) (Chapter III: Sources and Sinks: 10.1, p. 169) Perhaps we can we just retain X as the domain, but note however that in many contexts (e.g. recursion theory), the domain of a partial function f can mean instead: f^-1(Y). Paul August ☎ 20:51, 31 December 2005 (UTC)

I once did a course called something like "Mathematical foundations of quantum mechanics" in which we discussed unbounded linear operators. You would have a linear map T : L^2 -> L^2 (for example the "differentation" operator), but even though it was written like that, it wasn't defined on all of L^2. The part of L^2 that it was defined on (which includes, for example, the smooth functions) was called the domain of T, denoted I think dom T. Unfortunately I can't find anything on wikipedia which backs up this usage, probably because I don't actually know anything about quantum mechanics or functional analysis. Dmharvey 20:00, 31 December 2005 (UTC)

See the article Closed operator, which treats this topic. The convention I've seen is to call T in your example an operator on L², and use domain of T to denote the subset of L² on which T is actually defined. Brian Tvedt 18:12, 1 January 2006 (UTC)

For what it's worth, IMHO, X is not used outside of category theory and related morphism topics. Domain is used for the range of f^-1 (seems better terminology than trying to say f^-1(Y)) in almost all other contexts. I'm not attempting to back this up with Wikipedia usage, just with common mathematical terminology. -- Arthur Rubin | (talk) 23:08, 31 December 2005 (UTC)

Yeah, I agree with Arthur; we don't usually need a name for the X (it would just be convenient to have a name for it in the Partial function article). The set of values for which f is defined is a more useful concept, and more standardly called the domain of f (though the article should mention the other usage, which does seem to show up on a few websites). I'll make the appropriate edits if no one objects (could be a little while; I've got to get on a plane back to the Great White North very early tomorrow morning). --Trovatore 01:54, 1 January 2006 (UTC)

My preference is that in any context where it is necessary to distinguish between X and the preimage of f, use the category-theory terminology: call X the domain. To even speak of f as a partial function, it must be the case that the domain and preimage are different. Unfortunately, the mathematics community has never standardized terms across all fields, so issues like this will continue to appear. The category-theory usage was adopted because it works better in general; but if it is not a convention that is familiar and comfortable in a narrower context, best practice would be to alert readers to the conflict and to state clearly the convention to be used in the article in question.

Incidentally, the Unicode character U+0290D, "⤍", is better notation than "→" but requires a font like Code2000 to display. --KSmrq^T 07:04, 1 January 2006 (UTC)

The problem with "preimage of f" is that it isn't standard (standard terminology would be "the preimage of Y under f", which is too long-winded). OTOH the terminology "the domain of f" for the set of all points where f is defined is clearly the majority usage. --Trovatore 07:16, 1 January 2006 (UTC)

Again, these "standards" vary with context. I'm more familiar today with usage where the definition of a mapping includes its source and target, so that "the preimage of f" is perfectly well-defined, as is "the preimage of S⊂Y under f". Yet in my (distant) youth, the convention was exclusively that the domain of f was as you say. The conflict is real; we can't wish it away. Best practice remains clarity of definition and full disclosure of potential conflicts. --KSmrq^T 08:58, 1 January 2006 (UTC)

OK, in accordance with the above discussion, I've edited Partial function and Domain (function) to indicate the existence of both usages. I've edited Recursively enumerable set and Uniformization (set theory) to specify which sense of the term is in use. But there are bunches more articles that link to Partial function and/or Domain (function); I'm not likely to get around to checking them individually any time soon. --Trovatore 23:37, 4 January 2006 (UTC)

JA: Seems like "domain" is standard for the designated set, after all, what if it's just a relation L c X x Y ? And I think that "domain of definition" is used for the other thing by many folks in computing contexts, for example, Arbib et al. Jon Awbrey 07:40, 14 January 2006 (UTC)

Jan 2006 – Feb 2006

This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

Help with Simple harmonic motion

A newbie, Itzchinoboi, rewrote Simple harmonic motion. The new article is more elementary, which is good. To me both the original version looks good, and the rewritten version looks good, although the latter is full of newbie mistakes. See the diff. Anybody knowledgeble willing to spend some time understanding the changes and see how to deal with all this matter? Note that a plain revert is not an option, it seems that the user spent half a day on that article. Oleg Alexandrov (talk) 22:31, 2 January 2006 (UTC)

Scalar (mathematics)

This newly created page is an abomination. Please help. Michael Hardy 02:41, 3 January 2006 (UTC)

I've had a go. Dysprosia 04:20, 3 January 2006 (UTC)

Nice one, D. This seems to be rather an uphill battle. It would be good to get the thoughts of others regarding the article introduction - see this bit of the talk page. Thanks! — merge 04:14, 12 January 2006 (UTC)

Tensor wars

We may be in for more of the traditional troubles at Tensor. Category:Tensors now has 70 articles. I really think the main tensor article should reflect that (at least - some of the more algebraic pages are in Category:Multilinear algebra or elsewhere).

There is a sub-issue, rank of a tensor, which might be tractable on the basis of some sourced research.

Charles Matthews 17:02, 3 January 2006 (UTC)

Articles listed at Articles for deletion

Set descriptions in colloquial English (AfD discussion)

Uncle G 01:03, 4 January 2006 (UTC)

Wikipedia talk:Stable versions#Certification gang

would you like to create certified articles in mathematics? -- Zondor 03:19, 5 January 2006 (UTC)

Hmmm ... I have major issues with this idea. How do you decide who can join your gang ? You wouldn't want to let just anyone in, would you ? They might start doing stuff that you disagreed with. It sounds awfully like a self-elected technocracy. I would be more worried if I didn't think that the chances of reaching critical mass on this idea are really, really small. Gandalf61 09:46, 5 January 2006 (UTC)

It will start out as a gang but eventually to something professional like a league. -- Zondor 13:35, 5 January 2006 (UTC)

Certification is an interesting idea, but its not yet completely fleshed out. Its primary utility is to handle articles where there have been significant edits wars, or get a lot of inappropriate edits from newbies, or even regular vandalism. This is maybe less than 1% of all math articles. The goal is to certify one particular version of the article, and then let anon hack on it. If one comes back in a month or two and its a horrid mess ... well, so what, at least the certified version is good. This is much better than the battle fatigue of having to defend an article on a daily basis. linas 15:20, 5 January 2006 (UTC)

But if you don't defend an article on a daily basis, then it will get messed up, and after a month or two you won't be able to sort out any good edits from the rubbish, so the only way forward will be to roll back to the "certified" version. In effect, you have frozen the article - no one will bother to make any serious contributions because they will all be lost in the next purge. Gandalf61 16:23, 5 January 2006 (UTC)

Our energy can be spent better in places other than in certifying articles. If you come back to an article months later and it's "messed up", you should take the time to go through the diff and find out what went wrong, and then either revert there or fix it by hand. Reverting to an outdated "stable" version is too crude a tool.

Meekohi 19:05, 5 January 2006 (UTC)

The energy is well spent if creating a Wikipedia:WikiReader project for Mathematics. -- Zondor 15:10, 7 January 2006 (UTC)

Yes, well, these points should be argued there, not here. My take is that I've seen too many good editors get wiki-fatigue and wikistress and have some of them leave, because they were unable to defend thousands of articles on a daily basis. If you can do this, great. Like many other "old-timers" (ok, I've been here a year), I now spend more time watching articles, trying to ward off decay, than I do on actually writing. That is wrong. It should not be a herculean effort to stave off wikirot. (See above, Wikipedia talk:WikiProject Mathematics#Help with Simple harmonic motion for a real-life example. Oleg watches a lot of these kinds articles, and can't keep up with the changes. The old version should have been declared "stable", and stay that way till the new one is done.) linas 21:25, 5 January 2006 (UTC)

This is getting offtopic, but I gave up watching articles by the thousands. After going under 1000 I actually found time to write new stuff every now and then. :) Yes, open acces is the biggest asset but also the biggest disadvantage of Wikipedia. But seems to work so far. :) Oleg Alexandrov (talk) 01:03, 6 January 2006 (UTC)

The single most important thing for stable versions is to have a guarantee of accuracy and reliability otherwise it is no different to the system we already have. So at any given time, we can demand a print edition of Wikipedia 1.0. Whereas, the wiki version serves as the playground for boldness, experimentation and to be cutting edge. Once you have made the published version, you can forget about it and concentrate on the wiki version. Eventually, it becomes better than the previous stable version, you then supplant it after it has been certified for accuracy. -- Zondor 01:02, 6 January 2006 (UTC)

Math Collaboration of the Week

I hope nobody is too opposed to the requets for nominations at the top of the page. I think we need it if we're going to get MCoW up and running again. Meekohi 20:06, 5 January 2006 (UTC)

Nevermind, apparently the big man minds. ;) Meekohi 20:07, 5 January 2006 (UTC)

Uhh, I've never really seen Oleg, but I would bet he's not really that big. Nevertheless as Fropuff suggested below it will get more attention here anyway. Paul August ☎ 03:46, 6 January 2006 (UTC)

What units do you want it in, feet, meters, edits per second? Oleg Alexandrov (talk) 18:59, 6 January 2006 (UTC)

It's alright, many people watch the discussion on this page. For those of you who don't know User:Meekohi is trying to get the Mathematics Collaboration of the Week going again (it has been dead for about four months now). If you are interested in participating please list nominations on that page. -- Fropuff 20:42, 5 January 2006 (UTC)

Perhaps that page should scale back to a less ambitious "Math Collaboration of the Month". Paul August ☎ 17:58, 6 January 2006 (UTC)

Well, is it flogging a dead horse? The discussions have always seemed to show up the way people here have rather disparate interests, within mathematics. We could have Algebra COTM, Geometry COTM etc., running in parallel.Charles Matthews 18:03, 6 January 2006 (UTC)

Honestly I feel it should be the Fortnightly collaboration since that is about how long it takes to get an article up to par, but it wouldn't fit in with all the other Weekly Collaborations we have in other subjects. Meekohi 15:45, 13 January 2006 (UTC)

A new project idea

I have an idea for a new math project that provides a somewhat concrete way of evaluating progress. I call it the "Let's Beat Mathworld" project; its goal is for every topic listed on Mathworld, to write a better article on the same topic. We've already done so for many of them, but I bet we can cover them all. We can make a project page listing all the topics in the Mathworld hierarchy with links. We have to watch out for copyvio, but I think it's a great source of useful topics that we may be failing to touch on or that may currently be stubs. Deco 04:25, 6 January 2006 (UTC)

For all that's worth, the mathworld articles already are listed at Wikipedia:Missing science topics (Math1 through Math7). Whoever did that seems to to have avoided copyvio by shuffling things and possibly mixing with entries from other places. Oleg Alexandrov (talk) 04:47, 6 January 2006 (UTC)

I was unaware of those lists. I've now added a link to them in the "Things to do" table on the main project page. (By the way Oleg, just how big are you?) Paul August ☎ 05:06, 6 January 2006 (UTC)

~~If you are asking how I got to know about that project, then the answer is that there was an announcement on this page a while ago, and actually Linas and Rick Norwood got there long before me. :)~~

Answered above. Oleg Alexandrov (talk) 04:17, 7 January 2006 (UTC)

By the way, there is also a User:Mathbot/List of mathematical redlinks, which I made at Fropuff's suggestion, containing 11,000 redlinks found in existing math articles. Oleg Alexandrov (talk) 07:38, 6 January 2006 (UTC)

Wow, 11k links. I wonder if it would be helpful to somehow categorize those missing links/ topics. I mean missing theorems, lemmas, formulas, problems, scientists... (Igny 14:45, 6 January 2006 (UTC))

A good chuck of those are nonmathematical. You would need artificial intelligence to sort out theorems from problems and from scientists. Yeah, I don't know how helpful that list is, but it exists. :) Oleg Alexandrov (talk) 15:01, 6 January 2006 (UTC)

Many of those 11K links are now blue. Oleg, do you plan on updating this list anytime? I don't know about other people, but I find it useful. Thanks again for doing it. -- Fropuff 15:26, 6 January 2006 (UTC)

I updated them now, and will do every couple of weeks or so. Oleg Alexandrov (talk) 04:17, 7 January 2006 (UTC)

I asked permission to used those list a few months ago, but received this reply

Rudy, Thank you for your mail. We appreciate your effort to secure proper permission before using our material. Our lists *do* represent original works of authorship and, as such, enjoy copyright protection. Further, the value of our editorial work is evidenced by your desire to incorporate the material into your project. We understand your need for such a list, and we would very much like to support Wikipedia -- as I am sure you would like to support the continued development of MathWorld. It is worth noting the relative dearth of links to Mathworld from Wikipedia. Regardless, it isn't obvious how reproducing MathWorld (which already offers unfettered, free access) furthers the goals of Wikipedia. Are there other areas of mathematics/science that are in greater need of free web-based exposure that we could help Wikipedia develop? Benson Dastrup Wolfram Research, Inc.

—Ruud 10:02, 6 January 2006 (UTC)

I really think we can set our own agenda now. Why not lead rather than follow? This is more likely to attract active research workers. Charles Matthews 15:22, 6 January 2006 (UTC)

I second Charles' opinion. MathWorld should be asking for our lists. If you see an article on MathWorld that doesn't have good coverage here, just post a request on Wikipedia:Requested articles/Mathematics. -- Fropuff 15:29, 6 January 2006 (UTC)

Well, that's if it's actually worth covering here. MathWorld's topic selection can be, to put it kindly, quirky (cf the Somer-Lucas pseudoprime article, which along with Somer pseudoprime probably ought to be deleted). --Trovatore 15:49, 6 January 2006 (UTC)

Trovatore, I don't understand you at all. Why would any article with substantiated content be deleted? Why would any topic not be worth covering? As for beating Mathworld, I do believe we already did, but in any case I think it will be much more efficient if every Math Wikipedian will, once in a while (or multiple times in a while), go to "random entry" in Mathworld, and make sure that Wikipedia has a better coverage of the encountered topic. If not, improve it or put a request for it. While this could create a little duplicate effort, it will solve many of the aforementioned problems (copyright issues, alleged statement that we are not as good as Mathworld, manageability of large lists of topics) as well as guarantee that changes to Mathworld will not be overlooked. --Meni Rosenfeld 17:01, 6 January 2006 (UTC)

Okay, perhaps those articles aren't as substantiated as I thought at first. Stil, I think the direction should be attempting to substantiate such articles, rather than delete them. --Meni Rosenfeld 19:50, 6 January 2006 (UTC)

I've noticed that while in many cases, we have better articles than mathworld, their articles will have a much larger section of raw often obscure formulas and identities. Those can detract from the quality of an article, as they're not very readable, but they're still important and useful, for any reference work. And remember, we're a reference, not a textbook. -lethe ^talk 04:25, 7 January 2006 (UTC)

The emphasis on formulas at MathWorld is surely to do with the Wolfram connection in the site's origins. Anyway I like classical formulae myself, but a more wordy style is indeed better for WP. Charles Matthews 08:01, 7 January 2006 (UTC)

It would probably be best to include such formulae, perhaps placing the less important ones near the end of the article so as not to be a distraction. --Meni Rosenfeld 15:09, 7 January 2006 (UTC)

While on one hand I agree that attempting to merely reproduce Mathworld's extensive quality entries might seem silly, on the other hand as the above e-mail demonstrates, their articles are not libre: we need to make the same information available to everyone to use, and update, in any way they please. Also, for the sake of our reputation, it would be neat to say that we unequivocably have even better coverage than a site as well-known as Mathworld. Deco 06:56, 10 January 2006 (UTC)

Mathematics Portal

I've been doing some work on the Mathematics Portal recently. It has been in fairly poor shape for most of the last year as very few people have bothered to maintain it. If you have any suggestions for improvement please mention them on Portal talk:Mathematics. I do need suggestions for future featured content. You can list these at Portal:Mathematics/Suggestions. Thanks. -- Fropuff 17:32, 6 January 2006 (UTC)

I think the new portal looks great. Paul August ☎ 17:45, 6 January 2006 (UTC)

Multivariable calculus help

If someone who remains div, grad, curl better than me would have a look at the van Hove singularity article I've just written, I'd be pleased. I can't recall the name of the series expansion $\mathrm{f(x) = f(0) + f'(0)x + 1/2f''(0)x^2 + \ldots}$ . Probably there's a math article on this expansion that I could point to. Also, I have a feeling that the change of variable I'm doing where I go from a volume integral over k to a surface integral over E is the result of one of those fundamental theorems, (Gauss? Stokes? Green?) but I'm not sure which one. Perhaps in addition I have made an egregious notational faux pas. Thanks for any suggestions you have. Alison Chaiken 18:58, 8 January 2006 (UTC)

The series expansion you mentioned is the Taylor series. Unfortunately I don't remember multivariable calculus well enough to offer any additional help. --Meni Rosenfeld 19:28, 8 January 2006 (UTC)

The change of variable may have a more specific name, but "generalized Stokes theorem" would suffice. --KSmrq^T 20:31, 8 January 2006 (UTC)

Well, looks to me like this is about pushing forward a measure/density, and the only difficulty indeed would be at a critical point (mathematics). Not that that page is a great help. The thing about the square-root singularity comes out of the Morse lemma, and so is only generically true (true in practice ...)? That anyway is why you only get cases like the quadratic form cases to worry about. (Sorry Alison, this is hardly helpful, talking amongst ourselves here.) Charles Matthews 20:46, 8 January 2006 (UTC)]]

Thanks Charles for your editing. I added a link in the van Hove singularity article to critical point (mathematics) in the hope that it will improve eventually. I'm contemplating a link to the Morse lemma or Stokes theorem articles but need to think about it more. Alison Chaiken 03:23, 9 January 2006 (UTC)

The above expansion is, to be more specific, the Maclaurin series (the Taylor series about zero). Same article though. Deco 06:57, 10 January 2006 (UTC)

Formal calculation

During my studies, I have encountered the concept of a "formal calculation", in the sense of, roughly, a calculation for which the steps are not completely substantiated, and yet the result can give us insight about the true answer to the problem in question. I want to write an article about that concept, but I haven't found any references to it on the web, so I'm not sure how widely it is used and whether I understand the concept properly. Any ideas? --Meni Rosenfeld 18:34, 12 January 2006 (UTC)

On the contrary, I think of a "formal calculation" specifically as a calculation in which every step is very clear and verifiable. I'm not sure I know a name for what you're referring to. Meekohi 20:43, 12 January 2006 (UTC)

I think I know roughly what Meni is trying to say. I would have thought you might find it at heuristic or heuristic argument or something similar, but they seem to be run by philosophers. Dmharvey 20:47, 12 January 2006 (UTC)

A formal argument is when you just follow what the syntax seems to suggest your reasoning, without proving the reasoning is sound. Like when you prove that, in a ring, if (1+ab) is invertible, then so is (1+ba) by using power series. Power series don't exist in a ring, but but you can still make formal arguments using them. -lethe ^talk 21:58, 12 January 2006 (UTC)

Lethe's example is what I would call a heuristic inference. It seems very strange to me to call this "formal": it's good because of informal gut feeling experience, not in virtue of the formal structure of the problem. --- Charles Stewart 22:02, 12 January 2006 (UTC)

Lethe's reply coincides with my experience. I suspect that it may be hard to find good references, but I remember reading about it recently. Bear with me … -- Jitse Niesen (talk) 22:05, 12 January 2006 (UTC)

Here we are. Stuart S. Antman, Nonlinear Problems of Elasticity, Applied Mathematical Sciences vol. 107, Springer-Verlag, 1995. Page 1 contains the paragraph: "I follow the somewhat ambiguous mathematical usage of the adjective formal, which here means systematic, but without rigorous justification. A common exception to this usage is formal proof, which is not employed in this book because it smacks of redundancy." (his emphasis). -- Jitse Niesen (talk) 22:28, 12 January 2006 (UTC)

I think the term systematic calculation would be far more fitting nomenclature, but that doesn't really carry the connotation of being subtly incorrect that we're looking for. Meekohi 02:02, 13 January 2006 (UTC)

I wouldn't call it incorrect: it is, after all, an excellent heuristic. I'd rather say it was non-well-founded. --- Charles Stewart 02:13, 13 January 2006 (UTC)

Are all in favor of creating a stub, bearing the title "Formal calculation", based on the definition Jitse found, and beating it around until we reach something we can agree upon? --Meni Rosenfeld 13:40, 13 January 2006 (UTC)

I don't know, personally I'm fairly opposed. To me the term Formal Calculation distinctly implies that it is rigorously correct. The reference Jitse gave doesn't really give much support in my mind, seeing as he points out this is ambigous usage. If we are going to make an article on it, I think the main article should describe what it means to be rigorous/systematic, and then there should be a short section pointing out that it is possible to be apparently systematic, but still incorrect. Meekohi 14:05, 13 January 2006 (UTC)

I know that "formal calculation" seems to imply a rigorous one, and actually that did confuse me the first times I encountered the concept. But I got the impression that, while perhaps ambiguous, it is usually used in the sense I described - Much like in the probably more common term formal power series. In this sense, "formal" actually means of form, namely, the form of the objects matter and not their underlying meaning - making the calculation perhaps systematic, but not really rigorous because we are using properties without any justification to why these properties should hold. We could always delete the article later if we can't seem to rich any consensus. --Meni Rosenfeld 14:59, 13 January 2006 (UTC)

Formal power series are just sequences over a ring with convolution as multiplication. Since all sums involved are finite, this is a rigerous mathematical topic. Convergent power series is a different topic requiring the ring to be a Banach algebra. In france there is a state wide research association called "Calcul formel", which would probably translate as symbolic calculus or even symbolic algebra. The research and design of computer algebra systems is part of that.--LutzL 15:09, 13 January 2006 (UTC)

Of course formal power series are ultimately defined in a rigorous way, but the inspiration for this definition comes from a non-rigorous application of properties of convergent power series to arbitary power series. That's where the term "formal" comes from. --Meni Rosenfeld 15:12, 13 January 2006 (UTC)

I think the originally-proposed topic is a 'derivation', universal in (say) theoretical physics. It's not a particularly good topic for an article, though. Charles Matthews 16:20, 13 January 2006 (UTC)

I think that this is a good topic for an article, and it may well prove useful for my planned article on Boole's algebraic logic (to be carefully distinguished from Boolean algebra, since Boole's system allows terms that do not have set-valued denotations). They can be seen to be similar to the status of polynomials prior to the discovery of complex numbers: onbe can know the sum and product of the roots of a quadratic and know furthermore that those roots don't exist. If we are to resort to neologism, why not optimistic calculation? --- Charles Stewart^(talk) 16:29, 13 January 2006 (UTC)

I think "formal" in "formal calculation" has the same meaning as in "formal power series". In my experience, it is often used in the following context (for instance, in a talk on Kolmogorov-Arnold-Moser theory which I just attended): We want to prove that a function f_epsilon with a certain property exists for epsilon sufficiently small. We know f_0, so we expand f_epsilon in a power series in epsilon. If this is possible (i.e., if we can find all the coefficients in the power series), we have a "formal solution". To prove that this is actually a solution, we have to show that the power series has a positive radius of convergence.

So, formal is not just optimistic. And I don't think "formal" in this meaning is a neologism either, as Meni, Lethe and I have all heard of "formal" in this meaning. -- Jitse Niesen (talk) 18:08, 13 January 2006 (UTC)

Another example: formal group law. Dmharvey 21:16, 13 January 2006 (UTC)

It appears that the phrase is used in the proposed sense. It also appears to be understood in other ways, and it appears that some folks feel that the proposed sense is not a good sense. For an inclusionist (not necessarily me), Wikipedia should have an article. The article should note the opposition and provide disambiguation. However, a major unresolved question is: What is the primary meaning of "formal calculation"? The answer to that I do not know, but I'm inclined to think it's the "rigorous" sense, not the proposed sense. --KSmrq^T 01:23, 14 January 2006 (UTC)

I believe the phrase is commonly used in physics in the sense of "we know this can't possibly be right, but by shoving symbols around on a page, here's what you can come up with". For example, "formally", one has 1+2+3+...=-1/12, which is clearly both "right" and "wrong" in various deep ways. That is, its ambiguous without further clarification about how in the world this could possibly be a valid manipulation; but in physics, further clarification is often too hard to provide. A formal calculation is one step up from handwaving. linas 06:01, 14 January 2006 (UTC)

In a nutshell, I think my original proposition of creating a stub and beating it around is fair. I'll do that now. Be sure to check it out for any flaws\omissions\whatever as I am an inexperienced editor. Formal calculation. --Meni Rosenfeld 15:20, 15 January 2006 (UTC)

Yeah it seems that there is enough support for the idea now that we should have an article, even though I still don't like the terminology ;) Meekohi 15:28, 15 January 2006 (UTC)

Red links

Is there a handy way, given a red link, to figure out what articles link to it? Some of the red links we have seem like they just need to be reworded to link to something more appropriate. Meekohi 15:41, 13 January 2006 (UTC)

To find all articles linking to Magnus series, for instance, follow the red link and then click on "What links here". -- Jitse Niesen (talk) 15:59, 13 January 2006 (UTC)

Ha ha, hiding from me in the toolbox all this time. Thanks! Meekohi 18:29, 13 January 2006 (UTC)

70.22.128.220

Could an admin keep an eye on this IP? I've reverted two of their edits. They obviously know a little about the material they are editing, but are still make some pretty serious false claims and mistakes. I've put the details up on the Talk page. Meekohi 16:10, 13 January 2006 (UTC)

Well, you'd better explain your concern some more. Apart from the deletion of one reference, which is not explained, this looks like a technically proficient editor. Charles Matthews 16:16, 13 January 2006 (UTC)

For Scale-free networks he deleted the entire formal definition from the page, and for Complex networks he made claims that preferential attachment was the first generative model for power-law distribution graphs, which is false (and was stated as false in the article already). I'm not saying he's not technically proficient, but he's altering articles for the worst. Meekohi 16:35, 13 January 2006 (UTC)

The more you can document these points on the Talk pages of the articles, the easier it is for others to follow the changes, and contribute to the discussion. Charles Matthews 17:14, 13 January 2006 (UTC)

Math Will Rock Your World

Seems that math made it as the cover image at businessweek.com. See article. Admittedly this is not a Wikipedia related post, however, I found it interesting. The article ends with "Yes, it's a magnificent time to know math.". Oleg Alexandrov (talk) 20:05, 13 January 2006 (UTC)

That head is some kind of scary ;) Meekohi 20:22, 13 January 2006 (UTC)

History of Science WikiProject being formed

ragesoss is trying to start up a History of Science Wikiproject; add your name here and help him get started. linas 05:50, 14 January 2006 (UTC)

proof of impossibility

Someone's just started proof of impossibility, which seems like it could end up being quite nice. I've created a redirect from impossibility proof, which I think is a more common term. Perhaps we should move the original? Dmharvey 02:19, 15 January 2006 (UTC)

I chose the name. Either is fine for me. Deco 08:43, 15 January 2006 (UTC)

List of decimal expansions

Is there an article "List of decimal expansions of mathematical constants"?

If so, where is it located?
If not, does anyone think it would be a good idea to create one? Where should it be placed?

--Meni Rosenfeld 16:17, 15 January 2006 (UTC)

If you mean a list of mathematical constants sorted by magnitude, with 50 or so decimal places given, then sure, it would be a good idea. I started a Swedish such list a while back. Fredrik Johansson - talk - contribs 16:23, 15 January 2006 (UTC)

That seems like a potentially useful list, although I'm not sure if it's encyclopedic enough to be added. It would be better if rather than listing them bby magnitude (which is fairly meaningless) you catagorized them in some sensible way. Meekohi 16:58, 15 January 2006 (UTC)

Maybe I'll sort them by order of popularity or something like that. I'll try to see what I can put up... --Meni Rosenfeld 17:02, 15 January 2006 (UTC)

The page mathematical constant already provides such a list (for some definition of "popularity"...) Fredrik Johansson - talk - contribs 17:14, 15 January 2006 (UTC)

Well, this page will have to do for now - Although I do think a list with more digits per constant, perhaps without all the additional information, could be interesting. Perhaps we could also add binary expansions and factorial base expansions (which could be argued to be less arbitary than decimal). Maybe I'll try to compose something over the course of time. --Meni Rosenfeld 17:22, 15 January 2006 (UTC)

Decimal expansions of constants and other tables of numbers should go to Wikisource (see [41]). Samohyl Jan 18:42, 15 January 2006 (UTC)

Areas of mathematics article

To quote from the start of the article, "The aim of this page is to list all areas of modern mathematics, with a brief explanation about their scope and links to other parts of this encyclopedia, set out in a systematic way." Although this has been done for some areas, others are most definately lacking. (All the Analysis, Non-physical sciences and General sections, plus about half the Algebra and Physical sciences sections). Due to the wide ranging nature of the topics in question, this needs contributions from plenty of people. Even if you are only able to expand on a bullet point or two, that would be a definate help. Tompw 11:38, 16 January 2006 (UTC)

Subset notation

As far as I can tell, the conventional notation for "subset" in most of mathematics and in WP is $\subseteq$ . However, it has been argued that in probabilty theory the notation $\subset$ is used. Which one of the symbols should be used in the article shattering, which deals with a topic in probability theory? --Meni Rosenfeld 19:39, 16 January 2006 (UTC)

I believe that $\subset$ refers to a proper subset, while $\subseteq$ does not necessarily refer to a proper subset. NatusRoma 19:55, 16 January 2006 (UTC)

Unless the article specifically states that ⊂ may refer to nonproper subsets it seems wise to use ⊆ for the general case and ⊂ for proper subsets. I don't see why this should be any different in probability theory. -- Fropuff 20:16, 16 January 2006 (UTC)

To NatusRoma: Yes, that is the common convention - However it seems that in probability theory, a different convention is used, where $\subset$ means a not necessarily proper subset.

To Fropuff: That is what I also think, but it has been argued that probabilitists will be confused when they read an article in their field which uses a different convention than they. I would like to hear more opinions to make sure we have consensus on using ⊆. --Meni Rosenfeld 20:22, 16 January 2006 (UTC)

Probabilists use $\subset$ (⊂), to mean subset -- however they seem never to use $\subseteq$ (⊆), so the mathematically correct usage shouldn't confuse them. Arthur Rubin | (talk) 22:21, 16 January 2006 (UTC)

I have proposed a convention regarding this issue. Discuss it here. --Meni Rosenfeld 09:41, 17 January 2006 (UTC)

Chaos theory needs help

The Chaos theory page needs help. There is a Wikipedia user that insists in inserting comments about biotic motion into the page. Several contributers have tried to point out the problems with biotic motion to the contentious user, but to no avail. What should be done about this?

The long discussion in the Chaos theory talk page has brought up a series of difficulties with the published work in bios theory: lack of mathematical definitions, one common author in all the six papers in citation indices, no reference to a century of work in dynamical systems, simple analytical arguments not made, etc.

Despite the results being published, I find it hard to see how a topic that has failed to attract attention for seven years should be included as a major idea in the Chaos theory article.

XaosBits 03:08, 18 January 2006 (UTC)

Editors need help at function (mathematics)

There is a dispute going on at function (mathematics), where substantial rewriting (with reverts) has been going on, with the two editors unable yet to agree on how the article should be rewritten. Rich Norwood is requesting other editor's views. Please help out. (I will be away for a few days but I will try to lend a hand when I get back.) Thanks all. Paul August ☎ 15:20, 18 January 2006 (UTC)

Mathie

I nominated this for deletion. Votes (either way) welcome. :) Oleg Alexandrov (talk) 01:57, 19 January 2006 (UTC)

Shape or set?

I am having a dispute with Patrick over at shape. Here's the relevant diff to Patrick's version. I would argue that Patrick is a bit pedantic insisting on the word "set" instead of "object" and that it makes the article less clear for the general public. Patrick's explanation is in the edit summary to that edit, stating "object is undefined; e.g., there is unclarity about color". I would like some comments, on this page, which I will later move to talk:shape. Oleg Alexandrov (talk) 01:03, 21 January 2006 (UTC)

Yeah, it should be object. To talk about shape, there's already an implicit assumption made that the set has a metric. There's also an implcit assumption that there's a space so that rotations, translations, etc. are defined. By contrast, true "sets" don't have metrics and can't be rotated or translated. So insisting on "set" is kinda goofy. linas 01:25, 21 January 2006 (UTC)

Maybe we should use the word "object", and add a comment like "object here is taken to mean a subset of a metric space"? This will make it more or less accurate, while maintaining readability. -- Meni Rosenfeld (talk) 06:40, 21 January 2006 (UTC)

Real projective line

Hi everyone.

It seems that currently the only reference in Wikipedia on the real projective line ( $\mathbb{R}\cup\{\infty\}$ ) is this 3-line subsection. I believe there is much more to be said about it, elegantly extending analytical properties of reals to it. The problem is that I've never really read about such definitions (I'm not very proficient in the mathematical literature), but it seems natural to me that these are things that should be defined. Examples are to say that $\lim_{x \to a} {f(x)} = \infty$ iff for every M > 0 there is ε > 0 such that $| f (x) | > M$ for every |x - a| < ε. In this way, $\lim_{x \to 0} {\frac{1}{x^2}}$ , $\lim_{x \to 0} {\frac{1}{x}}$ and even $\lim_{x \to 0} {\frac{1}{x sin{1/x}}}$ are all equal to $\infty$ . Since we don't want to use signed infinities, classical limits like $\lim_{x \to +\infty} {f(x)}$ and $\lim_{x \to -\infty} {f(x)}$ become $\lim_{x \to \infty{-}} {f(x)}$ and $\lim_{x \to \infty{+}} {f(x)}$ (approaching the point at infinity either from the left, through increasingly positive numbers, or from the right, through increasingly negative numbers). The concept of continuous function can be extended. The notion of intervals can be extended, for example if a > b, we define the open interval $(a, b) = (a, +\infty) \cup\{\infty\}\cup (-\infty, b)$ . This way, we have for example the nice propety: The image of the interval (a, b), under the funtion $f(x) = \frac{1}{x}$ , is $(\frac{1}{b}, \frac{1}{a})$ , no matter what the values of a and b are.

I want to write an article on these topics (more specifically, turn real projective line from a redirect to an article). The questions are these:

Is there a place in WP where these concepts already appear?
Does anyone know a reference where these definitions appear, to make sure I'm not inventing anything?
Does anyone think this is not a good topic for an article?

I'll be grateful for any comments. -- Meni Rosenfeld (talk) 15:24, 22 January 2006 (UTC)

There are three more lines in a more abstract setting at compactification (mathematics) (look for the one-point compactification). It seems to me a good topic for an article if you can find some references and I expect these references to exist. -- Jitse Niesen (talk) 15:40, 22 January 2006 (UTC)

Have you heard about these concepts? That would be a good start. Unfortunately I do not know of any references. Would it be okay to create the article now, and add references as we find them? -- Meni Rosenfeld (talk) 16:11, 22 January 2006 (UTC)

No. I think you shouldn't write an article without consulting references. Personally, I even make mistakes if I know the stuff very well unless I have a book lying next to me. -- Jitse Niesen (talk) 00:50, 23 January 2006 (UTC)

It wasn't clear to me from your answer whether you have heard about these definitions. It is important to me to know, because if not I will have a mind to put this matter to rest. In either case, is there anyone who has heard about it, and preferrably, know of a reference to it? -- Meni Rosenfeld (talk) 06:34, 23 January 2006 (UTC)

Oh, and I've just found this. It doesn't address all of the above ideas, but it's a good start, no? Is it enough for starting an article with just what is mentioned there? But please do tell me if you've heard about the limits thing. -- Meni Rosenfeld (talk) 08:34, 23 January 2006 (UTC)

I have no definite recollection of the limit thing. On the other hand, I doubt I would remember it if I had read it somewhere as it seems quite natural to me and a consequence of general topology.

I'm quite sure I've seen the thing of how division of intervals might result in an interval containing infinity in a paper on interval arithmetic. This is also mentioned in the MathWorld link. -- Jitse Niesen (talk) 11:42, 23 January 2006 (UTC)

Yeah, I figured this is a special case of more general topologic spaces. But the reason I think these explicit definitions are of notable interest is because they are an elegant extension of the good old real numbers, a structure we all know and love. Also I don't know much topology so I'm not proficient in all the structures that exist.

I think we have sufficient grounds to at least start an article, which I will begin working on now. It will be called Real projective line. Everyone be sure to check back in a few hours and leave some feedback. -- Meni Rosenfeld (talk) 09:08, 24 January 2006 (UTC)

Hmm I don't like that name so much. Mostly because it's not a name that anyone uses. The space you're talking about is called (in my experience) the real projective line or else the one point compactification of the real line. -lethe ^talk 09:15, 24 January 2006 (UTC)

Okay, I thought it would be a good idea to call it this way because that's how it's called in Mathworld, but if you say it's uncommon I'll change that. -- Meni Rosenfeld (talk) 09:22, 24 January 2006 (UTC)

While we're at it, what is the most common notation for this space? -- Meni Rosenfeld (talk) 09:30, 24 January 2006 (UTC)

$\mathbf P^1(\mathbf R)$ perhaps. Double-struck if you prefer. Dmharvey 13:33, 24 January 2006 (UTC)

Hmmm not so sure now. You seem to be talking about a set with certain arithmetic operations, and the notation I suggested doesn't really cover that. Dmharvey 13:48, 24 January 2006 (UTC)

Functions, partial, pre-, proto-, total, etc.

JA: I'll be introducing some language under the heading of Relation (mathematics) to cover these cases and more, as they arise within the setting of relations in general. Stay tomed. Jon Awbrey 15:48, 22 January 2006 (UTC)

Notation for positive infinity

Another question on a loosely related subject: Is there a notational convention in WP regarding positive infinity? I think it is most commonly denoted $+\infty$ in the literature, but I've seen places in WP where it is denoted just $\infty$ . Should the + sign be added for consistency and clarity? -- Meni Rosenfeld (talk) 16:40, 22 January 2006 (UTC)

As a rule the plus sign is used only if it is necessary to distinguish a positive infinity from a negative one. Also, some contexts require other ways of denoting infinities, such as ω or ℵ₀. --KSmrq^T 18:39, 22 January 2006 (UTC)

My experience is that it's referred to as $+\infty$ only where it is necessary to distinguish it explicitly from negative infinity, such as in the limit of some real-valued functions. In some contexts such as complex numbers there are an uncountable number of different kinds of infinity. Generally I think just $\infty$ is fine for most purposes. Deco 18:43, 22 January 2006 (UTC)

Maybe this example will clarify the question... Don't you agree that the + sign should be used there? These are statements about plain real numbers, not a projected line, a Riemann sphere, cardinalities, non-standard analysis and all the other stuff (which are all very nice but have little to do with my question). -- Meni Rosenfeld (talk) 18:47, 22 January 2006 (UTC)

I don't agree. For the same reason we don't need to write +1 to distinguish it from –1, we don't need +∞ to distinguish it from –∞. -lethe ^talk 00:15, 23 January 2006 (UTC)

I don't see any harm in using +∞, except that it seems maybe a little pedantic. It does serve a colorable purpose in distinguishing +∞, not from –∞, but from "unsigned infinity". --Trovatore 00:18, 23 January 2006 (UTC)

I like +&infinity;, especially when writing down an integral or sum. Also helps to distinguish from unsigned or complex infinity. —Ruud 00:28, 23 January 2006 (UTC)

I once thought like lethe, but have since come to realize that, like Trovatore and Ruud said, you don't need to distinguish +1 from an "unsigned one", but you do need to distinguish $+\infty$ from unsigned infinity. So what do you say? Should we use $+\infty$ consistently for this purpose? -- Meni Rosenfeld (talk) 06:30, 23 January 2006 (UTC)

OK, the point that infinity can be signed or unsigned while finite numbers are not is well-taken. I'm still not sure of the absolute necessity for adherence to this convention here. Seems to me that it will always be clear in context which is meant. In short, I think it's OK for you to use this convention, but I don't believe it's necessary to ask that everyone use it everywhere in the project. -lethe ^talk 06:40, 23 January 2006 (UTC)

I agree that no harm is done by not following such a convention, but I do believe that it can only improve things. I have proposed the convention, discuss it here. -- Meni Rosenfeld (talk) 07:54, 24 January 2006 (UTC)

Division by zero

I am having a dispute with Rick Norwood regarding division by zero. The problem is that I want to write about structures where division by zero is possible, while he systematically tries to prove that defining division by zero is "wrong" and that you mustn't do it, because it leads to problems. I will appreciate your comments (either way) on the issue.

And while you're at it, I would also like to hear your opinions regarding the size of inline fractions in the article. -- Meni Rosenfeld (talk) 06:41, 23 January 2006 (UTC)

Technically, you can come up with you own theory, which defines division by zero through axioms somehow. However, I think you will have a difficulty proving consistency of your theory. (Igny 13:36, 23 January 2006 (UTC))

We already have wheel theory, which purports to be such a theory. But such things are better structured as 'see alsos' to the main article. Charles Matthews 13:47, 23 January 2006 (UTC)

If I had to invent such a theory myself, I probably would have encountered difficulties formulating it; Fortunately, the theories are well developed and it is well known what is or is not true. About the wheel theory, I don't know much about it, but I think it may indeed be too advanced to be discussed thoroughly in this article. But things like the Riemann sphere are certainly more than mere curiosities, and should be discussed in such an article. -- Meni Rosenfeld (talk) 20:04, 23 January 2006 (UTC)

Not really. There are places like birational geometry, rational map and so on, where it can better be put into context. Charles Matthews 13:45, 24 January 2006 (UTC)

Sets of sets

A new but promising editor, User:MathStatWoman, has written an article called sets of sets, apparently in response to some talk-page discussion that I can't really remember where to locate at the moment. I think the article has two major problems. First, it seems to be more a personal essay than a verifiable encyclopedia article. Second, I don't think it's really correct: It claims, essentially, that locutions like "collection of sets" are preferred over "set of sets" because of the Russell paradox. I don't think that's the reason at all; when people discuss sets of reals and collections of sets of reals, the Russell paradox is not remotely in the same time zone as the objects being discussed, which can all be coded in V_ω+2. The reason for preferring the word "collection" is that it helps to keep the types straight in the reader's mind (and for that matter, in the author's mind).

I really think the article should go to AfD, hopefully without any prejudice to MathStatWoman. Any thoughts on the matter, or alternative suggestions? --Trovatore 04:36, 24 January 2006 (UTC)

AfD for sure -lethe ^talk 07:59, 24 January 2006 (UTC)

I agree that, at least in some contexts (possibly most), "collection of sets" is used for clarity rather than for accuracy. But I can't see why it looks to you like a personal essay. In any case, call me an inclusionist, but I think it's worth having an article with this name. Perhaps some of the content should be removed, some can be disambiguated (something like "'collection' is sometimes used for clarity, and sometimes because it really isn't a set"), and perhaps some words about the simple fact that an element of a set can be itself a set, a concept that is difficult for some first-year students. -- Meni Rosenfeld (talk) 08:03, 24 January 2006 (UTC)

The article is problematic. I saw the it late last night just before I went to bed, and was too tired to do anything about it then. I had planned to contact User:MathStatWoman and discuss it with her this morning. I don't really think we need such an article and as it stands it is misleading and inaccurate — but I had really hoped to avoid AfD. I hope we don't end up alienating the author. Paul August ☎ 13:22, 24 January 2006 (UTC)

No offense taken; no, you have not alienated the author. :-) But indeed there is a reason for not declaring certain collections sets. Some groups of things are not sets. Agreed, there are some sets of sets that are ok, when logical inconsistencies or incompleteness does not come into play. But we probabilists often run headlong into difficulties with certain particular peculiar collections, classes, or families of sets (and with AoC, and with measurability problems, too, by the way) My suggestion: let's keep the article sets of sets for now, discuss the issue, and clean it up together. with references and examples. Seem ok to all of you? Thanks for the input. I like a good debate like this one. You were all polite and kind, and I appreciate that. MathStatWoman 15:37, 24 January 2006 (UTC)

You said:

we probabilists often run headlong into difficulties with certain particular peculiar collections, classes, or families of sets

What are these problems, and how does this article address or resolve the problems? linas 16:23, 24 January 2006 (UTC)

First, please let me preface the answer: The article on empirical processes is under development; anyone else who works in this field is welcome to contribute, of course; that would be excellent, in fact. But I am struggling with the markup language, so it takes me a very long time to add very little information. Now the answer: Anyway, once the article is expanded,it will be evident that the study of empirical processes involves classes of sets, and also collections of functions related to those sets. It is well known that functions are related to families of subsets, since a particular function, (e.g. indicator functions, important in empirical processes and statistics), often can be viewed as a subset; hence we would end up using sets that could contain themselves, or not contain themselves; hence a paradox unless we use terminology such as families, collections, or classes of sets. See, for example, Vapnik and Chervonenkis, Pollard's, Wellner's, R. M. Dudley's, and R.S. Wenocur's works in V-C theory, empirical processes, and learning theory...they always use terms "classes of sets or collections of sets or functions to avoid these paradoxes. In some cases, a class" of sets cannot be a set itself, or we have inconsistency. Hope that clarifies the issue a bit for now. I would like us all to work more on the article sets of sets rather than delete it. I can add references soon, if that would help. MathStatWoman 17:00, 24 January 2006 (UTC)

MathStatWoman, I'm going to have to call you on this claim that the Russell paradox is relevant to anything that comes up in probability theory. I just don't see it happening. The Russell paradox fundamentally arises from a confusion between the intensional and extensional notions of set; no doubt one could code that confusion into probabilistic language, but only in an attempt to turn probability theory into foundations, and I've never heard that probabilists were into that. If you're going to stick to this claim, please find a minimal example and explain it here. --Trovatore 17:28, 24 January 2006 (UTC)

I have to go to work/schoool now, so just a few quick words; no time for markup language; please forgive my using plain typesetting here. Please understand that this is not a joke; it is serious mathematics; I am not trying to play games here. In probability theory, the probability space Omega and the sample space X can be anything; its elements can be sets (or, equivalently, functions, which can be viewed as sets, e.g. all functions from set Y to {0.1) is equivalent to the collection of all subsets of Y, i.e. its power set 2^Y. We use indicator functions in empirical processes. To show that we need to restrict sets under consideration to V-C classes of sets, or uniform Donsker classes of sets, or P-Glivenko-Cantelli sets, etc...we need counterexamples that involve e.g. X being the class of all sets. Cantor's Paradox and Von Neumann-Bernays-Gödel set theory (in which we do not speak of sets of sets apply here. When empirical process article develops, all this will become apparent. Let's just make the sets of sets article better, or, as an alternative put it (cleaned up and referenced) into Von Neumann-Bernays-Gödel set theory, how does that seem? Talk to you later. gtg now MathStatWoman 17:58, 24 January 2006 (UTC)

The notion of proper class is discussed in several places, I think; I don't see any need for a new article
If you really meant to say that NBG doesn't use sets of sets, that's wrong. In fact all sets in an interpretation of NBG are sets of sets. Yes, NBG also has collections of sets that are not themselves sets.
I'm still extremely skeptical that you're going to be able to show us how the Russell paradox attaches to VC theory or probability theory. Please give a minimal example. --Trovatore 21:33, 24 January 2006 (UTC)

I believe that this article should be deleted. If something needs to be said about sets and classes it should be said in proper class or class (mathematics) (the considerations here are too elementary for NBG, I think). "Set of sets" is the wrong title, because sets of sets per se are ubiquitous and unproblematic. There might be some issues here which should be moved to proper class or class (mathematics), though -- after being clarified; the existing text is confusing. Randall Holmes 03:59, 27 January 2006 (UTC)

On looking at these articles, I think the proper context for a discussion of these issues would as I said be class (set theory) (which is the same article as proper class, class (mathematics)); adding some informal examples with explanation to this article would be the right way to achieve the author's apparent purpose. There are some technical points: in most mathematics, a finite set which is one of its own members (used in one of the examples) will not arise; in the standard set theory ZFC, no set is an element of itself. And in the standard set theory ZFC all sets without exception are sets of sets; sets of sets is not the right title. Like Trovatore, I would be very interested in seeing any relevance of this topic to probability theory (though I wouldn't be surprised if there were some; mathematicians are ingenious :-) Randall Holmes 04:11, 27 January 2006 (UTC)

I should also add, lest I seem too encouraging, that the only real content in the article sets of sets seems to be a discussion of Russell's paradox, on which there is already an article. I do notice that class (set theory) might (or might not) benefit from an informal summary of reasons why certain classes (the Russell class, the class of all ordinals) actually are proper classes, and this might do what is wanted in sets of sets. If there are specific applications of the set/class distinction in probability theory, these might make a subject for an article. Randall Holmes 04:17, 27 January 2006 (UTC)

another point: the mere possibility of having sets which are elements of themselves does not in itself imply any danger of paradox. Aczel's theory of non-well-founded sets has this kind of circularity (and I suspect this may be all that is needed in the theory of empirical processes) and doesn't come anywhere near needing proper classes or risking Russell's paradox. Applications of hypersets may be the issue here. Randall Holmes 04:19, 27 January 2006 (UTC)

Lethe for admin

In case some of you don't follow Wikipedia:Requests for adminship, I nominated one uf us, Lethe, for administrator, which, in my opinion, was long overdue. If you are familiar enough with Lethe's work, you can vote at Wikipedia:Requests for adminship/Lethe. Oleg Alexandrov (talk) 17:06, 24 January 2006 (UTC)

Mediation needed in big dispute at relation (mathematics)

There is a big argument at talk:relation (mathematics), with Arthur Rubin and Randall Holmes on one side, and Jon Awbrey on the other side. I did not study the matter in a lot of detail (and am not an expert in the matter), but it seems that Jon Awbrey is making things more complicated than necessary and is rather pushy at enforcing his version (judging from the edit history. Anyway, help would be very much appreciated. Oleg Alexandrov (talk) 18:57, 24 January 2006 (UTC)

Proposed changes to mathematics

I've proposed some changes to the "Major themes in mathematics" section of the mathematics article, see: Talk:Mathematics#Proposed changes to "Major themes in mathematics" section. Paul August ☎ 21:35, 24 January 2006 (UTC)

Question about bases

Hi all, Base (mathematics) gets very little (if any) traffic so I'd like to ask this here. The question is on Talk:Base (mathematics), at the bottom, about integers vs. numbers (please respond there as I'm not watching this page). I'm not a mathematician, just an enthusiast, so this is me asking experts for (knowledge and) advice with the article (be warned, it is unreferenced and possibly inaccurate). Thanks :-) Neonumbers 10:02, 25 January 2006 (UTC)

another problematic article

The article SuperLeibniz law seems to be complete nonsense. I would have put it on AfD, but a search makes it look like a superLeibniz law might be something real (see e.g. Poisson superalgebra). However all the hits seem to be Wikipedia reflections, and Poisson superalgebra doesn't give any clue as to a definition for SuperLeibniz law. Poisson superalgebra was written by User:Phys, who hasn't been around since November. Unless someone knows what a SuperLeibniz law is supposed to be, I still think AfD is where it's headed. --Trovatore 03:30, 26 January 2006 (UTC)

Oh, I should amend the claim that Poisson superalgebra doesn't give any clue as to a definition; it does in fact give an example. But it's not clear whether it's the only example, nor what would characterize any others. --Trovatore 03:32, 26 January 2006 (UTC)

I see a red link for the article you mention, and searching didn't turn it up either. Did someone speedy delete it already? -lethe ^talk 03:41, 26 January 2006 (UTC)

Ooops, I've found it SuperLeibniz Law here. -lethe ^talk 03:45, 26 January 2006 (UTC)

Ahhh, the thing that is mentioned in Poisson superalgebra is what I know as a graded derivation or an antiderivation. It's defined in derivation (abstract algebra). The stuff in SuperLeibniz Law is, as you suggest, patent nonsense. The question is whether we want to redirect or just delete. Is that name attested anywhere? -lethe ^talk 03:47, 26 January 2006 (UTC)

The notion of a super Leibniz law is a valid one, although what was SuperLeibniz Law was patent nonsense. The concept usually goes by the name of superderivation or graded derivation. If V is a superalgebra and D is a (graded) linear operator on V, then D satisfies the "super Leibniz law" if

$D(ab) = (Da)b + (-1)^{|a||D|}a(Db).\,$

I'll will amend these articles shortly. -- Fropuff 04:50, 26 January 2006 (UTC)

Yep, that's it. The Lie derivative, exterior derivative, and inner derivative satisfy that equation with degrees 0, 1, and –1 respectively. I've not heard it called a superderivation before, but it sounds like a reasonable enough name. -lethe ^talk 05:01, 26 January 2006 (UTC)

I added a section to derivation (abstract algebra). -lethe ^talk 05:16, 26 January 2006 (UTC)

I think the name graded derivation is a more general term applying to Z-graded algebras, whereas the name superderivation means a graded derivation of superalgebras. Maybe a separate article at graded derivation would be best, but I'm fine with a redirect to derivation for now. -- Fropuff 05:48, 26 January 2006 (UTC)

Isn't a superalgebra just a Z₂ graded algebra? -lethe ^talk 05:54, 26 January 2006 (UTC)

Yes it is, but one can have graded derivations on algebras with a more refined grading than just Z₂; e.g. the exterior algebra. It is not common to refer to the exterior algebra as a superalgebra (although it is one). More importantly, it is important to keep track of the more refined grading for linear maps. As you say, the exterior derivative and the interior product have grades +1 and −1 respectively, but as maps of superalgebras I would say they both have grade 1 (i.e. they are both odd). -- Fropuff 06:05, 26 January 2006 (UTC)

Right, right. I think I thought you made a complaint that you didn't actually make, now that I reread your complaint. I added graded derivation to that article, when really what we wanted was superderivation, which is a special case. And I didn't mention it the term at all.. Antiderivation is already there, which is pretty close, but not it. As for whether it should get its own article, I'm not opposed to the idea, but I'm not going to do it. I've got to think about dual spaces some more. -lethe ^talk 06:25, 26 January 2006 (UTC)

I think I thought you made a complaint that you didn't actually make. That's got to be the quote of the day ;) -- Fropuff 06:29, 26 January 2006 (UTC)

Appeal to clean up the page on "list of paradoxes"

There are so many items in the list of paradoxes that are not paradoxes. I commented on just a few examples on that page's discussion page. Could we please collaborate to clean up that page and remove what does not belong? MathStatWoman 09:05, 27 January 2006 (UTC)

No genuine paradoxes in mathematics. So we should just cut the maths? Actually it is OK by me for list of paradoxes to list things called a paradox, and then annotate/comment in individual articles as to the aptness of the name. Lists are mostly a navigational tool; 'added value' in terms of comment is good, but judge them mainly by the help they can give in fiding what you were looking for. In that sense, Category:Paradoxes might need to be more rigorous. Charles Matthews 10:30, 27 January 2006 (UTC)

So there are two ways of understanding the word paradox and people often talk past each other until they notice that they're using the word differently. Both of you seem to be using it to mean simply "contradiction". In my usage a paradox is an apparent contradiction. Paradoxes are much more interesting than contradictions. A contradiction just tells you that one of your assumptions is wrong, which is commonplace. A paradox tells you that something about your intuition is wrong, and that your intuitions need to be reconstructed to fit the facts. --Trovatore 15:21, 27 January 2006 (UTC)

W.V.O. Quine says the same thing in an essay on paradoxes. He identifies "veridical" paradoxes, which are arguments that prove apparently absurd results that are nevertheless correct, such as the Banach-Tarski paradox, and "falsidical" paradoxes, which are apparently-correct arguments that nevertheless prove false results, such as Zeno's paradoxes. -- Dominus 17:06, 27 January 2006 (UTC)

I'm not quite so ignorant. For example Smale's paradox is really Smale's counterintuitive result? But Bertrand's paradox is really a verbal trick about 'uniform'? There is a bit of history on this, monster barring and so on. Charles Matthews 16:43, 27 January 2006 (UTC)

I didn't mean to imply you were ignorant. But what can it mean to say there are no genuine paradoxes in mathematics? (As I said on Talk:List of paradoxes, "genuine paradox" puts me in mind of "genuine faux pearls", a bonus offered on TV ads for those who call now.) --Trovatore 16:50, 27 January 2006 (UTC)

No contradictions in a consistent formal system. But 'paradox' actually connotes only semi-formalised reasoning. Charles Matthews 08:29, 28 January 2006 (UTC)

Article intro text

I'm sure this has come up before, but I'd like to ask - what thought has been given to how "technical" the first paragraph of maths articles should be. I'm of the opinion that the introduction should try only to explain what an interested non-mathematician would understand and find useful - what it is, why it's important, and what it's used for, all in non-technical terms. The detailed technical information can follow later. What do you think? --Khendon 21:10, 28 January 2006 (UTC)

Non-technical is always a great goal. But it may be a challenge. It took an hour of rewrites to get the first line of the dynamical systems article. And I am not sure how useful it is. It is very tempting to say: a dynamical systems is a tuple [M, f, T] where M is ... There are many technical reviews available on the WWW, but I feel there is a lack of non-technical reviews. The reader I try to keep in mind (but often loose) is the college freshman. XaosBits 23:52, 28 January 2006 (UTC)

Right. It is good for the intro to be motivational. See also the math style manual. Oleg Alexandrov (talk) 23:55, 28 January 2006 (UTC)

One should not try and "dumb down" articles too much. It is important to make sure the article explains everything following from the article (such as any further definitions, concepts, etc that need to be made), but the article should not spend time trying to teach concepts that a reader should already be familiar with. Motivational explanations and examples are a Big Plus. Dysprosia 08:26, 29 January 2006 (UTC)

I agree that the article as a whole should not be "dumbed down". However, I think there are two readers of maths articles - the casual reader who's heard the word "topology" and wants to know what it means, and the mathematician. I think we should cater to both --Khendon 09:41, 29 January 2006 (UTC)

It's important to cater for both sure, but we shouldn't sacrifice "encyclopediality" (to coin a phrase) to do so. Dysprosia 13:01, 29 January 2006 (UTC)

Does the Wikipedia model really work for mathematics?

I am developing a fundamental doubt after spending time watching relation (mathematics) and function (mathematics). I don't see how we can possibly have sensible articles on core concepts on whose definition everything else depends unless someone competent writes them and they are then frozen and edited (by a manager or by a limited class) after consultation only. This doesn't apply to all topics, but these two articles (for example) are about ideas about which many people have ill-informed, strongly held ideas and about which other people, perhaps not so ill-informed, have ideas based on philosophical or pedagogical ideas which deviate too far from the norm for easy accommodation. It was interesting to be able to write an article on New Foundations for people to read -- this is unlikely to attract the attention of too many people of the categories mentioned; articles about obviously technical subjects are not usually subject to this kind of problem, and seem to look pretty good. But central ideas of mathematics (especially ones about which silly statements are prevalent in low-level textbooks or in the popular literature) must require a constant painstaking watch which in the end may not be a sensible use of the time of competent people. (Jon Awbrey should not necessarily assume that I am referring to him). Maybe this does work out in the long run, but I'm certainly finding a watch on these articles to be much less productive and much more frustrating than watching technical articles in set theory... Randall Holmes 02:33, 29 January 2006 (UTC)

Welcome to the real world. :) Randall, both you and Jon are rather new, and I believe that's part of the problem (I remeber my bitter fights with Linas a year ago :) Yeah, the Wikipedia model has its advantages and disadvantages, takes a while to get used to it, and yes indeed, constant watch and occasional frustrations are part of the game. Sorry I can't say something more meaningful, hopefully others will have better insights. Oleg Alexandrov (talk) 06:57, 29 January 2006 (UTC)

Yes, well, Randall none-the-less does bring up a valid point. My response has been to ignore articles on pop topics, but this is not really a "good" answer. I don't know the answer, but direct interested parties to Wikipedia:Stable versions linas 17:06, 29 January 2006 (UTC)

Mirabile dictu, both articles which are bothering me are looking mostly correct today, though the text is becoming increasingly dense and qualified... Randall Holmes 21:57, 29 January 2006 (UTC)

GSL GFDL Copvio problem.

Please see discrete Hankel transform. The article incorporates text taken from GSL, which is GFDL'ed. However, the GSL license has "invariant front and back-cover texts" which the copy did not preserve, resulting in a copyvio dispute. Surely WP has a GFDL sources policy? I don't understand that policy, but links to where it is explained would be handy. linas 17:11, 29 January 2006 (UTC)

Another small step towards MathML support in MediaWiki

Jitse and I have been making progress with MathML support in MediaWiki.

Try out the test wiki.

See also the announcement at the village pump, and our page on Meta.

Please direct all discussion to the talk page on Meta.

Dmharvey 01:50, 30 January 2006 (UTC)

You da' man, David! Major kudos for working on this. I really hope blahtex makes it into MediaWiki someday soon. I'm happy to help out testing. -- Fropuff 02:17, 30 January 2006 (UTC)

I am looking forward to the day when math on Wikipedia will look good, when we won't worry about \, vs \! to PNGfy things, when html and TeX live in peace and harmony, blah, blah, blah... Oleg Alexandrov (talk) 03:41, 30 January 2006 (UTC)

Oleg, given your comments on MathML in the past, I'll take that to be your way of trying to sound encouraging :-) Dmharvey 04:14, 30 January 2006 (UTC)

I never had anything gainst BlahTeX or MathML. It is just I was (and still am) very skeptical about the pace of introduction of MathML and the timing of when we won't need to worry about PNG and HTML and all that. My skepticism is based on my past experiences with other (cool!) things. But you are doing great work, and I hope things will work better/sooner than I think. :) Oleg Alexandrov (talk) 21:16, 30 January 2006 (UTC)

Scepticism is good, action is better. -- Jitse Niesen (talk) 22:10, 30 January 2006 (UTC)

You've got to admit that at least we look a bit better than PlanetMath... Dysprosia 10:48, 30 January 2006 (UTC)

I'm still holding my breath for Safari to implement MathML before I get excited. -lethe ^talk 11:20, 30 January 2006 (UTC)

Me too. Paul August ☎ 19:38, 30 January 2006 (UTC)

That's true. At least HTML/PNG is compatible on nearly *all* browsers. Dysprosia 11:53, 30 January 2006 (UTC)

Don't get me wrong. I'm looking forward to being excited about it. I was even toying with the idea of trying to pitch in to MathML implementation in Safari. I think one day a lot of browsers will have it. -lethe ^talk 12:26, 30 January 2006 (UTC)

I didn't really mean it like that; the fact that MathML isn't supported in Safari highlights the problems a lot of people may have if we eventually switch to MathML. I tend to use Lynx or w3m a lot sometimes in browsing things, and MathML would be unreadable in those circumstances. Dysprosia 00:35, 31 January 2006 (UTC)

I'm of the opinion that we should push for MathML implementation in MediaWiki as soon as possible, regardless of whether or not major browsers such as IE or Safari have native MathML implementations (the PNG/HTML option will still be available to those users). In fact, I think having a high profile site like Wikipedia making heavy use of MathML will be a major motivation for browser developers to implement MathML in their browsers (lest everyone switch to Firefox/Mozilla). -- Fropuff 19:55, 30 January 2006 (UTC)

I like this argument a lot. -lethe ^talk 23:51, 30 January 2006 (UTC)

In fact, the process that Fropuff is alluding to has already started happening (sort of). At the time I released the previous version of blahtex (August 2005), MathML development in gecko (i.e. mozilla/firefox) had been close to moribund for a few years. But as soon as they heard that wikipedia was planning MathML support, a few developers there started fixing all kinds of bugs, and indeed fixed the majority of the really nasty ones that I specifically pointed out to them. I haven't yet seen any evidence of other browsers getting their act together, but maybe with a working demo wiki now available, they'll take more notice. Dmharvey 21:14, 30 January 2006 (UTC)

Thats encouraging. Maybe wikipedia will be the killer app which makes maths on the web finally happen. Its been do-able for at least 10 years now (since the geometry center folks were developing WebEQ) but its never been a priority and never got that critical mass. I'm all for a push for MathML in MediaWiki, might be able to help with coding. There is a MathML (if possible) option in 'my preferences', don't know if it has any functionality. --Salix alba (talk) 22:09, 30 January 2006 (UTC)

The "MathML (experimental)" option presently only produces MathML for the very simplest things like "x + y = 2". Give it a superscript and it stares back blankly at you. But that's besides the point: it is also necessary to deliver the entire document as XHTML, get the browser recognising the MIME types, and a few other things, without breaking browsers that don't understand any of that. Currently MediaWiki doesn't do these things. Dmharvey 22:39, 30 January 2006 (UTC)

BlahTex now work in Internet Explorer (Win) with the MathPlayer plugin. I've also created a page meta:Blahtex/Compatibility to list how well it works with different browsers. Testing of the blahtex wiki welcome. --Salix alba (talk) 15:22, 5 February 2006 (UTC)

Definition of "computational mathematics"

The term "computational mathematics" turns up over half a million Google hits; most seem to come from names of institutions or courses. I've thought of starting a stub, but I'm not sure how to define the term and relate the field (if there is one) to others. My intuitive understanding is that, roughly speaking, computational mathematics is to mathematics what computational science is to science; i.e. it comprises the study and/or use of algorithms for the purposes of mathematics (including discrete and symbolic mathematics, in addition to numerical analysis). Is this correct? Fredrik Johansson - talk - contribs 19:09, 30 January 2006 (UTC)

Good luck with coming up with a definition. I'd say that it's the study of algorithms for mathematical problems, regardless whether the ultimate application is in mathematics or without. My list of fields which can be considered part of computational mathematics: obviously numerical analysis (including optimization and approximation theory), symbolic mathematics, computational number theory, learning theory, computational geometry, image processing, and some complexity theory. But generally it is very hard to define a research discipline, especially one of these fashionable multidisciplinary ones. -- Jitse Niesen (talk) 20:13, 30 January 2006 (UTC)

Springers journal has a nice def [42]

Foundations of Computational Mathematics (FoCM) publishes research and survey papers of the highest quality, which further the understanding of the connections between mathematics and computation, including the interfaces between pure and applied mathematics, numerical analysis and computer science.

a non copyvio rewrite of that could be a good place to start. --Salix alba (talk) 20:40, 30 January 2006 (UTC)

Don't bother rewriting it - just quote it in the intro. I think this will make a great high-level topic for linking lots of more specialised areas - it might even be a good idea to link it directly from Mathematics. Deco 00:39, 31 January 2006 (UTC)

Yes please; cf Talk:Mathematics#Request for link to mathematical computing. Hv 16:53, 31 January 2006 (UTC)

I'am a bit confused by this discussion. Fredrik, you said above, that you understand it similarly to computational science, so, by this analogy, do you mean application of computational methods to mathematics itself (like experimental mathematics and automated theorem proving)? But then, what other people said, it seems that they mean study of computational methods mathematically, regardless of the application field. So which one of these two possibilities is "computational mathematics"? Samohyl Jan 19:21, 1 February 2006 (UTC)

I mean the former. I don't think "study of computational methods mathematically" would be correct; nor does this phrase, as far as I can tell, agree with what others here have suggested. Fredrik Johansson - talk - contribs 23:14, 1 February 2006 (UTC)

Actually, I meant the second of the possibilities that Samohyl mentioned. On rereading my comment, I still agree with myself ;) -- Jitse Niesen (talk) 23:20, 1 February 2006 (UTC)

And now I'm confused ;-) I'm reading "study of computational methods mathematically" as "mathematical study of algorithms", which seems to be the opposite of "algorithms for mathematical problems" as you said first. Fredrik Johansson - talk - contribs 23:29, 1 February 2006 (UTC)

Sorry, let me try to explain using an example. For weather forecasting, you need to make a mathematical model of the atmosphere (basically a PDE), gather the initial data, solve the PDE, and interpret the result — apologies to the people involved for the huge simplifications. The step of solving the PDE is part of computational mathematics, in my interpretation of the term. The problem you are solving is mathematical on one level (a differential equation), but physical on another level (forecasting the weather). On the other hand, I'm not so sure that automated theorem proving is computational mathematics, because there is no computation involved.

I think the definition from JFoCM is a good start, especially since it is verifiable and does not involve the comments of random Wikipedians. -- Jitse Niesen (talk) 16:15, 2 February 2006 (UTC)

I think the best way to view it is in the context of computational modeling:

Step One- Model Setup/Knowledge of the Problem: Engineer/Scientist. Requires thorough knowledge of the physics etc (i.e. can fluid flow be treated as potential flow or not = engineer not mathematician). Sets up the basic equations to be solved.

Step Two- Formulation of the numerical scheme and method of solution (espicially method of solving large matrix equations): Mathematician. This is, in my mind, the biggest aspect of Computational Mathematics. Usually, mathematicians design this part and Engineers/Scientists scan the literature and use those methods developed (ex GMRES, SOR, etc).

Step Three- Implementation of the numerical scheme: Computer Scientist. Here is the science of actually writing the code on the computer, implementing massively parallel computations, etc. Best done in the hands of a computer scientist.

Step Four- Data Analysis/Insight: Engineer/Scientist. Running the simulations, coming up with conclusions, verification of data.

Of course sometimes, one person does everything, but in the "ideal world" that would be how the process works and explains the specific role/ability each type of scientist can bring to the table.

Differentiation of functions of matrices with respect to matrix

Moved to talk:Matrix calculus'. 09:34, 2 February 2006 (UTC)

Functions of matrices

Do we have an article on functions of matrices? I can see some specific cases like Matrix exponential but not a general discussion. Also (and this question overlaps) what about convergence of series of matrices (such as the theorem that a pwoer series of matrices converges if it converges for all of the eigenvalues of the matrix)? Thanks. --Zero 03:58, 2 February 2006 (UTC)

I'm glad to see that you volunteer to write an article on functions of matrices ;) The closest we have is holomorphic functional calculus, but that's probably too abstract. Look at matrix logarithm, somewhere near the bottom, for how it applies in concrete situations. -- Jitse Niesen (talk) 13:21, 2 February 2006 (UTC)

The power series thing is holomorphic functional calculus, but is also clear enough from Jordan normal form, I guess. Charles Matthews 14:08, 2 February 2006 (UTC)

History of manifold

Hey, if there are any experts reading this talk page, it would be great to see the Manifold#History section fleshed out. Thanks. –Joke 04:24, 2 February 2006 (UTC)

It's not so bad now. Query what Weyl actually did in his book on Riemann surfaces, though. Charles Matthews 14:15, 2 February 2006 (UTC)

Surely it is possible to say more about it than that Riemann and Weyl contributed? What about its influence on other branches of mathematics, and vice versa? What about the relationship to physics? What about the development of modern differential geometry, the contributions of Sophus Lie, etc...? –Joke 15:22, 2 February 2006 (UTC)

Yes, always more to say. However the story about the basic, underlying manifold idea is not the same as that of the history of differential geometry, or of Lie groups. (In a strange way, the technical development of manifolds lagged behind.) Charles Matthews 15:32, 2 February 2006 (UTC)

I agree, but the manifold did not develop in a vacuum. Well, maybe if you believe in the Hartle-Hawking state it did. The page differential geometry and topology has no reference to any history either. My point is that saying Riemann did this, then Poincaré conjectured, then Weyl made it abstract seems a little haphazard. Maybe I should try and do some research. –Joke 16:03, 2 February 2006 (UTC)

Template for deletion

Template:Axiom

Seems pretty useless to me. - Gauge 23:41, 4 February 2006 (UTC)

I would think it would be a nice template if it weren't so goddamn ugly. All math books have demarcation for theorems, axioms, definitions, etc. Unfortunately, I don't see how this can be accomplished with current wiki markup. Maybe someday, but not today; this one's gotta go. -lethe ^{talk +} 00:35, 5 February 2006 (UTC)

What appearance would you like? Wiki markup is not the only option; CSS is more powerful. --KSmrq^T 01:24, 5 February 2006 (UTC)

CSS or not, adopting those boxes in any way will make Wikipedia look like American calculus books; with each theorem, lemma, definition, and important formula, in its own shiny box, with different colors for each and so on. Gosh, I hope we don't get there. Oleg Alexandrov (talk) 02:03, 5 February 2006 (UTC)

Agree with Oleg; American calc textbooks are very ugly in their presentation. I don't think we want to be emulating that. If you have lots of axioms, having boxes around each would get out of hand really quickly. I don't see any compelling need to have such a template. - Gauge 06:34, 6 February 2006 (UTC)

If we had something, it would have to be at most an indentation with a boldfaced Theorem inline heading, as is common in textbooks. Putting things in boxes is just ugly (and this particular box is uglier than most). -lethe ^{talk +} 02:42, 5 February 2006 (UTC)

I think it's quite a pretty box. All those purple dots. Look:

Template:Axiom Dmharvey 02:52, 5 February 2006 (UTC)

The template takes only one argument at present, which would have to change if the axiom name is to be bolded automatically. But indentation (left and right), bold, and italics should be possible otherwise.

Axiom 3 (Composition): Given f:a→b and g:b→c, the composition g○f:a→c exists.

This is merely an example. Styling details can be tweaked per taste. --KSmrq^T 04:30, 5 February 2006 (UTC)

I don't think colored text is a good idea. Simply indenting an axiom and making italic should be enough I would guess. Oleg Alexandrov (talk) 04:55, 5 February 2006 (UTC)

I'm not recommending color, only presenting it as an option for people who like purple dots. ;-)

Also, the style can do more than indent. Observe a longer "axiom":

Axiom 9 (Greek): Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.

Notice the "indentation" of the right margin as well as the left; again, an option. --KSmrq^T 07:52, 5 February 2006 (UTC)

I think all axioms in boxes should be stated in Latin as above ;-) - Gauge 06:34, 6 February 2006 (UTC)

This is my little typographers' joke. The text of the "axiom" is explained at lorem ipsum. And "greeking" means either "to display text as abstract dots and lines in order to give a preview of layout without actually being legible", or to fill with meaningless text like "lorem ipsum". Of course, I would never actually use the florid style in the example, with its ugly and distracting background color and small caps. --KSmrq^T 16:34, 6 February 2006 (UTC)

What, pray tell, is wrong with a simple bullet point? Dysprosia 08:16, 5 February 2006 (UTC)

For one thing, you can't put math tagged equations in a bulleted item without resorting to HTML. -lethe ^{talk +} 10:00, 5 February 2006 (UTC)

$\cos{x}+3\,$

Looks like you can? Dysprosia 10:25, 5 February 2006 (UTC)

That's fine for a list of formulas, but doesn't work for a theorem or axiom. See this:

Theorem 1: A right triangle with sides a, b and c obeys

$a 2 + b 2 = c 2$ where c is the hypotenuse and a and b are the legs.

or with the usual indentation for math tags:

Theorem 1: A right triangle with sides a, b and c obeys

a 2 + b 2 = c 2

where c is the hypotenuse and a and b are the legs.

It sucks. When I want to make things like this, I resort to HTML tags. And as Jitse will tell you, I often forget to close them. But you get this:

Theorem 1: A right triangle with sides a, b and c obeys

$a 2 + b 2 = c 2$

where c is the hypotenuse and a and b are the legs.

If there were a template that would give some indentation like that, but without the bullet point, and put theorem, definition, axiom according to an argument, I would consider using it. -lethe ^{talk +} 11:17, 5 February 2006 (UTC)

Theorem 1: A right triangle with sides a, b and c obeys $a 2 + b 2 = c 2$ where c is the hypotenuse and a and b are the legs.

This looks like it works fine. One doesn't have to always indent with math tags unless it's supposed to be displayed. And if there is content that needs to be displayed, it shouldn't be in the one line.

Theorem 1: A right triangle with sides a, b and c obeys

$a^2+b^2=c^2\,$

where c is the hypotenuse and a and b are the legs.

In the second case, observe that using another colon to indent appears to solve the indenting problem. However, there appears to be a minor spacing issue there...

The template option sounds like a good idea, by the way. Dysprosia 11:25, 5 February 2006 (UTC)

your first case is not so great because it has the math png inline. The second one is a bit awkward, but it would serve if nothing else were available. But the html tags are available and do better in my opinion. Anyway, a nice template might be nice. -lethe ^{talk +} 12:13, 5 February 2006 (UTC)

That's if you use the PNG always option. I don't. Dysprosia 12:19, 5 February 2006 (UTC)

To play with the concept I created a template Template:Pfafrich/Axiom which has a configurable style option so the look can be changed.

no style same as a blockquote

Theorem 1: A right triangle with sides a, b and c obeys

$a^2+b^2=c^2\,$

where c is the hypotenuse and a and b are the legs.

user defined style

Theorem 1: A right triangle with sides a, b and c obeys

$a^2+b^2=c^2\,$

where c is the hypotenuse and a and b are the legs.

default style

Theorem 1: A right triangle with sides a, b and c obeys

$a^2+b^2=c^2\,$

where c is the hypotenuse and a and b are the legs.

It turns out the axiom box fails when used with * its just that TfD notice hides this. So in a wiki * bullet point we have

Theorem 1: A right triangle with sides a, b and c obeys

$a^2+b^2=c^2\,$

where c is the hypotenuse and a and b are the legs.

The green box should surrond the whole theorem. It fails because MediaWiki does template substitution before interpreting the * bullet syntax. MediaWikis does the simplest thing when it finds a * - it just puts li tags at beginning and end of line, closing whats necessary. The upshot is that its imposible for a template to box multiline theorems in a * bullet point. Using html <li> will work.

Theorem 1: A right triangle with sides a, b and c obeys

$a^2+b^2=c^2\,$

where c is the hypotenuse and a and b are the legs.

--Salix alba (talk) 23:28, 6 February 2006 (UTC)

I find all the frameboxes, regardless of how they look, to be not so pleasing. In my opinion, they give an unprofessional/naive appearance to the Wikipedia pages, while not helping in understanding the concepts. Neither mathworld nor planetmath use them, nor any books or math publications (as far as I am aware), save again for American calculus and college algebra books. If one really wants an axiom to stand out, I would think indenting it would do a better job. Oleg Alexandrov (talk) 03:49, 7 February 2006 (UTC)

I agree with Oleg that outlined boxes are terrible. Why are you making us look at them? Oleg is right, indentation should be enough. But of course a template might be a nice way to accomplish an indentation (because of the math tags issue). Your first one, the one with no outline, I might consider using that. Maybe I should change the axiom template and then change my vote. -lethe ^{talk +} 04:12, 7 February 2006 (UTC)

Lethe is right, why are you making us look at them? Oleg Alexandrov (talk) 04:21, 7 February 2006 (UTC)

I agree with the both of you. A bullet point suffices. Dysprosia 11:17, 10 February 2006 (UTC)

Copula (statistics)

Can someone take a look at this article, specifically the value of theta at the end of the Archimedean copula subsection? A couple of months back, it said theta=+1. I looked there, and though I don't know the topic, it seemed to me it had to be -1. I changed it and marked it as uncertain. Today I noticed that an anon with no other edits has changed it to theta=0. Once again, I think that's likely wrong, but I don't have the knowledge or time to fully think it through. Can someone check? I want to be sure we don't have some sneaky vandalism happening. Martinp 19:06, 7 February 2006 (UTC) (a lapsed mathematician)

0 it is.

$\lim_{\theta \to 0}(a^\theta+b^\theta-1)^{1/\theta} = a \cdot b$

Arthur Rubin | (talk) 19:57, 7 February 2006 (UTC)

Good. Thanks. That's an interesting limit, btw. Would make a good exam question... Martinp 15:40, 8 February 2006 (UTC)

New stub cat (topology)

Following prescribed discussion, I've created a new stub category, {{topology-stub}}. Assistance in populating it would be appreciated (a lot of articles marked with {{geometry-stub}} are really topology, and there are many articles marked with just {{math-stub}} that are topology). --Trovatore 19:29, 7 February 2006 (UTC)

Proofs and derivations

In many of the pages on wikipedia, articles go over proofs and derivations of forumlae and other such things. Most of the time I don't need a proof, and in some cases the proof obscures the end formula. I think a very clean and elegant way to include proofs would be to link to a separate page that goes through a proof or derivation. This way, an article can be kept uncluttered and clean, while being complete and non-mysterious. (btw, is this the wrong place for this suggestion?). I'd like to know if anyone feels the same way I do. Fresheneesz 22:01, 7 February 2006 (UTC)

We've had previous discussion on this. Basically proofs should only be here if they have some merit or interest. Charles Matthews 22:07, 7 February 2006 (UTC)

See Wikipedia:WikiProject Mathematics/Proofs for discussion, and the Math_style_manual#Proofs for the policy. Oleg Alexandrov (talk) 22:51, 7 February 2006 (UTC)

Here are a few examples like what you suggested: Proofs of Fermat's little theorem, Proofs of Fermat's theorem on sums of two squares, Proofs of quadratic reciprocity. I'm sure there are plenty of others. Dmharvey 03:54, 8 February 2006 (UTC)

Dmharvey references the very finest proofs, those that are well-enough written to be deserving of real articles. By contrast, the dirty, ugly ones that got ripped out of articles can be found in Category:Article proofs. This is, I believe, what you are talking about. linas 04:26, 8 February 2006 (UTC)

So would it be ok if I randomly snatch proofs from articles, and put them in their own page, if I think the page they're on would be more readable with just a link to the proof? Fresheneesz 21:29, 8 February 2006 (UTC)

If you think it improves readability, be bold! Dmharvey 22:27, 8 February 2006 (UTC)

I think I have nothing to do here

I was hoping to help in the areas that I like (not abstract algebra), but all of these are full. Only abstract algebra articles are available to give a respectable edit, the problem is: I'm really not interested in abstract algebra but I want to contribute here, what should I do. juan andrés 03:32, 8 February 2006 (UTC)

I hardly think any area is "full"! However you would be a pretty unusual sixteen-year-old if you could just pick mathematical topics at random that you know well, and easily find important subjects that don't already have articles. Why don't you start by looking at some stub articles, and seeing if you can expand them? You don't necessarily need to already know the material you'll be adding; looking it up is considered better procedure anyway, and as a byproduct you'll learn some interesting things.

Look at Wikipedia:WikiProject Stub sorting/Stub_types#Mathematics to see the various stub categories listed, pick something that looks interesting, and have fun! --Trovatore 03:41, 8 February 2006 (UTC)

There are 300+ articles in Category:Elementary mathematics and its subcategories, and almost all are in poor condition, are poorly explained, are missing details, etc. Do not be mislead by the word "elementary": while all of these topics can be first taught/introduced at an elementary level, many also can lead to very sophisticated mathematics. My favorite example is the torus, which appears in many many places, including leading edge research. If you can take some elementary topic, and fill it out so that it connects with higher math, that would be excellent. linas 04:20, 8 February 2006 (UTC)

Per linas's comment, also don't forget that "elementary mathematics" doesn't mean the same thing as "mathematics that is easy to explain". I should spend some more time around there some day. Dmharvey 05:09, 8 February 2006 (UTC)

Thank you. That's what I was talking about. Sorry if I could not answer but I was very busy with school homework. I know is very difficult to explain because you have to go back to the basics. juan andrés 20:21, 18 February 2006 (UTC)

blahtex 0.4.1 released

No bug fixes today, but one very nice new feature: correct vertical alignment of PNGs. This is something that PlanetMath has that I think is very cool (actually it's their underlying converter LaTeX2html that does it), but I'm using a different, somewhat experimental strategy. :-)

Try it out on the interactive demo, and also have a look at what it does with the equations from Wikipedia (which I've just updated from some more recent database dumps).

It's not enabled yet on Jitse's test wiki. It might be some time before it gets enabled, not because it's technically difficult, but for other semi-technical reasons that might be discussed another day...

Also, the blahtex manual is now online in HTML format, should make it easier to read.

Enjoy, Dmharvey 04:06, 9 February 2006 (UTC)

This is totally awesome. Deco 04:16, 9 February 2006 (UTC)

Blahtex Compatibility Project — seeking volunteers

Hi math(s) people,

As you all know, Jitse and I are working on developing some MathML support for Wikipedia/Mediawiki. For this to actually happen, a lot of things have to go right simultaneously.

One of the issues we need to deal with eventually is that blahtex's input syntax is ever-so-slightly different from texvc (i.e. the current input syntax on wikipedia). In fact, blahtex's input parsing is much closer to TeX's parsing than texvc is. Here are some examples of where they differ:

The characters $ (enter/leave math mode) and % (denoting comments) are illegal in blahtex, but texvc treats them as literally the $ sign and the % sign. The correct TeX for these is \$ and \%.
You can leave out curly braces in texvc sometimes, where TeX wouldn't allow it. For example: "\hat\overrightarrow x" is OK on wikipedia now, but not cool in TeX or blahtex; it should be "\hat{\overrightarrow x}". Similarly "x^\left( y \right)" is legal in texvc but not in blahtex or TeX.
Because of the way TeX handles macros, certain constructs like "x^\cong" are illegal in TeX (needs to be "x^{\cong}), even though other ones like "x^=" are ok.

These differences between blahtex and texvc are entirely deliberate. The idea is that we should make it as easy as possible to translate wikitext into other formats, using standard tools. The closer we are to TeX, the easier it is to do this.

So the question is: if and when we ever switch over to using blahtex for MathML support, what will happen to all the existing equations on Wikipedia that break under blahtex?

The good news is that only about 1,000 out of 180,000 equations on Wikipedia (this data includes the ten largest language versions) have problems, and of those, most of them fall into easily defined categories, like the $ and % sign issues described above. A complete list can be found on the blahtex website (http://blahtex.org) under the "Wikipedia samples" section.

I propose that we fix these equations, one by one, over the next few months, or however long it takes, and I would like to ask people here to volunteer to help out with the effort. Probably some of it can be automated (it's easy to change $ into \$) but some of it probably requires some human attentiveness.

This is not an entirely trivial task, and I think it would be best if someone volunteers to organise the effort. I don't have time myself to organise it right now; besides real life, I have code to write! This "Director of Blahtex Compatibility" might consider doing the following: setting up a page where people can volunteer to fix up "blocks", based on (say) the md5 of the equation. If you need the list of equations in a different format, I can provide that; I have code that can extract it from the Wikipedia database dumps fairly easily. Also they might want to write a page explaining what this is about, so that people can use a link to the explanation page in their edit summary. And they might want to find someone willing to write a bot to handle the automate-able parts of the project.

Please put up your hand if you're willing to organise this. And of course please speak out if you think this is a really stupid idea. Dmharvey 18:05, 9 February 2006 (UTC)

I'm willing to take responsibility for dewiki.--gwaihir 00:11, 10 February 2006 (UTC)

The other major problem is malformed html tags written directly in (i.e. not using MediaWiki code). For example

<ul>
<li>line one
<li>line two
</ul>

this is legal html but not legal xhtml, and it breaks the BlahTex wiki. It might be possible to integrate HTML-Tidy into the code so that we get pure xhtml out, but its going to be a major problem. Malformed html abounds for example Help:Formula had an extra </table> tag (now fixed on meta).

I might be up for helping with compatibility (director sounds too grand).

Testing on various platforms also appreciated. --Salix alba (talk) 00:31, 10 February 2006 (UTC)

Thanks Gwaihir.

The issue raised by Pfafrich (Salix Alba) concerning malformed HTML is an important one (a *very* important one), but not on topic :-). Here I'm only talking about the stuff inside <math> tags. Dmharvey 00:51, 10 February 2006 (UTC)

I suppose I can answer Pfafrich's point a little better here. HTML tidy is already integrated into mediawiki. But it's switched off on blahtexwiki at the moment, because HTML tidy doesn't like math tags. Jitse is working on a clean solution to this. So it's not as big a problem as it sounds. Not easy, but not insurmountable. Dmharvey 01:10, 10 February 2006 (UTC)

Fixed occureces of $ in main article namespace (a few left in Talk and old ref desk) see User:Pfafrich/BlaxTex $ bugs for all occurences . A possible earier way round the problem is to search for malformed latex from the database dumps, a relatively simple grep and sed found all the $'s. --Salix alba (talk) 03:50, 10 February 2006 (UTC)

Pfarich, nice work. We need that done on the other languages too :-) I'm concentrating on the ten largest ones: en, de, ja, fr, it, es, pt, pl, sv, nl. Maybe this will help: I've put up a list of all the problem equations (i.e. all the ones I have listed at blahtex.org) in a simple text format at http://blahtex.org/errors-20060203.txt. Be careful: if you feed the data to a machine, keep in mind that some entries have more than one web address listed; use the "-----" line to work out where. Let me know if a different format would be more convenient. Dmharvey 14:01, 10 February 2006 (UTC)

Is this the right place to ask specific questions (like: what's wrong with $x\not\subset y$ ? Error message given here reads: "No negative version of the symbol(s) following "\not" is available"; but TeX doesn't complain).--gwaihir 10:55, 10 February 2006 (UTC)

Yes it is the right place to ask. The answer is: that's a bug in blahtex, and it's on my list to fix. Don't worry about those ones for now. Thanks. Dmharvey 14:01, 10 February 2006 (UTC)

Update: I've corrected this behaviour for blahtex 0.4.2. This particular one (\not\subset) will be translated correctly now, and I've also added all the others that have specific MathML characters associated to them. If you try one that blahtex doesn't know (like "\not\partial" which occurs in fr:Matrice de Dirac), it will now only give up on the MathML output, and will still succeed for PNG output. A similar issue is errors like "The symbol "1" is not available in the font "bb"", which should give you $\mathbb{1}$ . The updated behaviour is that it gives up on the MathML output but still does the PNG output. This is not ideal, but it's something I will revisit later. Dmharvey 22:44, 10 February 2006 (UTC)

Well, \mathbb1 is nothing more than a dirty hack for some missing macro/mathchardef. It should not work. If this symbol is needed, a corresponding command should be made available.--gwaihir 23:34, 10 February 2006 (UTC)

Well said. This is why it's not a priority. Soon I will expand coverage of symbols to get as much as possible of LaTeX and AMS-LaTeX. Dmharvey 23:39, 10 February 2006 (UTC)

My own view would be to have BlahTex be as compatible with texvc as possible, and introducing the feature which allows it to be more compatible with TeX (and less wtih texvc) later. That because having MathML be accepted and working on Wikipedia would already be hard enough, thus, worrying about slight incompatibilities with the existing system would be an unnecessary distraction. Oleg Alexandrov (talk) 20:08, 10 February 2006 (UTC)

I agree, but it's a fine line to be walking. The earlier versions of blahtex (0.2.1... or perhaps even earlier ones that I never released) were in fact more compatible with texvc, because they used a yacc-based parser, as texvc does. But I discovered that to be able to do more interesting things, this approach had to be abandoned. On the other hand, blahtex has a command line option "--texvc-compatible-commands" which enables use of all of the texvc commands which are not standard TeX/LaTeX/AMS-LaTeX. This is enabled on Jitse's wiki, and I expect it to be enabled if blahtex ever gets deployed on the real thing. Here's the list of commands, i.e. commands that work on wikipedia but in no latex installation that I know of: \R \Reals \reals \Z \N \natnums \Complex \cnums \alefsym \alef \larr \rarr \Larr \lArr \Rarr \rArr \uarr \uArr \Uarr \darr \dArr \Darr \lrarr \harr \Lrarr \Harr \lrArr \hAar \sub \supe \sube \infin \lang \rang \real \image \bull \weierp \isin \plusmn \Dagger \exist \sect \clubs \spades \hearts \diamonds \sdot \ang \thetasym \Alpha \Beta \Epsilon \Zeta \Eta \Iota \Kappa \Mu \Nu \Rho \Tau \Chi \arcsec \arccsc \arccot \sgn. These ones could of course be easily simulated by means of macro definitions (and that's in fact how I implement them in blahtex :-)). In contrast, the real problems (the ones I mentioned above) are the ones that *cannot* be solved by adding a few macros. For a while I even tried writing *two* parsers that could live side-by-side.... but it was too much trouble. I spent quite a while analysing how much of a burden this would be, and the net result is that 1000 equations --- across ten different languages --- is actually not so bad. I decided it was worth making a clean break. I can assure you that compatibility has been uppermost in my mind, but compromises had to be made. I think this is the least bad solution. Anyway, it was a good chance to fix tons of other things in texvc which are partly a consequence of its parsing strategy. For example, it's annoying that \mathop{\rightarrow}^f doesn't put the "f" above the rightarrow, like it should: $A \mathop{\rightarrow}^f B$ . (And the spacing's wrong there too.) Actually, given what pfafrich has been up to, I wouldn't be surprised if we were already down to 900, and with a few more helping hands, the issue will pretty much disappear before we get around to considering deployment... Dmharvey 20:35, 10 February 2006 (UTC)

A short comment, hope it's not too much of a nonsequitur as I don't know much about how you're implementing blahtex: why don't you resort to standard TeX to get certain "difficult" things done instead of falling back on LaTeX and nothing deeper? For example, won't the AMS \buildrel do what you need instead of \mathop (which I gather is a LaTeXism)? Dysprosia 05:24, 13 February 2006 (UTC)

I don't completely understand your question, but I can make two comments: (1) I don't know AMS-LaTeX nearly as well as I should, so for example, I've never used \buildrel, and (2) \mathop is buried even deeper than LaTeX, it's a TeX thing. Any advice you have is appreciated. (Hmmm... wikipedia is very broken today... can't seem to log in.... so this is Dmharvey, 15:35, 13 February 2006 (UTC))

LaTeX is built on TeX. TeX is not the evil twin of LaTeX ;) I don't know what you're doing in the backend of blahtex, but if you're interfacing with LaTeX, presumably you can include plain TeX commands. So, if you figure out how to do something in plain TeX, why not give the plain TeX code to LaTeX and get it to do what you like? If you don't want to use the entire complement of AMSTeX or AMSLaTeX, you can always just snip out the bits you want from the AMS code. Sorry I'm not more precise on this. If you'd like me to attempt something specific, let me know and I can give it a shot. Dysprosia 06:15, 22 February 2006 (UTC)

Carathéodory theorem

I found out that there is no real entry on Carathéodory theorem in wikipedia. The article Carathéodory's theorem (measure theory) links back to outer measures, and you cannot find the definition of Carathéodory theorem for extension of measures on algebra. I don't know what you think, but the article is really not clear about what the theorem is, and I would consider this theorem fundamental in measure theory. Ashigabou 11:29, 10 February 2006 (UTC)

Are you talking about Carathéodory's theorem (convex hull)? Probably renaming the article is in order. (Igny 13:51, 10 February 2006 (UTC))

Oh, you meant absence of the Caratheodory extension theorem as defined in [43].(Igny 14:01, 10 February 2006 (UTC))

exactly. I know the theorem myself, but I am not that familiar with other "abstract theories", as I studied it recently in the theoritical fundations of probability; I wouldn't be able to link it to other fields. I created a stub, but I am not sure that semi-ring is the standard naming convention (subset S of the power set of X, closed under finite union, and difference can be written as a finite union of elements of S). Ashigabou 15:32, 10 February 2006 (UTC)

#REDIRECT Carathéodory's theorem -- linas 23:52, 10 February 2006 (UTC)

Why is it Carathéodory's theorem but Cauchy theorem (as opposed to Cauchy's), which is also a dab page? Should we standardise? —Blotwell 01:57, 11 February 2006 (UTC)

Kramers-Kronig relation

Hello, up until a few minutes ago there were two different articles Kramers-Kronig relations and Kramers-Krönig relation. Having determined that Ralph Kronig spelled his name with o, not ö, I merged both articles to one named Kramers-Kronig relation. However, since I know nothing at all about math and physics, it would be very good if someone who actually understands the text could look at the new article and make any necessary changes. Thanks! Angr/talk 18:16, 12 February 2006 (UTC)

blahtex 0.4.2

Now can do every symbol from LaTeX/AMS-LaTeX. (Well, almost all of them.) Results may vary depending on the fonts you have installed. At the very least you should be able to see them as PNGs. Dmharvey 02:37, 13 February 2006 (UTC)

Cool! But won't this break texvc when blahtex is incorporated? That is, texvc will choke on a symbol that blahtex accepts. (Of course, the correct thing to do is fix texvc not handicap blahtex.) -- Fropuff 04:59, 13 February 2006 (UTC)

Um, yes texvc will of course choke on symbols that blahtex accepts, but I don't really that this is a problem. Right now on blahtexwiki, Jitse has set it up (hope I've got this right) so that both texvc and blahtex are attempted, texvc's output is used wherever it succeeds, and blahtex is used for anything else. This means that (1) all MathML output is generated by blahtex, (2) PNG output is generated by texvc whenever texvc can manage it, otherwise blahtex does the PNG output, (3) all HTML output is handled by texvc, because blahtex doesn't do any HTML at all. By the way, I started this whole project trying to "fix texvc", but I soon gave up on that, and started again from scratch. Hence, blahtex. (-- Dmharvey, who can't log in now, some time on Feb 13.)

What, every? Almost every. --Trovatore 05:02, 13 February 2006 (UTC)

That's what I said. Almost every. Soon, with everyone's eagle eyes, we'll hopefully be able to substitute "every". (-- Dmharvey, who can't log in now, some time on Feb 13.)

AfD: Foundational status of arithmetic

Up for deletion: Foundational status of arithmetic - an interesting if slightly unusual article on the history of arithmetic. Contains some non-standard views, but maybe it can be cleaned up? 17:42, 13 February 2006 (UTC)

Maybe. Looks like a chore, though. Could be tagged with NPOV in the meantime. It points to arithmetization of analysis, which seems equally problematic; it seems to take the astonishing view that analysis has been mapped into the arithmetic of the natural numbers. (It's just possible that it means this has been done in higher-order logic, which is arguably true.) --Trovatore 17:48, 13 February 2006 (UTC)

By inspection

I am rather unhappy with this article, both the name and the content. I would think that the best thing to do would be to have it deleted, but maybe there are ways of renaming it and rewording it to make it an acceptable mathematics encyclopedia article. Comments? Oleg Alexandrov (talk) 02:52, 14 February 2006 (UTC)

I wrote this little thing after using the phrase in another article, Evaluating sums, which I thought had potentially a naive enough audience that they would appreciate seeing an explanation of this piece of mathematical jargon. I was uncomfortable writing about jargon, but it's not strictly a dictionary definition so I thought it would be excusable. There's more to say than I felt comfortable shoehorning into mathematical jargon, though, so I gave it its own article; however, it is by far the least substantial of the jargons linked to from that page. I don't know if there's much more to say than what I and Charles Matthews have already written; perhaps it can just be put into mathematical jargon anyway.

However, that only addresses one aspect of it being a bad article. What is unacceptable about it to you? For example, aliter and one and only one are analogously brief; what do you think of them? Ryan Reich 03:07, 14 February 2006 (UTC)

OK then, what I don't like is the name. Maybe something like method of inspection or something, or indeed part of the mathematical jargon. Don't know. :) Oleg Alexandrov (talk) 04:09, 14 February 2006 (UTC)

The name is one thing I don't really dislike. However, some other jargons, like arbitrary and canonical, have solved the naming problem by merging into a much larger article on the word taken in all its contexts. There is an article inspection; should I perhaps insert the contents of by inspection there? Ryan Reich 04:21, 14 February 2006 (UTC)

Trigonometric and hyperbolic functions: create separate articles?

Our article trigonometric function lacks much information, but is huge and difficult to expand as is. I think it would make sense to create a separate page for each function (cosine, inverse cosine ...). MathWorld has very rich pages on the individual functions, which are much more useful than Wikipedia's overview for someone with a good basic understanding of the topic. Of course, the main article should be kept as an overview. Same thoughts go for the hyperbolic functions. - Fredrik Johansson - talk - contribs 03:33, 14 February 2006 (UTC)

I am not convinced. Sine and cosine overlap too much as it is. Septentrionalis 05:53, 15 February 2006 (UTC)

I have long thought that the inverse trigonometric functions, at least, needed their own page. I started a draft at User:Fropuff/Draft 5 but I didn't get very far. I'm ambivalent as to whether we should have separate article for each function. -- Fropuff 07:50, 15 February 2006 (UTC)

A separate page for the inverses would help. Fredrik Johansson - talk - contribs 16:10, 15 February 2006 (UTC)

Rather than a split by type of fnction, I's suggest a split by topic (which mirrors the current topics covered in the article): so, for example, there could be Trigonometric function history, and Trigonometric function series and Trigonometric function identities, and so on. linas 22:39, 15 February 2006 (UTC)

Well, we already have the long article on trigonometric identities. I don't think we really need a separate article on the history; it fits in quite nicely in the main article. -- Fropuff 01:40, 16 February 2006 (UTC)

Multi-variable articles

I am still not satisfied with multi variable calculus articles (some of them only). Jacobian and gradient are not developped enough in my opinion. My main point, I guess, is we should have an article which generalizes derivative in one dimension for many practical cases (domain, codomain being vector spaces , with a special treatment for matrix spaces); we have an article on Frechet derivative, but it emphasize the genral case (infinite dimension). I think that in finite dimension, having a good article on derivative with several variables in the context of Frechet is necessary: it has all the good properties we expect from the scalar case (composition rule, inverse rule, differentiability imply continuity, etc...) that partial derivative do not have, and could explain the gradient and Jacobian definition, and some really common rules (for example the multi variable change in integrals). Some people disagree with me on this view, but I started to really understand gradient, jacobian and matrix calculus only once I studied Frechet derivative, and this view is adopted in at least two different documents, one being a reference, I think (I am not a mathematician, so I may be wrong though; the book I am talking about being Analysis on manifolds, from Munkres). As I studied this point recently quite heavily, I am willing to write the article, but I am not sure about the title, and how to link it to other article in multi-variable calculus. Ashigabou 01:54, 15 February 2006 (UTC)

I am not sure what exactly you want, but I think it would be more useful to expand the articles we currently have. So, develop the article on Jacobi matrix and mention that it satisfies

$f(x+h) = f(x) + J_f(x) \, h + o(|h|) \qquad(*)$

and thus it is a Frechet derivative. If the "some people" refers to me, then I'm afraid I didn't express myself clearly. The property (*) is essential for understanding multivariate calculus. What I meant to say is that most people will encounter the Jacobi matrix before they have heard of Frechet derivatives, and therefore you cannot motivate the Jacobi matrix by saying that it's simply a Frechet derivative, but you can (and probably should) refer to property (*) in the motivation.

The article on chain rule (what you called "composition rule") mentions the rule with Jacobi matrices and Frechet derivatives, inverse function theorem has the rule for inverse function, etc. If you want to write a high-level overview, you can add some paragraphs to multivariate calculus (if it gets too long, you can always split of a part to, say, multivariate differential calculus). All these articles can be improved, and I suggest you concentrate on that rather than writing a new article. Don't be afraid of changing existing articles. This goes in particular for matrix calculus (I'll comment on your remarks there).

I don't know Munkres' book, but from what I've heard it's pretty good, but more of a text book than a reference work. However, Munkres has a more general setting in mind: calculus on manifolds, rather than calculus in Rⁿ. -- Jitse Niesen (talk) 12:03, 15 February 2006 (UTC)

Agree with Jitse. Do not confuse the Jacobean with the Frechet derivative: although similar, most calculus books are built on the Jacobean, not Frechet. Personally, I'd already had plenty of classes in "calculus on manifolds"; I'd known a half-dozen different concepts of derivatives, long before I'd ever seen the words "Frechet derivative". Focus on Jacobean, which does what you want for finite-dimensional spaces, and leave Frechet for the infinite-dimensional stuff, for which it was invented. linas 22:52, 15 February 2006 (UTC)

I agree that most calculus books are built on the Jacobian; whether it is a good thing or not is a different matter; I personnally think it is a mistake, because you cannot really understand matrix calculus. I agree that talking about Jacobian with an emphasize on the linear map it represents would be in the right direction (from my POV :) ), but how do you explains derivative of matrix with respect to matrix ? You both seem to think that Frechet is really useful for infinite dimension only, and I don't understand that (I am open to explanations, though, of course). I think taking a maybe somewhat original approach to multi variable calculus would be interesting. At least, I was never satisfied with the standard approach (using partial derivative only) during my undergraduate courses. Ashigabou 00:14, 16 February 2006 (UTC)

I will rephrase my point differently: when I wanted to understand multi variable differentiability, I was interested in a concept which generalized all the 'good' properties of the derivative in 1 dimension, that is differentiability implies continuity, etc... Wether calling it Frechet or not, I don't care, that's not really the point. I feel like an article about how to extend derivability in several dimensions while keeping most good properties would be good; something more than partial derivative. If you think this can be done without Frechet, then I would be glad to hear how. Ashigabou 00:26, 16 February 2006 (UTC)

I'm having great difficulties understanding what you mean, and why you think that you need the Frechet derivative. Si tu veux, tu peux écrire français. Is your point that a function may have partial differentials and thus a Jacobi matrix, without being Frechet differentiable? -- Jitse Niesen (talk) 14:00, 16 February 2006 (UTC)

I don't feel like the difficulty is coming from my English, but anyway: en scalaire, on apprends la definition de la derivée, et pas mal de théorèmes fondamentaux qui sont liés; derivabilité implique continuité, valeur intermédiaire, théorème de Taylor, dérivée de la fonction inverse, etc... Je trouve que ce serait intéressant d'avoir un article qui généralise ces concepts en plusieurs dimensions. In English: in undergraduate, we learn that if f has a derivative at the point a, f is continuous at the point a, that if f has derivative on [a, b], there is c in [a, b] such as f(b)-f(a) = f^'(c)(b-a), that if f is Cⁿ, f has a Taylor expansion of degree n, etc... When I had some courses about multi-variable calculus, we were told the concept of partial derivative, and that was about it, and on wiki, this is the same: gradient, jacobi, defined as vector of partial derivative; partial derivative are a bit strange, because even when they exist, f may not be continuous. I wondered for a long time how can you have a generalization of the derivative for multi variable functions with all the nice properties of the scalar, and the approximation of f(x+h)-f(x) by a linear map with respect to h is the natural extension. This is again related to my remarks in matrix calculus: for now, all the formula are said to be notations, and I think this is plain wrong, that all those matrices and tensor represent linear map which correspond to Frechet derivative (at least in the C¹ case). . When Linas says that Frechet is one of the derivative generalization, I don't agree; I think this is *the* natural generalization for 'nice enough' spaces (Banach spaces). I have some nice examples how to use the definition in Frechet context to find most formula in matrix calculus, but I am told this is different, this is just a notation, and I really don't agree, at least not with some more explanations (you know, those stubborn Frenchs :)... ). Thank you for your interest ! Ashigabou 00:55, 17 February 2006 (UTC)

Hi Ashigabou—I agree with your point that approaching the derivative through the concepts of linear maps and best local linear approximations is the way to go. As usual many undergraduate-level courses and texts are lacking here. There is no reason why this approach must be more difficult than focusing on matrix computations and partial derivatives; quite the contrary. I wonder if you'd like to take a look at a very remarkable book on these topics called (very modestly) Advanced Calculus by Shlomo Sternberg and Lynn Loomis. This is without question the finest treatment of this area of mathematics I've ever encountered. Is the approach to the derivative used in this book the sort of thing you had in mind? — merge 10:28, 18 February 2006 (UTC)

I'm not actually sure what this discussion is about. We can and should have multiple approaches to an area like multi-variable calculus, for which there are superficially-different approaches well documented in the literature. If Fréchet derivative is somewhat too abstract, we can take a more 'gradualist' approach there, or in some other article. Charles Matthews 10:50, 18 February 2006 (UTC)

Ashigabou, I still don't quite know what you want, but I think I mostly agree with you, except for some details. The only advice I can give you now is just to do what you think is best. Once we see what you've written, it will be clear where you want to go. Based on what I've read, I expect that it will be generally okay and it will fill a gap in our coverage of multivariate calculus. I agree that Frechet is the most natural generalization of derivatives in R^n. -- Jitse Niesen (talk) 15:13, 18 February 2006 (UTC)

PROD (Proposed deletion): Empty Summation Equations

I proposed Empty Summation Equations for deletion, using the new Wikipedia:Proposed deletion process. Since this process is only being tested, I thought it would be fair to let you know. I didn't follow the debate, but my interpretation is that Proposed Deletion is for those articles that fail the criteria for speedy deletion, but for which it is still obvious that they should be deleted. -- Jitse Niesen (talk) 14:05, 16 February 2006 (UTC)

Can the /Current activity bot be modified to include this new type of activity? Arthur Rubin | (talk) 14:53, 16 February 2006 (UTC)

Yes. With a bit of luck, the article will appear on Current activity tonight. -- Jitse Niesen (talk) 19:15, 16 February 2006 (UTC)

Revert war at Real number

See for yourself [44]. Comments? Oleg Alexandrov (talk) 19:39, 16 February 2006 (UTC)

It is clear that what DYLAN LENNON has been repeatedly adding is not appropriate for this article. I can understand this happening once due to a lack of knowledge about what is noteworthy, but the repetition makes this unwelcome, and knowingly disruptive. Elroch 20:40, 16 February 2006 (UTC)

Possibly not notable articles

I nominated Colloquium (College of Engineering, Guindy) and Ramanujan Rolling Shield for deletion, as as they appear nonnotable. Comments and votes welcome. Oleg Alexandrov (talk) 04:07, 17 February 2006 (UTC)

I nominated (yesterday) Hiroshi Haruki, and I nominated a couple of DYLAN LENNON's creations for speedies. Comments and votes welcome. (I also removed a number of his lines

"The easiest proof" of (this theory) is due to Name that I never heard of.

Arthur Rubin | (talk) 20:22, 17 February 2006 (UTC)

DYLAN is surely a problem user. Some anon wrote on his talk page a while ago that he was banned from the Japanese wikipedia for trolling. Wouldn't surprise me. Oleg Alexandrov (talk) 21:08, 17 February 2006 (UTC)

Although DYLAN is a problem, it now appears (from the comments made in the AfD) that Haruki is adequately notable, although the article surely doesn't reflect it. Is there a {{sub-stub}} tag? Arthur Rubin | (talk) 00:13, 18 February 2006 (UTC)

Believe it or not, but {{substub}} has been deleted. Six times. I'm sure it has been discussed extensively, and I don't want to know how many edit wars had been going on about whether some article was a stub or a substub. -- Jitse Niesen (talk) 02:22, 18 February 2006 (UTC)

Some of MR LENNON'S links to ja appear to be incorrect or misleading. Then again, some of them seem to be right. We need someone who knows a bit of japanese to review them. Dmharvey 17:45, 18 February 2006 (UTC)

Good articles list

If you look at Wikipedia:Good articles, you'll see that only four articles are listed. I am pretty sure that there are far more than four good mathematics aricles on Wikipedia. So, I would like t orequest that if anyone knows of any other articles that fulfill the required criteria, could they please list them. Tompw 13:22, 18 February 2006 (UTC)

You can usually get a hollow laugh out of mathematicians with lines like should not omit any major facets of the topic. We really don't do completeness, except in some classifications. What would it take, to say that of an article like homology theory or Lie group or partial differential equation? So those guidelines are not written for us. Charles Matthews 14:00, 18 February 2006 (UTC)

Where does it say that? The requiremnts given for a good article are that it:

Be well written
Be factually accurate (which means error-free for a maths articles)
Use a neutral point of view (generally get this one for free :-) )
Be stable
Be reference (which isn't always needed for maths articles)
Wherever possible, contain images to illustrate it. The images should all be appropriately tagged.

Anyway, actions speak louder than words... so will try and seek some out. Tompw 19:50, 18 February 2006 (UTC)

Right after your point 6, it says:

Good articles may not be as thorough and detailed as our featured articles, but should not omit any major facets of the topic.

Now I don't think that necessarily excludes math articles, even ones like homology theory. I would interpret it as meaning something like "any subfield of homology theory accounting for (say) ten percent of the total research effort in that field should get at least a mention". It's not reasonable to read it as meaning that we have to track down the content of every PhD thesis written in the area. --Trovatore 20:01, 18 February 2006 (UTC)

OK, I saw and was editing my reply, but you got in first. However, I agree with you that we have to interpret "major facet" in our own way. Tompw 20:08, 18 February 2006 (UTC)

ALthough the Wikipedia:Good articles process is "sub-optimal" (if not broken) in a variety of ways, it is "well intentioned". From what I can tell, "someday", there will be a print version of WP, and thus, the articles suitable for inclusion in a print version must be identified. There are now many wikiprojects trying to categorize all of thier articles into "good bad and ugly". Seperately, there is a debate at Wikipedia:Stable versions about mechanisms by which the correctness and authority of an article can be atested to. A "good bad ugly" classification will probably feed into that process. I'm not convinced that now is the time to launch into the busywork of classifying math articles, but now is the time to get famliar with the issues. linas 00:53, 22 February 2006 (UTC)

Wikipedia:Articles for deletion/Safe sex makespan

Despite the name, this is a combinatorics / operations research article. It could probably need some sources and a new name, but it's a somewhat interesting problem. If somebody here knows this problem (known as "Glove problem" on Mathworld), please comment at the AfD. Kusma (討論) 00:01, 19 February 2006 (UTC)

can't remember the name of something

I'm not sure, but I think we might be missing an article on something. Unfortunately I can't remember its name, but I can describe it. It should be related to articles like bifurcation diagram, Feigenbaum's constant, chaos theory, dynamical system etc. If you look at the bifurcation diagram, and list the periods of the stable orbits from left to right (including the "islands of stability"), you get some ordering on the positive integers, which starts out 1, 2, 4, 8, ... but then does funny things in a non-well-ordered way. The picture is confusing me a bit (especially since it looks like 6 shows up twice, which is not suppoed to happen !!!), but I'm sure this has a name, it's called "so-and-so's ordering", but I can't remember who. And I seem to remember that the same sequence crops up no matter which dynamical system you choose, kind of like feigenbaum's constant, well at least for some reasonable class of systems. Anyone know about this? Dmharvey 15:30, 20 February 2006 (UTC)

ok, got it now: Sarkovskii's_theorem Dmharvey 15:34, 20 February 2006 (UTC)

blahtex compatibility update

Thanks to the efforts of Pfafrich on en, and of gwaihir and LutzL on de, and possibly others too, the blahtex compatibility project has been making substantial progress. Here's a table showing the number of problem equations on each wiki. The first column is the numbers before they got started, and the second column shows the counts for today's dumps. ("Today's dumps" means "today" for en, de and ja, but is still lagging by about two or three weeks for the other languages.)

      BEFORE   AFTER
en      342     287
de      372      68
fr      103      92
it       81      69
pl       57      49
es       37      32
pt       35      35
nl       34      16
ja       28      32
sv       10       9

TOTAL  1099     689

So already almost 40% of problems have been dealt with.

(Note: some proportion of the decrease -- not sure exactly how much -- is attributable to changes in blahtex. In particular it is now more permissive about using font commands in strange ways like $\mathcal{a}$ , so these aren't reported in the second column.)

An updated list of errors is available at http://blahtex.org/errors-20060220.html.

I encourage anyone who feels like helping us to jump in! Dmharvey 23:00, 20 February 2006 (UTC)

I should add that the samples on http://blahtex.org/ have not been updated with the new dumps, and they won't be updated for a little while yet. Dmharvey 23:08, 20 February 2006 (UTC)

If people are interested in helping on en-wiki I've created a set of pages detailing some of the imcompatabilities User:Pfafrich/Blahtex en.wikipedia fixup, and listing their status. So far all the errors are very minor using % rather than \%. People are welcome to fix bugs listed there, about 100 articles. --Salix alba (talk) 16:42, 21 February 2006 (UTC)

Real, again

OK, it seems we indeed have a problem user, the same DYLAN LENNON, recently reincarnated as WAREL. See the last 100 entries in the history of real number. [45] He was also inserting things at Proof that 0.999... equals 1 and other places. Seems to know math, but has unreliable edits, and is very perseverent. I would like to ask some of you to put real number on your watchlist. So far, it was mostly Jitse and me (with Zundark and an anon) who tried to keep this user at bay. Don't quite know what to do about this. Oleg Alexandrov (talk) 17:02, 21 February 2006 (UTC)

Applying WP:3RR should at least alleviate the problem; I see it's been tried. Septentrionalis 05:57, 22 February 2006 (UTC)

Frivolous articles on little-used geometric terms

See ana (mathematics), kata (mathematics), and spissitude. I don't mind these being merged and redirected to some sensible place, but giving them individual articles tends to give the false impression that the terminology has some currency.

The articles fourth dimension and fifth dimension have related problems. From fourth dimension:

The cardinal directions in the three known dimensions are called up/down (altitude), north/south (longitude), and east/west (latitude).

Well, come on, no they're not, not in general. These articles all seem to take for granted that there's some sort of preferred coordinate system with respect to which we can name directions. I think fourth dimension and fifth dimension should be moved to four-dimensional space and five-dimensional space, respectively, and substantially rewritten to address this problem. --Trovatore 20:12, 21 February 2006 (UTC)

Those articles on ana and kata and spissitude are unlikely to get any bigger than the stubs they are now so they should be indeed combined in a single article describing the terminology.

About moving fourth dimension to four-dimensional space, that may be more complicated. That article is rather big, and is partially about the four dimensional space, but it has sections devoted exclusively to the fourth dimension. Food for thought. Oleg Alexandrov (talk)

I remember debating "the fourth dimension" with grade-school playmates; this is a valid topic for anyone who has no math education beyond addition and multiplication. It should be dealt with at that level. (I also remember hearing about "the fifth dimension" in some movie, or an Outer Limits episode maybe, and thinking "that script-writer got it all wrong, there ain't no such thing") linas 01:34, 22 February 2006 (UTC)

So what exactly can we sensibly and accurately say to such a person about "the" fourth dimension? Which fourth dimension? I think the article as it stands is just wrong; there is no sensible ordering of dimensions (though of course in GR spacetime there's a timelike dimension that can be distinguished from the other three spacelike ones). --Trovatore 03:33, 22 February 2006 (UTC)

Presumably, the fourth dimension would be one orthogonal to the 3-dimensional space we live in (whether it be a timelike dimension or a spacelike one). Whether or not such a dimension exists is debatable, but we can at least ascribe some meaning to the term. -- Fropuff 05:20, 22 February 2006 (UTC)

There isn't any unique 3-dimensional space we live in; there are various spacelike slices. Which one do you pick? --Trovatore 05:32, 22 February 2006 (UTC)

All of them, if you wish. Look, I'm not trying to say the term has a precise definition, but rather loosely binds some related ideas that people like to think about. The article doesn't fall completely within the scope of mathematics (or even physics) and shouldn't be treated as such. -- Fropuff 05:37, 22 February 2006 (UTC)

I'm not sure what's stated in the article has any clear meaning at all, mathematical or otherwise. That's my objection to it. --Trovatore 05:41, 22 February 2006 (UTC)

Well, I agree with you there. I'd say it could do with a complete rewrite (although I'm not volunteering). -- Fropuff 05:43, 22 February 2006 (UTC)

These are references to fairly notable speculations about a physical/psychological fourth (space-like) dimension; see Charles Howard Hinton or John William Dunne, I forget which. (I presume the reference to Henry More the Platonist is at least half true, however.) Cat as history of mathematics and forget about them. Septentrionalis 06:02, 22 February 2006 (UTC)

I had 4D in fairly good shape last time I had a stab at it. Pity it seems to have gone south from there... Dysprosia 06:09, 22 February 2006 (UTC)

Alas, its probably one of those articles which takes constant vigilence to keep the nonsense at bay. Sometimes I think the whole stable versions idea isn't half bad. -- Fropuff 06:21, 22 February 2006 (UTC)

Lists of PRNGs

I see that list of pseudorandom number generators ran into copyright trouble, and was deleted about a week ago . This really needs recreation, with more care to avoid whatever caused the trouble (something about the GNU manual, some eejit copying in too much). I can get back the old text, if someone wants to work on this. Charles Matthews 12:11, 22 February 2006 (UTC)

Just wrote a new stub. Dysprosia 12:21, 22 February 2006 (UTC)

Found the old text from the database dump, see talk page. Is it fair use to have copyvio material on talk page for discussion? --Salix alba (talk) 13:46, 22 February 2006 (UTC)

Better really not to have it back on the site, in the history. It is very likely still on some mirror sites, but perhaps with corrupt formulae and so on. I'll email the text to anyone who needs it. Charles Matthews 15:49, 22 February 2006 (UTC)

If this is GSL-related, then I want someone to explain to me why copying GFDL'ed material from a Gnu/FSF GPL'ed software is considered to be a copyvio. (I ask because there are a few other WP articles that have gotten take-down notices from the GSL authors, which were mostly ignored). linas 17:21, 22 February 2006 (UTC)

From what I can tell Wikipedia:Cleanup Taskforce/List of pseudorandom number generators it was not copyvio which led to its deletion, more just a case of list cruft, not meeting wikipedia standards for an article. Looking at the licence it is OK to include GFDL material, as long as its source is acknowledged. It might be better to take your Q to Wikipedia talk:Copyrights where they will know more on such issues. --Salix alba (talk) 20:15, 22 February 2006 (UTC)

According to the deletion log

22:30, 14 February 2006 Splash deleted "List of pseudorandom number generators" (GFDL article, but with front- and back-cover texts which WP does not permit per Wikipedia:Copyrights)

so I don't think the cruftiness is why it was deleted. It is a good argument against recreating it as it was, though; the stuff on the talk page does not look like a good article. I don't actually know what is meant by "front- and back-cover texts".) --Trovatore 00:58, 24 February 2006 (UTC)

"front- and back-cover texts" is a reference to an optional part of the GFDL, see http://www.gnu.org/licenses/fdl.txt. Dmharvey 01:08, 24 February 2006 (UTC)

A question about differential equations

Hi everyone. This is probably not the best place for this request, but seeing that no-one has replied to a question I have posted in the reference desk, I was wondering if anyone here would be so kind as to help me with a problem that has been troubling me for eons, thus earning my undying gratitude. -- Meni Rosenfeld (talk) 20:20, 23 February 2006 (UTC)

combined set theory

This, according to the author of the page Avrill, is a bit of original research, and Arthur Rubin and Trovatore agree, see here and here. So I prodded the article. After which Avril blanked the page (thereby removing the "prod" tag), meaning it is technically no longer a valid candidate for an uncontested deletion. However, I'm inclined to interpret Avril's blanking of the page as a request for deletion, but since I was the one who added the "prod" tag, I don't think I should be the one to delete it. Would some other admin please take a look and delete it if you think it is appropriate? Thanks. Paul August ☎ 23:56, 24 February 2006 (UTC)

You're being overly process minded. Blanking a page is a nonadmin way of marking a page for deletion, as is recognised in the speedy deletion policy. It's obviously the right thing to do, so just go ahead and do it. --- Charles Stewart(talk) 16:11, 25 February 2006 (UTC)

blahtex 0.4.3

is now available at http://blahtex.org/. The main changes are: now supports \color, support for \not is cleaned up a lot, and a few other bugfixes. The new version hasn't been installed on the test wiki yet (http://wiki.blahtex.org/) because Jitse is out of town for a while.

Also, the sample pages have been updated with the more recent dumps. I'm throwing in russian, chinese and hebrew now (ru, zh, he) as well.

Compatibility project update

More progress has been made with blahtex compatibility on Wikipedia. We are now down to 463 errors across 13 wikipedias. I know there's a few people working on this in the background; I'm starting to tackle some of the smaller wikis myself. It's a bit frustrating that the wikipedia dumps are updated so infrequently (most of them are almost a month old now), making it hard to locate equations that haven't already been dealt with. Therefore, for the convenience of people working on this project, I've written a script that pulls down (via CURL and Special:Export) a live copy of all equations which were broken in the most recent dump, runs blahtex on them, and produces an up-to-date list of errors. So this list will miss any brand new errors that showed up since the last wikipedia dumps, but I expect the number of these to be miniscule. I will try to run this script every few days, and the results will be kept at http://blahtex.org/errors.html, so we can monitor progress. Many thanks to those who have been helping with this. Dmharvey 22:05, 25 February 2006 (UTC)

341 and counting.... and it looks like both de.wikipedia and fr.wikipedia are finished. Good stuff folks! Dmharvey 13:46, 26 February 2006 (UTC)

Ruud for admin

Luck has it that we mathematicians are a close-knit bunch who do good work. :) I nominated another one of us (Lethe was promoted serveral weeks ago), for admin, namely Ruud. If you are familiar with Ruud's work, you can vote at Wikipedia:Requests for adminship/R.Koot. Oleg Alexandrov (talk) 04:00, 26 February 2006 (UTC)

what's happened to planetmath?

When I go to planetmath.org, I see a weird "coming soon" message and a link to a mysterious wiki. Does anyone know what's going on with that? -lethe ^{talk +} 08:01, 28 February 2006 (UTC)

Worksforme. Dysprosia 08:05, 28 February 2006 (UTC)

Weird. It's still not working for me this morning. -lethe ^{talk +} 14:47, 28 February 2006 (UTC)

Works fine now. Oleg Alexandrov (talk) 16:12, 28 February 2006 (UTC)

Mar 2006

This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

recategorizing recreational mathematics

I've been being WP:BOLD with the subcategories of Category:Recreational mathematics. In particular I've emptied its rather ill-defined subcategory Category:Mathematical recreations and puzzles; a lot of its articles have found much better homes, but those that really did want to be somewhere under both Category:Recreational mathematics and Category:Puzzles I've put in one of a few joint subcategories such as Category:Mechanical puzzles. (Putting "puzzles" as a subcat of "recreational mathematics", as suggested on one talk page, isn't really an option: there are a lot of puzzles there that really aren't mathematical.)

While I was at it I also emptied Category:Puzzle games, which had an identity crisis as some people thought it was Category:Puzzle computer and video games while others couldn't tell it from Category:Puzzles.

Anyway, I expect I've offended innumerable people one way or another. If I've put your favourite article somewhere you don't think it belongs, please don't hesitate to move it (hopefully not into the categories I've carefully emptied). If you dislike the entire new categorization, please don't hesitate to argue with me about it. Though I can't imagine I've made things worse, since everything was categorized more or less at random to begin with. —Blotwell 14:35, 1 March 2006 (UTC)

Category:Mathematicians by religion

Category:Mathematicians by religion has a single subcategory, Category:Jewish mathematicians. I would think that being Jewish does not necessarily mean being religious. And do we actually need to categorize mathematicians on whether they were relegious, and if yes, what relegion they were practicing? Oleg Alexandrov (talk) 23:48, 1 March 2006 (UTC)

Being a jew does not, of course, make one religious, any more than being a christian makes one religious. So the categories' names do not imply that the mathematicians in question are religious - They just state to which religion they belong. And I think such categories are useful, in the same way that categories of mathematicians by nationality are useful. But obviously, additional categories for other religions, not just judaism, are in order for it to be meaningful. -- Meni Rosenfeld (talk) 07:19, 2 March 2006 (UTC)

I note that Category:Christians in science is applied both to Blaise Pascal, a Christian writer, and Bernhard Riemann, where as far as I can see it does little. I didn't much like like classifying mathematicians by nationality, when it came in; but it was inevitable with the growth, and the issue of several nationalities has the solution of including all of them. There are problems with all such classifications, and I'm not keen on them. Charles Matthews 09:05, 2 March 2006 (UTC)

Hmm, I wonder if Voltaire belongs in the Category:Christians in science, as, like me, his parents were Christian? I don't like this kind of categorization either; I think its basically some subtle political POV-pushing. May I suggest one possible cure: IF the person preached a religion (other than math) at one point in thier life, or published articles on faith (in newspapers, as letters to the editor, etc), THEN they may be classified by faith. However, if they had the bad luck of having Christian, or Jewish parents, that alone is not a reason to classify. I would insist on proof of religious activity before allowing classification. linas 14:49, 6 March 2006 (UTC)

french spelling

Um, I don't actually know french, but I thought only the first "e" in "etale" had an acute accent. So is this edit incorrect? Dmharvey 03:11, 2 March 2006 (UTC)

I think in this context, it's correct: the term in Hartshorne is "éspace étalé". Ryan Reich 03:30, 2 March 2006 (UTC)

So how do you know when it's étale and when it's étalé? Dmharvey 03:36, 2 March 2006 (UTC)

As far as I can tell, it's étalé here, and étale for morphisms. "éspace étalé" means roughly "slackened space", or "stretched-out space", which is reasonable given what it is, while an "étale morphism" is simply a "slack morphism". The metaphor is roughly the same, in that the slackness refers to a space constructed from layers laid out flat, and the grammatical difference distinguishes the "slackened space" constructed from something which was not, of itself, slack, from the "slack morphism", which is inherently so. Of course, "éspace étalé" is not used much anyway. Ryan Reich 03:56, 2 March 2006 (UTC)

It is certainly espace (not *éspace) étalé in French, but this leaves open the question of what the English translation of this expression is. I had been under the impression that it was called the étale space nevertheless, but Google seems to support both usages. —Blotwell 05:12, 2 March 2006 (UTC)

Étaler being a verb, étalé is the past participle (has been spread out, roughly). My MicroRobert says étale, adjective, can be applied to the sea as 'calm', when the tide is about to turn. We have been using sheaf space for espace étalé, which is not so common in English. HTH. Charles Matthews 09:13, 2 March 2006 (UTC)

Please continue with sheaf space. Septentrionalis 21:08, 6 March 2006 (UTC)

After a check in the "Annales de l'Ecole Normale Supérieure", the good term is "espace étalé". --pom 11:18, 2 March 2006 (UTC)

Location of "elementary function" article

I think Elementary function (differential algebra) should be moved to Elementary function, currently a disambiguation page with little value. Despite the title, said article covers the concept of elementary functions in the general sense. Fredrik Johansson 23:50, 2 March 2006 (UTC)

I think it would simplify a few links and a line could be added to the article pointing to the list of common functions. When Elementary function (differential algebra) was created what is currently List of mathematical functions was in an article called Elementary functions, so I had to create something else. XaosBits 02:10, 3 March 2006 (UTC)

Could someone execute the move? Fredrik Johansson 04:56, 6 March 2006 (UTC)

Definition of General Linear Group

Charles Matthews and I are having a discussion about the correct definition of general linear group. It might be useful to have more input. The question is whether it should be defined initially in terms of rings or fields. Talk:General_linear_group A5 22:19, 4 March 2006 (UTC)

LaTeX

I have created a template to tag articles in need of LaTeX formatting. My concern is that it uses the LaTeX logo, which may or may not be a problem. The image was created using LaTeX, and using LaTeX to create images like $\frac{q}{2}$ doesn't seem to be a problem; yet, the image is still a logo with questionable copyright status. I was wondering what everyone else thought? Isopropyl 00:04, 5 March 2006 (UTC)

I would like to note that per the math style manual html formulas are perfectly acceptable (unless they look awful, like Σ_i=1ⁿ). It is also advised that one not modify somebody else's formulas by converting them from HTML to LaTeX or viceversa.

In fact, formulas which become PNG images may actually be preferrable in HTML, as then they show up as text, and look better on the page, also per the math style manual.

All in all, I don't see any pressing need for putting the {{LaTeX}} template on articles which are properly formatted, but only in HTML. Of course, one may use this template for articles which have no formatting whatsoever, like people writiting x_2 or x2 without bothering to use proper markup or math tags. That's what I would think.Oleg Alexandrov (talk) 23:37, 5 March 2006 (UTC)

Thanks for your input! I'll keep it in mind in the future. What is your opinion on the logo used in the tag? Isopropyl 23:42, 5 March 2006 (UTC)

Should a page use a combination of LaTeX and HTML formatting, or should its use be consistent throughout an entire article? I have tagged sections with {{LaTeX}} when the section in question deviated from the precendent set by the rest of the article. Isopropyl 23:45, 5 March 2006 (UTC)

I don't quite know, and for myself I would be fine with a mix. But if you find it stylistically ugly to have html mixed with LaTeX, then a better solution would be maybe to just convert the html to LaTeX right away, rather than put a "work needed" template on it and hoping that a kind soul would do it some time. There is a huge amount of articles needing serious work, as listed at Wikipedia:Pages needing attention/Mathematics, and I think that labeling an article as needing work because of TeX/HTML inconsistency would be probably not good. Cheers, Oleg Alexandrov (talk) 23:57, 5 March 2006 (UTC)

I agree with Oleg. Paul August ☎ 01:48, 6 March 2006 (UTC)

Most linked to and least linked to maths articles

I've been playing around with the database dumps and extracted the most links and least linked mathematics articles.

The top linked articles might be useful for directing our efforts as these are probably most visited pages. The orphaned articles and redirects could help with some housekeeping. For example there is Squircle which seems quite dubious, and there are several highly linked redirects which indicate a need for some topics to be expanded. --Salix alba (talk) 13:54, 6 March 2006 (UTC)

Heh. Pi has 314 links... Ryan Reich 14:15, 6 March 2006 (UTC)

No way.... Dmharvey 14:33, 6 March 2006 (UTC)

And it holds slot 77 which is almost pi/4. linas 15:31, 6 March 2006 (UTC)

I wonder about the correctness of these lists. I was browsing the "orphaned" list and I was very surprised to see Stone–Weierstrass theorem, which of course is linked to from many articles. Paul August ☎ 17:15, 6 March 2006 (UTC)

It is quite a tricky job, especially where redirects are concerned. For Stone–Weierstrass theorem the only pages which link directly to it are 6 redirect pages [46]. For some technical reason, I've not included redirects in the count of articles. So these lists are the bests my little scripts can produce at the moment. If people feel the need, I'll try to update them to get closer to a real number. In the case of Stone–Weierstrass, I'd actually say the appearence in the list is a good thing. Looking closely, the hyphen in the article name is an odd unicode character (0xE28093) rather than a regular ascii hyphen (0x2D). I'd say this would be a good case for the article to be moved to the name with the ascii hyphen. --Salix alba (talk) 18:31, 6 March 2006 (UTC)

Ok I see. Yes I noticed the odd name. I think I will move the article. Paul August ☎ 19:51, 6 March 2006 (UTC)

JA: I thought we were standardizing the use of ndashes, not hyphens, for conjoining names of distinct people, as distinguished from hyphenated names of one person. Jon Awbrey 20:04, 6 March 2006 (UTC)

Were we? I missed that. Why would we want to do that? Paul August ☎ 20:12, 6 March 2006 (UTC)

JA: I'm sure I was directed to do that by some WikiPundit or other -- I just assumed it was to mark an obvious logical distinction for the sake of better hyper-indexing or sumting. Jon Awbrey 20:25, 6 March 2006 (UTC)
- Somebody likes m-dashes and n-dashes, hardcoded by use of — and – and goes through substituting them. I'm not sure why; portability, maybe? Septentrionalis 21:13, 6 March 2006 (UTC)
  - I think I would strongly oppose that policy, on ground of human nature. Most editors will use the ascii hyphen, never get to see the policy on ndashes, leading to the same redirecting problems we have seen on Stone–Weierstrass. --Salix alba (talk) 21:31, 6 March 2006 (UTC)
    - Well, I haven't seen these improvements in article names; only in text. But there does seem to be a tendency to avoid hyphenated article titles: loan word not loan-word. Septentrionalis 23:26, 6 March 2006 (UTC)

JA: YARTIW (yet another reason to ignore wikipundits). Jon Awbrey 21:40, 6 March 2006 (UTC)
dear reader, for a more complete view of the status of the discussion, please do have a look at User_talk:Jon_Awbrey#En-Dash_Protocol_Reigning_Over_Polynominal_Titles_.28EDPROPT.29

Endashes

I knew we'd have to discuss this one eventually. The arguments for the A-endash-B theorem if A and B are two people are (a) it parses uniquely if you don't happen to be able to recognise double-barrelled names, and (b) it is a more professional piece of format. I would, however, always recommend creating [[A-hyphen-B]]'' first, as a precaution, so as to pick up any hungry red links; and only then move to the endash version. Charles Matthews 21:58, 6 March 2006 (UTC)

Yeah, I didn't like it at first, but after thinking about it (and looking at typeset documents) I have to agree. Not so much for the unique parsing, which is a good argument in principle but not so much in practice (you can't reliably conclude that Burali-Forti is a single person just because the article is at Burali-Forti paradox, even assuming you do notice the difference in the length of the dash/hyphen, which I wouldn't have if it hadn't been pointed out). But the endashes really do make the title look more like typeset documents and less like Usenet.

Maybe someone could send a bot around to look for article names that are duplicates except for the hyphen-endash distinction (these should always redirect to the same place), and for articles with endashes with no corresponding hyphen redirects (redirects should be provided). --Trovatore 22:24, 6 March 2006 (UTC)

Agreed. Some folks care as much about typographical niceties as mathematicians care about proof validity, or musicians care about pitch correctness. Lack of personal interest or awareness of these subtleties is no good excuse for hostility toward the interests of those who do care. Accents and quotation marks are another common battleground. With redirection, there is no need to fight. The hypen-redirects-to-dash idea seems like a reasonable compromise. --KSmrq^T 22:26, 6 March 2006 (UTC)

dear reader, for a more complete view of the status of the discussion, please do have a look at User_talk:Jon_Awbrey#En-Dash_Protocol_Reigning_Over_Polynominal_Titles_.28EDPROPT.29

Three forms of mathematical induction

This article was intended to be comprehensible to all mathematicians.

It was not intended to teach mathematical induction. It was not intended to explain what mathematical induction is, nor how to use it.

It was nominated for deletion by those who did not understand it. To some extent, they did not understand it because it was a stub and failed to explain what audience it was intended for and what its purpose was.

A bunch of (mostly) non-mathematicians looking at the stub form in which the article appeared when it was nominated from deletion saw that

It was not comprehensible to ordinary non-mathematicians who know what mathematical induction is, and

The article titled mathematical induction is comprehensible to ordinary non-mathematicians, even those who know --- say --- secondary-school algebra, but have never heard of mathematical induction,

...and voted to delete.

And so I have now expanded the article far beyond the stub stage, including

Substantial expansion and organization of the introductory section.

Two examples of part of the article that is probably hardest to understand to those who haven't seen these ideas.

An prefatory statement right at the top, saying that this article is NOT the appropriate place to try to learn what mathematical induction is or how to use it, with a link to the appropriate article for that. It explains that you need to know mathematical induction before you can read this article.

Therefore, I have invited those who voted to delete before I did these recent de-stubbing edits, to reconsider their votes in light of the current form of the article.

I also ask others here to vote on it by clicking here.

(Nothing like nomination for deletion to get you to work on a long-neglected stub article!) Michael Hardy 23:42, 6 March 2006 (UTC)

WAREL

My assumption of good faith in User:WAREL (formerly User:DYLAN LENNON) is being sorely tested. I know I'm not the only one who has wasted a lot of time over the past few weeks dealing with him/her. I'm wondering whether anyone else here has any thoughts about how to deal with WAREL, short of deploying an automatic WAREL-edit-reverting-bot. Dmharvey 18:00, 7 March 2006 (UTC)

For context, see the following article histories Decimal representation, Real number, Twin prime conjecture, as well as User talk:WAREL (Link to today's version, as WAREL likes to delete things he does not like. See especially the bottom section.) Oleg Alexandrov (talk) 19:47, 7 March 2006 (UTC)

I left a comment at Wikipedia:Administrators' noticeboard/Incidents#Disruptive_contributor to_mathematics articles. Oleg Alexandrov (talk) 05:47, 9 March 2006 (UTC)

al-Khwarizmi

This isn't about mathematics, but it is about a mathematician. Anybody who has spare time and is willing to read a long talk page is kindly request to comment on the dispute regarding al-Khwarizmi's etnicity at Talk:al-Khwarizmi. Cheers, —Ruud 14:49, 9 March 2006 (UTC)

How about showing the whole lot of them the way to Wikinfo, which wants editors like that? ;-> Septentrionalis 19:24, 9 March 2006 (UTC)

Somehow I doubt that most persons involved are interested in updating his biography beyond the first two sentences. —Ruud 19:30, 9 March 2006 (UTC)

Articles for the Wikipedia 1.0 project

Discussion moved to Wikipedia:WikiProject_Mathematics/Wikipedia_1.0 Tompw 16:40, 13 April 2006 (UTC)

Wikipedia talk:Scientific peer review

Notice: interested contributors may wish to participate in the Wikipedia talk:Scientific peer reviews by working scientists.

--Ancheta Wis 17:10, 11 March 2006 (UTC)

Can you guys have a look

Gallagher Index is a Political Science article and subject. But currently it could probably do with a mathematicans eye (alongside a few more things as well). Essentially, is there a neater or nicer way of doing the table at the bottom as an example of how the index is generated? Cheers, --Midnighttonight 08:47, 13 March 2006 (UTC)

Categorizing articles

On my suggestion, Salix alba made a list of Wikipedia articles which are not categorized, but which are linked from a math article. That list has a bunch of false positives, but also articles which are math and are not categorized. I suggest we start a cat wiki-pet (short for a Categorizing Wikiproject), going through those articles and categorizing them.

I split the list into 47 sections of 50 articles each. One may choose a section to work on, and sign at the bottom when done. I did the first three, and found roughly 3-5 articles out of 50 which may need categorizing. See the list at User:Salix alba/maths/uncategorised maths. Oleg Alexandrov (talk) 20:14, 14 March 2006 (UTC)

I don't know much about the category system, but if I just tag relevant articles with Category:Mathematics, is that enough to get them on the radar? (i.e. should I mark a section as "done" if I do this?) Dmharvey 03:03, 15 March 2006 (UTC)

I'd shoot for at least one level more specific than Category:Mathematics. The names of the big categories are pretty intuitive: Category:Algebra, Category:Mathematical analysis, Category:Mathematical logic, Category:Geometry, Category:Topology, Category:Number theory. Just make sure to remember the "mathematical" before "analysis" or "logic". --Trovatore 03:16, 15 March 2006 (UTC)

Sometimes one can pick the right category by looking at the articles going from the current one. But yes, putting them in Category:Mathematics is a good first option. Then my bot will list them to the list of mathematics articles, so more people will see them and may refine the categorization further. So yes, marking a section as done if the articles there are listed in some category is good, thanks. Oleg Alexandrov (talk) 03:18, 15 March 2006 (UTC)

ok guys thanks Dmharvey 03:27, 15 March 2006 (UTC)

I made the sections be 20 items rather than 50, as those were too big I think. To continue with the note at the top of this section, the person who does most work will get a cat as a wiki-pet (the Wikipet which anybody can touch (and edit)). Oleg Alexandrov (talk) 05:08, 15 March 2006 (UTC)

Oleg, you are SO going to award it to yourself. That is, like, so totally not fair. Dmharvey 19:48, 15 March 2006 (UTC)

Not all is lost, the race is still fully open! By the way, if you look at my bot's changes page, you will see a good harvest of math articles for March 15. Awesome work! Oleg Alexandrov (talk) 03:37, 16 March 2006 (UTC)

Now, I eager to get the wiki-pet, reviewed a section, categorized around 10 of the 20 there, felt good of myself, and when I got to editing the section to say "done", I see the section was done already! Dmharvey, now that's unfair. :) Oleg Alexandrov (talk) 04:55, 16 March 2006 (UTC)

Perhaps people should mark their territory -- in a nice way -- at the top of the score of items when they start work on it? Jon Awbrey 05:00, 16 March 2006 (UTC)

I doubt it is worth it; I meant it to be a silly joke rather than a complaint. Oleg Alexandrov (talk) 05:01, 16 March 2006 (UTC)

$''\!$ Jon Awbrey 05:32, 16 March 2006 (UTC)

Cheaters!!!! Hey, I noticed that some of the "finished" sections are still contain uncategorized articles. Even if the article is not about math, please do make an effort to put it into some category, somewhere!!! linas 01:08, 18 March 2006 (UTC)

Be my guest, my friend. :) Oleg Alexandrov (talk) 02:10, 24 March 2006 (UTC)

History of human knowledge about pi

This is the new title of History of pi. Even I think this is pædantry, so it may be over the top. Can we discuss this here, away from the Pi day crowds? Septentrionalis 00:48, 15 March 2006 (UTC)

"History of pi" deserves an article. To think that a table of the history of numerical computation of pi is the same thing as a history of pi is very silly. I've moved the table to another article, and labeled this article a stub. Michael Hardy 01:40, 16 March 2006 (UTC)

Agree w/Michael. I remember reading, as a young student, of plenty of interesting snippets about Egyptians knotting strings, silly legislation in kansas about pi=3, and what not. It deserves an article. linas 22:26, 17 March 2006 (UTC)

LOL... I remember adding that to (what is now called) Chronology of computation of pi (see under 1897), except the reference I have is for Indiana not Kansas. Dmharvey 22:34, 17 March 2006 (UTC)

MathWorld

Hi guys,

I was wondering why I can find so many maths-related articles here that do not reference relevant pages from MathWorld. I'm not sure what their license model is, but I can only assume that this is the reason why it's not popular around here? Please let me know if you think including their articles as references is a desirable thing. I'm watching this page, so do reply here. - Samsara (talk • contribs) 13:18, 15 March 2006 (UTC)

Obviously, we can't include relevant sections of MathWorld articles, as that would be a copyright violation. The reason for not referencing MathWorld articles is probably the uneven quality (yes, even by our standards) and the presence of clear errors (possible copyright traps) and probable neologisms. (I don't think the neologism being published as part of Mathematica makes it any less a neologism.) — Arthur Rubin | (talk) 13:56, 15 March 2006 (UTC)

I agree with Arthur and the reasons he provides. A policy of providing links to mathworld just doesn't make sense for us. However, if you come across a particular article where they have a much stronger version, then certainly linking to theirs would be useful (even better: bring ours up to snuff). -lethe ^{talk +} 15:30, 15 March 2006 (UTC)

Yeah, making it a policy to link to mathworld does not make sense, but I would think we should be encouraged in making external links to mathwolrd on case-by-case basis when those links are relevant (not necessarily much stronger than ours :) Oleg Alexandrov (talk) 16:11, 15 March 2006 (UTC)

Just to clear up a possible misunderstanding: I was referring to the license model because Planet Math is more frequently linked to. Is quality really so divergent between the two? I'm not trained as a mathematician, so I admit my judgement is poor. - Samsara (talk • contribs) 16:17, 15 March 2006 (UTC)

We actually copy planetmath articles, see WP:PMEX, that's why we must refer to the original versions, per their site license. Oleg Alexandrov (talk) 16:21, 15 March 2006 (UTC)

I second Arthur's comments. Just in the past month or so, I've had to remove several external links to MathWorld because when I checked them out, I found out they contained major errors. Sometimes these MathWorld articles can be good, but other times, it looks like a real hack job. So it's definitely not good to just unilaterally add the MathWorld links. I think it best for editors working on particular articles in their area of knowledge to add the links they actually found the most useful. --Chan-Ho (Talk) 10:20, 10 April 2006 (UTC)

Please vote on this proposed deletion

at Wikipedia:Articles_for_deletion/Proof_that_22_over_7_exceeds_π#.5B.5BProof_that_22_over_7_exceeds_.CF.80.5D.5D.

The delete votes seem to be from non-mathematicians who erroneously think they understand the article. The main idea is this:

$0<\int_0^1\frac{x^4(1-x)^4}{1+x^2}\,dx=\frac{22}{7}-\pi.$

Therefore 22/7 > π.

But the article also includes exposition, discussion, and mention of the appearance of this problem in the Putnam Competition.

One "delete"-voter says this is no more significant than, for example, a proof that π > 3.14159 or the like. The fact that 22/7 is a convergent in the continued fraction expansion of π seems to mean nothing to that person or to escape his notice altogether. The fact that this particular integral is so simple and has a neat pattern also seems to escape them. Another shows signs of thinking that all articles on π-related topics should get merged into one article (see list of topics related to pi). Michael Hardy 02:22, 16 March 2006 (UTC)

arXiv

So what's the deal with linking to the arxiv? This has come up quite a number of times in the last little while. Someone has gone trigger-happy recently on some papers there by Diego Saá, and it took a lot of convincing to get User:WAREL to stop linking there. (Or maybe he/she is still at it.) I would think generally such papers do not qualify for linking from Wikipedia, unless there are very good reasons to the contrary. Somehow a link to the arXiv has an air of respectability that you don't get from your home page on geocities etc, but it's not deserved, and we shouldn't be misleading people into thinking that the arXiv is a reliable resource. Dmharvey 02:16, 17 March 2006 (UTC)

I agree. One should only use references to books and peer-reviewed journals. Oleg Alexandrov (talk) 02:54, 17 March 2006 (UTC)

That's not how it works in mathematics research, and I see no reason why Wikipedia should adopt stricter rules for citations in its mathematics articles than most of the mathematics community itself. Wikipedia would only be shooting itself in the foot. --Chan-Ho (Talk) 05:08, 25 March 2006 (UTC)

Well, we should prefer refereed references. Of course for journal references that are also on the arxiv, we should provide an arxiv link (not everyone has access to an academic library). Furthermore, there are worthwhile things on the arxiv which don't get published in journals. A lot of times, Witten, for example, publishes a lot of his papers only through the arxiv, he doesn't feel that journal referees are qualified to vet his papers. And there are précis on the arxiv which are very good resources but not original work, and therefore not appropriate for journals. But of course, there is also crackpottism on the arxiv, so care is certainly required. -lethe ^{talk +} 04:07, 17 March 2006 (UTC)

You definitely need a lot of care when citing papers by a guy who "doesn't feel that journal referees are qualified to vet his papers". :) Oleg Alexandrov (talk) 15:49, 17 March 2006 (UTC)

That is a dangerous attitude; but in the case of Witten I suspect many of the referees would agree, and are probably relieved that they do not have to try to keep up! --KSmrq^T 16:17, 17 March 2006 (UTC)

Off-topic: but Alexander Grothendieck stopped publishing in journals as well. linas 23:32, 17 March 2006 (UTC)

The arXiv is mostly reliable, except for the general mathematics (GM) section which is where the crank articles seem to get listed. I removed all the links to Diego Saá's papers that I could find; they were added by User:Diegueins, who claims to be his son. R.e.b. 05:57, 17 March 2006 (UTC)

In the last six months, I have found there a paper proving P=NP and another proving P $\neq$ NP. No comments... pom 16:18, 18 March 2006 (UTC)

Please sign up on the participants list!

If you have this talk page on your watchlist, then you should add your name, field(s) of expertise and interests to the Wikipedia:WikiProject Mathematics/Participants page! I know there are some newcomers who haven't yet signed up, and I suspect there are some old-timers as well. linas 22:15, 17 March 2006 (UTC)

I meant to sign up at some point, but I glanced over the list and, frankly, many of you guys seem to be so good that it's kind of scary (I'm only an undergrad student) :-) - only half joking. But now, if you say so... AdamSmithee 00:20, 18 March 2006 (UTC) And after signing up, I see that my nick and the alphabetical ordering puts me on top of the list :-D AdamSmithee 00:28, 18 March 2006 (UTC)

I would join but you see, I'm on vacation. Good luck to you all. -- 127.*.*.1 01:17, 18 March 2006 (UTC)

Let me also add, feel free not to add yourself to that list or any others, for any reason. I myself don't see what purpose the list serves, and don't like adding myself to lists like that, though I did so eventually. -lethe ^{talk +} 03:41, 18 March 2006 (UTC)

Obviously the list doesn't have any kind of official status, but it does create a kind of community, as well as crystallizing one's own role in the Mathematics project in one's own mind. Mostly it seems sort of like the ritual of everyone gathering in a circle and placing hands one above another to seal a pact. And I'd encourage AdamSmithee to put his name on the list simply because he feels out of place; doing so will put him correctly in place :) Ryan Reich 06:18, 18 March 2006 (UTC)

Actually, I got into a discussion recently about how many particle physicists there are working in WP; looking at the participants list help put a lower bound on the number. This is a lot like any department directory or phonebook or census: rarely looked at, but terribly useful when its really needed. That, and indeed, the community feeling of the historical "I was here" thing. In 20 years, the list may be interesting to review: "I remember old so-n-so." linas 02:58, 19 March 2006 (UTC)

Statistics on User:WAREL

I submit the following statistics as an argument to block WAREL for, I suppose, a few days.

User:WAREL was born 17th Feb 2006. He/she has a total of 242 edits since then. The following survey includes 99 of those edits (41%), plus a few of User:DYLAN LENNON's edits (WAREL is a reincarnation of DYLAN LENNON).

Perfect number: 23 edits. At least 13 immediately reverted. Many prior edits by DYLAN LENNON going back to July 2005 -- generally not reverted
Twin prime conjecture: 17 edits, all reverted
Real number: 12 edits, 11 reverted (As DYLAN LENNON: 14 edits, 10 reverted)
Decimal representation: 11 edits. 10 reverted.
Zeta constants: 6 edits, 3 reverted
Finite field: 6 edits, 3 reverted, the other 3 self-reverted
Proof that 0.999... equals 1: 5 edits, all reverted
Decidability (logic): 5 edits, all reverted
Riemann hypothesis: 5 edits, 1 reverted
Chen prime: 4 edits, 2 reverted
Decimal: 3 edits, all reverted
Halting problem: 2 edits, both reverted.
Fermat's last theorem: 1 edit, reverted
Soliton: 2 edits, both reverted
Wiener's tauberian theorem: 1 edit, reverted
Cousin prime: 1 edit, reverted
List of real analysis topics: 1 edit, reverted

Of these 113 edits, there are at least 88 reversions, which is 78% of the edits listed above, or 36% of all edits logged.

He/she was even reverted twice on his/her own talk page.

WAREL has been reverted by at least 17 distinct editors: User:Jitse Niesen, User:JoshuaZ, User:Dmharvey, User:EJ, User:Schildt.a, User:Arthur Rubin, User:ANTI-WAREL, User:Oleg Alexandrov, User:Elroch, User:Mfc, User:Trovatore, User:Zundark, User:Fropuff, User:Fredrik, User:Paul August, User:KSmrq, User:Melchoir, many of whom you will recognise as being respected contributors to mathematics articles.

On the other hand, I note that WAREL has also made several nontrivial, non-reverted contributions to several mathematics articles: Riemann hypothesis, Perfect number, Hilbert's fifth problem, Perfect power, Proof that the sum of the reciprocals of the primes diverges. He/she also makes plenty of edits to articles in which I am not competent, especially relating to Japanese mathematicians and musicians. Therefore, in my opinion, a permanent block is not (yet) warranted, even given the fact that he/she was permanently blocked on the Japanese wikipedia.

Dmharvey 01:23, 20 March 2006 (UTC)

I wrote a note on his talk page a few days ago about his revertions at decimal representation, and Jitse wrote one today about perfect number (see User talk:WAREL).

I have a silly suggestion. How about writing a petition on his user talk page, telling him that if he engages in any disruptive activity again, at any article, he will be blocked for 12 hours? Then we could all sign it, and then, should he disrupt again, any of us administrators would be able to block him with a clear heart. Wonder what you think. Oleg Alexandrov (talk) 06:53, 20 March 2006 (UTC)

Your suggestion is not silly. I think it would be important to emphasise in this petition that although some of his/her contributions have been appreciated, his/her almost complete disregard for other editors' opinions is not. I've spent enough time on this now; if someone else writes it, I will sign it. Dmharvey 13:11, 20 March 2006 (UTC)

<math> rendering bug

Just noticed at perfect number (at the bottom of the section on odd perfect numbers), this math tag:

 <math>2^{4^{n}}</math>

is getting rendered as this html:

 <span class="texhtml">2<sup>4</sup><i>n</i></span>

to appear as:

  $24 n$

.. which is clearly wrong.

I wasted some time tracking down the paper to check the clearly wrong result before realising that it was the rendering rather than the text that was at fault. I don't know if this is a well known bug, but a brief search on Mediazilla didn't throw up any candidates. I have reported it to the Wikitech-l mailing list mailing list. Hv 16:12, 20 March 2006 (UTC)

I've noticed this before. It's actually not a bug in the LaTeX => HTML converter. It has to do with HTML tidy, which is a program that processes the HTML after the converter is done with it. The correct translation would be something like 24n. I think what happens is that HTML tidy sees the second and assumes that the author forgot the slash. So it inserts an extra slash producing 24n. Then it sees the next and can't find a matching so it kills that one too. Finally the last dies. This is just a theory, but I'm pretty sure that texvc gets the conversion right in the first place. Dmharvey 18:30, 20 March 2006 (UTC)

See for example http://bugzilla.wikimedia.org/show_bug.cgi?id=108. Dmharvey 18:35, 20 March 2006 (UTC)

Thanks for the pointer. Is this HTML Tidy we're talking about? Because if so I'm surprised there's no mention there that it is being used on WP. (I also had a quick browse of the HTML Tidy bugs database, and saw no related item there.) If not, can you point me at some details of the HTML tidy you mean? I'd like to track this problem further ... Hv 19:52, 20 March 2006 (UTC)

Yes, that's the Tidy I mean. There is a flag $wgUseTidy in the mediawiki source which enables use of HTML Tidy. I'm pretty sure they use it on WP itself. You could try asking User:Jitse Niesen, I know he's at least one person who's been thinking about Tidy recently :-) Dmharvey 20:16, 20 March 2006 (UTC)

Indeed, I do know about it. This is fixed in the current version of HTML Tidy, but that is not yet installed on the MediaWiki servers. Details are in mediazilla:599. I haven't yet seen your post to the mailing list (perhaps it's help up in a queue), but the solution is to upgrade HTML Tidy. -- Jitse Niesen (talk) 23:16, 20 March 2006 (UTC)

Cool, I even managed to find the changelog that fixed it ([47]) but I guess that's redundant now. (I also followed up with a "never mind" to my wikitech mail, so it may never get through to the list.) I look forward to the new version. Hv 23:23, 20 March 2006 (UTC)

Decimal representation or decimal expansion?

There is a discussion on which name is more appropriate at talk:decimal representation. Comments welcome. Oleg Alexandrov (talk) 03:39, 21 March 2006 (UTC)

Problem at transfinite number

There is an editor, User:Jagged 85, whom you may recognize as being interested in the contribution of Indian mathematicians. At transfinite number he has been making edits that attribute the concept to certain ancient Jaina mathematicians/philosophers. The evidence presented is, in my estimation, of the sort that would be accepted only by someone who either has an agenda, or who does not really understand the contemporary concept. I'd appreciate it if some interested folks would drop by and take a look. --Trovatore 21:46, 22 March 2006 (UTC)

I fully agree with your assessment. In fact, I'll go further: this is obvious crackpotism. Various ancient philosophers have made dubious or meaningless claims about infinity (I had found a quote by Aristotle stating that the number of grains of sands on a beach was "infinite"), but none of them corresponds to what we now view as transfinite numbers; and Indian mathematicians were so proud of their invention of the decimal system that they had fun writing very large numbers as cosmic cycles, and sometimes they confused them with infinity, but obviously this has nothing to do with the modern concept. I support any move toward removing the incriminated section. --Gro-Tsen 22:04, 22 March 2006 (UTC)

It is no more (and no less) nonsense than Galileo's work on infinite numbers, in which he found that the natural numbers were equinumerous with a subset (the set of squares) and recoiled in horror. It is not the transfinites. Septentrionalis 22:41, 22 March 2006 (UTC)

Well, if it could be documented that the Jaina had the notion of equinumerosity (as witnessed by one-one matching), that would already be a step in the right direction, though I still don't think it would be enough to use the word "transfinite". As I understand it the historical context is that Cantor didn't want to use the word "infinite" because he was talking about things that were not absolutely infinite. They were trans-finite, beyond a limit, but not in-finite, without limit. That last sentence may be a bit of retrospective etymology on my part, but I think it really is the basic idea, whether or not Cantor had that specific etymological reasoning in mind. --Trovatore 22:46, 22 March 2006 (UTC)

A section reviewing the general history of eastern and western ideas about infinity, including Aristotle's ideas, as well as Gaileo's shock, would not be out of place somwhere on WP. We do, after all, have Category:History of mathematics and the topic of infinity, just like the question "what is four dimensions", was a legit intellectual excercise over the millenia. No doubt Immanuel Kant had some pronouncemnts as well. linas 00:54, 25 March 2006 (UTC)

Never mind. That article exists, its called infinity, and the Indian stuff should be moved there. linas 01:02, 25 March 2006 (UTC)

Another tedious orthography question

Vladimir Arnold or Arnol'd? Vladimir Drinfel'd or Drinfeld? We should be consistent: and preferably across all references to them in WP. (In both cases we currently use the apostrophe sometimes, but far from consistently.) —Blotwell 06:46, 24 March 2006 (UTC)

For Арнольд, we may as well defer to the way it appears on his books and web page, "Arnold". --KSmrq^T 02:02, 25 March 2006 (UTC)

Transliteration of the soft sign ("ь")—which does not so much represent a sound as a modification—is problematic, and conventions vary. But for names, it appears that in a context like this, appearing before a consonant, it would typically be omitted. Wikipedia allows us to choose that one as primary, for the article name, and use redirects for the variants. --KSmrq^T 18:35, 25 March 2006 (UTC)

Springer Encyclopaedia of Mathematics

I just stumbled across the Springer Online Encyclopaedia of Mathematics it claims to be

the most up-to-date and comprehensive English-language graduate-level reference work in the field of mathematics today. This online edition comprises more than 8,000 entries and illuminates nearly 50,000 notions in mathematics

and seems to live up to its description. It seems like this could be a useful resouces for many articles. --Salix alba (talk) 00:14, 25 March 2006 (UTC)

Yes, and its pretty good too, at least for the 3-4 articles I looked at. I created a template fr this, which may be usd as the following (for example:) {{springer|id=f/f041440|title=Fredholm kernel|author=B.V. Khvedelidze, G.L. Litvinov}} which results in

B.V. Khvedelidze, G.L. Litvinov, "Fredholm kernel" SpringerLink Encyclopaedia of Mathematics (2001)

linas 00:47, 25 March 2006 (UTC)

Would be a good idea to add those entries to Wikipedia:Missing science topics. I will try to look into that these days. Oleg Alexandrov (talk) 06:45, 25 March 2006 (UTC)

First article I hit was the normal distribution [48] I was quite disappointed in that it doesn't have a single graph of it. That said, it'd be worth copying the index into a new article or added to the missing science topics. Cburnett 06:56, 25 March 2006 (UTC)

No, you can't do that; this came up before with MathWorld. It's a copyright violation.

The Springer encyclopedia seems pretty weak in set theory. --Trovatore 07:29, 25 March 2006 (UTC)

Also compare the article on Self-adjoint operator in WP to the one in Springer. Tell me which one is better.--CSTAR 14:45, 25 March 2006 (UTC)

Ours is definitely more self-adjoint:

C^*=C.

Oleg Alexandrov (talk) 19:30, 25 March 2006 (UTC)

Is it worth an article SpringerLink Online Encyclopaedia of Mathematics? --Salix alba (talk) 20:21, 25 March 2006 (UTC)

I would think it's probably worth an article (I never heard of it before this discussion, but we're not talking about something put up by some random hobbyist; this is Springer). The issue is how to write a neutral review that's not original research. That's a problem to which I have not thought of any good answer (it's why I slapped my own article on Kunen's book, Set Theory: An Introduction to Independence Proofs, with an OR tag). --Trovatore 20:53, 25 March 2006 (UTC)

See what reviews it has in the scholarly press. Scholar.google.com should have something (this should solve the Set Theory problem, anyway.) If that fails, it can be put in WP space, as a resource. Septentrionalis 21:26, 25 March 2006 (UTC)

They have a lot of great articles. They're beating us in a lot of areas, and already kick the crap out of mathworld (soon it'll be time to put mathworld out of its misery). However, have you seen their diagrams? Complete garbage! -lethe ^{talk +} 17:23, 26 March 2006 (UTC)

I have merged their lists of entries into the Wikipedia:Missing science topics. I highly doubt that this is a copyright violation in any way, as while their lists may be copyrighted (the order of entries I guess :), individual items in the list are not, and after merging together the mathworld links and the springer links and removing the bluelinks, little if any resemblance is left to their orginal lists.

By the way, I brought some order in that Wikipedia:Missing science topics by completing incomplete entries (mathworld had those), putting things in lowercase, regularly removing the bluelinks, and providing links to google search and google books for each entry. Those lists can be rather good at suggesting new redirects, new articles, or judging where we are lacking. Oleg Alexandrov (talk) 21:28, 26 March 2006 (UTC)

Actually, I will send Springer an email asking if they mind using their list as a resource for our redlinks list. Just to be safe. :) Oleg Alexandrov (talk) 00:19, 27 March 2006 (UTC)

I've looked things up in the library's copy one or two times; good to see I don't have to go all the way there now... :-) Anyone know if the online edition differs significantly from the one in print? Fredrik Johansson 00:32, 27 March 2006 (UTC)

none of the springer links seems to work. how does one get to it from the springer website? thanks. Mct mht 07:15, 5 April 2006 (UTC)

The Springer server is down every now and then. Will come back eventually. Oleg Alexandrov (talk) 02:36, 6 April 2006 (UTC)

blahtex 0.4.4 released

Major changes since 0.4.3 are:

support for Japanese and Cyrillic in PNGs
much faster PNG output, because we're using dvipng rather than dvips/imagemagick

Useful links:

test wiki at http://wiki.blahtex.org (recently got attacked by spammers :-))
page illustrating blahtex's features
blahtex home page
updated error list (currently 337 errors)

Dmharvey 14:10, 26 March 2006 (UTC)

The dx in \int f(x) dx doesn't look right in the MathML output (it's rendered "d x"). Fredrik Johansson 14:45, 26 March 2006 (UTC)

Which browser+version are you using? This was a known problem with earlier versions of Firefox. Dmharvey 14:48, 26 March 2006 (UTC)

Firefox 1.5.0.1. Fredrik Johansson 14:58, 26 March 2006 (UTC)

Hmmm... does the same thing happen at all font sizes? Dmharvey 20:54, 28 March 2006 (UTC)

Normal, no style, enlarged.

Essentially. Increasing the text size a few times doesn't change the absolute width (it stays at 3 pixels); it looks normal if I use an obscenely large font. By the way, the space gets one pixel narrower if I disable the page CSS style (but still looks too wide, though this could be in my imagination). See image. Fredrik Johansson 21:28, 28 March 2006 (UTC)

That's a bummer. Thanks for pointing this out. I looks like Firefox is interpreting the "d" and "x" as belonging in separate "frames" and doesn't want to overlap them; therefore because the "d" is italicised and tall, it pushes the "x" to the right. I'm not totally sure about this, especially since there's a one pixel overlap in your second example, but that could just be some rendering thing that happens after the frames have been positioned. I will put it on my list of bugs to pursue; it's probably something that the Firefox folks will need to deal with. Dmharvey 03:39, 2 April 2006 (UTC)

gradient issues

There is some disagreement on what to include in the gradient article. It is argued by some parties that it should be a disambig. Comments welcome at talk:gradient#Should gradient be a disambigutation page? Oleg Alexandrov (talk) 17:20, 26 March 2006 (UTC)

Programs for linear algebra illustrations

What programs would people around here recommend for making images to illustrate geometry and linear algebra concepts (and the like)? I'd like to manually input coordinates for vector arrows, line segments, points, etc., choose colors and line styles, and output the result to SVG. Eukleides looks good, but it doesn't do 3D and I need that. Fredrik Johansson 23:45, 26 March 2006 (UTC)

Matlab gives you complete control, 3D, and output to color EPS. Here is a (free) program which it seems outputs to svg [49]. May be more. Of course, Matlab costs money, but should be available at any university, if you are in academia. Here are some pictures I made with it. Oleg Alexandrov (talk) 00:16, 27 March 2006 (UTC)

Yeah, I have access to Matlab, but not at home (not conveniently, anyway). Fredrik Johansson 00:22, 27 March 2006 (UTC)

You could learn a scripting language and roll your own tool. It shouldn't be that difficult. Dysprosia 02:41, 27 March 2006 (UTC)

Next thing you build your own rocket in your backyard, and could as well write your own encyclopedia. :) Oleg Alexandrov (talk) 04:03, 27 March 2006 (UTC)

Been there done that SingSurf, good for algebraic surfaces. It relies on JavaView which is quite good for 3D maths and is free as in beer but not speach. Also see Interactive geometry software for others. --Salix alba (talk) 12:04, 28 March 2006 (UTC)

IE compatibility

I wonder what people think of a policy of changing unicode html tokens to tex tags in order to ensure compatibility with Internet explorer browsers which apparently have problems with some unicode symbols. I guess compatibility with IE takes precedence over our own MoS guidelines, right? What do you folks say? -lethe ^{talk +} 11:53, 28 March 2006 (UTC)

We shouldn't use Unicode gratuitously in articles anyway. Unicode is far from being a ubiquitous standard, and when someone tries to edit in something that isn't Unicode capable, it screws up the entire article. That's not good behaviour. Dysprosia 11:57, 28 March 2006 (UTC)

When I work on my Windows laptop I don't see some Unicode characters on Wikipedia, even though I use Firefox and not IE. I guess it is a problem of missing fonts more than browser.

Changing unicode to LaTeX may be a huge amount of work, and may yield expressions which are a mix of both html and TeX. It would be fine I think if people do it on a case by case basis, but I would not be sure about making that a policy.

To comment on Dysprosia's comment, Unicode is a fact of life on Wikipedia given interlanguage links and foreign names/words. Luckily not that many browsers screw Unicode anymore, maybe just Lynx or really old browsers. Oleg Alexandrov (talk) 18:52, 28 March 2006 (UTC)

Well, I happen to use Lynx some times when I don't have access to a graphical browser, or (less often for me), when I use other operating systems I may use a browser that may not support Unicode. I'm not saying that Unicode should be completely removed from articles, it just shouldn't be used when there are other more portable equivalents out there that won't be mangled if someone edits with something that's not Unicode compatible. For example, one shouldn't just use a Unicode alpha when an α will be just as suitable. Dysprosia 22:55, 28 March 2006 (UTC)

I don't understand your example. Isn't that a unicode alpha that you've displayed? We shouldn't use unicode when unicode will suffice? -lethe ^{talk +} 23:04, 28 March 2006 (UTC)

No, it's a HTML entity, edit the section and have a look: α renders as α. Dysprosia 23:08, 28 March 2006 (UTC)

Oh, I see. But uh, don't the web browsers render the HTML tokens with unicode? I thought they did, and so therefore HTML tokens and UTF-8 text are equivalent (for viewing purposes). Or am I mistaken? -lethe ^{talk +} 23:11, 28 March 2006 (UTC)

The difference is that the Unicode alpha is just another character in the text, like "t", or "q". The HTML entity is the string "α". All good computer systems should support ASCII, and the HTML entity consists of only ASCII characters, so no matter if you use a computer that supports Unicode or if you don't, the string will be unchanged. However, some browsers that don't support Unicode simply ignore the Unicode characters, so if someone edits with one of those browsers, it will look like all the Unicode characters in the article have suddenly disappeared. If the browser chooses to render "α" with a Unicode character, that's fine, but it doesn't mean that that Unicode character is somehow equivalent to the HTML entity -- they aren't. Hope that explains things a bit better... Dysprosia 23:16, 28 March 2006 (UTC)

Yes, I understand now. UTF-8 text will get lost in the edit box by some browsers, even though it renders the same. Thank you for explaining. -lethe ^{talk +} 06:58, 29 March 2006 (UTC)

Replacing Unicode would be bad policy. This question was already decided when the wiki software switched over to UTF-8 as a standard. The world has gone Unicode, and that includes even standards-flouting Microsoft. To the best of my knowledge, all contemporary browsers can display Unicode characters if configured with adequate fonts. Usually Code 2000 will suffice. --KSmrq^T 21:29, 28 March 2006 (UTC)

I brought this up because some user went on a crusade to replace all instances of ℵ with $\aleph$ inline and display mode alike. I didn't like it, but apparently IE doesn't display ℵ correctly even if you have a font for it (which we learned because it displays if he changes web browser). -lethe ^{talk +} 23:08, 28 March 2006 (UTC)

PNG shouldn't be used inline. Dysprosia 23:10, 28 March 2006 (UTC)

That is also my opinion, but do we not have an obligation to lower our standards to support IE? Some might say we do. -lethe ^{talk +} 23:16, 28 March 2006 (UTC)

The HTML entity ℵ looks like it works... Dysprosia 23:25, 28 March 2006 (UTC)

Are you saying that ℵ displays differently from ℵ in IE? Septentrionalis told me once that he couldn't see ℵ correctly (I don't know for sure what setup he was using). --Trovatore 23:33, 28 March 2006 (UTC)

Doesn't work for me, either. I certainly prefer ℵ, regardless, as it's difficult to distinguish ℵ from the Hebrew letter by inspection if they were in Unicode, and those may display differently on different browsers. — Arthur Rubin | (talk) 23:36, 28 March 2006 (UTC)

I'm saying that ℵ should work on IE, that is, it should actually display. It shouldn't matter that much that it "looks different". I don't have IE so I can't check this. Dysprosia 23:56, 28 March 2006 (UTC)

I do not see the point of distinguishing ℵ from the Hebrew letter. Next we will be wanting an α different from alpha. I'm using a computer in the same cluster; both ℵ and ℵ now display well (and almost identically) in this IE set-up, but the second is a little square box in the edit window. Septentrionalis 00:08, 29 March 2006 (UTC)

alefsym definitely looks better alongside roman text than a Hewbrew aleph. The Hebrew aleph is too big. Do you not also find it so? -lethe ^{talk +} 07:05, 29 March 2006 (UTC)

I don't understand what you're talking about. If you want an aleph, you have ℵ, which actually does work. Dysprosia 00:10, 29 March 2006 (UTC)

OK, when I reboot into Windows to look at this in IE, I just see a square for the ℵ character. This is in IE 6.0.2900.someothernumbers, SP2, WinXP Home Edition, Version 2002, SP2. I suppose to really figure out what's going on I should say what fonts I have installed, but there are too many to conveniently list. --Trovatore 00:43, 29 March 2006 (UTC)

It's probably not a font issue, since if you try another browser on the same system, it will display. It's an IE issue. Now the question is, do we want to replace inline HTML token/UTF-8 with tex to support IE? -lethe ^{talk +} 07:05, 29 March 2006 (UTC)

I am the "user [who] went on a crusade to replace all instances of ℵ with $\aleph$ ". I was just replacing characters which I could not read with IE in those articles which I was trying to clean up for other reasons. alefsym causes the same problem as "ℵ" in IE. Also there is an element symbol which does not display correctly; and a proves symbol. Although these are rare. Oddly, I think that the actual Hebrew letter aleph works (at least I see the Hebrew letters OK in Google when I switch languages). JRSpriggs 05:24, 29 March 2006 (UTC)

Why do novices constantly "fix" things that obviously are not broken for most people? If the Unicode characters are in the article, there is nothing wrong with the characters for the author, and presumably for most readers. Adjust your own browser, your fonts, your configuration. Common sense and common courtesy suggest you at least ask before launching an ill-conceived massive alteration campaign—especially if you haven't been editing long enough to create a User page!

Suggestion: Look at this page and adjust the things under your control so you see as few missing characters as possible. (Note: For me, none are missing. Again, I highly recommend Code 2000.) This is a page in my personal user space; do not edit it! --KSmrq^T 07:07, 29 March 2006 (UTC)

I have been editing here for about two months. I did not create a user page because I have no interest in talking about myself for the public. I have a User-talk page to communicate about our shared work here. You are wrong to say that these characters are "obviously are not broken for most people". Most people use Internet Explorer 6.02 or earlier. So most of our readers will not be able to read the characters in question. And remember, this is an encyclopedia for the general public, not a private domain for you and the other authors to glory in their own words. Do not worry, I will not edit your user pages. JRSpriggs 07:33, 29 March 2006 (UTC)

Don't get defensive. KSmrq has a good point. We have a community here with established conventions. You can do whatever you like, make whatever decisions you want, decide what's the best format to use in articles, but we have the same rights, and in order to keep from devolving into continual revert wars, we try to respect consensus and community guidelines. When you've been here a while, you get a stronger feeling for that. Now, obviously you feel that wikipedia has to conform to IE's capabilities. Maybe you should try to win people over to your view instead of fighting with them. At the moment, I'm on the fence, but about to fall on the other side. -lethe ^{talk +} 07:43, 29 March 2006 (UTC)

Several distinct issues are at play. One is the recurring integration of novices into the community, with the usual exuberant misstep and jaded correction. A second is the display of the rich panoply of Unicode characters, whether mathematical or otherwise, in articles as viewed with a diversity of browers and fonts. Almost always the problem is with the fonts and browser settings. The Unicode characters are here to stay, especially when BlahTeX generates MathML for Wikipedia. A third issue is what appears in edit windows. The wiki software could be conservative and convert non-ASCII characters to named or numeric entities, but a browser that can display a page with Unicode characters can probably edit them as well.

But my point is none of these. I'm genuinely puzzled by the hubris of editors who assume that the article is broken because their view of it shows missing characters, especially when the same character appears in many articles. Do they think everyone else is stupid or blind? I don't know the statistics for Wikipedia readers, but one browser watch site shows slightly over 50% IE6 users, so it would seem reasonable to assume that many people had viewed any given Wikipedia article in IE6 without complaint. Yet these editors inexplicably fail to draw that conclusion.

Which leads to a design question: Is there anything we can do to head off these edits before they occur? The insert menu already shows a large assortment of non-ASCII characters, but obviously that's not enough of a hint to some editors. Should every article page have a prominent link to help with missing characters? --KSmrq^T 09:10, 29 March 2006 (UTC)

I know what we need. Here pages that use indic fonts include a template which indicates that they're being used and that if you want to view the page, you have to make sure your system is ready. If we want to use stuff in a math article which doesn't have widespread support, we could have a template like that one. That would probably keep new editors from changing font stuff, right? -lethe ^{talk +} 12:26, 29 March 2006 (UTC)

This page contains Indic text. Without rendering support, you may see irregular vowel positioning and a lack of conjuncts. More...

What about the difference between ''x''² x² and ''x''2 x²? I'd say the latter looks better on my screen. --Salix alba (talk) 23:39, 29 March 2006 (UTC)

Only a few superscript characters have Unicode points, so consistency weighs in favor of the tags. For example, look at x²x³ = x⁵ versus x²x³ = x⁵. Similarly, a few special fractions have Unicode points, while most do not. For example, compare ¾ (entity frac34) to ³⁄₇ (using entity frasl, and tags and ). --KSmrq^T 01:21, 30 March 2006 (UTC)

Move of "Ruler-and-compass constructions" to "compass and straightedge"

John Reid moved the article "Ruler-and-compass constructions" to "Compass and straightedge". As the article currently stands, I think there are problems with the new name. I intended to move the article back to its original name, until we can reach a consensus, but I inadvertently left out the hyphens and moved it instead to Ruler and compass constructions. Please share your views on any of this at Talk:Ruler and compass constructions. I will volunteer to make any necessary changes after we arrive at a consensus about what to do. Thanks — Paul August ☎ 17:58, 28 March 2006 (UTC)

Poll on "ruler" vs "straightedge"

Some of us can't agree on how to properly call the article Ruler and compass constructions, with the other option being Compass and straightedge. "Votes" at Talk:Ruler and compass constructions are solicited. :) Oleg Alexandrov (talk) 21:49, 29 March 2006 (UTC)

Neusis

Please see Jim Loy's angle trisection page. He shows a few methods using forbidden tools; I call your attention to the so-called tomahawk and to the movable, marked carpenter's square. Is the use of these tools not equivalent to neusis? John Reid 18:33, 31 March 2006 (UTC)

Please! Neusis? Yes? No? John Reid 19:59, 7 April 2006 (UTC)

Apr 2006

This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

Parametric coords

Hi all. I saw there wasn't any article on parametric coords. I am willing to create one, if needed. However, since it might be the same thing as curvilinear coordinates, I've just put in a redirect for now. I've asked the question on Talk:Curvilinear coordinates, but so far nobody can tell me if they are identical, or just related, topics. Please take a look and post your conclusions at that talk page. StuRat 21:24, 1 April 2006 (UTC)

If someone does write the article, please don't use that name, but spell "coordinates" out in full. Ryan Reich 22:14, 1 April 2006 (UTC)

Absolutely. I do like to add redirects from short names to full names, though. This allows users to enter shorter words like "coords", "lab", "gym", etc., which are both more convenient and less likely to contain spelling errors. StuRat 02:31, 2 April 2006 (UTC)

Parametric coordinates really require a parameterisation, for example a parameterised curve or surface. For that reason I've now made parametric coords redirect to parametric equation. --Salix alba (talk) 09:40, 2 April 2006 (UTC)

Yes, but not all parametric equations describe a parametric curve or surface. Therefore I feel that an article specific to this application of parametric equations is justified. StuRat 02:29, 3 April 2006 (UTC)

Direct logic

Could someone take a look at Direct logic? I see some potential problems with this, given who the author is. —Ruud 16:01, 2 April 2006 (UTC)

IMHO, it looks like this is original research and doesn't belong. How does one tag an article to indicate as much?Lunch 18:42, 3 April 2006 (UTC)

Petition on WAREL's talk page

For background, see Wikipedia talk:WikiProject Mathematics#Statistics on User:WAREL several sections above.

Fresh out of his most recent 48 hours block, WAREL/DYLAN has been engaging in edit wars at field (mathematics) and division ring, moving, incorrectly, interwiki links from the former to the latter, see WAREL's contribs and DYLAN's contribs.

I wrote a petition on the top of his talk page asking him to stop revert wars, as this has been going for too long. If you are familiar with WAREL's edit warrior activity, and think that it's a bad thing, you may help by signing the petition. I doubt WAREL/DYLAN will learn anything from it, but it may give more legitimacy to future attempts at blocking him for disruption. Oleg Alexandrov (talk) 17:46, 3 April 2006 (UTC)

I've tried to figure out what this editor's motivation could possibly be, and my current working hypothesis is that he's engaged in a "destructive testing" experiment to figure out exactly how much it's possible to get away with before drawing blocks/RfC/permanent ban. Otherwise it's hard to understand why he keeps pushing just inside the edge of written rules, trying to get trivial changes kept, ones it's hard to believe he thinks would make any real difference.

Is it time to think about bringing the experiment to a successful conclusion? --Trovatore 21:06, 3 April 2006 (UTC)

Guys, make it an RfC. It's what that is for. Charles Matthews 21:35, 3 April 2006 (UTC)

I am currently editing Wikipedia:Requests for comment/WAREL -lethe ^{talk +} 22:30, 3 April 2006 (UTC)

I guess the RfC has to be certified by other people, so anyone who cares to, certify it. -lethe ^{talk +} 22:55, 3 April 2006 (UTC)

Great, thanks! I guess the RfC has been certified, I see a lot of names there. I now unblocked WAREL so that he can comment in the RfC. Oleg Alexandrov (talk) 00:04, 4 April 2006 (UTC)

DYLAN and finite fields

While I am not sure on what to do about the current dispute at field (mathematics), which is centered on the use of "field" at the Japanese Wikipedia, DYLAN LENNON now claims that a finite division ring is not the same as a finite field, and removed the interwiki link from our "finite field" to the Japanese "finite division ring". Comments welcome at talk:finite field. Oleg Alexandrov (talk) 18:57, 6 April 2006 (UTC)

My Muddle

I have frequently had an unpleasant experience when looking up mathematical terms in Wpedia. I go to the article I want and, reading the definition of the term, I encounter another term I don't understand. If there is a link connected to the term I open a new tab to find the definition of the second term. In reading the second definition I find the need to look up a third, then a forth, fifth, sixth. I am soon swamped by "hanging" definitions. But, not infrequently, a term is used without any attempt to define it. Do mathematicians write these articles only to communicate with other mathematicians? Surely an encyclopedia is meant to educate people about things they don't already know. Too Old 00:19, 7 April 2006 (UTC)

This is more or less of a problem depending on the topic in question and how much effort has been spent on writing it. If you mention it here, or on the discussion page of the relevant article, it's more likely to get fixed. Dmharvey 00:25, 7 April 2006 (UTC)

Hmm...I sometimes find that some calculus-related articles make more sense on Wikipedia than Wikibooks — Ilyan e p (Talk) 00:38, 7 April 2006 (UTC)

Wikipedia is not meant to teach you the background knowledge you need. Wikipedia is an encyclopedia, not a collection of tutorials. If you want that, try Wikibooks. Dysprosia 00:40, 7 April 2006 (UTC)

Yes, it is good to keep things accessible, that means having relevant links to all concepts encountered. That of course does not mean it is Wikipedia's fault if you start reading an article about a term you don't know only to run into links to other terms you don't know. Wikipedia is (and should be) after all a loose collection of essays, not a course (and even for a course, you have prerequisites :) Oleg Alexandrov (talk) 01:08, 7 April 2006 (UTC)

An encyclopedia should not be of use only to a specialist, like a physician's medical database. An encyclopedia is, IMHO, meant to be a resource for the generally well-educated layperson, who might need the occasional definition, but definitely should not need a tutorial to understand an article. The background you speak of should not have to be extensive prior knowledge of the subject. When I consult, for example, the article on steel, I find an extensive treatment of the subject, occasionally having to find a definition, but not having to undertake a course in metallurgy in order to understand the article. When I go to look up a definition in that article, I need not go further and further afield in order to understand the definition. Too Old 01:37, 7 April 2006 (UTC)

An encyclopedia is a reference work, a collection of facts that are explained well and do not attempt to excessively mollycoddle the reader. You are comparing apples and oranges with your example of steel there -- mathematics, as well as certain other fields, are necessarily reliant on your accumulation of prior knowledge. A more apt analogy is expecting to understand an article on quantum spin. That article does not and should not teach you the basics of physics before launching into the actual article content, but it can give some motivation and make some simple insightful analogies. Dysprosia 01:52, 7 April 2006 (UTC)

I would like to dispute you on one point without arguing with the intent. The argument that "math is special" because it is more structured (or more rigorous, or constantly evolving, or any other argument I've seen used at various times) is very silly and I don't think it's good here. There are a lot of topics that can be covered with only elementary background. What do I mean by elementary? Well, read steel carefully and see what it assumes: right off the bat it talks about alloys, various chemical elements, technical ideas like "ductility" and "tensile strength", and the notion of atoms. All fundamental ideas in chemistry and physics. Too Old seems to have had no problem with these, yet I don't feel that this corpus of prerequisites is any larger than asking people to know calculus or Euclidean geometry. But I don't know that this was his problem, since he never said which articles he's found too technical.

I guess my point is that I feel like "math is hard" pulls too much weight around here even (especially!) when spoken by mathematicians. A reasonable article should assume the reader's knowledge of terms which form a language of discourse for the subject, so that each sentence need not be interrupted with definitions and qualifications, but anything that (in the context of the discursive standard) could be taken as technical should be explained. Rather than telling Too Old to go off and get an education, we should at least extract some productive information from his complaints and see what sort of stylistic changes might be needed around here. Ryan Reich 03:03, 7 April 2006 (UTC)

The companion matrix article, for instance, assumes you know what a polynomial is (and knowing what a polynomial is requires its prerequisites), knowing what a matrix is and the necessary basic matrix algebra necessary, plus a little more advanced matrix theory such as the characteristic polynomial is, diagonalizability, plus if you'd like to get through the rest of the article, assumes you know some basic field theory and linear algebra. There are articles and areas of mathematics with much worse prerequisites than that -- there are a lot of extremely deep areas, just pick something that is right near the bottom of that "depth". Mathematics does build on prior knowledge and decreeing this fact as "silly" doesn't quite make much sense.

No one is telling Too Old to "go off and get an education", though one should not blame the article for one's gaps in knowledge. Of course, a bad article can and does exist where it explains the concepts in an illucid way, and that of course should be fixed, but an article should not aim to teach the reader prior knowledge -- that responsibility is up to the reader, not the reference work. Dysprosia 03:43, 7 April 2006 (UTC)

My complaint was that the claim that math has special depths of prerequisites is silly. Go look at any science; they're just as bad. In particular, the use of this claim in this context, namely in response to someone who was almost certainly referring to articles that an amateur might be interested in reading, is silly, since such articles can without doubt be disposed of without using advanced concepts (of course, later in the article advanced ideas may arise. That has never been part of this discussion, though). In particular, I was not claiming that all math can be done at an elementary level (actually, I think I made allowances for the opposite). The example you give simply supports my contention that a common language be established at the start of the article. What might not be a good idea, in this particular case, would be for the article to introduce the theory of companion matrices in the context of modules over a PID, since it can be done more simply. This is the sort of distinction I'm making, yet I'll bet some people (I might be one of them, depending on my mood) will argue that the article should talk about companion matrices this way, since it's "more correct". That argument only works if it doesn't sacrifice clarity. Ryan Reich 04:12, 7 April 2006 (UTC)

I don't understand why you make the claim because I never did claim myself that math has "special depths of prerequisites" -- I said "mathematics, as well as certain other fields", and made special note that physics is just as bad. Otherwise I think we may be in violent agreement. Dysprosia 04:37, 7 April 2006 (UTC)

Oleg, you've absolutely hit the nail on the head. Dysprosia 01:52, 7 April 2006 (UTC)

Two sources of difficulty are obvious: (1) the structure of the subject, and (2) how it's presented. It is a fact of life that knowledge is a web, not linearly structured in dependency. Knowledge of A supports understanding of B, but also knowledge of B supports understanding of A. A writer of a text must work hard to order the presentation linearly, and at best achieve only partial success. Often a text read a second time will make more sense, because the additional context is available. A writer of a web article has no control over order of access. The only option is to include definitions, not just link to them; but taken too far, these intrusions become an obstacle themselves. Instead, some people use popups to get a quick look at a linked definition without opening a tab (or a window, in an antiquated browser). --KSmrq^T 01:24, 7 April 2006 (UTC)

Pop-ups are life savers (well okay time-savers) — Ilyan e p (Talk) 01:31, 7 April 2006 (UTC)

We don't write our articles solely for mathematicians; we endeavor to make them as readable as possible. Accessibility is definitely a consideration for us. But only one of many, so sometimes an article is not as accessible as we might like. If you think the articles need help, then you know what to do. This is a wiki, be bold, edit. Complaining about the quality of some difficult work done for free by volunteers in their spare time is not going to win you any friends. -lethe ^{talk +} 01:57, 7 April 2006 (UTC)

For the record Talk:Hilbert_space#The_Layperson, Talk:Calabi-Yau manifold, Talk:Lie_group#is_this_useful.3F, some more examples of people with the exact same complaint. Happens a lot, I guess. If there were some magical way to easily write mathematics articles that were easy to learn, I would employ it in my writing. -lethe ^{talk +} 04:00, 7 April 2006 (UTC)

Per Ryan Reich, please make the complains specific. There are reasonable complaints, and there are unreasonable ones. :) Oleg Alexandrov (talk) 03:13, 7 April 2006 (UTC)

Well, it seems that I am not alone. But, people, I did not mean to attack your virtue. There was a suggestion that I should "be bold, edit". Were I 30 or 40 years younger, and had the resources, I might take up the serious study of mathematics. I then might find a way to rewrite some of these articles to make them more accessible. But, life is too short... I have had my say. I leave you now to play The Glass Bead Game among yourselves. If you have any thing to say to me I shall be happy to read it on my talk page, or you may email me. Too Old 07:11, 7 April 2006 (UTC)

Sorry, but sciences just aren't for everyone; you have to have a certain basic knowledge to be able to understand more complicated concepts in mathematics, physics, and so on. There's only so much we can do about that. —Nightst a llion (?) ^{Seen this already?} 14:51, 7 April 2006 (UTC)

I think Too Old has a valid criticism, frequently repeated. The coverage of mathematics is often at too high a level, organisation of articles is confusing, core topics like Algebra are woefully inadaquate. Yes we have done good work todate, our coverage is extensive, but there is still a long way to go.

I propose creating Wikipedia:WikiProject Mathematics/Essential articles where we can identify which are the most important mathematics articles, assess then for quality and also mathematical level required. An example we could follow is Wikipedia:WikiProject Computer and video games/Essential articles which nicely organises that fields core material. This would also fit in with the Articles for the Wikipedia 1.0 project discussed above.

Is anyone interested in helping on this? --Salix alba (talk) 23:09, 8 April 2006 (UTC)

WAREL/DYLAN indef blocked

Well, the RfC and all our pleas seem to have no effect on his behavior. I blocked both accounts indefinitely, and wrote a note at Wikipedia:Administrators' noticeboard/Incidents#Indef block of WAREL/DYLAN LENNON.

This will generate serious questioning, as we are talking about an indefinite block, no less, so your comments there are appreciated, to make the case that this is a community-backed decision. Oleg Alexandrov (talk) 17:49, 7 April 2006 (UTC)

formal laurent series

Should formal Laurent series redirect to Laurent series (as it currently does) or to formal power series (my preference)? Dmharvey 18:20, 7 April 2006 (UTC)

I think formal power series is better, especially since the doubly infinite Laurent series cannot be treated formally (with rare exceptions). — Arthur Rubin | (talk) 18:52, 7 April 2006 (UTC)

Maybe the section on formal laurent series in the article Laurent series should be merged into the corresponding section of formal power series. -lethe ^{talk +} 18:54, 7 April 2006 (UTC)

Done. Dmharvey 17:03, 9 April 2006 (UTC)

references: multiple page numbers for same book

I've been trying out the new cite.php tool, i.e. with the <ref> and </references> tags. See for example quasi-finite field. But it looks a bit silly there, because I have two different page numbers for the same book. Does anyone know a slicker way to handle this? Dmharvey 18:22, 7 April 2006 (UTC)

David, I've made an edit at quasi-finite field, to suggest another way of handling your situation. However, I don't really like the look of the cite tool, I prefer the rf/ent templates, so I've also made a second edit using the rf/ent templates, to see if you like the way they look better. Paul August ☎ 21:49, 7 April 2006 (UTC)

I gotta admit I don't like any of the options very much. What I really want is something like LaTeX's \cite command, i.e. each reference gets e.g. a number or sequence of letters, and then you can specify the page number inline. So for example it would read like "according to [Se, p.198] you can do ..., or you can see later on [Se, p.204] suggests blah blah blah", and then in the references it just has one item, "[Se] Serre, Jean-Pierre, Local fields, etc". But it doesn't look like any of the automated mechanisms allow one to do this. Dmharvey 02:27, 8 April 2006 (UTC)

Solicit help organizing topics relating to approximation theory

I have recently created some material in the approximation theory page, relating to polynomial approximations to special functions. This is related to function approximation, Chebyshev polynomials, and polynomial interpolation, but in ways that I'm not clear about. I'm not an expert in the taxonomy of this area of mathematics, only in the specific things about which I wrote. In particular, I know that there is a field of interpolating polynomials through given data points, and that Chebyshev polynomials (and their roots) are involved in this. I can't believe that "approximation theory" is just about Remes' algorithm or use of Fourier/Chebyshev analysis to make optimal polynomials. So this whole area may be somewhat messed up, and my material might be in the wrong place. Would someone who knows his/her way around in this area be willing to take a look and move things around?

William Ackerman 00:40, 8 April 2006 (UTC)

Copies of long essay on multiple talk pages

User:BenCawaling has added apparently identical copies of a 2,500 word essay titled "About the incomplete totality of the infinite set of prime numbers" to the following talk pages:

Talk:Riemann hypothesis

Talk:Gödel's incompleteness theorems

Talk:Cantor's theorem

Talk:Cantor's diagonal argument

Talk:Bijection

Talk:Prime number

Talk:Fermat's last theorem

I don't think that Wikipedia is the right place for this diatribe, and we certainly don't need multiple copies of it - but as it's all on talk pages, I don't know what policy or guideline could be quoted in support of removing it. Does anyone have an opinion on what should be done about this (if anything) ? —The preceding unsigned comment was added by Gandalf61 (talk • contribs) 11:41, April 8, 2006 (UTC)

I think we should remove it as a kind of spam. Paul August ☎ 15:36, 8 April 2006 (UTC)

Replace all but one of them with a link to the remaining one? Or replace all with a link to his userspace? -lethe ^{talk +} 15:37, 8 April 2006 (UTC)

I suppose any of these things would be OK, but there's a risk that it would constitute paying him too much attention. At least he's been good enough to confine his ramblings to a single section on each talk page, and as far as I've seen no one's bothered to respond. If it stays that way, maybe he'll get bored and go away, and the screeds will eventually pass harmlessly into archives. Of course if he were to start editing article pages, or injecting irrelevancies into other discussions on talk pages, then action might have to be taken. --Trovatore 18:32, 8 April 2006 (UTC)

You are right about the unnecessary multiple copies of some of my discussion text. I have just downloaded Wikipedia's "How to edit a page" and would make the deletions and links to one in "Prime number" article talk page. For now, you may do as you please with my "contributions".

You are wrong about no one's responding --- countless with positive reactions do in my Yahoo e-Mail address (I intentionally include it because, just like David Petry's last comments "As I see the situation now" in his "Controversy over Cantor's theory" article, the majority of Wikipedian administrators and editors are Cantiorian fanatics who (loking at their user pages (where there are any) are not at all mathematically qualified to discuss these stuff and whose best response is bad-name-calling (just read the next 3 messages) or appeal to their or their idolized "authoritative knowledge" but not actually refuting the arguments proferred even though they cite only elementary mathematics understandable by even honor high school students. The Yahoo e-Mail messages that I received confirms to me that Wikipedia articles are widely read by mostly amateur mathematicians or stidents. I was hoping to give them alternative understanding of the most controversial issues in modern mathematics to discuss with their professors.—The preceding unsigned comment was added by BenCawaling (talk • contribs).

A better idea would have been to actually contribute to the creation or update of an article, instead of spamming multiple pages. By the way, thanks for insinuating that we are nothing but name-callers, then accusing us of being "Cantorian fanatics". Isopropyl 03:21, 14 April 2006 (UTC)

Crank spam. Delete. Charles Matthews 18:39, 8 April 2006 (UTC)

Agreed; delete. Talk pages are explicitly devoted to discussions about the article itself. --KSmrq^T 22:05, 8 April 2006 (UTC)

Agreed; crank spam. There is lots of that in talk pages in violation of the stated purpose of talk pages, unfortunately. However, in most cases enforcing this policy is probably a pain. In this case there's so much of it that it should all be deleted. So I guess the message to crank spammers is this: if you have something cranky to say, keep it short.--CSTAR 22:34, 8 April 2006 (UTC)

I have moved this essay to User:BenCawaling/Essay and replaced each copy on an article talk page with a link to its new location. Gandalf61 08:46, 14 April 2006 (UTC)

WAREL is back

This is getting interesting: two socks at the same time: [50] [51]. And an anonymous edit: [52]. Oleg Alexandrov (talk) 19:57, 8 April 2006 (UTC)

How sure do we have to be that these are him before we permban the socks? That's my inclination. -lethe ^{talk +} 20:32, 8 April 2006 (UTC)

I was under the impression that on-sight permabanning of socks was reserved to Willy on Wheels-level offenders. Isopropyl 20:40, 8 April 2006 (UTC)

Oleg, just do it. We'll pick up the pieces later. We can always apologize to anyone blocked by mistake; it's not like any huge permanent damage is done. --Trovatore 20:50, 8 April 2006 (UTC)

Oh, and by the way, this last incident should more than justify restoring the permanent ban on WAREL. --Trovatore 20:52, 8 April 2006 (UTC)

Someone made the comment that WAREL isn't learning anything from these repeated blocks. I think that if we keep unblocking him and he continues along the same path, we're the ones who aren't learning anything. Those who are about to block, we salute you. Isopropyl 21:25, 8 April 2006 (UTC)

I banned 64.213.188.94 (talk • contribs) indefinitely. -lethe ^{talk +} 22:33, 8 April 2006 (UTC)

I asked Lethe to shorten the block for a day, as IP addresses can be shared, unlike user names. On the more general problem, I start thinking that WAREL may actually not only be a highly arrogant user but also have some kind of compulsive disorder. In the worst case scenario he will play a cat and mouse game making new accounts just as we block them. No easy solution in sight. Oleg Alexandrov (talk) 00:25, 9 April 2006 (UTC)

Interesting common line of thought there. I almost posted a comment that when the permanent ban is put into place, a suggestion to seek psychiatric help should be posted on his user page. That would make it clear we have WAREL's interest at heart. On a practical matter, what IP addresses have the named accounts used by WAREL had? Elroch 00:56, 9 April 2006 (UTC)

Looking through the "contributions" of 64.213.188.94, from day one I see lots of silly vandalism and trolling of the worst sort, interspersed by occasional relatively lucid postings on the very mathematics subjects WAREL and DYLAN LENNON like to post, such as Perfect number and Masahiko Fujiwara. I also see some fascination[53][54][55][56] with one Doyle Farr, apparently a black student at Franklin Pierce College. Whether shared IP or not, I can't say that a permanent ban would be a big loss to Wikipedia. Lambiam ^Talk 04:04, 9 April 2006 (UTC)

I don't think this anecdotal evidence makes a very strong case that the next person who tries to edit from that IP won't be a legitimate, good-faith contributor. Let's keep our responses targeted. OTOH I think immediate permanent blocks should be imposed on User:DEWEY and User:KOJIN and future recognizable sockpuppets as they appear. If we make a mistake it can always be corrected. --Trovatore 16:28, 9 April 2006 (UTC)

Length of an "arc" or of a "curve"?

At Talk: Length of an arc I added a comment arguing that the title ought to be Length of a curve (presently a redirect to Length of an arc). Please discuss there if you care (one way or another). Lambiam ^Talk 03:18, 9 April 2006 (UTC)

{numbers}

Number systems in mathematics .
Basic
$\mathbb{N}\sub\mathbb{Z}\sub\mathbb{Q}\sub\mathbb{R}\sub\mathbb{C}$ Natural numbers $\mathbb{N}$ Negative numbers Integers $\mathbb{Z}$ Rational numbers $\mathbb{Q}$ Irrational numbers Real numbers $\mathbb{R}$ Imaginary numbers Complex numbers $\mathbb{C}$ Algebraic numbers Transcendental numbers Transfinite numbers Split-complex numbers $\mathbb{R}^{1,1}$
Complex extensions
Bicomplex numbers Hypercomplex numbers Quaternions $\mathbb{H}$ Octonions Sedenions Superreal numbers Hyperreal numbers Surreal numbers
Others
Nominal numbers Serial numbers Ordinal numbers Cardinal numbers Prime numbers p-adic numbers Constructible numbers Computable numbers Integer sequences Mathematical constants Large numbers Pi π = 3.141592654... e = 2.718281828... Imaginary unit $i 2 = - 1$ Infinity ∞

Here is the {{numbers}} template. Today is the second instance when somebody felt templated to insert it in all the articles linked in there (first time was a while ago). I feel this is the case when being in Category:Numbers is enough for these articles, and the gain given by this template in all articles is not offset by the huge size of the template and the distraction it causes on the page. Comments? Oleg Alexandrov (talk) 04:01, 10 April 2006 (UTC)

The template is certainly sort of obtrusive visually. On the other hand these are all articles aimed at a pretty elementary audience. Maybe it is useful for them to have this reminder of how the various sets of numbers fit together. Could we find some of them to ask? --Trovatore 07:39, 10 April 2006 (UTC)

This is an absurd template. How many times and places do we need to know about, say sedenions? Perhaps if the template limited itself to the basics it might be justifiable. --KSmrq^T 08:41, 10 April 2006 (UTC)

I agree. It's absurd. I'm very skeptical as to its utility even for the "elementary audience" Mike mentions. I would think an appropriately placed link to number systems or whatever would be better; I think we all know how to keep a brower window or tab open :-) --Chan-Ho (Talk) 08:49, 10 April 2006 (UTC)

This is the sort of thing I made {{otherarticles}} for. Septentrionalis 22:31, 10 April 2006 (UTC)

Neusis again

I'm a bit miffed that my original post on this topic seems to have been blown by without comment. I'm not an expert and I really don't know the answer.

Maybe it's just that no-one here knows the answer. Dmharvey 02:23, 11 April 2006 (UTC)

A curious fact of life in posting to forums like this is the extreme differences in volumes of responses questions can provoke, differences which sometimes seem to be independent of the merit of the questions. The answer to your question requires technical study of the tools in question. The general situation is that we know compass-and-straightedge constructions only allow solutions to linear and quadratic equations; the additional tools allow solutions to broader classes of equations such as cubics. This much every serious mathematician knows. However, it may not be obvious which additional classes any particular tool admits. For example, we know a number of different tools that can be shown sufficient to solve cubics (hence permit trisection); but that does not mean they are equivalent in power. So my short answer to your question is, "I don't know." If everyone who does not know the answer to a question posts a statement to that effect, we are overwhelmed with useless noise; therefore the convention is that only those who know (or, sigh, think they know) post — which in this case may be none of our regular readers. After a respectful amount of time with no response, it is acceptable to ask a followup question. A good followup: "Is there a problem with my question?" :-D --KSmrq^T 03:34, 11 April 2006 (UTC)

I believe the movable square is equivalent to neusis; I think, but am less certain, that the tomahawk is. I have no proof of either right now, which is why I haven't posted. Septentrionalis 03:55, 11 April 2006 (UTC)

(rolling eyes) Oh, that I should have asked mathematicians for opinions! "What color is that tree?" "It might appear to be some shade of green on the side that was visible at the time of obseveration." ;-) It really would be informative to hear a number of expert users say "I don't know."

It's okay. For the immediate, ugly, practical purpose of editing the project, it's enough that I think both are cases of neusis, Pmanderson suspects it, and nobody yet is ready to say they're not. That's enough information for me to proceed with my rounds. If an expert has more information later, well, we'll change it. Thank you. John Reid 18:22, 12 April 2006 (UTC)

Edit war over Jaina "mathematics"

Before I continue the edit war which has developed between "Jagged 85" and myself (with some others), I would like to bring the case to our community. Jagged 85 has been adding (what I consider) irrelevant material to several articles in the "Cardinal numbers" category (and I think elsewhere as well). I removed it once. Now he has put it back. This inspite of the fact that there is an already existing article on Indian mathematics to which he has been adding. See Talk:Cardinal number for more information. In my opinion, he is just cluttering up these articles and making them hard to read. There are no mathematical theorems or hard facts in his writing, just attempts to grab credit for the Jaina. JRSpriggs 03:20, 11 April 2006 (UTC)

Yeah, this is a bit of an ongoing problem, and not just about the Jains, but about ancient Indian mathematics in general. Jag, and maybe a couple of others, repeatedly make "anti-Eurocentric" claims that strike me as having a political axe to grind. See especially Kerala school#Possible transmission of Keralese mathematics to Europe, which consists mostly of speculation that European mathematicians could have learned of these claimed precedents and thus may not really have made their discoveries independently. Now, he does have lots of sources; my guess is that they have a political agenda as well, but that's speculation on my part, given that I haven't seen the sources. --Trovatore 04:03, 11 April 2006 (UTC)

A political agenda won't surprise me. I recall the dispute at Arabic numerals, which was moved to Hindu-Arabic numerals and back in total 12 times hist, and see also Talk:Arabic numerals. That not meaning to say that I have anything against India or its great contributions. Oleg Alexandrov (talk) 04:34, 11 April 2006 (UTC)

Long, long, long, long, LONG "stub" articles!

Please look at:

Template:Algebra-stub

I've deleted the "stub" notice from a few dozen of these. Please help. Click on one. If it's too long to be called a "stub", deleted the {{algebra-stub}} notice. Start at the bottom, since I started from the top, so the ones NOW near the top have been dealt with. Some are AMAZINGLY long articles, and are called "stubs". Others are fairly short and could use more material but are clearly too long to be called stubs.

Then we can go on to "geometry-stub", etc., etc., etc., etc.......... Michael Hardy 03:09, 12 April 2006 (UTC)

I've checked every article in the category [57]. --MarSch 11:59, 12 April 2006 (UTC)

Weisstein reliability (or not)

Debate is getting a bit heated at Wikipedia:Articles for deletion/Radical integer and Wikipedia talk:Articles for deletion/Radical integer, with one contributor arguing that it's not within our purview as editors, even if experts, to judge the reliability of anything written in Weisstein's encyclopedia, unless some other source directly contradicts it.

That idea strikes me as a recipe for disaster. Weisstein's work has so much overlap with our project, and is so full of idiosyncracies, that we have to view with caution any article on which he's the only source. If our hands are tied on this, the quality of WP math articles is at risk. Please come and state your views. --Trovatore 21:34, 13 April 2006 (UTC)

I think you're right, as knowledgable editors, we have to use some discretion about what sources are allowable for original material to be included; otherwise we will have to allow all kinds of crackpot material. However, I don't really see a need to take a hardline stance about Weisstein. We can also use our discretion about what of his meanderings should be allowed, which is why I haven't really entered into that debate. -lethe ^{talk +} 00:12, 14 April 2006 (UTC)

Oh, of course. I'm not saying we should automatically reject material just because it comes from him. I'm just saying it needs extra scrutiny when it comes only from him. More scrutiny than might be required with regard to sole-source material from a recognized specialist in whatever the subject matter is. --Trovatore 01:06, 14 April 2006 (UTC)

Well then we're in complete agreement. -lethe ^{talk +} 01:10, 14 April 2006 (UTC)

Also agree (on both points).--CSTAR 02:23, 14 April 2006 (UTC)

Soni's theorem

Has a trivial subject and I could not find any google hits. Should it stay? Oleg Alexandrov (talk) 04:10, 14 April 2006 (UTC)

I'd say no. --Trovatore 04:14, 14 April 2006 (UTC)

I couldn't find anything about it either --MarSch 11:47, 14 April 2006 (UTC)

I would say this article is a strong keep. It has been refined by another user, and I believe the content is much clearer now. This theorem is not trivial, it is like the Trivial Inequality (I don't know if non-mathematicians will understand that reference, so I will explain). This theorem is useful by itself, and not at all obvious. However, when combined with other things, such as De Moivre's, this can be incredibly useful. It should not be deleted for any reason. perhaps a more experienced mathematician can refine it... Mysmartmouth

I nominated it for deletion using the WP:PROD process. So, if nobody objects in 6 days, it will get speedy deleted. Oleg Alexandrov (talk) 20:42, 14 April 2006 (UTC)

Deprodded by author, listed on AfD by me. --Trovatore 23:01, 14 April 2006 (UTC)

Please add your comments to the AFD page.--Chan-Ho (Talk) 23:30, 14 April 2006 (UTC)

Help with matrix groups

I've been working on the matrix group page and need some help with the content. In particular I'm trying to summarize the types of classical groups but don't have the necessary background to do so. Some of the changes involve generalizing the definitions on other pages (such as unitary group) to arbitrary fields as well as possibly adding some pages (such as projective special orthogonal group).

I've put a summary of the changes I think would be helpful on Talk:Matrix_group. TooMuchMath 05:00, 14 April 2006 (UTC)

Update: The page is starting to come along, however we now have some redlinks if anyone wants to take a shot at them:

TooMuchMath 17:39, 21 April 2006 (UTC)

Well as you can see the links are no longer red and the classical groups portion of the page is looking pretty good. More contributions are welcome, of course! TooMuchMath 22:52, 24 April 2006 (UTC)

The links have become redirects, but have the target articles added the necessary discussions? For example, "projective special orthogonal group" redirects to "orthogonal group", but that article says nothing specific to support the redirect. --KSmrq^T 23:09, 24 April 2006 (UTC)

references for basic topics

Since we seem to be discussing references/sourcing so much recently.... can I ask what is the deal with references for all of our articles on more basic topics? For example, none of the following articles have any book/journal references: irreducible polynomial, normal subgroup, null space, vector space, affine scheme, group (mathematics), symmetric group, function composition. And there are plenty more, they're very easy to find. For such articles, sourcing would have two primary purposes: (1) historical information about where the concept first appeared, possibly in nascent form (this is hard because it involves genuine historical research), and (2) pedagogical, i.e. "where you can learn more about this idea". The second one is obviously problematic because in some cases there are many thousands of textbooks that cover the relevant material. On the other hand, sometimes I feel like there are some double standards going on in the background: for topics which all of us here know are important and standard, we don't require any sourcing, but things like "radical integer" make sparks fly.... Dmharvey 12:20, 14 April 2006 (UTC)

I certainly think that for basic subjects, referencing one or more modern textbooks on the subject would be really useful. For example, something like "An introduction for Undergraduates is given by 'Algebra' Splodgett and Madeup (Cambridge 2003). A textbook more suitable for postgraduates is 'Introduction to Algebra' Spurious and Fictitious (Springer Verlag 1998)." (I pick on Algebra because I was recently looking at [Elementary Algebra] and that has poor references (though I didn't know of a good one to use myself). There's no way that a wikipedia page, no matter how good, can teach a basic mathematical topic and therefore a textbook reference (and some insight into what level of student it would suit) would be very helpful. I realise this could possibly cause issues with people recommending their own books or particular favourite texts. --Richard Clegg 14:10, 14 April 2006 (UTC)

There are double standards and double standards; I think this double standard is absolutely rational and legitimate. I am unembarrassed to say I think we should have that double standard. Just the same, the point is well taken: While not as essential for topics we know about than those we don't, sourcing is still useful and the article isn't really complete until it's provided. --Trovatore 19:34, 14 April 2006 (UTC)

Well, sure, we should source things properly. If they aren't, then we shouldn't include it. On the other hand, we often give editors the benefit of the doubt. If there are no sources for something, then if the creator of the article is a known, respected contributor, not known for randomly inserting crazy crap into Wikipedia, then we give him/her time to find a source. I think it's perfectly fine to rely on the trust built among known contributors. In this case, it was a respected contributor Henrygb who had created the article, even giving a source. However, in this case, another respected contributor questioned the source, as upon investigation the source cited a mailing list which is not available for view and other searches through the usual methods, Google, MathSciNet, etc., were unable to find the term "radical integer". In this case, it's not applying a double standard to ask, "Should we allow this material?" It's natural and perfectly fine to engage in discussion, even amongst contributors who hold a great deal of trust for each other. Such discussion acts as a "reality check", making sure we don't get carried away and making sure we ultimately uphold the standards.

Even when the editor is an anon, we often give the benefit of the doubt, investigating how common the terminology is and whether the results are mentioned in some well-known resources. I'm even amazed at the lengths people sometimes take to investigate rather dubious-sounding claims, in the interest of completeness and fairness.

So I would say there is no double standard here. We often allow anyone to edit and insert material without citing, as if we didn't, we wouldn't gain a lot of content. On the other hand, to make sure we don't allow the crap to build up, we rely on trust of known contributors and also our expertise, e.g. "hey, this guy says some cubics can't be solved by radicals; that's not what I learned in undergrad algebra!" Eventually, though, we should be adding sources, and indeed some people are clearly going through articles and added citations where needed. So it's not accurate to say we don't require sources for some articles. --Chan-Ho (Talk) 20:18, 14 April 2006 (UTC)

Let's not mix apples and oranges. Sources for mainstream mathematical content act as enrichment, "See also". The content is not in dispute, perhaps with a few lunatic exceptions. Many of the algebra topics, for example, could cite Mac Lane and Birkhoff's Algebra (ISBN 0023743107), or van der Waerden, Moderne Algebra (ISBN 0387974245), or Artin's Algebra (ISBN 0130047635), or numerous other texts; and they should. In other cases, we have questions of proof, or notation, or history, or who-knows-what. It is not practical to referee every article like a journal paper, and even then many assertions are accepted without proof. We concentrate our demand for references on statements that raise suspicion. In principle, we should be able to defend "1+1=2", but in practice that level of citation would be absurd. --KSmrq^T 22:41, 14 April 2006 (UTC)

I would agree with KSmq. The rules for when a reference is not required (as I remember from high school) is if the information is "widely known" (which in high school meant that it was avaliable in three or more sources). "Moscow is the capital of Russia" would not need a citation for this reason. Even when we do run into problems with conflicting definitions ("St. Petersburg is the capital of Russia" was true for a time) citations aren't strictly required if both definitions are or have been widely used. In fact a discussion of the historical (or motivational) reasons for differing definitions is often more useful than a citation in these cases. A citation is required only when a definition is obscure. Aside from the academic integrity motivations for proper citation, this is particularly important on Wikipedia to ensure the "no original research" policy as well as to weed out the junk science. That said, a good reference or two can enrich the content substatially, so even for widely known topics it would be a good idea to add references. TooMuchMath 18:16, 15 April 2006 (UTC)

That's nicely put. This is the "rational double standard" I was advocating above. However I wouldn't formalize the "three sources" standard; I think the appropriate test is more whether an ordinarily prepared worker in the specialty would know the facts asserted. --Trovatore 19:26, 15 April 2006 (UTC)

OK, I agree with the bulk of what everyone's saying here, certainly I agree with the "rational double standard". I intended my comment to focus more on the educational usefulness of Wikipedia, rather than its veracity. In fact, if I had more time available now, I would consider trying to organise a "let's find book/pagenumber references for all those unreferenced basic topics articles" project, for the sole purpose of assisting those who are using Wikipedia as part of their mathematics studies. It's getting to a point now where an undergraduate and even a graduate student (like myself) can profitably use Wikipedia as their first stop when looking stuff up, and it would be incredibly helpful to have more pointers to denser sources of information. Unfortunately I don't have the time now. (nudge nudge wink wink) Dmharvey 19:47, 15 April 2006 (UTC)

This is a problem I have encountered when ever I nominate maths articles for Good Article status - they very often comment on teh lack of sources. The trouble is that many of the common topics (groups, vectors etc.) are written entirely of own knowledge, which means the source is out own knowledge hence the lack of physical references. That said, I think we should always list *some* references, if only to provide a place for readers to verify the info or find out more. Don't forget it says under any edit box that "Content must not violate any copyright and must be verifiable". Any book which know contains infomation for the article in question is suitable. Putting the article name in Amazon's search box often provides something suitable. (Although the references I list tend to come from the reading list for my uni's maths course). Tompw 20:01, 15 April 2006 (UTC)

PDE Surfaces

Copied from Talk:Mathematics --Salix alba (talk) 14:18, 15 April 2006 (UTC)

This seemed like the best place to get people's attention about the article PDE Surfaces, written by Zer0 cache. I suspect that it's promoting research, but I can't be sure. It would be appreciated if other editors can check this out. I've also left a small query at PDE surfaces talk page. MP (talk) 11:28, 11 April 2006 (UTC)

it seems fully referenced... hmm I guess Salix Alba fixed it already. --MarSch 17:43, 15 April 2006 (UTC)

Hm, what about the naming? I've already downcased it, but it didn't occur to me at the time that it would probably be more standard to move it to PDE surface, assuming there is such a thing as a PDE surface that makes sense in isolation from other PDE surfaces. On the other hand, if it's the description of a method rather than a kind of mathematical object, should it perhaps be method of PDE surfaces? --Trovatore 17:48, 15 April 2006 (UTC)

mathematics for AID

mathematics is curerntly going very well on Wikipedia:Article Improvement Drive. Maybe you want to vote for it --MarSch 18:13, 15 April 2006 (UTC)

debate over external link at Talk: Serge Lang

There's an extremely heated debate going on the talk page for Serge Lang between two editors, User: Revolver and User: Pjacobi. The issue is whether an external link to an article on the AIDS wiki (which was written by Revolver) should be allowed. I've just made my thoughts known there, and I also noticed that an RFC had been filed, but no comments had been made here (which is requested on the RFC page). --Chan-Ho (Talk) 04:18, 17 April 2006 (UTC)

Theorem 1

I nominated Theorem 1 for deletion. I tried using {{prod}} first but its author disagreed. Comments welcome. Oleg Alexandrov (talk) 03:55, 18 April 2006 (UTC)

Delete. The author says "There is a list, and this is #1." I'm not aware of any cosmic list of theorems. Now it does have something of a place of distinction -- postulate #4 of book 1 of Euclid's elements. But it isn't "theorem #1". Will there be a theorem #2? William Ackerman 17:16, 18 April 2006 (UTC)

There is no point in commenting here. To find the discussion, go to the article in question, and follow the link at the top of the page. --Trovatore 17:17, 18 April 2006 (UTC)

NPOV dispute at geostatistics, kriging, and spatial dependence

There is an NPOV dispute at the above articles: we need expert advice from statistician(s), especially those familiar with spatial statistics.

Briefly: User:JanWMerks claims that geostatistics is a scientific fraud, and has repeatedly edited these related articles to reflect that POV. Myself, User:Antandrus, and others were trying to point out Wikipedia rules, such as WP:NPOV, WP:VERIFY, and WP:NOR. Much edit warring ensued.

Now, the dispute (at spatial dependence) is over whether the F-test is a valid statistical test for spatial dependence. Also: several references (at geostatistics and kriging) are being used to support the claim that kriging is invalid, and I don't have easy access to a good library to check these references.

I hope that someone is willing to research the claims of invalidity better than I can, or perhaps simply provide a third opinion about the dispute.

Please feel free to visit Talk:Geostatistics, Talk:Kriging, and Talk:Spatial dependence to help out. Thanks!

-- hike395 17:40, 22 April 2006 (UTC)

cron vs hedron

I wonder if these two Greek suffixes mean the same or almost the same thing. Then, the following redirects may make sense:

Great dirhombicosidodecacron --------> Great dirhombicosidodecahedron
Great dodecahemicosacron --------> Great dodecahemicosahedron
Great dodecahemidodecacron --------> Great dodecahemidodecahedron
Great icosihemidodecacron --------> Great icosihemidodecahedron
Small dodecahemicosacron --------> Small dodecahemicosahedron
Small dodecahemidodecacron --------> Small dodecahemidodecahedron
Small icosihemidodecacron --------> Small icosihemidodecahedron

I stumbled into them at the Missing science project, and don't know what to do about them. Thanks. Oleg Alexandrov (talk) 18:55, 22 April 2006 (UTC)

I think the ones on the left are duals of the ones on the right or something. They should be given seperate articles. -- 127.*.*.1 20:33, 22 April 2006 (UTC)

Indeed the coverage of dual is week at the moment. I've mentioned this on Talk:Polyhedron. --Salix alba (talk) 22:39, 22 April 2006 (UTC)

Delete "Category:Continuum theory"?

This category called "Category:Continuum theory" is a subcategory of "Set theory" and of "General topology", but it contains no articles. Should it be deleted? How can I propose it for deletion? JRSpriggs 07:20, 26 April 2006 (UTC)

Wikipedia:Categories for deletion explains the deletion process. It might be applicable for speedy deletion. --Salix alba (talk) 07:34, 26 April 2006 (UTC)

Yup, WP:CSD says that empty categories can be speedied. I'm going to do it. This category defines a continuum as a compact connected metric space, which isn't right. The real line is not compact. -lethe ^{talk +} 07:56, 26 April 2006 (UTC)

Continuum has more than one meaning in mathematics. In continuum theory, which is related to dynamical systems, continuum does indeed mean what the category said. Perfectly cromulent articles which would have belonged in this category include pseudo-arc, indecomposable continuum and solenoid (mathematics). —Blotwell 14:49, 26 April 2006 (UTC)

Well, if the category had a correct definition, and also there are articles which could live in it, then the deletion was inappropriate. I will now undelete, and promise to be more careful when speedying things in the future. Thank you. -lethe ^{talk +} 20:34, 26 April 2006 (UTC)

Help requested at hyperbolic 3-manifold

An editor insists on removing red links as "cleanup". I think the participants here realize the importance of red links to this project (and Wikipedia in general). I'm puzzled why anyone would insist on removing them, but this editor has been quite stubborn, insisting that the articles *must* be created before links to them can be included in this article. --Chan-Ho (Talk) 00:41, 28 April 2006 (UTC)

I've made some comment's at the user's talk page (User talk:PHDrillSergeant); hopefully, this should be enough. --Chan-Ho (Talk) 01:01, 28 April 2006 (UTC)

Edward R. Dewey

A stock market "analyst" who sold a correspondence course on "cycle analysis".[58] This link includes a table of contents which I think makes clear how trivial Dewey's "system" is; please comment on Wikipedia:Articles for deletion/Edward R. Dewey. Septentrionalis 19:13, 28 April 2006 (UTC)

Should Radical integer be deleted?

A newly created article Radical integer has been listed for deletion. Should it be kept or deleted? Note that the article resolves a long-standing redlink in Algebraic integer listed on Wikipedia:Missing_science_topics/Maths8. Weigh in. Lambiam ^Talk 17:50, 9 April 2006 (UTC)

I'm the one who listed it for deletion, because the given source (MathWorld) looked hinky and in a quick search I couldn't find the term clearly and independently attested. I'm not a number theorist, so if it's not something one of Eric Weisstein's buddies just made up one day, by all means say so. --Trovatore 17:59, 9 April 2006 (UTC)

Someone somewhere has got to have a short name for Algrebraic integer expressible by radicals, but this doesn't seem to be it. Septentrionalis 22:33, 10 April 2006 (UTC)

Radical extension, extension by radicals, or (most common, I think) pure extension is standard, and radical number I think I've seen. Radical integer is logical and has a MathWorld article to go with it, which speaks in its favor. It seems to me that all of this should be discussed somewhere in an article on solvable extensions, but I can't find any such article. Should I write one? I don't want people deleting it if I do. Gene Ward Smith 21:25, 13 May 2006 (UTC)

Let me summarize the history as I see it:

The article radical integer was sourced only to MathWorld and all the Google hits seemed to trace back there. So I nominated it for deletion as one of Eric Weisstein's neologisms (as you'll have gathered, I don't think the existence of a MathWorld article speaks particularly well in favor of it; it's not a strike against it per se, but certainly not enough support for an article by itself).
During the discussion it emerged that there was more than a not-so-interesting definition involved, but rather an actual putative theorem, which (if true) goes as follows: Consider all numbers that can be expressed by starting with the naturals and closing under addition, multiplication, subtraction, division, and extraction of natural-number roots. Intersect that class with the algebraic integers. Then any number in the intersection can be expressed by starting with the naturals and closing under the previous operations, without division.
That theorem, if it is one (which I think it probably is), is very interesting, and clearly justifies the creation of a term for an element of the class. Unfortunately at the current time the theorem cannot be sourced, except to MathWorld, which IMO is not reliable. Moreover I think it's a reasonable principle that sources for putative theorems ought to point the reader to an actual proof, and the MathWorld source does not do that. --Trovatore 17:26, 25 May 2006 (UTC)

It might be posible to get a better source, the theorem was discussed on the math-fun mailing list, which I presume is on the web somewhere. In an email to me Rich Schroeppel said he would try to dig up the archive when the tax season was over. If anyone is interested this would be great to follow through. --Salix alba (talk) 17:35, 25 May 2006 (UTC)

Oh, one more small point: What I said about "sourced only to MathWorld" is not strictly true; I'm including Weisstein's encyclopedia of math as part of MathWorld. With that addendum it's true. --Trovatore 17:35, 25 May 2006 (UTC)

It seems to me if I understand the claim that Schroeppel's theorem is too trivial to use as a reason for an article. If μ is an algebraic integer, then it has a monic polynomial, and expressing it as a root expresses it without division. Expanding on that, the ring of integers in any number field has an integral basis; it can be written as c₁ μ₁ + ... + c_n μ_n, where the c's are ordinary integers and the μs are algebraic integers in the field, so in terms of this basis everything in the ring of integers is precisely everything which can be expressed without division.

So, what exactly is the statement of this theorem? Gene Ward Smith 19:47, 25 May 2006 (UTC)

I think I've already stated it exactly; here's the example that came up as to why it's not trivial. The golden ratio is a root of x²−x−1=0, so it's an algebraic integer. It's also obtainable from the naturals by iterating the operations listed, including division, as

$\frac{1+\sqrt{5}}{2}$

However it's not immediately obvious that you can get it from the naturals by iterating the operations not including division. But you can. It's

$\sqrt[3]{2+\sqrt{5}}$

(Thanks to Lambiam for that representation.) Unless I've misunderstood it, the argument you give does not prove this. --Trovatore 19:55, 25 May 2006 (UTC)

Here's a sketch of an almost-proof. "Almost" because I'm left with a denominator of at most 2.

Let S be those numbers obtainable from the natural numbers by addition, subtraction, multiplication, division, positive integer roots. (I want to call this the maximal radical extension of Q, but I'm slightly concerned about roots of unity. Never mind.) Let R be the "radical integers", i.e those numbers obtainable from naturals by addition, subtraction, multiplication, and positive integer roots (but not allowing division). First I claim that any x in S is of the form y/d for some y in R and some integer d. This is done by induction on the structure of x. Clearly addition, subtraction, multiplication pose no problems. Integer roots also fine (i.e. $(y / d) 1 / n = y 1 / n d (n - 1) / n / d)$ ). Division is slightly more troublesome, you need some kind of "rationalising the denominator" trick.

So now suppose we have x = y/d as above, and suppose further that x is an algebraic integer; we want to prove that x is itself a radical integer. Let K = Q(y), and let O be the ring of integers of K, so x is in O. As Gene pointed out above, O has a finite Z-basis, and the basis elements are polynomials in y with coefficients in Q, so for a large enough integer m we find that mO consists entirely of radical integers. Split m into a product of powers of prime ideals in O, say $m = \prod_P P^{r_P}$ . By looking at the rings $O/P^{r_P}$ , we can find some large integer n such that xⁿ is congruent to either 0 or 1 modulo each $P^{r_P}$ . Then $x 2 n - x n$ is in mO, so is a radical integer, say z. Then we have $x = \left(\frac{1\pm\sqrt z}2\right)^{1/n} = \frac{2^{(n-1)/n}(1+\sqrt z)^{1/n}}2$ , which is a radical integer possibly divided by 2.

Anyone buy that? Getting rid of that last 2 seems a little problematic. Dmharvey 00:26, 26 May 2006 (UTC)

Oh yeah, by the way you can apply that proof to the golden ratio case quite easily. We already have $x = \frac{1+\sqrt5}2$ presented in the right form. Let O be the ring of integers of $\mathbf Q(\sqrt 5)$ . Then the ideal (2) is inert in O because the polynomial

x 2 - x - 1

is irreducible mod 2. So the quotient O/2 is GF(4), so cubes of anything nonzero are congruent to 1. So

x 3 - 1

is in 2O, so is a radical integer. And indeed $\left(\frac{1+\sqrt5}2\right)^3 - 1 = (1 + \sqrt 5)$ is twice an algebraic integer, so must be a radical integer, which is I suppose where Lambian's formula comes from :-) Dmharvey 00:33, 26 May 2006 (UTC)

OK, here's the rest of the proof to handle that annoying factor of 2. You need to treat the residue characteristic 2 a little carefully.

Again suppose x = y/d where x is an algebraic integer. Let $\theta = (1+\sqrt 5)/2$ be the golden ratio. Consider the extension $K = \mathbf Q(y, \theta)$ , let O be its ring of integers. Again we can find some m so that mO consists entirely of radical integers. Consider all prime ideals P of O of residual characteristic 2, suppose their multiplicites in m are given by r_P. Take some high power of x, call it x₂, which is = 0 or 1 modulo each $P^{r_P}$ . Then x₂ + θ is not in any

P

, because θ is not 0 or 1 modulo 2 (i.e. neither θ nor θ−1 is twice an algebraic integer). So some high power of x₂+θ, let's call it x₃, is congruent to 1 modulo every $P^{r_P}$ . Then x₃−1 is = 0 modulo every $P^{r_P}$ . Now consider all the other primes Q of various other residue characteristics, which have multiplicities

r Q

in m. Then some high power of x₃−1, let's call it x₄, is either 0 or 1 modulo each $Q^{r_Q}$ , and is still 0 modulo every $P^{r_P}$ . Now look at x₄+1; it's either 1 or 2 modulo each $Q^{r_Q}$ , and it's 1 modulo each $P^{r_P}$ . Since the residue characteristics of the Q are not 2, some high power of x₄+1, say x₅, is 1 modulo all of the $Q^{r_Q}$ and all of the $P^{r_P}$ . So x₅−1 is in mO, and therefore a radical integer. If you unroll your way through x₅, x₄, x₃, x₂, back to x itself, you get that x is a radical integer. Whew! Dmharvey 02:48, 26 May 2006 (UTC)

Applause. Now get that published in the Journal of Number Theory and we can write an article about it :) --Lambiam ^Talk 16:21, 26 May 2006 (UTC)

Update on the lists of missing math topics

The lists at Wikipedia:Missing science topics#Mathematics now contain entries from MathWorld, Springer Encyclopaedia of Mathematics, Charles Matthews' maths lists (thanks Charles!), St Andrew's, and PlanetMath. There are 15465 redlinks and 9700 bluelinks (in separate lists), which is a progress of 38.55% towards eliminating the redlinks. For many redlinks it is likely that the information exists on Wikipedia but under a different name, so creating redirects is a good way to advance that project forward. The harvest is great and the workmen are few[59] (since it's Easter today :) Oleg Alexandrov (talk) 22:21, 16 April 2006 (UTC)

And I finally got permission from Springer to use their lists in our project. Oleg Alexandrov (talk) 03:25, 25 April 2006 (UTC)

Really? That's very generous of them, I didn't think they would. I think mathworld wasn't willing. Neat! -lethe ^{talk +} 03:32, 25 April 2006 (UTC)

If Mathworld was not willing, how come the Wikipedia:Missing science topics was created to start with? Before I got there, all the math entries from there were copied from MathWorld, all the way to incomplete entries, like Archimedean Spiral Inv.... Oleg Alexandrov (talk) 03:37, 25 April 2006 (UTC)

I seem to recall a discussion here on the wikiproject talk page, where someone created a carbon copy of the mathworld index of topics, and someone emailed them, and they indicated that it was indeed a violation of their copyright. In fact, my recollection is that you were in this converation, though I could be mistaken. Anyway, I don't know where the content of Wikipedia:Missing science topics comes from, but unless I'm misremembering something, to have their index is a copyright violation. I guess I should see if I can find that old conversation. -lethe ^{talk +} 07:37, 1 May 2006 (UTC)

That's really good news. I'm not so surprised though, that Springer was willing but MathWorld not. There are people at Springer that are truly committed to what they're doing and I've seen Springer do things that strictly speaking, they did not need to do. --Chan-Ho (Talk) 07:27, 1 May 2006 (UTC)

listing variable names after formulas

I wonder what people think of these multiply-indented lists to define all the variables that appear in a formula. An example is found here. It is claimed that this format is somewhat standard here at wikipedia and is found in hundreds of articles, but I've never seen it, and furthermore don't really like it, I prefer instead a regularly indented paragraph of text. What are your opinions of this format? -lethe ^{talk +} 00:52, 22 April 2006 (UTC)

It takes too much space. -- 127.*.*.1 03:26, 22 April 2006 (UTC)

Yes, that is quite an unfortunate presentation style. A simple paragraph of explanation would be much better. — merge 08:07, 22 April 2006 (UTC)

From a dyslexic point of view I have problems parsing large blocks of text and tend to find lists easier to read. I had a play about with a more compact format using tables. Compare

The Schrödinger equation is:	i	the imaginary unit,
	t	time,
$H(t) \left\| \psi (t) \right\rangle = i \hbar {\partial\over\partial t} \left\| \psi (t) \right\rangle\qquad$	${\partial\over\partial t}$	the partial derivative with respect to t,
	$\hbar$	reduced Planck's constant (Planck's constant divided by 2π),
	$ψ(t)$
	H(t)	the Hamiltonian - a self-adjoint operator acting on the state space.

The Schrödinger equation is:

$H(t) \left| \psi (t) \right\rangle = i \hbar {\partial\over\partial t} \left| \psi (t) \right\rangle\qquad$

where i is the imaginary unit, t is time, ${\partial\over\partial t}$ is the partial derivative with respect to t, $\hbar$ is the reduced Planck's constant (Planck's constant divided by 2π),

ψ(t)

is ...., H(t) is the Hamiltonian - a self-adjoint operator acting on the state space.

--Salix alba (talk) 09:27, 22 April 2006 (UTC)

If a list seems necessary, why not use a list?

The Schrödinger equation is:

$H(t) \left| \psi (t) \right\rangle = i \hbar {\partial\over\partial t} \left| \psi (t) \right\rangle\qquad$ ,

where:

i is the imaginary unit
t is time
${\partial\over\partial t}$ is the partial derivative with respect to t
$\hbar$ is the reduced Planck's constant (Planck's constant divided by 2π)
$ψ(t)$ is ....
and H(t) is the Hamiltonian - a self-adjoint operator acting on the state space.

— merge 09:42, 22 April 2006 (UTC)

I wonder if those explanations of the symbols make this equation any more comprehensible to someone not familiar with the notation. If you don't know what the symbol is for partial differentiation then IMO it is very likely that you don't know what partial differentiation is and the same goes for the imaginary unit.--MarSch 09:55, 24 April 2006 (UTC)

I don't think it's necessary to explain certain things, such as the imaginary unit, time, or the partial derivative. Articles assume some basic knowledge, so we should rely on this (however, we should clearly attempt to make the number of assumptions as smallest as sensibly possible). Dysprosia 10:05, 24 April 2006 (UTC)

The Schrödinger equation is:

$H(t) \left| \psi (t) \right\rangle = i \hbar {\partial\over\partial t} \left| \psi (t) \right\rangle\qquad$

where H is the Hamiltonian, ψ is the state and t is time,

but even better is probably

A physical system with Hamiltonian H and initial state vector ψ₀ can be described at time t by the state vector ψ(t) which is a solution of the initial condition ψ(0) = ψ₀ and the differential equation called the Schrodinger equation

$H(t) \psi (t) = i \hbar {\partial\over\partial t} \psi (t)$

--MarSch 10:09, 24 April 2006 (UTC)

I'm in favor of lists for equations. The main reason is that I don't like to read the whole article - and lists of variables show a clear spot where I can find all the information I need. This is of course provided that its written properly. If the variables in the equation are fully clear, then theres no need. However, in the case of the schrodinger equation, almost none of the variables and symbols are familiar to most people. Also, most always, all variables do need description. Leaving out variables leaves the equation incomplete, and even a reader who assumes the right meaning might question himself, and end up having to double check the formula somewhere else. Stuff like simple operators probably don't need explaining, but I've found a good compromise in that respect to define the derivative of something rather than the dervative operator (for example: "dp/dt is the instantaneous rate of change of the momentum").

Another main consideration is consistancy. If equations are written in 5 or more different forms, users will have a harder time sorting through the formats to find what they need. Almost always, variables are written below the equation, and when they're not - I find it difficult to follow. The list format makes it easy to find the perhaps one or two variables you don't know, and refer back to it without losing your place.

We as editors should consider that wikipedia isn't only used by people wanting an in depth overview of a subject, but may also want a quick reference. Articles that distinguish different parts of the article (like equations, subject headers, examples vs generalities) are much easier to read and use. The faster a reader can find the information they are looking for is (in my opinion) far more important than making the page compact. Fresheneesz 07:25, 2 May 2006 (UTC)

AFD - How to get the prime factors of a number

I have nominated How to get the prime factors of a number for deletion. Comments welcome. -- Meni Rosenfeld (talk) 16:46, 26 April 2006 (UTC)

It seems like useful information, although it could be better written. Is this info in some other article? If not, maybe the article should stand. PAR 16:58, 26 April 2006 (UTC)

Please take comments on the merits to the AfD page. --Trovatore 17:04, 26 April 2006 (UTC)

Deleted. -lethe ^{talk +} 05:17, 1 May 2006 (UTC)

May 2006

This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

"Tone", pronoun use, etc. in math articles

The other day, I left a pretty extensive comment on Talk:Knot theory, in response to two editors who complained about the article's tone. One specific complaint was the use of pronouns and that the article sounded like a teachger giving a lesson. Now, I just noticed that Braid group has been tagged (by someone else) with a "tone" tag, and the talk page mentions for example, that the use of "we" is bad and that it sounds too much like a "math lesson instead of an encyclopedia".

My thought is that while some of the pronoun use could be favorably excised, I am definitely starting to get the feeling (especially after examining the articles in question) that these particular editors do not understand the conventions in mathematical writing, e.g. "We consider blah as doing blah..." is ok. They also may not understand that sometimes a procedural description should be given, e.g. "take such and such and do such and such...". See my long comment linked above. I would like to know what those who normally work on mathematics articles think about all this, so please drop by those pages and make some comments. --Chan-Ho (Talk) 03:58, 1 May 2006 (UTC)

We is pretty much mathematical jargon; one is better for the general reader. Charles Matthews 11:45, 1 May 2006 (UTC)

I believe the passive is the preferred thingy. "We consider..." becomes "... is considered". --MarSch 14:08, 1 May 2006 (UTC)

But then... "is considered", er, by whom? By a deity? (Igny 15:33, 1 May 2006 (UTC))

This reflects a certain diference about using We. In a statement like We can deform a knot in 4D it can easily be rewitten as a knot can be deformed in 4D and the prounoun can easily be dropped. However We consider... are subjective statments and in a paper the we is used to indicate the opinion of the authors. In wikipedia such subjective statements need appropriate qualification most mathematicians consider 4D knots to be very boring. --Salix alba (talk) 19:04, 1 May 2006 (UTC)

I've responded where requested; see for details. Passive is not preferred; just the opposite. Overuse of "one" also makes reading drag. Technical writing has a tradition of such conventions, not to its credit. --KSmrq^T 19:15, 1 May 2006 (UTC)

A MIT style guide says to use "we" in the active voice. I see now that I was mistaken in thinking it too personal, and yes, I did not understand mathematical writing conventions as pointed out by Chan. I will try to not be an ignoramus in the future. --Reader12 03:57, 2 May 2006 (UTC)

Well, you live and learn! I tried to carefully explain how the situation appeared to me without being patronizing or rude; I hope you weren't offended. At any rate, I think it's been a very fruitful discussion thus far with a variety of people voicing their thoughts and it's still ongoing! --Chan-Ho (Talk) 08:08, 2 May 2006 (UTC)

No, no offense taken. This has been very instructive to me. Thanks! --Reader12 21:40, 2 May 2006 (UTC)

I've just come across a great book on Algebraic topology by Allen Hatcher which can be downloaded [60]. To my mind he has a very good writing style, which avoids the problems of overly technical writing, whilst still being technically correct. I fell there is quite a bit which could be learnt by examining how he structures his writing. I think a lot of illustrations help, the sub project /Graphics has reciently been set up to try to improve the illustrations of the maths articles. --Salix alba (talk) 09:21, 2 May 2006 (UTC)

Naming: "fixed-point" vs "fixed point"

Several articles are named inconsistently. I prefer "fixed point". Any opinions? Post here or at Category talk: Fixed points. Staecker 21:18, 1 May 2006 (UTC)

It's my experience that "fixed point" is way more common in the literature, so we should stick with that.--Deville (Talk) 22:25, 1 May 2006 (UTC)

Not so fast; there's a grammatical distinction. As a noun phrase, we would write the "fixed point" of a recursive function, without the hyphen. But as an adjective, we often write "fixed-point" thingy, with the hyphen. In the case of theorem names, the former applies, as in "Brouwer fixed point theorem". And what about "Kleene fixpoint theorem"? It should redirect. --KSmrq^T 22:59, 1 May 2006 (UTC)

I don't mind making the distinction, but I don't think I understand as you've stated it. In "Brouwer FP Theorem," it sounds like an adjective phrase to me (modifying "theorem"). Is this an exception? When would the hyphen be appropriate? Something like "fixed-point set"? That sounds like an adjective phrase to me, but I never write it that way myself. Come to think of it, I don't ever use the dash regardless of context. (Except when I have to link to Lefschetz fixed-point theorem) Staecker 23:19, 1 May 2006 (UTC)

You want me to explain why punctuation conventions make sense?! I wish. I can say that I would never hyphenate in a situation like "Every rotation has a fixed point." The article on hyphen discusses some common rules. So why not "Brouwer fixed-point theorem"? I suppose because it's a ritual thing, with "theorem" doing the modifying. Or it's an example of the general guideline that hyphens are for clarity, and if we don't need them we don't use them. The still more general guideline is to tread carefully in this territory, and don't rush to accuse anyone of doing it wrong just because their choice is not yours. (But you knew that already, yes?) --KSmrq^T 02:47, 2 May 2006 (UTC)

My usage would be like KSmrq's. The underlying reason may be that a "fixed-point set" is a set which consists of fixed points (or is a fixed point, if you're doing category theory); but a "fixed point theorem" is a theorem about fixed points: a more distant relationship, analogous to the difference between mathematics and metamathematics. Septentrionalis 18:58, 5 May 2006 (UTC)

Are you sure there's an inconsistency? A fixed-point theorem (with a hyphen) asserts the existence of a fixed point (with no hyphen), and it is completely appropriate to use a hyphen in one case and not in the other, because of the difference in the way the phrase is being used. That is not an inconsistency. Michael Hardy 20:09, 5 May 2006 (UTC)

hyphens generally

By the traditional conventions concerning hyphens,

A man-eating shark (with a hyphen) scares people away from beaches, whereas
A man eating shark (with no hyphen) is a customer is a seafood restaurant.

The traditional usage is still followed by nearly all newspapers and magazines and in novels, and people are accustomed to seeing it. But many educated people, including many authors of scholarly papers and books no longer follow the traditional rule. I've tended to be conservative about it and I moved the Wikipedia article titled "light emitting diode" (with no hyphen) to light-emitting diode (with a hyphen) and have done the same with various other articles. I think in some cases, the hyphen is a magnificently efficient disambiguation device. Michael Hardy 20:14, 5 May 2006 (UTC)

Nice example, copied from hyphen:

semantic changes caused by the placement of hyphens:

Disease causing poor nutrition, meaning a disease that causes poor nutrition, and
Disease-causing poor nutrition, meaning poor nutrition that causes disease.

Michael Hardy 20:18, 5 May 2006 (UTC)

A fixed point theorem is a point theorem that was found to contain an error, which now has been repaired. Lambiam ^Talk 21:13, 6 May 2006 (UTC)

Blahtex and wikimania

The poster deadline for wikimania is fast approaching. I think it would be really good if we could have some presence there as a step to getting meta:Blahtex integrated into the main encyclopedia sites. Neither User:Dmharvey or myself are able to attend, but posters can be submitted without having a physical presence. Questions: is anyone here planning to go to wikimania Aug 4-6, in Cambridge MA? Anyone happy to spend some time standing next to a Blahtex poster? For those who don't know Blahtex is a extension which converts LaTeX maths into the MathML XML markup which allows for improved rendering of mathematics in MediaWiki with moder browsers. --Salix alba (talk) 10:05, 2 May 2006 (UTC)

Bogus AfD of proof article

Loom91 has been goaded by Melchoir into nominating "Proof that 0.999... equals 1" for deletion, on the grounds that Wikipedia should not contain proofs like this. The archives of sci.math currently show well over a thousand postings related to this topic, which is therefore included in the sci.math FAQ; yet it appears that Wikipedia covers the topic far better. Those who are interested can register an opinion here. Caution: This topic (and perhaps this vote) attracts, um, non-standard thinkers, to put it delicately. (See the talk page archives for examples ad nauseam.) --KSmrq^T 10:31, 5 May 2006 (UTC)

Yeah, I feel bad about that; sorry, everyone! (In my defense, though, I did try to explain why the AfD would fail, after which I didn't think Loom91 would actually go through with it.) Well, at least it's attracting some fresh constructive attention, and it'll be useful to have on record. Melchoir 20:09, 5 May 2006 (UTC)

By the way, in case anyone hasn't seen it yet, the AfD closed with a keep. Melchoir 22:58, 5 May 2006 (UTC)

That's a understatement; it closed with a speedy keep, with overwhelming support and complaints about the nomination as violating WP:POINT. --KSmrq^T 22:31, 6 May 2006 (UTC)

Rewrite of Mode (statistics)

I rewrote the article Mode (statistics). Please review and correct errors, rewrite awkward sentences, simplify, embellish, supply sources, etc. It would further be nice to have some illustrations, both for a continuous density function and a histogram. Lambiam ^Talk 20:40, 5 May 2006 (UTC)

AfD for List of Mathematical Formulas

Should this be kept, deleted, merged, or should there be a category of "mathematical formulas"? (I wonder what the morphisms would be.) Visit Wikipedia:Articles for deletion/List of Mathematical Formulas and contribute your two cents. Lambiam ^Talk 21:04, 6 May 2006 (UTC)

As far as I can see, the chemists don't need Category:Formulas. We might not need it either, though. Charles Matthews 19:09, 7 May 2006 (UTC)

WAREL back?

See [61]. I don't read Japanese so I can't tell if the change is correct, but it's exactly the type of change we might expect from WAREL if he came back. --Trovatore 15:24, 10 May 2006 (UTC)

OK, I hate machine translation but it has its points. He changed the article to point to a nonexistent article on ja.wiki, called "Commutative field". It's WAREL alright; please block him with all deliberate speed. --Trovatore 15:41, 10 May 2006 (UTC)

KLIP (talk • contribs) blocked. -lethe ^{talk +} 17:20, 10 May 2006 (UTC)

James Stewart

Just created the page on Stewart, James Stewart (mathematician), your contributions would be most appreciated.--Jersey Devil 09:08, 11 May 2006 (UTC)

TeX font size

There is a discussion at the Village pump that might interest a few people here. —Ruud 01:09, 12 May 2006 (UTC)

Koszul-Tate

Is there anybody here interested in tackling the Koszul-Tate derivation topic listed on the "wikipedia:Articles requested for more than two years"? Thank you. — RJH 15:45, 12 May 2006 (UTC)

WAREL

is back again at Field (mathematics). --Trovatore 02:39, 13 May 2006 (UTC)

JLISP (talk • contribs). -lethe ^{talk +}

Zeration

Can someone please review zeration? Thanks. Samw 03:28, 13 May 2006 (UTC)

I'd give it thumbs down, in regard the Δ numbers. That is just wrong, even if referenced in the paper. The rest is more-or-less accurate, although I believe it falis WP:N.

As for hyperexponentials, my first paper (in 1966) references an earlier paper by Donner and Tarski which discusses hyperexponentials on the ordinal numbers. I doubt the primacy of the 1987 paper. — Arthur Rubin | (talk) 04:29, 13 May 2006 (UTC)

Referencing something from 2004 makes it a bit young and possibly fails "established research". Dysprosia 08:44, 13 May 2006 (UTC)

Duly sent to AfD, see Wikipedia:Articles for deletion/Zeration. -- Jitse Niesen (talk) 08:47, 13 May 2006 (UTC)

Spanish category

I wrote the following on Category talk:Mathematics; copying here.

An anon recently changed the Spanish link to es:Categoría:Matemática from es:Categoría:Matemáticas, or perhaps the other way around. It seems that both categories exist and are populated. Would someone whose Spanish is better than mine like to go tell them? I don't know how they handle these things over there; I think things like {{cfm}} are set up language-by-language. --Trovatore 14:54, 13 May 2006 (UTC)

It looks like es:Categoría:Matemática was created just today, by one es:Usuario:Ingenioso Hidalgo, who then took it upon himself to go around recatting over a hundred articles, then apparently got tired. Unless this was discussed somewhere this doesn't strike me as good behavior; someone should let them know. I don't know if they have any equivalent to WikiProject Mathematics. --Trovatore 15:21, 13 May 2006 (UTC)

On second thought, I suppose someone will notice, as the recats will surely show up on some watchlists. --Trovatore 15:35, 13 May 2006 (UTC)

P-adic numbers

There is a discussion on decimal-style notation for p-adic numbers, and what would be appropriate to use, on the talk page Talk:P-adic number which we would like comments on. I added a section which uses a notation which is unusual but not unprecedented, in the section intended to convey the intuitive idea of a p-adic number. It seems to me the notation I used does that more successfully than any alternative for people used to decimal notation. Gene Ward Smith 21:14, 13 May 2006 (UTC)

Real number

User:Oleg Alexandrov seems to me to be engaging in abusive reverts on this page, to a previous verison which is arguably incorrect mathematically and which removes a lot of new material, material for which he has given no argument for removal. He also says, falsely, that my attempt to satisfy his previous criticims amounted to "writing a one-liner" which seems to prove he hasn't even seriously looked at the version he is reverting from. I think we need other people to weigh in at this point. I am very much opposed to simply allowing it to say the real numbers have a number line and calling that a definition. My proposal to say they have a number line, with no "room" to fit additional numbers in, is an attempt to make the one-line introduction correspond to an actual rigorous definition, which will not be the case if we allow Oleg's revert. Gene Ward Smith 22:32, 13 May 2006 (UTC)

Comments at talk:real number are encouraged. My version of things is that Gene is convinced enough that he is right that he is prefers repeatedly reverting to his version to discussing things on the talk page. Oleg Alexandrov (talk) 22:51, 13 May 2006 (UTC)

I think you need to take your own advice; your reckless reversion was done without any discussion. Gene Ward Smith 23:28, 13 May 2006 (UTC)

Regardless of who did what, there is a discussion running at the talk page now. Please engage yourselves there. -- 127.*.*.1 23:35, 13 May 2006 (UTC)

Islamic mathematics

User:CltFn has proposed to move Islamic mathematics to Middle-Eastern mathematics. Please comment at the talk page. —Ruud 02:36, 15 May 2006 (UTC)

A typesetting subtlety

See if you can spot the difference between this:

$a+b+c+d\,$

$+e+f+g+h\,$

and this:

$a+b+c+d\,$

${}+e+f+g+h\,$

without looking at the TeX code, and guess how and—perhaps more subtly—why the difference was achieved.

I think perhaps this should be borne in mind in editing math articles. Michael Hardy 02:37, 15 May 2006 (UTC)

This is presumably because TeX does not apply its operator spacing rules in the first case, while since you've forced an empty group in the second, it does. Preferrably if you're continuing a sum onto two lines, one would add a \quad of space in the second or add a text indent (via a ":"), instead of relying on empty groups. Dysprosia 03:02, 15 May 2006 (UTC)

Sadly, I spotted the difference instantly, and even knew exactly where to look. This has been with TeX for decades, and Knuth explicitly calls attention to it in The TeXbook (ISBN 0201134489, p. 196). You'd never guess he was the type to pay extraordinary attention to detail, now would you? ;-D

"An extra ‘{}’ was typed on the second line here so that TeX would know that the ‘+’ is a binary operation."

The difference is a consequence of the operator handling rules. --KSmrq^T 04:27, 15 May 2006 (UTC)

Personally, I never noticed this until recently. I once asked Donald Knuth why he had issued an infallible pontifical decree about minute details of the design of the lower-case letter delta. He said it's because the design he prescribed was just obviously the right one. Anyway, in non-TeX mathematical notation, I've been something of a stickler about proper spacing with binary operations and binary relations, thinking all the while that there's no need to think about that in TeX, but in cases like this, there is. Michael Hardy 23:55, 15 May 2006 (UTC)

Dysprosia: How does a text indent via an initial colon achieve this result? It only adds space to the LEFT of "+". Michael Hardy 23:57, 15 May 2006 (UTC)

I wasn't exactly precise in what I was meaning above -- what I meant is that if one wants to continue a sum on two lines, one should add space to the left somehow, instead of keeping both lines of the sum aligned, for example

$a+b+c+d\,$

${}+e+f+g+h\,$

as opposed to

$a+b+c+d\,$

${}+e+f+g+h\,$

I probably should have added "and keeping the same indent" to the end of my comment. It's a shame that the TeX system in use here ignores initial spacing via quads and such. Dysprosia 08:46, 16 May 2006 (UTC)

Math error right on this page?

On this page there is a box telling us that hyperreal numbers, superreal numbers, and surreal numbers are "complex extensions"; in fact, they are all real closed fields. Gene Ward Smith 04:34, 15 May 2006 (UTC)

Zero-eigenvalue bifurcation

Could someone take a look at zero-eigenvalue bifurcation? It is proposed for deletion, but it do find some uses of this term on google scholar. —Ruud 00:17, 16 May 2006 (UTC)

The deletion, rather than redirection, seems summary and not necessary. Charles Matthews 11:03, 20 May 2006 (UTC)

I agreed with the deletion because I think that the term "zero-eigenvalue bifurcation" is hardly used by itself (in constract to more complicated phenomena like the "double zero-eigenvalue bifurcation", used as a synonym for "Bogdanov-Takens bifurcation"). But if you want to create a redirect, be my guest. -- Jitse Niesen (talk) 13:07, 20 May 2006 (UTC)

p-adic numbers notation

A debate is in progress at Talk:P-adic number about whether p-adic numbers should be written from right to left or from left to right. The article used to use the right-to-left notation, but was recently rewritten with the left-to-right notation. Contributions to the debate from a wider pool of wiki mathematicians would be helpful, to see if we can reach a concensus. Gandalf61 08:21, 16 May 2006 (UTC)

Okay, after some discussion on its talk page, I have now changed the p-adic number article to consistently use the right-to-left notation, but with a new section that mentions other alternative notations. Any comments on the partial re-write are welcome at Talk:P-adic number. Gandalf61 09:34, 26 May 2006 (UTC)

Moore closure

I propose to delete the bits about Moore closure in the article Kuratowski closure axioms; see Talk:Kuratowski closure axioms#Moore closure. --Lambiam ^Talk 09:05, 16 May 2006 (UTC)

Fine topology (suggestion needed for better name)

I have created a new page on fine topology (as in classical potential theory), but as the title "fine topology" already seems to be taken by a page about general topology (i.e. 'finer topology' rather than "THE fine topology"), I have called my page "classical fine topology" - seems like there ought to be a better solution - any ideas? —The preceding unsigned comment was added by Madmath789 (talk • contribs) .

(Copied from my talk page, I don't have a good answer to this. Oleg Alexandrov (talk) 23:30, 16 May 2006 (UTC))

Call the page Fine topology (potential theory) and use a

{{dablink|[[Fine topology]] redirects here. For the use in potential theory, see [[Fine topology (potential theory)]]}}

at the top of Comparison of topologies? Kusma (討論) 23:43, 16 May 2006 (UTC)

Thanks for that suggestion - I have renamed the page. In a similar vein, I am tempted to write 2-3 articles on the subject of 'thin sets' and 'polar sets' (as used in potential theory, subharmonic functions etc.) and find that these terms also link to pages mainly about set theory. Would it be sensible to call my new pages 'thin sets (potential theory)' etc. What do more experienced wikipedians think? Madmath789 10:10, 17 May 2006 (UTC)

Nothing links to Fine topology, so it might be better to turn this into a disambiguation page rather than redirect to Comparison of topologies, thereby avoiding an awkward disambiguation phrase in Comparison of topologies. Nothing links to Thin set either. --Lambiam ^Talk 11:07, 17 May 2006 (UTC)

Idea: when user clicks on an equation wikipedia explains it

Sorry if this is the wrong place / its already been suggested (I searched :-\), please direct me to the right place if here is incorrect (or tell me its not a worthwhile idea if you think so). This is a suggestion that when a equation is displayed (for example the one on this page) the user can click on the equation and is taken to a special page that explains the contents of the equation and what it means.

OK, let's try it:

UNIQ1603f57c73b030b5-math-0000D758-QINU

Weird! What I see is this:

UNIQ5f19c7bc44ccc704-math2f6e29f1133d184200000001

What I "should" see is this:

$\int_0^\infty 1\,dx.$

When I click on it, it takes me to the right place.

Is this browser-dependent? Michael Hardy 01:50, 20 May 2006 (UTC)

You are seeing artifacts of one of the intermediate interpretation passes that mediawiki does during math markup. When all goes well (e.g. properly formed or properly messed up math syntax) you'll either see the math, or some nice error note. If something unexpected happens (e.g. math in links, math in image captions, etc) then mediawiki will mysteriously dump out that garbage. Basically, you're causing an error that isn't specifically handled by the markup engine, so it gets confused. It's totally browser-independent.

As for the suggestion, I think such a thing would overly burden the database and the authors. It sounds like you're suggesting that a new page be created to explain every equation. That's a lot of new pages to store, and a lot to write. That style of writing probably wouldn't be very popular, since most of us are used to explaining equations in neighboring text. Plus, it would be quite a large programming task to add that functionality into mediawiki. Staecker 02:07, 20 May 2006 (UTC)

Ahh no I meant something automatically generated. By definition a mathmatical equation is exact and parsable by a computer. It will be a bit of work by someone to make it function, but I thought I'd put it out there as an idea.

In the page I referenced above, the reason for the equation is explained, but at the level of someone who understands equations already, not to someone who has no idea what the $\sum$ means. I thought it would make wikipedia more accessible to non maths experts and require the time of one developer (and not the time of every maths editor).

See User:RickiRich\Math_Example for an example of what I think could be programatically created, and a description of How it could be created without too much fuss. After exams I'll have a go at this if no one else has.

--RickiRich 01:01, 22 May 2006 (UTC)

I don't think this is a good idea, I doubt it will get used by anybody if it gets implemented, and I doubt the developers will ever bother implementing that. You should at least get some support for this feature before you decide to do anything about it. But again, I don't think this wil lead anywhere. Oleg Alexandrov (talk) 04:07, 22 May 2006 (UTC)

What Oleg said. Dysprosia 06:31, 22 May 2006 (UTC)

I think it won't work. A significant obstacle is that mathematical symbols can have many different meanings, and a computer just ain't smart enough to distinguish which one you mean. For example, the + symbol could mean addition, or it could mean the span of two vector spaces, or the concatenation of two strings, etc. So much depends on context. (Also you probably wanted a forward slash in the title of that page, not a backslash. See Wikipedia:Subpage.) Dmharvey 21:43, 24 May 2006 (UTC)

Intriguing idea, but I don't think its right for wikipedia. There have been some development along similar ideas both MathML and OpenMath formats have had some aspect of representing the meaning of an equation rather that its purely visible representation. OpenMath in particular has seen a lot of work with people developing Content Directories which are domain specific collections of mathematical definitions. There has been numerous papers on the subject, but I don't think its gained much acceptance apart from as a means of converting from one computer algebra system to another. In the wikiworld meta:Semantic MediaWiki is a wikipedia extension which allows some form of semantic markup.

Why its not right for Wikipedia: basically the wiki concept follows KISS principle (Keep it simple stupid) and this sort of system gets rather complex. Hopefully all the relevant terms should be linked in the text anyway. --Salix alba (talk) 22:17, 24 May 2006 (UTC)

Massive edits foil comparison operation in article history

Sometimes an editor goes thru an article and changes many minor things at once. For example: spelling corrections; deleting unneccessary spaces; replacing & alpha ; with α; etc.. When this is done, the function which shows changes in the history often fails. It may begin matching an old paragraph to the wrong new paragraph and then it never gets back in synch (until one reaches a section header, if that was not changed). Of course, this makes it very difficult to check that the change was done appropriately.

I think that it is probably impractical to correct this bug in the comparison. So I am suggesting that you-all try to avoid this situation in the first place. When you do such massive edits, please first do every other paragraph (to allow the software to get back in synch with an unalterred paragraph). Then do a separate edit to change the remaining paragraphs. Thank you. JRSpriggs 06:06, 20 May 2006 (UTC)

I think you'll need to provide a concrete example of this happening. Dysprosia 09:39, 20 May 2006 (UTC)

The most recent occassion on which this happened to me was in the 18 May 2006 edit of Constructible universe by UkPaolo, called clean up +spelling correction using AWB. See http://en.wikipedia.org/w/index.php?title=Constructible_universe&diff=53858793&oldid=53818751 and scroll down to the section named "L is absolute and minimal". JRSpriggs 09:05, 21 May 2006 (UTC)

For this example it would have helped if the diff algorithm ignored blank lines, that is, tried to match up the two versions after filtering out the blank lines (which should be re-inserted for the final presentation). I suppose there is a backlog of all kinds of wishes for the developers, and I don't know how important this really is, but it is relatively simple to implement. --Lambiam ^Talk 18:48, 21 May 2006 (UTC)

I think that the problem is more difficult than Lambiam thinks it is. In the section to which I referred, the only blank line was the next to last paragraph. Yet the mismatching of paragraphs began at the first paragraph in the section. Apparently the diff-software cannot measure the similarity of the contents of two paragraphs until after it has decided irreversably that they are matching paragraphs. That matching of paragraphs appears to depend only on whether they are identical, followed by interpolation (guessing) between identical pairs of paragraphs. JRSpriggs 07:12, 22 May 2006 (UTC)

Blank lines were removed in the edit following each and every section title. This doesn't show up clearly in the diff, but start an edit on both versions and compare the contents of the edit boxes, and it will be obvious. If then the next paragraph is also modified, the diff algorithm can't line them up. The silly thing in this massive edit is that many of the changes have no substance and consist of replacing two spaces after a full stop by a single space. --Lambiam ^Talk 10:06, 23 May 2006 (UTC)

You may want to mention this on Wikipedia:Village pump (technical) or check the bugZilla where there are currently 93 bugs related to the diff. In this case the edit summary gives some clue, the edits were done using the WP:AWB tool, they are mainly minor edits and it would be hard to break this up into smaller edits, by limitations of the software. --Salix alba (talk) 07:16, 23 May 2006 (UTC)

The problem is apparently caused by a feature of AWB, "Apply general fixes", which removes "excess white space" to which the diff algorithm is sensitive (Wikipedia:AutoWikiBrowser#"Set options"). --Lambiam ^Talk 10:15, 23 May 2006 (UTC)

resolve a revert war at dual space

I find myself in a revert war at the article dual space. It's mostly about style; how much information is too much, whether material looks good or fits. this diff shows the difference between the two users preferred revisions. See also this old version for a much longer revision that I reverted. I am pessimistic with how talks on the talk page are going. We seem not to see eye-to-eye. I would like to get some more opinions. -lethe ^{talk +} 04:42, 23 May 2006 (UTC)

Compound Poisson process question

Probabilists out there, I wonder if you could answer a question posted at Talk:Compound Poisson process. Oleg Alexandrov (talk) 17:25, 24 May 2006 (UTC)

looks right to me. (and the changes i made were mostly cosmetic.) Lunch 19:10, 24 May 2006 (UTC)

I added a final line to the moment generating function calculation, which should clarify matters further. The variance result looks OK, by computing them in terms of the moment generating function. — Arthur Rubin | (talk) 20:27, 24 May 2006 (UTC)

Looks OK to me, too. Michael Hardy 21:17, 24 May 2006 (UTC)

... and generally, the nth cumulant of the compound Poisson distribution, following the notation now in the article, is λt times the n moment of the distribution of the random variable that the article (in its present form) calls D_i. This can be shown via the law of total cumulance. The cases n = 1 and n = 2 are just what now appears in the article. Michael Hardy 21:20, 24 May 2006 (UTC)

Widespread mathematical delusions

I'd like to hear some opinions about the new article Widespread mathematical delusions. At the moment, the article lists only one delusion, and I am not sure what the delusion actually is, but it has something to do with statistical independence. In fact, the article Widespread mathematical delusions criticizes the lead section of statistical independence. Can somebody make sense of the new article?

The user who created the article has also written some articles on eventology, a theory which I haven't heard about. The article on eventology lists ten references, all by the same author, including some papers in good Russian journals so we might want to keep the article even though it violates the Wikipedia:Vanity guidelines. -- Jitse Niesen (talk) 05:12, 25 May 2006 (UTC)

0.999... ≠ 1 must be pretty widespread. And misconceptions about infinity are pretty common. -lethe ^{talk +} 06:58, 25 May 2006 (UTC)

I can't make much sense out of this rant. The "intuitive" meaning offered in the article Statistical independence appears to me to be an informal way of saying P(B|A) = P(B). Using the standard definition of conditional probability, this means P(A ∩ B)/P(A) = P(B), or P(A ∩ B) = P(A) P(B), in other words: events A and B are independent. Where is the delusion? There is no shortage of delusions, including mathematical ones, and the field of statistics and probability theory is particularly rich, but this doesn't seem to be one of them. Its like having a diatribe against saying that 1 < 2 means that 1 is less than 2, while it means nothing except "1 < 2". To AfD? --Lambiam ^Talk 11:16, 25 May 2006 (UTC)

I find it hard to understand exactly what this guy is ranting about, mainly because of the poor translation of his thoughts (presumably from Russian) into English. His maths seems to be correct, but only seems to show that conditional probability can be different in different situations. If this page is to be kept, it surely needs a different title? (and a lot of work on wording) I cannot believe that this really is a *widespread* delusion Madmath789 11:46, 25 May 2006 (UTC)

Whatever else it it is, it is surely OR. Paul August ☎ 11:51, 25 May 2006 (UTC)

The delusion consists in popular attempts to justify or to prove or to deduce the definition of independence of events: P(AB)=P(A)P(B) from other assumptions. Mathematical definitions do not demand proofs, especially in a preamble to encyclopaedic paper on probability theory. The criticism is directed only on style of a preamble. All other sections of paper “Statistical” are quite correct. Thanks for discussion. - Helgus 12:28, 25 May 2006 (UTC)

Helgus: I think you misunderstand what the lead section (what you are calling the "preamble") of Statistical independence, is saying. It is not trying to "prove the definition" rather it is simply trying to provide an intuitive understanding of the concept. In any case any criticism of that article belongs at talk:Statistical independence not in some other article. Paul August ☎ 15:52, 25 May 2006 (UTC)

Probably you are right. Especially it concerns the second section of paper. However the first section without doubts keeps within a well-known encyclopaedic category “Paradoxes in mathematics”. Russian mirror of this paper contains, for example, popular delusions which often meet at discussion on “Fermat's last theorem”, “Parallel lines in Lobachevsky's geometry”, “Events with zero probability”. Can be it is necessary to open a new category “Paradoxes in mathematics” into which this paper could enter? - Helgus 21:58, 25 May 2006 (UTC)

Yes AfD unless its moved to a different name and cleaned up to be less like Orignial Research, give it a bit of time though the page is less than a day old.

Also the eventology page is now proposed for deletion, although the other sub articles and the category are not. Either it should be all or none and I think AfD might be better than prod in this case. --Salix alba (talk) 12:58, 25 May 2006 (UTC)

If the page is to be kept, it should probably be renamed -- "delusions" is not quite neutral, perhaps "misconceptions" would be better. Dysprosia 13:03, 25 May 2006 (UTC)

The eventology pages look suspicious to me. The only reason I created Category:Eventology is too keep them all in one place. I agree that an AfD vote on all of them could be the things to do. Oleg Alexandrov (talk) 15:37, 25 May 2006 (UTC)

It really is OR and a rant. The title reads pretty bad as well, it probably should be deleted.--Jersey Devil 17:37, 25 May 2006 (UTC)

I've removed the prod tag from eventology, If we are to believe the references there, it isn't OR, although it may be non-notable. So I agree with Jitse's, I'm not sure we should delete this. Paul August ☎ 18:09, 25 May 2006 (UTC)

But User:Helgus is Oleg Vorob'ov, the author of 10 out of 11 of the references. Sounds like OR to me. Staecker 02:44, 26 May 2006 (UTC)

No, OR means writing about something which has not yet been published elsewhere. Paul August ☎ 02:48, 26 May 2006 (UTC)

You're right- sorry, I confused it with WP:AUTO. Not surefire grounds for deletion, but it gives me the willies. Staecker 02:57, 26 May 2006 (UTC)

Yes writing about your own work is problematic. And we should take special notice of such. Paul August ☎ 17:10, 26 May 2006 (UTC)

eventology, but not sub-pages now on AfD. --Salix alba (talk) 10:45, 28 May 2006 (UTC)

Lebesgue spine

Being a newcomer here, I would appreciate some brief advice: Lebesgue spine is listed somewhere as a missing link, but when I look at 'what links here', I only find things like Wikipedia:Missing science topics/Maths16. I could write a page about the Lebesgue spine, but would it be any use? Madmath789 20:35, 25 May 2006 (UTC)

Sure it would be useful. Paul August ☎ 02:45, 26 May 2006 (UTC)

Non-negative v. nonnegative

OED lists "non-negative" but Webster's lists "nonnegative". Is this a British/American usage split? I've looked through a few textbooks, but there doesn't seem to be any particular consistency (not all American books use "nonnegative" and not all European ones use "non-negative"). Any opinions? There seems to be a mix among Wikipedia articles (even within a single article) and titles. Thanks. Lunch 22:05, 25 May 2006 (UTC)

I use either when the mood strikes me. If there's no standard, what's the difference? Ryan Reich 22:39, 25 May 2006 (UTC)

I s'pose I was thinking consistency would make things easier to find, and any source I found was always self-consistent whereas the Wikipedia isn't. And now that I look through the textbooks sitting in front of me, four have "nonnegative" (five American authors) and only one has "non-negative" (two Frenchmen). Lunch 23:11, 25 May 2006 (UTC)

In my experience, in American papers and textbooks "nonnegative" is by far the most common. Older works may use "non-negative" to a greater frequency. --Chan-Ho (Talk) 01:52, 27 May 2006 (UTC)

Stone-Cech compactification name

Most of the references I've seen have a symbol over the "C", which I can't figure out exactly how to generate. (Also, there seems to be a convention that the "-" should be replaced by an n-dash "–".) — Arthur Rubin | (talk) 00:28, 26 May 2006 (UTC)

How about this: Čech? Dmharvey 02:51, 26 May 2006 (UTC)

When I open an edit window, below the Save page button is a box that says "Insert:", followed by numerous special characters. The character in question is one of them, and clicking on it causes it to be inserted into the edit box. JavaScript must enabled in the browser for this to work. --KSmrq^T 03:52, 26 May 2006 (UTC)

What a mess. We have Stone-Cech compactification and Stone-Čech compactification, and Čech points to neither, and probably we need Cech as a redirect as well. Dmharvey 02:56, 26 May 2006 (UTC)

Hm, apparently the redirect at Stone-Čech compactification is my fault; don't really remember doing it. Stone-Cech compactification should be moved to Stone-Čech compactification, but it won't let me move it because the redirect is to a different place. I'll tag the redir for speedy. --Trovatore 03:05, 26 May 2006 (UTC)

OK, fixed now. This time the endash thing came in handy. --Trovatore 03:12, 26 May 2006 (UTC)

How about Štone-Cech compactification? :-) -lethe ^{talk +} 04:01, 26 May 2006 (UTC)

Added. Hey, you never know. --Trovatore 22:34, 26 May 2006 (UTC)

Maths AfDs

A certain User:Mathguru has AfD'd Quasi-Hopf algebra and Quasi-bialgebra. I think it is notable, but as the author, I may be biased.Blnguyen | Have your say!!! 06:39, 26 May 2006 (UTC)

I'm a hair away from closing them both speedy keep. -lethe ^{talk +} 10:48, 26 May 2006 (UTC)

Too late now ... I closed them. -- Jitse Niesen (talk) 12:00, 26 May 2006 (UTC)

well, mathguru, Afd' the Australian Mathematics Competition as well.Blnguyen | Have your say!!! 08:00, 31 May 2006 (UTC)

Also closed as a speedy keep. -- Jitse Niesen (talk) 08:36, 31 May 2006 (UTC)

A query

Does anyone have a reference or proof for Kronecker's lemma? This has been bothering me, mainly in case absolute convergence of Σ x_n ought to be included. Charles Matthews 13:07, 26 May 2006 (UTC)

I think the statement is true as is stands, but I don't have a reference. Using summation by parts,

$\frac1{b_n}\sum_{k=0}^n b_k x_k = S_n - \frac1{b_n}\sum_{k=0}^{n-1}(b_{k+1} - b_k)S_k,$

where

S k

are the partial sums of the x's. Pick any epsilon > 0, choose N so that

S k

is epsilon-close to s for k > N. Then the right hand side is

$S_n - \frac1{b_n}\sum_{k=0}^{N-1}(b_{k+1} - b_k)S_k - \frac1{b_n}\sum_{k=N}^{n-1}(b_{k+1} - b_k)S_k$

$= S_n - \frac1{b_n}\sum_{k=0}^{N-1}(b_{k+1} - b_k)S_k - \frac1{b_n}\sum_{k=N}^{n-1}(b_{k+1} - b_k)s - \frac1{b_n}\sum_{k=N}^{n-1}(b_{k+1} - b_k)(S_k - s)$

$= S_n - \frac1{b_n}\sum_{k=0}^{N-1}(b_{k+1} - b_k)S_k - \frac{b_n-b_N}{b_n}s - \frac1{b_n}\sum_{k=N}^{n-1}(b_{k+1} - b_k)(S_k - s)$

Let n go to infinity. The first term goes to s, which cancels with the third term. The second term goes to zero. Since the b sequence is increasing, the last term is bounded by $\epsilon (b_n - b_N)/b_n \leq \epsilon$ . Dmharvey 13:41, 26 May 2006 (UTC)

Now transcribed to that controversial category Category:Article proofs. linas 01:43, 13 June 2006 (UTC)

Indiscriminate collection of information?

Don't pages like this, Derivative (examples), break with WP:NOT?--Jersey Devil 02:32, 27 May 2006 (UTC)

I have put it up for afd, your input would be appreciated.--Jersey Devil 02:36, 27 May 2006 (UTC)

Mathematics is Article Improvement Drive collaboration

Ladies and Gentlemen! Did you know that the article Mathematics is the current Article Improvement Drive collaboration? --Lambiam ^Talk 22:40, 27 May 2006 (UTC)

Voted for it on the AID page. One user commented that it is in the top ten most viewed pages on Wikipedia and therefore must be a featured article.--Jersey Devil 23:01, 27 May 2006 (UTC)

Eventology AfD

The article Eventology (by the same author as Widespread mathematical delusions) has been nominated for deletion. --Lambiam ^Talk 13:21, 28 May 2006 (UTC)

Delusions in probability theory and statistics on AfD

I've nominated the article Delusions in probability theory and statistics (earlier called Widespread mathematical delusions) for deletion. --Lambiam ^Talk 22:31, 28 May 2006 (UTC)

Disambiguation of sinc function

There are two possible definitions of the sinc function, namely

$\operatorname{sinc} \, x = \frac{\sin x}{x} \quad\mbox{or}\quad \operatorname{sinc} \, x = \frac{\sin \pi x}{\pi x}.$

One possible way to handle this is to split the article sinc function in two, sinc function (normalized) and sinc function (unnormalized), similar to the usual disambiguation process. We are having a discussion on Talk:Sinc function (unnormalized) whether this is the proper way to go about it, and I'm solliciting others to join. -- Jitse Niesen (talk) 05:21, 31 May 2006 (UTC)

Possible confusion over 'subadditive'

There is an article Subadditive which discusses functions satisfying $f(x+y)\leq f(x)+f(y)$ , and there is a link to this article from Sigma additivity in the category measure theory. There seems to be a different definition of 'subadditive' (and also 'countably subadditive') in use in measure theory:

$\mu(E \cup F) \leq \mu(E)+\mu(F)$

(used in developing the theory of 'outer measure'). My question is: do we need a separate page for subadditve set functions, or should we incorporate it into the existing subadditive page? (Or are subadditive set functions not notable and we do not need them?). I might be in a position to write something on the set function version of subadditive (if needed), but would appreciate some views about what might be done - and there are probably others better qualified to write such stuff anyway.Madmath789 11:27, 31 May 2006 (UTC)

I think you're right, subadditive (measure theory) deserves its own article. I don't know any measure theory, but I recall there being interesting theorems about set functions which are additive (on finite collections of sets) and countably subadditive. Dmharvey 11:37, 31 May 2006 (UTC)

Be bold! Write stuff, we move and fix later. Charles Matthews 11:46, 31 May 2006 (UTC)

Barry Simon article

The piece on Barry Simon is from a fan, it seems. Important guy for mathematical physics, and this should be better expressed and sourced, and have more technical stuff about the work. Charles Matthews 11:46, 31 May 2006 (UTC)

A good example of hagiography I guess. --CSTAR 18:54, 1 June 2006 (UTC)

Jun 2006

This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

E9 (Lie algebra)

My knowledge of Lie algebras is a single course, but this potentially confusing notation was never mentioned. Has anyone else heard of this? Septentrionalis 18:40, 1 June 2006 (UTC)

I have never heard of this notation. I note that my references list the notation as E₈⁽¹⁾. The subscript here is, as always, the rank. -lethe ^{talk +} 18:51, 1 June 2006 (UTC)

Please review

I have extensively revised and cleaned up Divisibility rule, so please take a look and help to improve it more. As I'm not fully experienced at all the editing tools, I'm sure the formatting and adherence to guidelines and standards could be improved.

I'd like to create a number of other pages related to mental math, so I'd like to get feedback on this one, the first I've heavily edited. (The current mental arithmetic has only the most basic, simple of techniques.

Walt 01:59, 2 June 2006 (UTC)

Category:Billion and cousins up for deletion

See Wikipedia:Categories_for_deletion#Category:Thousand. Oleg Alexandrov (talk) 18:57, 3 June 2006 (UTC)

Poincaré conjecture

Some Chinese news sources have picked up a story about a recent journal article by Cao and Zhu, experts on the Ricci flow, who have written what they (and the journal editors) claim is a "complete" proof of the geometrization conjecture, by giving more details of Perelman's work. Slashdot has also picked up on this. As a consequence, there has been several editors who have insisted on placing mention of Cao and Zhu's paper in the lead section. I have disagreed (see talk page discussion and also some of my edit summaries for extensive reasons). Please continue discussion there. I would also appreciate if people could pop in and check that things don't get out of control. Thanks. --Chan-Ho (Talk) 02:15, 6 June 2006 (UTC)

American Institute of Mathematics

The article on American Institute of Mathematics has been nominated for deletion by someone. R.e.b. 13:02, 6 June 2006 (UTC)

PlanetMath Exchange project milestone

The PlanetMath Exchange project has today reached a new milestone, with 40% of all PlanetMath articles reviewed.

For those of you who have not been following the project, I thought I would take this opportunity to report on the status of the project, and the progress which has been made to date. The purpose of the project is to review all PlanetMath (PM) articles (which are licensed under GFDL) and to incorporate any appropriate PM content not adequately covered on Wikipedia (WP).

There are over 4800 PM articles listed, of which over 1900 of which have been reviewed so far. Of the reviewed articles, 143 PM articles have been copied to WP, creating entirely new WP articles, and 121 have been merged into already existing WP articles. Additionally, a further 75 PM articles have been identified as needing to be copied, and 349 needing to be merged.

The project maintains 49 lists of PM articles grouped by topic (e.g. 11 Number theory, 26 Real functions, 54 General topology). The entire list of lists is compiled into a "Article lists" table, and statistics are maintained for each topic's list.

19 editors have identified themselves as participants, and 26 have reviewed at least one PM article (see Editor contributions).

Oleg Alexandrov, has provided several excellent tools to facilitate the project. He and Mathbot created the original 49 lists (first created in Feb 2005, and updated with new PM articles in March 2006). They also perform daily updates of statistics in the "Article lists", and "Editor contributions" tables. In addition, Oleg has created a convenient tool to assist in converting a PM article to wiki markup.

I heartily encourage everyone to join the fun.

Paul August ☎ 02:06, 8 June 2006 (UTC)

Direct logic up for deletion

See Wikipedia:Articles_for_deletion/Direct_logic -Dan 15:36, 8 June 2006 (UTC)

Another misguided nomination for deletion

Please vote at Wikipedia:Articles for deletion/American Institute of Mathematics. Michael Hardy 23:33, 9 June 2006 (UTC)

Yeah, R.e.b. told us already. -lethe ^{talk +} 00:48, 10 June 2006 (UTC)

I closed that AfD. -lethe ^{talk +} 00:54, 10 June 2006 (UTC)

Functional analyst needed

Hi, I left a question regarding the correct statement of the Ryll-Nardzewski fixed point theorem at Talk:Ryll-Nardzewski fixed point theorem. Cheers, AxelBoldt 04:10, 11 June 2006 (UTC)

As stated it's wrong. The semigroup is required to satisfy another property, that it be "distal". Also I don't think it can be used to prove existence of Haar measure on general locally compact groups, although I think for compact groups yes. I think this is in Rudin's functional analysis book for instance. Also see Frederic Greanleaf's little book (now horribly outdated) on "Amenable Groups".--CSTAR 12:41, 12 June 2006 (UTC)

Rewrite Poincaré_conjecture?

I invite interested parties to make comments at Talk:Poincaré_conjecture#Peer_review. --Chan-Ho (Talk) 12:48, 11 June 2006 (UTC)

Jaques Hadamard or Jacques Hadamard?

An anon recently redirected the wikilink in Chaos Theory from the first to the second. Is this legitimite? Are these the same person? — Arthur Rubin | (talk) 15:30, 11 June 2006 (UTC)

Yes, same person. Correct spelling is Jacques [62]. I have changed the Jaques page to a redirect and fixed the link in the single remaining article that used the wrong spelling. Gandalf61 15:53, 11 June 2006 (UTC)

Zipper theorem

I wanted to {{prod}} this article. But to be sure I thought I'd check. Is this article nonsense or not? I couldn't google the name, but that doesn't always mean anything. Garion96 ^(talk) 00:20, 12 June 2006 (UTC)

The theorem and its proof in the article are correct. The theorem was not known to me under this or any other name. --Lambiam ^Talk 00:53, 12 June 2006 (UTC)

Thanks, so I won't {{prod}} it. Anyone here wants to clean that article up? Cause the way it looks now, it's not understandable for the non mathematician reader. Like me. :) Garion96 ^(talk) 12:04, 12 June 2006 (UTC)

Hmm, perhaps I should have looked at at the article again. It already is cleaned up. Thanks. Garion96 ^(talk) 12:05, 12 June 2006 (UTC)

I think it's a neologism. I think it should be deleted without some evidence of that name having widespread currency. Dmharvey 12:15, 12 June 2006 (UTC)

I've heard it referred to in that way ("zipper theorem"); dunno if that's enough evidence for you. I also can't think offhand of a place I've seen it in print, though. I could ask around. Lunch 18:53, 12 June 2006 (UTC)

I'm skeptical that the name is very common. I can't imagine the theorem would even have a name amongst mathematicians. So I think the term would only be used in certain kinds of introductory course work. Google gives no results (off Wikipedia), so nobody that has mentioned it, for example, in a course webpage. The only place I can think the term may exist is in some textbooks somewhere. Even in that eventuality, I don't know if it's worth having an article based on that amount of usage. I guess it does no harm, but I'm also hard-pressed to imagine a situation where we would want to link to it. --Chan-Ho (Talk) 19:18, 12 June 2006 (UTC)

Merge it into Limit of a sequence#Properties? —Blotwell 17:01, 13 June 2006 (UTC)

I've asked a few people around, and none other than me have heard this result referred to as the zipper theorem. I guess it's not as popular a term as I thought. Maybe zipper lemma instead? ;) Maybe it'd qualify for a list of some sort of elementary properties of limits; if not, maybe stick it in the article on limits. BTW, this theorem is true for any metric space, but is it true for non-Hausdorff spaces? How much can the requirements of the theorem be relaxed? Lunch 21:57, 20 June 2006 (UTC)

The exact same proof, translating epsilons into open sets, proves it in every topological space. This result has about the same significance as, say, the linearity of differentiation, and should probably go in a list of limits like the list of derivatives. Ryan Reich 22:48, 20 June 2006 (UTC)

Sure, a list of limits article would be a good idea. And I guess you can just replace balls with neighborhoods; I think I was confusing myself with the non-uniqueness of limits in non-Hausdorff spaces. Lunch 23:33, 20 June 2006 (UTC)

Sorry if I was curt with that reply. I'll be happy to put together a basic list of limits. Actually, following the model of the list of derivatives, there isn't any need to touch zipper theorem, just link to it from the list. Unless we really don't like it for some reason. Ryan Reich 00:22, 21 June 2006 (UTC)

looks good! Lunch 17:58, 22 June 2006 (UTC)

integrable systems

Over at Talk:Constant of motion, I've been reduced to babling and waving my hands to the effect that a "system of differential equations with constants of motion == integrable system == system with symmetries" and conversely, "non-integrable system == system with no constants of motion". However, it occurs to me that I know of no grand theorems making this claim. Are there any? Is this in fact a collection of small results in narrow fields that have accreted into a grand truth? Guidance? How can one make this clear at a college-math level? It doesn't help that the article integrable system is somewhat foreboding in its current form. linas 01:30, 13 June 2006 (UTC)

Maybe I'm being lame? Maybe its just the Frobenius theorem coupled to the idea that the submanifold has a natural symmetry, ergo by Noether's theorem has constants of motion? I've never had formal skoolin in this matter. linas 03:13, 13 June 2006 (UTC)

I think I'm grasping for Liouville's theorem (Hamiltonian). I swear this stuff goes in one ear and out the other. I'm babbling even now. linas 03:27, 13 June 2006 (UTC)

You make a good point about the current article being somewhat forbidding. I would go a step further. I don't think integrable system should redirect to integrability conditions. An integrable system usually (?) refers to a Hamiltonian system with a full set of Poisson-commuting flows. Naturally, integrability conditions do play a role, but there is more structure a priori in an integrable system. For the point about conserved quantities for an integrable system, since the Hamiltonian flows commute, there should be loads of conserved quantities. (As you ask, is there a general theorem here? Does Noether apply? etc). Hence a system without "enough" conserved quantities will be non-integrable. I'm not so sure about the converse. Silly rabbit 13:15, 13 June 2006 (UTC)

Thanks. What I've been reading gives the name completely integrable system to the case of a full set of commuting Poisson brackets. Your "not being sure about the converse" would imply that there are non-integrable systems with a "full set" of conserved quantities. That certainly sets my mind wandering in wild directions. linas 23:27, 16 June 2006 (UTC)

Nice start on integrable systems. It certainly has helped me organize some of my own wild wanderings. I'm clearly not an expert, but it seems to be tricky to give a good definition of an integrable system. (Ok, so first off, yes I meant what you call completely integrable: which is unarguably a better term ;) In particular, there are issues of local versus global integrability. What does global integrability mean anyway? Do the all the level submanifolds have to be closed? Do the constants have to be found explicitly, or can they just be given in some implicit sense? Can a locally completely integrable system have degenerate Poisson brackets on some small dimensional locus, and still have functionally independent integrals? (Here is the "lack of converse" possibility -- if it exists to begin with.) Silly rabbit 23:37, 17 June 2006 (UTC)

Thanks. I'd say a Lie group is the prototype for something that is "globally integrable". I don't know of any systems that are "provably integrable" (constants of motion implicitly given), but whose solution is unknown (no explicit form). I suspect one can find level manifolds that are not closed, certainly things like the horocycle flow ( aka Anosov flow on tangent space of SL(2,C)) has the flavour of being non-compact but this is an off-the-cuff remark. I believe that the whole area of sub-Riemannian geometry is permeated with integrable systems that have cuts and isolated singularities and the like. Next, chaotic systems have "regimes" of regular and chaotic motion that's interspersed; the KAM torus being the famous example, although the easy-to-understand variants are in difference equations. Then there's all this stuff about homoclinic orbits, and stuff like Axiom A, which I dimly understand. Or things I dont:Smale's spectral decomposition theorem. I'm sort of learning this stuff as I go along.linas 04:57, 18 June 2006 (UTC)

Mathematicians for Wikipedia:Version 0.5 Nominations

On Wikipedia talk:WikiProject Mathematics/Wikipedia 1.0 there is a request for the most notable mathematicians whos biographies could be included in Wikipedia:Version 0.5 Nominations. Suggestions for celebratity mathematicians welcome. Possible also assesments of the quality of their article also welcome. --Salix alba (talk) 07:45, 15 June 2006 (UTC)

Thanks to great work by Lethe we now have a fairly comprehensive list of the the giants for mathematics on Mathematics/Wikipedia 1.0. A new template Template:maths rating has also been created together with a set of categories listing the quality and importance of mathematics articles. Mathbot will included these articles in Wikipedia:Version 1.0 Editorial Team/Mathematics articles by quality on a daily basis. Help is now needed in identifying the important maths articles and assigning then a grade (Feature Article/A/Good Article/B/Start/Stub), which can be done by including the template on the talk page. There are a few biographies which may be suitable for listing as good articles and several other on some key figures which are barely more than stubs and could do with expansion.

I'm also thinking that the list of mathematicians could make a good article in its own right, either as a section in Mathematicians or its own article, possible Influential mathematicians. --Salix alba (talk) 09:25, 16 June 2006 (UTC)

We already have list of mathematicians, but I guess you are thinking of a selective subset. I don't know if it is worth its own article. Oleg Alexandrov (talk) 15:37, 16 June 2006 (UTC)

Yes I was thinking of a more selective list, probably anotated as well, briefly describing their main acheivments. It could be an interesting way to tell the history of mathematics through the people involved and the new areas of study they started. This sort of presentation, is quite popular in science books aimed at the general reader and might appeal to certain wikipedia readers. --Salix alba (talk) 20:20, 16 June 2006 (UTC)

Well If you want a selective list one place to start would be Bell's Men of Mathematics. Paul August ☎ 20:55, 16 June 2006 (UTC)

Might I also suggest the obvious web site, MacTutor? --KSmrq^T 04:53, 17 June 2006 (UTC)

Probability/Measure theory glossary?

Does WP have a glossary that translates the language of probability theory to measure theory? I've got a complaint on my talk page that I'm trying to decipher; I don't understand Score (statistics) and Fisher information, although I suspect I would, if they were restated in terms of measure theory. The root of this interest is the rather astounding edit here, which is so remarkable, I abstract it here:

Fisher information is a powerful new method for deriving laws governing many aspects of nature and human society. B. Roy Frieden sets out in detail how Fisher information can ground a great deal of contemporary physical theory, including Newtonian mechanics, virial theorem, statistical mechanics, thermodynamics, Maxwell's equations, Lorentz transformation, general relativity, EPR experiment, Schrodinger equation, Klein-Gordon equation, Dirac equation, Rarita-Schwinger equation, and the fundamental physical constants. Frieden and coauthors have also used EPI to derive some established principles and new laws of biology, the biophysics of cancer growth, chemistry, and economics.

Surely, the ommission of M-theory and intelligent design is just an oversight? linas 00:38, 17 June 2006 (UTC)

See Talk:B._Roy_Frieden for a little bit of discussion and some links to external reviews of Frieden's work. He has some interesting ideas but, it seems, not quite the revolution he makes out for himself. The IP address of the edits is assigned to [http:/csc.canterbury.ac.nz Christchurch College of Education] in New Zealand. Maybe Frieden's been travelling? Lunch 03:49, 17 June 2006 (UTC)

user mathisreallycool

A new user mathisreallycool (talk • contribs) has made several edits which to my mind betray a fundamental lack of knowledge in certain mathematical topics. I have reverted several additions by this user, and I want to vet some other things by the user. For example, the article Konfisakhar space seems unobjectionable, it's referenced. However I've never heard of this idea, it's not in any of my texts, nor is it in my EDM2, and frankly, I find the idea of a fractal vector space hard to believe. Can someone (maybe with access to the book by Schaeffer) verify this concept? Otherwise, I shall want to AfD is. And maybe also this definition of semidirect products for monoids? -lethe ^{talk +} 07:14, 17 June 2006 (UTC)

A web search for Igor Konfisakhar suggests the work of a creative student, violating WP:NOR. The citation of the Schaeffer book is also not quite correct; the second edition (ISBN 978-0-387-98726-2) has two authors. I have no personal knowledge of the topic or the book, but I share your reservations.

PS: I've begun using 13-digit ISBNs, since the official transition is not far off. On online converter is available. --KSmrq^T 10:40, 17 June 2006 (UTC)

I've listed Konfisakhar space for deletion. "Professor Igor Konfisakhar" appears to be an undergrad, notable only for being a 3rd place winner in a Putnam prize contest, which is better 'n me but not good enough for this. linas 03:54, 18 June 2006 (UTC)

I know Igor Konfisakhar personally (or did), and can confirm that he is (at present) an undergraduate. Tesseran 03:21, 19 July 2006 (UTC)

The reference work listed is searchable online at Amazon (see [63]). I find no reference to "fractal" or "Konfisakhar". Paul August ☎ 04:35, 18 June 2006 (UTC)

Problems at Propositional Calculus

(Copied from my talk page. Oleg Alexandrov (talk) 07:51, 17 June 2006 (UTC))

JA: Hi, could you help sort out the continuing tangles at Propositional calculus? First there was that improper name change last month, and I let it go because the user who did it seemed fairly competent and added some good stuff, but now the word "logic" seems to be inviting anonymous users to take the article out of the mathematical logic designation and add any sort of half-baked exposition that they can cook up. I don't know my way around the procedures well enough to keep dealing with sort of stuff. Much appreciated, Jon Awbrey 05:15, 17 June 2006 (UTC)

There had been some noise in the past about moving propositional calculus to propositional logic or classical propositional logic. The move to propositional logic was affected by Charles Stewart via WP:RM last month, then reverted by a history-destroying copy-paste by Jon Awbrey this week. I reverted the copy-paste (restoring the history), then reverted the proper move (preserving the history), so now we're back where we started. If the move is to happen, a case will have to be made again. -lethe ^{talk +} 07:59, 17 June 2006 (UTC)

Use "iff", not "if", in definitions!

Some editors appear to believe that there is a convention which requires the use of "if" in definitions rather than "iff" (short for "if and only if"). A definition is a proposition which equates a new term to a compound expression composed of old terms. So using "if" is wrong. One should use "iff" or an equivalent, such as: "if and only if", "is", "is the same as", "means", "is equivalent to", "when and only when", etc.. JRSpriggs 08:20, 17 June 2006 (UTC)

Though you are technically correct, I don't think it's such a problem to use just an "if" in a definition. It's tedious to always write "if and only if" (and the abbreviation is esoteric), and the full meaning can always be inferred. Of course to require "if" in definitions is certainly bad. -lethe ^{talk +} 08:29, 17 June 2006 (UTC)

I am complaining because thrice recently someone has changed "iff" to "if" in a definition. JRSpriggs 10:03, 17 June 2006 (UTC)

If I saw that happen, I would probably revert. -lethe ^{talk +} 10:25, 17 June 2006 (UTC)

Well, "if" is brief, commonly understood, and colloquial; "iff" is brief, not commonly understood, and precise. What to do? Personal, I dislike "iff", so I either write out "if and only if" or use a phrase like "exactly when". My feeling is that anyone who understands the meaning of "iff" and feels comfortable with it also has enough of that fabled "mathematical maturity" to not misinterpret a definition using "if". I am not aware of a WikiMath guideline, nor a Wikipedia guideline that speaks to this slightly delicate issue involving both accessibility and formal correctness.

A recurring challenge with a multinational pool of editors is melding one's own training and taste with that of others. I cringe whenever I see the word "ditto" in an article, as to me it screams of informality, not suitable for an encyclopedia. I'd love to see both "iff" and "ditto" banned, but I have no sense of how much agreement I would find for that view. --KSmrq^T 11:01, 17 June 2006 (UTC)

I would agree with abolishing "ditto" but not with abolishing "iff". Anyway, I agree with Ryan below. The precision afforded by the usage "iff" is useful for theorems, but not so much for definitions. -lethe ^{talk +} 11:18, 17 June 2006 (UTC)

This doesn't follow any mathematical practice I've ever seen, so why should we insist on it simply because it's technically right? We don't make policy here, just record it. Besides, to counter your argument, "iff" is logically absurd in this context since the term to be defined has no prior meaning; whether or not it applies is determined by the text of the definition. In other words, "only if" is vacuous if the term is unique, and if not, it is erroneous. Someone reading an "iff" definition for the first time will wonder if they've missed some other discussion of the term, and anyone else will be annoyed because it departs from the usual style. I agree with lethe, though: any change of one to the other should be reverted. This is a personal preference. Ryan Reich 10:57, 17 June 2006 (UTC)

We are certainly allowed to make policy here. What we don't do is invent subject matter for our articles. So we can't invent terminologies, but we can certainly decide on conventions for our terminologies. -lethe ^{talk +} 11:18, 17 June 2006 (UTC)

I'd argue more but apparently you agree with me. My objection to inventing policy in this sort of case is that the choices are not all equally acceptable; it's not like choosing an indentation style for C code, where many different styles all have their widespread adherents. I've simply never seen "iff" in a definition. Ryan Reich 11:30, 17 June 2006 (UTC)

I can't quote chapter and verse, but I remember seeing a mathematical style guide recommending "if" in definitions. Personally I prefer "when", to distinguish it from the notion of logical consequence (as in: You are in a dilemma when you don't know which way to turn), although some may decry the temporal connotation. --Lambiam ^Talk 12:07, 17 June 2006 (UTC)

I much prefer "if", and that's what I observe as common mathematical practice. Dmharvey 12:57, 17 June 2006 (UTC)

~~I think "if" is somewhat unclear~~, but I have no problem with "only if", "if and only if", the equivalency arrow ( $\Leftrightarrow$ ) and other such language. The term "iff" I object strongly to, at least in basic math articles, on the grounds that it is jargon that is unfamiliar to many basic students of mathematics who have not done proofs. But don't take my word for it - I've seen countless edits where amateurs have "corrected" iff to "if". Deco 13:53, 17 June 2006 (UTC)

Something unseemingly asymmetrical about accepting "only if" (⇐) and rejecting "if" (⇒). I must say I do not understand your position. -lethe ^{talk +} 14:04, 17 June 2006 (UTC)

The words "only if" do not imply "given the sufficient condition that", and it is a myth that "if and only if" is the conjunction of "if" and "only if". It is merely a way of clarifying "if" using the additional qualifier "only if" that only serves to strengthen that "no we don't mean this is just a necessary condition" but in fact an equivalency is intended. If I say "a number is prime only if it has exactly two factors", the intepretation is clear; it does not even suggest that there might be a prime which doesn't have two factors. Deco 17:23, 17 June 2006 (UTC)

Indeed, "only if" implies "given the necessary condition that", and "if" means "sufficient". And in mathematics, "if and only if" certainly is their conjunction, at least in a formal context, but since this is a formal phrase that is to be expected. Using it in an informal context evokes its formal meaning and is just confusing when you start to split hairs about what it really means, especially given that syntactically, it definitely looks like the conjunction of "if" and "only if". Stating "only if" in a definition is redundant, since the term is intended to be deciphered, not encoded: if I see a long string of conditions which happen to have a nice definition but I don't know it, I will not go looking for one until it's necessary; on the other hand, if I see an unfamiliar term I will go looking for its definition. Putting "only if" in the definition would just mean "whenever you see this term, you can be sure it means this phrase", which is exactly what the process of defining the term means anyway. Combined with the common-sense reason that people just don't talk like that, I say "only if" should stay out. Ryan Reich 18:03, 17 June 2006 (UTC)

Oops, I switched necessary and sufficient, that's not what I meant. I don't object to leaving out "only if" if you find it unclear. ~~I'd like to avoid "if" due to ambiguity if possible~~, but my main concern is that that we avoid "iff", which people generally assume is a typo if they don't know about it. Deco 21:01, 19 June 2006 (UTC)

I strongly support the use of "if" in definitions over either "iff" or "if and only if". By the way this has (of course) been discussed before. I will now provide for your reading pleasure this oldie but goldi, this blast from our past:

(Start of copied text from talk page archives)

Charles Matthews 16:28, 21 Oct 2003 (UTC)

Onebyone 10:35, 22 Oct 2003 (UTC)

So, my understanding is that the Project isn't trying to prescribe, but is looking for some harmonisation. Charles Matthews 19:02, 22 Oct 2003 (UTC)

(End of copied text)

Paul August ☎ 18:38, 17 June 2006 (UTC)

In regards to Lambiam's comment on a style reference, a popular one is Nick Higham's "Handbook of Writing for the Mathematical Sciences." On page 20 of the second edition it says:

By convention, if means if and only if in definitions, so do not write "The graph G is connected if and only if there is a path from every node in G to every other node in G." Write "The graph G is connected if there is a path from every node in G to every other node in G" (and note that this definition can be rewritten to omit the symbol G).

In my own experience, I cannot recall ever seeing "if and only if" in a definition in formal mathematical writing. Can someone supporting the use of "if and only if" cite a current journal article with this usage or give reference to a style manual that advocates its use? Lunch 20:44, 19 June 2006 (UTC)

Oh, in definitions. I didn't realise this was regarding definitions and not theorems. My apologies for my dissent - of course it's redundant in a definition to state that it's an equivalency. I would not use any more verbose language in this case. Deco 21:03, 19 June 2006 (UTC)

If the consensus is that "iff" may be confusing because some lay-persons do not know what it means and it might be mistaken for a misspelling of "if", then I will not object when other editors change "iff" to "if and only if" or an equivalent. However, I still object to using "if" by itself between the definiendum and the definiens. JRSpriggs 03:52, 20 June 2006 (UTC)

Using a conditional rather than a biconditional in a definition is wrong

"Often ... the definition is a statement that expresses a logical equivalence between the definiendum and the definiens." When we define a mathematical symbol (constant, function, or relation), the definiendum (symbol defined) is a new word being added to our language; and it has no meaning other than that given to it by the definition. The definition is a postulate which gives meaning to the new word. Since it is not normally our intention to add strength to our set of axioms (as the axioms of ZFC), this must be a conservative extension. And we should be able to translate any sentence involving the new word into one which omits it and has the same meaning. If you put a conditonal ("if") rather than a biconditional ("if and only if") between the definiendum and the definiens, then you are doing one of three things:

Using "if" to mean "if and only if" when in the context of a definition. This is potentially confusing to the readers. First, they may not realize that "if" is being used for "if and only if". Second, they may learn to read "if" as "if and only if" in other circumstances where it is mistake to do so.
You are using "if" to mean "if", i.e. you really intend the postulate which is the definition to be a conditional rather than a biconditional. In this case, one could not prove the negation of the new word was ever appropriate. For example, if we defined "measurable cardinal" via "κ is a measurable cardinal if it is an uncountable cardinal with a <κ-additive, non-principal ultrafilter.", then we could not prove that 17 was not a measurable cardinal.
You are assuming that anything which is not provably true is false. Surely, since Gödel's incompleteness theorems, it is clear that this is not a tenable position.

In conclusion, definitions should not be conditionals. JRSpriggs 03:52, 20 June 2006 (UTC)

If you were working in a formal logic, you would not be phrasing your definitions as English sentences at all, and this would not be an issue. The use of "if" in definitions is just one of many places that context is conventionally used to establish the meaning of a symbol. If you did want to make a definition that was not biconditional (for some reason) you could simply use more explicit language such as "A implies that B", "A is a sufficient condition such that B", or implication arrows. Finally, I think the language "B if A" should be avoided in theorem statements in favor of "if A, then B" or "Given A, we have B" or "Whenever A holds, it follows that B", or something a bit less vague; such use would preclude confusion about the meaning of that sentence structure. Deco 04:18, 20 June 2006 (UTC)

The "if" in a definition is not a conditional. It's an assignment, like the = sign in C. This is a well-established linguistic convention (and it doesn't mean "if and only if"; as I said, it's an assignment, and not any sort of proposition at all).

Moreover I have a strong antipathy to using "iff" in formal writing (in any context, not just definitions). It's acceptable on a blackboard, like "wrt", but it should not appear in articles. --Trovatore 04:27, 20 June 2006 (UTC)

Agree with Trov on both counts. That being that "if" in deffintions is perfectly acceptable, while "iff" in definitions is a bit iffy. :) Oleg Alexandrov (talk) 04:39, 20 June 2006 (UTC)

In a context that makes clear we are offering a definition, "if" works for me.

We say that a foo is a bar if it satisfies mumble.

In a context which is not clearly a definition, we must be more careful.

… A foo is a bar if it satisfies mumble. …

Can a foo be a bar even when it does not satisfy mumble? Here I don't know!

So now we come to the question of what to write in Wikipedia articles. Often definitions are not highlighted as such, but appear inline in a form that is ambiguous about the intent. I myself would never use "iff". I would try to word the statement carefully so that it was clear what I meant. When we write, we know what we mean, so we don't always see the possible confusion our words may cause a reader. But when we see a potential problem, the better solution is to reword to make our intent clear, not to throw in jargon like "iff". Flag a definition as a definition, and our readers will thank us. (Well, no. Actually they'll read happily along, never knowing the confusion we spared them. Bad writing is what gets noticed.) --KSmrq^T 14:33, 20 June 2006 (UTC)

I guess I am agreeing with Oleg and Trovatore here. I am happy to go along with pretty much all the authors I respect (Rudin, Lang, Halmos, Ahlfors, ...) and NOT use 'iff' or 'if and only if' in a definition. Either would looks stilted and also be more confusing than helpful to less experienced readers. Madmath789 14:47, 20 June 2006 (UTC)

As KSmrq said "Often definitions are not highlighted as such, but appear inline in a form that is ambiguous about the intent.". For that reason, if no other, we should use language the same way in definitions that we do elsewhere to avoid confusion. JRSpriggs 05:43, 21 June 2006 (UTC)

When KSmrq said In a context that makes clear we are offering a definition I took it to mean that a phrase such as we say that or a foo is called bar if or we define a foo to be a bar if is used. This doesn't mean that Definition. has to appear in front of the sentence. By wording the sentence carefully, it can be made clear that a definition is occuring. If it isn't clear, putting in if and only if won't make it clear; that will only make it look more like a theorem if it already looked like one. I agree with several others, by the way, that common usage avoids the phrase if and only if in a definition. CMummert 12:36, 21 June 2006 (UTC)

We should also make definitions clear by italicising what we are defining. Dysprosia 12:39, 21 June 2006 (UTC)

I can't believe this is still going on. I've already made all the arguments I think are necessary to oppose "if and only if", but I do have two questions: is there anyone, anywhere, who has become confused due to the use of "if" in definitions? Would you actually want to read an article so reeking of pedantic formalism? Also, to respond to your comment above: a more important consistency principle than internal consistency is external consistency; our articles must follow common English writing practice. As KSmirq said, it is always possible to set apart definitions from the text (and this would constitute better writing), thus obviating the internal consistency problem, but it is never possible to set apart Wikipedia from the experience of a native English reader. Ryan Reich 12:50, 21 June 2006 (UTC)

Redirects in the list of mathematics articles

Currently we have 12102 articles in the list of mathematics articles. Out of them, 1070 are redirects (see the complete list). Redirects get created in several ways

Plugging in some redlink in the list (not anymore, as all redlinks are removed automatically)
Merging an article to a bigger article
Renaming an article.

In my view it is the third which makes for most redirects.

While redirects are very important, I see no good reason for why they should stay listed in the list of mathematics articles (I estimate that there are at least 2000 math redirects which are not there).

I wonder what people think of a big purge, removing all redirects from the list of mathematics articles. Of course, if at some point a redirect becomes back an article, my bot will add it back to the list. Thanks. Oleg Alexandrov (talk) 22:37, 17 June 2006 (UTC)

So if I create a redirect to a math article, but the redirect isn't already a redlink from the list, then it doesn't get added to the list? -lethe ^{talk +} 22:57, 17 June 2006 (UTC)

No. The bot adds to the list of mathematics articles via categories. So, if your redirect is made to be in a math category (which it won't, most of the time), the bot will add it to the list. Otherwise it won't. The primary purpose of list of mathematics articles is to list articles I think, not redirects, although a separate list of redirects to math articles may be found useful by some people. Oleg Alexandrov (talk) 23:55, 17 June 2006 (UTC)

Well whatever uses there may be for a list of math redirects, this list cannot serve, since it doesn't contain them all. Therefore, you have my full endorsement to remove them. There is simply no reason to have only some of the math redirects in a list, right? -lethe ^{talk +} 00:00, 18 June 2006 (UTC)

I'm not sure what purposes the list serves. Take Circular arc, which is currently a redirect to Arc (geometry), but the concepts are distinguishable and Circular arc might eventually grow into a separate article. In an index it would be reasonable to include it. If the purpose is to have a way to visit every maths article to check if its conforms to a new policy, then you'd prefer to skip it. (By the way, it currently is not categorized.) Perhaps math-categorized redirect pages could be listed, but rendered in italics, like with the All pages search. (<-This comment was by User:Lambiam who forgot to sign it. JRSpriggs 11:08, 18 June 2006 (UTC))

OK then, so if a redirect is important enough, it should be categorized, and then my bot will add it in. About making redirects italic, that is harder to do, as I would need to daily download a lot of articles to see which are redirects. Oleg Alexandrov (talk) 16:25, 18 June 2006 (UTC)

Done. The log is at User:Mathbot/Changes mathlist. Oleg Alexandrov (talk) 02:39, 19 June 2006 (UTC)

MathML / improved TeX support

Hi people. For those of you who have been watching developments concerning m:blahtex, MathML support on wikipedia, etc, I'm sure you've noticed nothing much has been happening for a while. Well, for the past few months, Jitse and I have been trying pretty damn hard to push buttons in the background to make things happen, but sadly the core developers simply haven't taken the bait. It seems to be a case of "yeah, it looks interesting, but we've got like 10,000 other things we're trying to do, and we just haven't got around to checking out the code yet...". It seems that wikipedia just doesn't have enough engineer-hours to give us the attention we need to get this going, and there's only so much pushing that Jitse and I can do without becoming annoying pains in the arse.

The status now is that I'm certainly not spending any more time on the code until I have some indication that there's a chance wikipedia is going to use it. And I've had enough of all the promotional "hey everyone isn't blahtex wonderful and y'all should be using it". It's tiring and not really my style. I enjoy writing code, not selling it.

So unless the people who hang out on this page somehow band together and make the developers realise that MathML is something that people want, the project is going to die a serene death. I took the initiative about a year ago, and wrote 13,000 lines of code to prove that it was possible. I'm happy to help out some more, and of course I look forward to the day when there is good mathml support in wikipedia. But someone else needs to take the initiative now, because I'm through.

Anyway, I think I'll go to bed now, make sure I'm bright and fresh to watch Australia defeat Brazil 6-0 tomorrow.

Good luck guys. Dmharvey 03:57, 18 June 2006 (UTC)

Perhaps a petition signed by the user community? Which is then passed up to Jimbo? This is an important chunk of code that is being laid at the feet of the sysadmins; surely its something that should be picked up. A few words of caution: (1) although the code may work well for you, sysadmins concerned with high-availability servers have a very very very different view of what it means "to run reliably". You might not have given them warm fuzzies on this issue. (2) The WP servers seem often overloaded, there may be unvoiced concerns about impacting performance. If you think these issues are under control, then a public appeal may be the right route to get attention. If they're wobbly, you might get blown out of the water. linas 04:18, 18 June 2006 (UTC)

I've explored the BlahtexWiki and I have to say, I'm quite impressed. I just have two main concerns for implementing MathML on Wikipedia, if those were fixed, I would gladly push the developers to implement it.

Browser compatability. Almost nothing works for me in IE 6.0
Fonts. It appears as if you need to download special fonts for MathML to display correctly. I'm not sure how many people would want to do that. Also, the radical symbols do not display correctly in Firefox for me.

I would be glad to push for the implementation of MathML in WP if we can somehow figure something out for those two problems. —M e ts501 (talk) 04:26, 18 June 2006 (UTC)

There is no way around the issue of downloading fonts. As far as I can tell, Firefox often lacks some fonts by default. For IE I think one needs the MathPlayer extension.

It is no surprise the developers are weary at accepting a huge chunk of outside code, especially there is not really a huge demand for MathML from users. Any ideas of how to convince the developers to take this step would indeed be much appreciated. Oleg Alexandrov (talk) 05:14, 18 June 2006 (UTC)

Thank you, thank you, thank you for all of your work. Having written some mathematical typesetting code myself at one time, I have a feeling for what a challenge it is to do a good job. There are so many subtle issues of fonts and stretching and spacing and symantics and positioning and compatibility and on and on, that only someone who has been in the trenches can really appreciate the magnitude of this endeavor. It really takes a champion, like Roger Sidje on the Mozilla project or David Harvey on BlahTeX.

I believe I can speak to systems programmers with some credibility, and I would be happy to do so on behalf of BlahTeX. A noisy outcry from Wikipedia's technical writers might also prove influential. Beyond mathematicians, we have physicists, chemists, biologists, and engineers of all stripes, all of whom could benefit.

The latest word from the STIX Fonts Project is

"After reviewing the tasks required for completion of the project, September was established as a revised target for the beta test. The final production release will likely occur in December, but the TeX package may not be ready until January 2007."

Although the STIX project has not been exemplary in meeting its targets, it does appear that it is real, it is happening, and in a matter of months there will be little excuse to complain about a lack of fonts for MathML.

I cannot imagine that server load is a realistic concern. Currently MediaWiki converts <math> mkup to images, which requires parsing, pseudo-TeXing, image generation, and then serving the images. Unless BlahTeX is very poorly written indeed, it is unlikely to be more of a load. All BlahTeX has to do is transcribe TeX syntax to MathML syntax; and bloated as it is, MathML is still much smaller to serve than the equivalent image. Caching may be used currently to amortize the cost of image creation, but there is no good reason the same could not be done for BlahTeX. And, again, storing cached images requires more space than storing cached MathML.

That leaves the concern of bullet-proofing. For that, we have the empirical argument that the code has been tested against every single equation currently used at Wikipedia, of which there are hundreds of thousands. Yes, a few hundred do not translate; but that's a small matter of manual conversion because they depend on the bastardized TeX currently supported (texvc). In compensation, future editors will have use of a broader range of TeX features, something arrow-pushers will appreciate.

It occurs to me that if the developers are recalcitrant, perhaps Jimbo Wales might be persuaded. Pressure from the top could then be more effective than pressure from the bottom.

Thanks again for all the hard work so far. Given Wikipedia's culture of consensus, it seems only fair that others now help shoulder the burden. --KSmrq^T 10:33, 18 June 2006 (UTC)

But so what is the next step? Campaign to get it installed on test.wikipedia.org? What can we do to help? Send messages to mediawiki-l? I notice searching through the archives, that you have previously announced releases of blahtex to that mailing list, and they have never had any response. Have you ever had any dialogue with anyone from mediawiki development about this code? Whom do we talk to? -lethe ^{talk +} 10:43, 18 June 2006 (UTC)

At the risk of sounding too critical, how difficult would it be to make things work for the current "bastardized TeX"? The idea of breaking old revisions of articles without it being obvious why that is makes me kind of queasy ...

Is this a major issue? How do things fail after the change? Backwards compatibility is something that needs to be addressed, even if it cannot be guaranteed.

Not that I think this is a huge problem, if the scope is that small.

Otherwise, I'm with lethe. Whom do we talk to, and what's their favourite ice cream flavour (for bribes, you know)?

RandomP 11:00, 18 June 2006 (UTC)

We have a list of all the broken bastardized tex instances. There are a couple of hundred, which we've slowly been fixing, one at a time. We would obviously want to finish them off before we went live. -lethe ^{talk +} 11:21, 18 June 2006 (UTC)

I'd just like to qualify my remarks: it seems that even today, "history" won't get you anything like the old version of an article, at least when that article uses images from the commons.

I think it would be really cool if someone wrote, essentially, a simulated wayback machine for wikipedia, that went back to the wikicode, images, and math layout as they were when the revision was created. I thought that's what history was, but apparently, not so.

So that's not an issue either, and can we please have mathml now?

RandomP 14:09, 18 June 2006 (UTC)

Brief replies to above questions

Linas's question about server overload. This is a complete non-issue for several reasons, some already mentioned by KSmrq. I haven't done any benchmarking for a while, but here's what I remember. Both blahtex and texvc spend almost all of their time (at least 90%) on PNG generation. Blahtex is somewhat faster at PNGs, maybe 2 or 3 times faster, since I switched to dvipng instead of using imagemagick+dvips. (And Brion Vibber has endorsed the use of dvipng in the past, ask Google for more information.) MediaWiki already has code for caching the images, so this time only gets spent during the first edit, not on subsequent page views or edits. Second, I haven't directly compared the parsing and mathml generation time of blahtex to the parsing time of texvc, but I do know that my desktop machine can generate mathml for the entire wikipedia corpus in about 30 minutes. There's 200,000+ equations in there, so it's not lightning speed, but you ain't gonna overload their servers. And MediaWiki also has code already for caching the mathml, so again that only happens on the first edit. Third, some tests Jitse and I ran a while back suggested that texvc's parsing is unbearably slow on long input data; blahtex on the other hand processes that kind of input really fast.
Linas's point about reliability. Of course it's got bugs. All software has bugs, especially software that hasn't yet been exposed to the real world. Someone mentioned above that it's been tested against all the input in wikipedia and doesn't pretty darn well, which is a start, but of course that's not the point. The real question is whether it survives a determined adversary with source code access. Well, I don't know, I suppose most likely it's not secure. But all software has to start somewhere. I'm not asking to have the code installed tomorrow and force everyone to use it. Heck, at this stage I'm not even asking for the "minimal interesting configuration", which is that it's only available for registered users who select MathML in their preferences, and that we stick to texvc for all PNG output, and only allow mathml for the equations for which texvc can already generate graphics. All I'm asking for is that some core developer gives us more than ten seconds of their time to render an opinion. If they tell me the code is crap and I'm a chump, that's fine, I can live with that, at least it's an answer. If they tell me I need to rewrite it in COBOL, that's fine, it gives me something to do. If they tell me I need to write a comprehensive test suite, that's great, I can do that. But so far the longest reply I've had from people like Brion Vibber, Tim Starling, etc, is a one-line email from Brion:

It sounds great, but I've not had a chance to look at it yet...

He also replied on the mailing list once, here's what he said:

Neat!

I understand 100% where he's coming from, but it's still incredibly frustrating.

Mets501's question about fonts. As KSmrq points out, the STIX fonts project is going to get there eventually, not tomorrow or the next day, but eventually. I believe it will solve all the font problems, because e.g. Firefox will just be able to bundle the fonts in the default installation and it will all Just Work. So for now, no good answer, but eventually, yes.
Mets501's question about browser compatibility. Short answer: it sucks. Firefox/Mozilla is the best out there in my opinion, and it's not quite good enough yet. (I've heard about your problem with broken radical signs; I believe it's a recent regression.) I think the reason browsers haven't quite made it yet is because there just isn't the content out there yet. Well, we can change that, because if wikipedia switched on mathml support, it would overnight become the largest repository of mathml on the web. (I don't have stats for that, it's just a guess.) And here's something else: when I first mentioned to the firefox people, like roger sidje, that wikipedia was planning mathml support, suddenly a whole raft of mathml-related bugs in firefox got fixed, bugs that had been lying around unattended for 2-3 years. These open-source guys love wikipedia. If we deliver, they will follow. On the other hand, I don't have any illusions about MSIE.
RandomP's question about backward compatibility. It's a minor problem in my opinion. See http://blahtex.org/errors.html for a complete list, as of March. Maybe that list looks long, but remember it's across 13 languages, and represents about 0.1% of the total. We could fix them all in a few days. And anyway, Jitse's glue software falls back on texvc if blahtex fails, so it's easy to make the problem vanish entirely.
Everyone's question about who to talk to. I don't know. I've run out of ideas and energy. That's why I'm turning the initiative over to all of you. If enough of you make enough noise, and if the powers that be are hearing voices other than that of the guy who wrote the program, maybe something will happen. Dmharvey 12:28, 18 June 2006 (UTC)

Caching: As KSmrq suggests, the MathML is cached and hence it needs to be generated only once.

Backward compatibility: To expand on what David says, the code as currently written uses texvc to generate HTML and PNG and blahtex for generating MathML. If texvc fails, then blahtex will also generate PNG. Therefore, the few formulae that are not understood by blahtex (for instance because they use invalid latex syntax) will still be rendered as PNG, but there won't be any MathML. In other words, just like the present situation. -- Jitse Niesen (talk) 13:02, 18 June 2006 (UTC)

my email

I sent this email to mediawiki-l just now:

From: lethe at charter dot net
Subject: Blahtex: what's the next step
Date: June 18, 2006 8:08:37 AM CDT
To: mediawiki-l@Wikimedia.org

David Harvey and others has been working hard on Blahtex, the next generation in MediaWiki math rendering technology. Visit http://www.blahtex.org/ for more information and http://wiki.blahtex.org/go/Main_Page for a running demo hosted by Jitse Niesen.

Harvey suggests that blahtex will afford a significant performance advantage, but the main impetus is the ability to render MathML. Support for MathML is not widespread at the moment, so the need for Blahtex is not urgent, but it is the future, and we have reason to believe that Wikipedia's adoption could goad browser developers to speed their efforts (the answer to the old chicken and egg of who comes first, browser support or use by web pages could be: Wikipedia comes first).

It has to happen someday, and today is as good a day as any. Harvey says the software is ready for the next step, and wants to move forward, but doesn't know whom to talk to in order to make this happen. I'm writing you to voice my full support for Harvey's and Niesen's efforts, to find out what needs to be done to take the next step towards rolling this software out, and to ask if there is anything I can do to help the developers to get this software ready for deployment.

Thanks
lethe

I was hoping that several others of you would chime in on the mailing list. If we had a chorus of complaining voices, we would be harder to ignore. Currently, the developers watching that mailing list have ignored me completely. What should I do? Send another, more plaintive, email? -lethe ^{talk +} 11:51, 20 June 2006 (UTC)

Are you sure this is the right way to go? I'm not sure about the relation between mediawiki, the software that actually serves wikipedia, and that mailing list. Is the authoritative version of mediawiki the one serving en:? Are decisions about changes to that software, beyond bugfixes, made on that mailing list, the meta wiki, wikipedia (en) talk, or where?

RandomP 11:56, 20 June 2006 (UTC)

The short answer is, I don't know. Where is the right venue to discuss changes in the software, and who is the right person to talk to? I don't know. Does anyone know what is the right course of action to take? How to we get software changes evaluated and committed? As for whether en runs the official version, the answer is yes. They rollout new versions on test.wikipedia.org first, I think. But then they roll it out for en.wikipedia.org. Should I email Brion Vibber or Rob Church or something? I don't want to be a nuisance, but I think Dmharvey's request to get a response from them at least to say "sorry, we can't accept this" is not unreasonable. -lethe ^{talk +} 12:20, 20 June 2006 (UTC)

Hmm. This is a problem. I've looked around for a good place, but the best I've found is the MediaWiki bugzilla, which currently has two bugs [64] [65] matching blahtex, and I don't think either is what we want.

Can someone create a new feature request there and link to it (I'd also suggest linking back to a Wikipedia page from the new bug, so we can have discussions without all getting out to get accounts on yet another bugzilla)?

That might be a first step to, at least, documenting we're trying to get it in through the official channels ...

Again, I'm just confused by the whole thing. There's a wiki, a mailing list, a bugzilla, and apparently an IRC channel, and I still don't know where and if development discussions happen. However, at least a bugzilla is permanent and will get someone's attention, one would hope ...

Can we move the discussion to Wikipedia:Blahtex or something? It's of interest to physicists, economists, biologists, etc, too! (Or should be.)

RandomP 12:53, 20 June 2006 (UTC)

m:Blahtex would be a place to have a centralized dicussion, after we sent spam to all the physicist, economist, etc Wikiprojects. But that would only be necessary if we are completely unable to open up a discussion with developers in one of the developer channels. If we can do that, then let's just have the discussion there. -lethe ^{talk +} 13:02, 20 June 2006 (UTC)

I have submitted a bug report and sent another email to mediawiki-l. You can vote for the bug at this location. I have no idea what voting for bugs accomplish; I wouldn't be surprised to find out accomplishes nothing. -lethe ^{talk +} 13:23, 20 June 2006 (UTC)

I'm told that most discussions take place on IRC, but I haven't seen any. There are two relevant mailing lists: mediawiki-l for the software as used on Wikipedia, other Wikimedia sites, and other wikis not related to Wikimedia; and wikitech-l for technical matters (hardware and software) involving Wikimedia (Wikimedia is the foundation running Wikipedia, Wikibooks, Wiktionary, Wikisource etc). Either list would be appropriate, and I think they mostly have the same readership. Then there is bugzilla, as mentioned by Lethe, and we also have Wikipedia:Village pump (technical) here. There are also two central wikis, http://meta.wikimedia.org/ which used to contain everything related to the software, and http://www.mediawiki.org/ where the documentation is being brought over to. So it is rather confusing.

I put the items in the order that seems to be best to get the attention of the powers to be (with IRC on top). However, in the end it boils down to an individual developer taking a decision. The concept of consensus plays rather a small role on that level.

I'd advise against emailing the developers individually. -- Jitse Niesen (talk) 14:02, 20 June 2006 (UTC)

I guess the response you may get from IRC depends on who's in the room. I went there first, before anything else, a few days ago as soon as Dmharvey posted his request, and got no biters there. They suggested I might have better luck on the mailing list. Perhaps I try IRC again at a busier time. -lethe ^{talk +} 14:08, 20 June 2006 (UTC)

Discussion continued

I'm not a developer, nor am I Jimbo, but putting myself in their shoes I'd be much more worried about the font issue than about accepting an apparently well-tested huge chunk of outside code. In fact, not being in their shoes this worries me. Many people access Wikipedia from computers they have no control over, and are in no position to download and install fonts for, even if willing to do so. Others may try to and fail. Most wouldn't even try, and miss out on all Wikipedia has to offer that involves formulas. I think it is important to keep blahtex alive, but aim at introduction after the availability of the required fonts has become common. --Lambiam ^Talk 13:53, 18 June 2006 (UTC)

Thus MathML won't be enabled by default. Only people who know what it is, have capable computers, and want to see it, will see MathML. When the day comes that every windows, mac, and linux computer has by default MathML able browsers and plenty of fonts, then we can have MathML by default. But for today, let's have Blahtex which is smarter in all ways. This is a non-issue. -lethe ^{talk +} 14:22, 18 June 2006 (UTC)

Yes, I agree. I will help push for this to be implemented as much as I can. I do think, however, that the default should not be MathML (yet). Users who sign up for an account should be able to select MathML from the preferences page, but the option should link to a page called Wikipedia:MathML, which would say what MathML is, which browsers support it, and which fonts/whatever is needed for MathML to work. I would definitely not give up on this project and I hope that it will be implemented soon (I love experimenting on the BlahTeX wiki!) —M e ts501 (talk) 16:54, 18 June 2006 (UTC)

We've really got to stomp out some myths. The most important fact is that BlahTeX only adds capability to MediaWiki, it does not force removal or breakage of anything that already works. A complete set of mathematics fonts will be available Real Soon Now to everyone on every platform with every browser. Don't have the necessary fonts on the computer you happen to be using? Not a problem; stick with the old-fashioned images and HTML hacks. Browser not set up to support MathML? Not a problem; don't ask for MathML. In other words, adoption of MathML is strictly voluntary.

So why BlahTeX? Because it offers so much more than texvc, which is old and seriously deficient. BlahTeX handles a broader range of TeX input, including things that are currently a real pain to work around. Even when it generates PNG output, not MathML, BlahTeX is superior to texvc.

And why MathML? Because it is the future of mathematics on the web, for reasons such as the following.

A text-to-speech processor can read MathML aloud for vision-impaired users, or for ordinary folks who merely want to know how a formula is spoken.
All the fonts and layout of a MathML display can be scaled up or down, just like the rest of the text on a web page, to either zoom in on a detail or zoom out for an overview.
MathML can include arbitrary Unicode characters, something texvc is unlikely ever to do.
A MathML formula is smaller and faster to serve than a PNG.
MathML can allow internal line breaks, while images cannot.
Programs like Mathematica allow cutting and pasting MathML formulae, so an equation can be transfered easily for evaluation or graphing.
MathML has already found favor on technical blogs, like The String Coffee Table.
Because MathML is built on XML, it can be processed with XSLT and used across diverse media. In particular, MathML will be much more compatible with print than any fixed-resolution PNG rendering.
One of my favorite benefits is that the contents of a MathML formula are available to search in my browser, whereas a PNG is an opaque monolith.

Note that the MathML 2.0 Recommendation from W3C was released on 2001 February 21, and the 1.0 version dates back to 1998 April 7. That's an eternity ago in web time!

But to reiterate: BlahTeX offers considerable benefits even for those who do not choose to view MathML. It can't hurt. It can only help. Please support its rapid adoption by MediaWiki, in whatever way suits you best. --KSmrq^T 19:22, 18 June 2006 (UTC)

I think you should put that in an email to the mailing list. Perhaps wait until mine shows up and make it a reply so it's all in one thread though. We want to generate some noise so that it seems like there is a whole rabble of us clamoring for this. And of course we have to quelch the false assumptions that people will make to justify not using the software. -lethe ^{talk +} 19:29, 18 June 2006 (UTC)

Thanks, KSmrq, that's a nice piece of writing. Not for the first time, I admire your writing skills.

Apparently, the best way to contact the developers is via IRC (#mediawiki on irc.freenode.net). Another thing we haven't done is to contact our colleagues at the other language Wikipedias. I imagine that especially editors writing in a different script than ours would be interested. -- Jitse Niesen (talk) 04:23, 19 June 2006 (UTC)

Hey, KS, I think maybe this nice list of yours should be copied over to m:Blahtex where it would be the skeleton of a FAQ. A central repository that we can refer to easily to stop out myths. What say ye? -lethe ^{talk +} 14:38, 20 June 2006 (UTC)

If you like it, use it. --KSmrq^T 20:14, 20 June 2006 (UTC)

Do you think that we should write an email to Jimbo about this? Do you know how aware he is of BlahTeX? If we could convince him, it would definitely get implemented. —Mets501 (talk) 20:40, 20 June 2006 (UTC)

Let's try to confine our efforts to those people who will actually have a hand in the software direction, which I don't think Jimbo does. Anyway, the latest correspondence sounds like Vibber is going to set up Jitse with an SVN account. We might be in business, so let's wait to hear from Jitse and Dmharvey what happens with that. -lethe ^{talk +} 20:47, 20 June 2006 (UTC)

[via edit conflict] Hang on for the moment guys. Brion gave a more positive reply to one of Lethe's recent emails, see here. Jitse and I will work out what to do with this development, and we'll keep you all posted. Dmharvey 20:49, 20 June 2006 (UTC)

Yay! Good luck guys! Make sure to let us know about any developments. —Mets501 (talk) 13:11, 21 June 2006 (UTC)

Some progress has been made

See here. I'm not precisely sure about terminology here, but perhaps this makes Jitse a Developer. This is good news, but I don't promise mathml tomorrow. Still some work to do. We'll keep you posted. Thanks guys for your encouragement, and especially lethe for the insistent emails on mediawiki-l :-) Dmharvey 12:00, 22 June 2006 (UTC)

Or perhaps he's saying that he's responding to Jitse, and he will be adding the BlahTex extension (because he put in a comma). Either way, its good. —Mets501 (talk) 12:35, 22 June 2006 (UTC)

It only makes me a minor developer. The standard tariff is to sacrifice one virgin every full moon as otherwise Bad Things Happen. However, I can also be placated with papers on which I can put my name as co-author. ;) -- Jitse Niesen (talk) 13:19, 22 June 2006 (UTC)

Well, I can give away my virgin mathbot as a groom to the brand-new bride-to-be Jitse's bot (who am I am sure is a she, or otherwise can be made so just by flipping a bit). Oleg Alexandrov (talk) 16:10, 22 June 2006 (UTC)

So who is "jitsenielsen" anyway? Dmharvey 14:11, 22 June 2006 (UTC)

I'm pretty sure Brion Vibber made a spelling error :-) —Mets501 (talk) 14:30, 22 June 2006 (UTC)

Request for book recommendations

Maybe this is not the place for this (I am aware that this is not un all-purpose forum), but here it goes. I intend to order some math books from Amazon, but I'm not sure what to get. As it seems to me that there are some very good mathematicians here, I think you could help me a lot with some recommendations. Now for some background, to understand what I specifically need: I'm an undergraduate math student (though also an economics graduate and working economist) and I pursue math mostly for my own curiosity and because I truly enjoy it (more than economics :D). I need something mainly appropriate for self-learning, so I'm targeting good classic texts on major fields or other good books. I prefer books that don't shy away from advanced/abstract concepts, but preferably give motivation for concepts and some intuitive explanaition/interpretation. Also, I learn the most from books which include examples worked-out in detail and/or solved relevant problems. Also, note that unfortunately cost is an issue, so don't recommend too many books that are only somewhat helpfull (though by all means recommend books that you consider good, even if they are not very popular). Hope that you will have some advice for me... AdamSmithee 20:48, 18 June 2006 (UTC)

A great place to ask this question, which is indisputably appropriate (unlike here, which is apparently disputably so :)) is the sci.math newsgroup. You can get there through Google groups if you don't already know. This page is really just for discussing the Wikipedia mathematics project. Ryan Reich 20:57, 18 June 2006 (UTC)

I am sure that we could give a great deal of advice (though some of us will contradict each other!), but we do need a bit more info about your mathematical interests and level: which branches of maths are you most interested in? what sort of level are you at in that level? Perhaps it might be best if you could tell us some maths books that you believe you have mastered, and we could suggest some books that would make a "good next step"? Madmath789 21:02, 18 June 2006 (UTC)

Myself, I'm a graduate student and I like algebraic geometry and sometimes number theory. Or did you mean him? :) Ryan Reich 21:42, 18 June 2006 (UTC)

LOL! I did mean 'him', but our edits crossed, and I got the indentation wrong :-) (but if you want some suggested reading on algebraic geometry, I can probably oblige :-) ) Madmath789 21:46, 18 June 2006 (UTC)

The most affordable route is used books, especially if you live in or near a decent university or college. Some of the much older books are easier to learn from, because not so long ago mathematics texts had a bad habit of being horribly written for learning, though packed full of detail for reference. More recently there may have been a corrective swing, so that one can benefit from both a modern viewpoint and decent pedagogy. But in a field like algebraic geometry, the really old stuff has lots of geometry while the modern stuff has almost none. Depending on your tastes, one may appeal more than the other. Another fact about older books is that often recent books try not to duplicate the work of the early masters, so if you want to get the original insights from the folks who had them you have to step back in time. It reminds me of something that was said about the programming language ALGOL, that it was an improvement on many of its predecessors, and also on many of its successors. Lastly, it is vital to choose books at the right level at the right time, lest an otherwise great book become a doorstop. --KSmrq^T 22:39, 18 June 2006 (UTC)

Well, first of all tx for replying! As I said, I know this is not the place (and I'll probably try sci.math, which I didn't know about), but I tried it because I came to trust many of you guys. As for my background and interests: I'm an undergraduate student in math at this time. So far, my exposure was almost entirely to Romanian textbooks, which are very tightly written and unfortunately are generally very good for reference but not for learning (this is somewhat of a characteristic of Romanian academic books). On the other hand, I've read quite a few American graduate level textbooks in economics and I noticed that, generally, they are much better for learning (also, reading some freely available online math books lead me to believe this is also true for math). To give an example, at this time I'm struggling with linear connections and covariant derivative, but my (Romanian) books insist to much on tightely written modern coordinate-free stuff, giving virtually no motivation and no explanation, and I'm having trouble understanding why the stuff is defined that way, what does it mean and what is it good for.

At this moment my interests are rather wide and I just want to get a reasonable background in the main fields. However, I do have a sweet spot for abstract algebra, and I'm interested in probability and statistics (including links to measure theory, numeric analysis etc.) for the aplications to economics. But I'm also very interested in stuff like differential geometry for instance. As an example of one book that I have heard about, and I might get, I know about Jacobson's 'Basic Algebra' (though I don't know how that is), but I have no idea what else is there.

Regarding level, it is hard to say what undergraduate in Romania means compared to other education systems, but it is possibly more advanced than American undergraduate level (?maybe?). AdamSmithee 23:25, 18 June 2006 (UTC)

Hi, I suggest browsing Dover Publications online catalogue (use Google to find, I am lazy :P). They republish a lot of classical and important texts. By rule of thumb, eastern Europe is more advanced in beggining of undergraduate studies. -- 127.*.*.1 01:14, 19 June 2006 (UTC)

Poussin proof

I have just had a brief look at the page Poussin proof, and apart from being a short stub, at least half of it seems to be mathematical rubbish. I would like to have a go at making this into a sensible article - but about the Dirichlet divsor problem (the first sentence of the Possin page), as I can't find anything about this elsewhere. If I have missed it, and there really is a page about the Dirichlet divisor problem, plase let me know before I waste too much time ... Madmath789 12:11, 19 June 2006 (UTC) (OK, having read it again, it is not total rubbish, but badly worded.)

Change of project scope at Wikisource

(I've copied the following from Talk:Mathematics. — Paul August ☎ 16:56, 19 June 2006 (UTC))

I would like to call the communities attention to and personally protest a decision at Wikisource to exclude and delete a significant portion of the material that was part of its original charter. Prior to April 29 of this year, Wikisource:What is Wikisource? listed the following as included material:

"Some things we include are:

1. Source texts previously published by any author
2. Translations of original texts
3. Historical documents of national or international interest
4. Mathematical data, formulas, and tables
5. Statistical source data (such as election results)
6. Bibliographies of authors whose works are in Wikisource
7. Source code (for computers) that is in the public domain or compatible with the GFDL"

On that date the project page was changed to explicitly exclude:

Mathematical data, formulas, and tables
Source code (for computers) that is in the public domain or compatible with the GFDL
Statistical source data (such as election results)

Obviously, this represents a major change in the scope of the project. It is based on a single poll conducted between April 4 and 27, 2006 Wikisource:Scriptorium/Archives/2006/04. Previous discussions had been held with opposite results Wikisource:Wikisource talk:What Wikisource includes. A primary reason given for the new change is that the editors participating do not feel competent to maintain this material and have little interest in it. However apparently no effort was made to notify participants in the previous discussions, nor to recruit new editors that might have an interest. Note that there are many active projects pages in mathematics and the sciences where such people might be found.

There was also no discussion of methods for reducing the load on editors, such as locking material after review. In general, reference material does not need or benefit from frequent edits.

I certainly respect the efforts of the regular editors on Wikisource and agree that their views should be shown some deference. However the process they chose is not sufficient. At the very least, I think there needs to be broader community input into such a massive change in the scope of a Wikimedia project. Even if this material is best excluded from Wikisource, I believe it deserves to be part of an encyclopedia and that any material already contributed should be moved elsewhere rather than be deleted. The simplest solution would be to move mathematical and scientific reference material to Wikipedia, where there are large communities to evaluate and protect this information. An argument could be made that mathematical data belongs in Wikicommons because it is, or potentially can be, language neutral. Or perhaps there should be a new Wikireference project. Computer source code deserves a separate discussion, since there are so many other open source code repositories available.

At this point hundreds of articles have been marked for deletion. See Wikisource:Category:Deletion requests/Reference data Some material has apparently aready been deleted. There is nothing left in Category:Mathematics. I would propose that all article deletions on Wikisource based on this change be frozen until a fuller, community-wide discussion can be held.

I have also posted these comments at Wikisource:Scriptorium, where I think the primary discussion should be held.--agr 16:01, 19 June 2006 (UTC) --agr 16:01, 19 June 2006 (UTC)

This call to arms would look better at Wikipedia talk:WikiProject Mathematics. It is about mathematics at wikipedia, not about the article Mathematics on wikipedia. -lethe ^{talk +} 16:12, 19 June 2006 (UTC)

(end of copied text)

It was actually my intent to post the here. I just messed up. I am removing the link from the math talk page.--agr 20:16, 19 June 2006 (UTC)

(Cross-posted from Wikisource)I would like to quote my own remarks on opening up this disscusion back on April 3:

I realize this has been discussed several times in the past, to the agreement of accepting such material. However, the current state of reference data on Wikisource is unacceptable. The community members who are active on this site have little interest, and in some cases understanding, of the data we have been hosting. Although there have been editors that were adamant that this material should be included here, they have not remained active in the organization nor matainance of it. Much of this material is beyond the active administrators ability to even distinguish vandalism from corrections. Because of this current state of affairs there have been nominations for deletion for some of this data. However I feel we need discuss the larger questions of the place of reference material on Wikisource before we make any deletions.

It is disingenuous to suggest we ignored previous discussions or made no efforts to find other solutions short of deletion. In fact I opened up the discussion back then to put a stop to this material being brought up piecemeal at Proposed Deletions. In all honesty, at the beginning of the April disscussion I expected that we would arrive at a solution for keeping a portion if not a majority of this material. No one who was interested in this material bothered to even suggest any alternatives much less volunteer to implement any solutions in over 2 months since then. As for calling this to the "community's attention", you imply we are trying to hide it or be secretive. This is false. I personlaly have left notes on WP talk pages of people showing recent interest, as well as mentioned the decision in passing on foundation-l. Not to mention the write up done by Pathoschild in Wikisource news during and after disscussion. The decision was also mentioned on wikisource-l. The idea that this was "based on a single poll" is also misleading. It is based on consensus taking into account ideallistic comments made in prior disscussions as well as the pragmatic reality of maintaining this site. (Added Note: Not a single person spoke up for inclusion) My negative opinions about inviting in the entire Wikimedia community into these sorts of decisions are given in much detail at the foundation-l archives. The thread begins with this post (Note this thread is not about Wikisource, but deals with the subject of alerting other Wikimedia projects to dissucions of policy changes within one sister project). I will quote myself from a later email in that thread:

I think [Ec has] hit the nail on the head with "Good rules support existing practice rather than shape it." The problem with the original suggestion is such advertisement would atract people who have no understanding of existing practice. That is my concern. I feel anyone familar with existing practice will be aware of policy disscussion through the normal in-project channels.

The deletions are proceeding slowly and carefully with any wanted info being moved to other sites. There were no mass deltions on April 29th. If you can find a home for anything we could not I will restore the pages for your access, please give me a list. I think the topic of this post is out of line and [agr's] proposal has little merit. Especially the idea that we should hold this material until and new sister project of "Wikireference" gets off the ground--Birgitte§β ʈ Talk 18:16, 19 June 2006 (UTC)

Added Note. This disscussion as seen by those unfamilar with Wikisource may be misleading in our inclusion policy. I just want clarify that if there is an otherwise acceptable publication with apendices of Mathmatical tables, the enitre work including the tables is accepted at Wikisource. The exclusion only regards standalone data which is not a transcription of an acceptable publication such as s:Trinary numbers.--Birgitte§β ʈ Talk 18:27, 19 June 2006 (UTC)

Yes, I would like a list of the material that has been deleted. I think it is totally reasonable to expect some notice and time for us to decide what should be kept and where. I get the message that this material is not wanted at Wikisource, but that is no excuse for simply deleting it without informing anyone who might be interested. The fact that no supporter of the material spoke up during the April discussion should have been a clue that there was not adequate notice. --agr 20:16, 19 June 2006 (UTC)

I find your topic header both here, and on the Scriptorium, to be inflammatory, inappropriate, and wildly out of place. To quote from our own article on book burning: "Burning books is often associated with the Nazi regime." Jude (talk) 00:14, 20 June 2006 (UTC)

I certainly was not trying to suggest that anyone is behaving like Nazis and I apologize if the title is too harsh. As I said in my original post, I believe the regular editors at Wikisource are due some deference in their decision making. But I find the wholesale deletion of articles belonging to topics no longer in favor, Mathematics in particular, to be very disturbing. It is one thing to change the scope of a project, another to simply discard material submitted and accepted in good faith.--agr 00:38, 20 June 2006 (UTC)

Just to clarify, nothing was deleted because the topic fell out of favor. I would love to see mathmatical texts added. We actually have some being worked on now. Data is being excluded no matter the topic. --Birgitte§β ʈ Talk 00:58, 20 June 2006 (UTC)

The entire category of mathematics was wiped out. Absent a list of what was deleted there is no way to tell what might have been of interest.--agr 11:54, 20 June 2006 (UTC)

Of the 1741 pages that have been deleted since April 29, 2006, on Wikisource, and June 18, 2006, 1381 of them were in the main namespace. Of those 1381 deletions, 152 pages contained "efer" or "ref" in the deletion summary. You can find the complete list of them here. Jude (talk) 13:26, 20 June 2006 (UTC)

(edit conflict)Categories are currently little used at Wikisoucre (i.e. s:Category:Epic poetry lists 5 poems, believe me there plenty more), that one is empty does not mean we have nothing on the topic. I do not know how narrowly you define Mathmatics but some projects currently underway are s:A Treatise on Electricity and Magnetism (the proofreading of OCR is being done on the image pages); s:The New Student's Reference Work#Arithmetic; s:1911 Encyclopædia Britannica/Infinitesimal Calculus These are just a few example of current work. Most anything listed on this website would also be a welcome addition as I believe they are all out of copyright. The topic of Mathmatics has not fallen out of favor!

You are complaining that pages you might have been interested in (if you had a list of them to examine, as you do not seem to know what actually existed) were deleted by people who examined and disscussed them on project's main discusssion page as well as at Proposed Deletions. This complaint's scope is based on an empty category on a project that does not currently use categories in an organized fashion. This complaintent despite speaking for the inclusion of data at Wikisource in November, never made a single edit towards the maintanence or organization of that material in the 5 months between then and the April disscussion. Despite your strong interest in the deleted data, you refuse to do the legwork on compilng a list of titles for me to restore. Titles which you did not put up, did not edit and did not add to your watchlist. I dislike turning this in your direction, but I really dislike the the misrepresentations being made about what happened at Wikisource. I will repeat that this topic heading is quite out of line and would appreciate it if you struck it. I imagine you realize the Plan on phasing out reference data will procede without interuption, please make any requests for temporary restoration on my talk page.--Birgitte§β ʈ Talk 14:15, 20 June 2006 (UTC)

To cool things down a bit, I have changed the topic heading here and at scriptorium. User:Bookofjude has finally provided a list of the material deleted after others told me to search through the logs. That is a big help. I really don't want to make this personal, but I must point out that after the November discussion led to a clear consensus on keeping reference material, I submitted a detailed proposal on what tabular material to include to the discussion page on January 18, 2006. It received no further comment. I think I had every reason to think the matter was settled. --agr 14:52, 20 June 2006 (UTC)

Thank you for the alteration. I sympathize that you believed things were settled, but I have learned that settled doesn't exist on a wiki.--Birgitte§β ʈ Talk 15:13, 20 June 2006 (UTC)

Although I am a bystander in the debate, though in favour of keeping math tables on wikisource, I would like to remark that I read Wikipedia Signpost regularly and I don't remember any remark about voting about massive deletions of existing material on Wikisource. Considering that fact that Wikisource is not so high profile and people here could be interested in the voting, I think it's a bit unfair. Samohyl Jan 16:47, 20 June 2006 (UTC)

I read the Signpost regularly as well. Although they seem to report very well on Wikimedia Foundation issues, I think their coverage of other projects and other languages is quite minimal. I don't know that I would say it is unfair of them, after all the Signpost a product of the English Wikipedia. Anyone interested in Wikisource policies should regularly read the Scriptorium. There is nothing of importance that is not at least mentioned there. I think the archives are quite nicely organized as well for those interested.--Birgitte§β ʈ Talk 17:08, 20 June 2006 (UTC)

Deleted math articles

As best I can determine, here is a list of the math-related articles that have been deleted. Birgitte§β has kindly restored them temporarily:

Wikisource:Prime deserts - a fairly short short list of gaps in the primes
Wikisource:Fibonacci numbers 1-500
Wikisource:Mersenne primes - up to number 30, 2^132049−1
Wikisource:Phi to 30,000 places - There was also an article listing Phi to 20,000 places

Also there were computer source code articles with the following titles:

I'm not sure these have mcuch value. Finally, I believe there were once articles listing pi and e to a million places. These would be easy to reconstruct if anyone wants to make a case for them.

I think a case can be made for moving at least the first two or three articles above to Wikipedia, presumably retitled as "Table of..." Comments?--agr 18:35, 20 June 2006 (UTC)

Babylonian mathematics, Ibn al-Banna

The section Old Babylonian Mathematics (2000-1600 BC) of this article seems to be a copy of this page (starting with "Perhaps the most amazing aspect of ..."). It's especially funny in sentences like "In our article on Pythagoras's theorem in Babylonian mathematics we examine...", where in reality, no such article exists on Wikipedia. What should be done about it?

On a somewhat related issue, User:Chem1 has created the article Ibn al-Banna (1256-1321), to whom he attributes the invention of the iterative process $x_{n+1} = \frac{1}{2}(x_n + \frac{N}{x_n})$ for finding the square root of a number - aka the "Babylonian method". This doesn't seem right. -- Meni Rosenfeld (talk) 14:41, 21 June 2006 (UTC)

I'll take a shot at a re-writing and wikifying the Old Babylonian Mathematics (2000-1600 BC) section. Gandalf61 14:54, 21 June 2006 (UTC)

I've removed that section from Babylonian mathematics as well as and following section as possible copyright violations, leaving a notes on the talk page of that article, and the editor who added it. Paul August ☎ 15:31, 21 June 2006 (UTC)

Okay, I've now trimmed, re-written, wikified and re-ordered the offending section. I think it is now sufficiently different from the source to be no longer copyvio, so I have put the re-written version back into the article. Gandalf61 13:17, 22 June 2006 (UTC)

Iff in formal writing

I would like to propose that all usages of "iff" to mean "if and only if" be replaced by "if and only if", as iff is not a very common abbreviation. Thoughts? (I actually did a bit of this but Oleg Alexandrov advised me to ask here – if there is a consensus for me to remove those edits it will be no problem for me to do it.) —Mets501 (talk) 20:24, 21 June 2006 (UTC)

I disagree that iff isn't very common, but I support removing it in favour of "if and only if", particularly in articles that might be of use to people who aren't expert mathematicians. RandomP 20:28, 21 June 2006 (UTC)

I would say that iff is quite common in textbooks, and I use it all the time, personally, but this is an encyclopedia, and I believe (quite strongly) that iff should be avoided everywhere (especially in definitions, whether formal or informal!) Madmath789 20:45, 21 June 2006 (UTC)

Yeah, iff is a bit of a neologism (which I think fell out of fashion by now :) and should surely be avoided in defintions. Is it a good idea however to just do a mass iff removal from all math articles? Makes me wonder if it is worth the trouble. Oleg Alexandrov (talk) 21:05, 21 June 2006 (UTC)

It's not really trouble. It just takes a bit of time, but I'll put the time in if we get enough consensus here to remove it. —Mets501 (talk) 21:08, 21 June 2006 (UTC)

I prefer "if and only if". Life is short, but if your life isn't that short, I say go ahead and change them. Just be careful with articles like if and only if and IFF. Dmharvey 21:14, 21 June 2006 (UTC)

(Edit conflict) Well it may not be trouble for you to do it, but you have kind of washed out my watchlist. This is slightly annoying, but tolerable for a good cause. Is there any precedent for bot flags for people using AWB? -lethe ^{talk +} 21:15, 21 June 2006 (UTC)

No precedent that I know of. I'm sorry about the watchlist, I know what you mean (my watchlist is full of math articles too). Hopefully I can get it all done today so that only one day's watchlist is screwed up :-) —Mets501 (talk) 21:18, 21 June 2006 (UTC)

If I recall, "iff" is allowed in any Springer book or journal. It is in the Merriam-Webster dictionary (supposedly). I think that disqualifies it from being a neologism. I personally never use it, but I wouldn't impose a moratorium. Don't you think this is a bit heavy-handed? Silly rabbit 21:39, 21 June 2006 (UTC)

It's there. At least it's in their online version, and I predict that iff (heh) it's there, it's either in their print edition, or will be in the next print edition. --Jay (Histrion) (talk • contribs) 17:33, 22 June 2006 (UTC)

I support making this change, with the exception of "iff" used in definitions which should be changed to "if". In fact I think we should expand the Math Manual of Style to discourage the use of "iff".Paul August ☎ 21:56, 21 June 2006 (UTC)

I support editing out all uses of "iff" from Wikipedia, and augmenting the MSM to discourage future use. However, I think a more delicate touch is required. In definitions that are clearly such, change to "if". Elsewhere, it is often better to rewrite the sentence rather than merely changing "iff" to "if and only if". I realize that may be much more labor intensive, and require more insight and judgement on a case-by-case basis, but the alternative could look ugly. Uglier than "iff", I don't know. My practice has been simply to make this kind of change as I encounter instances, and as the mood strikes me. A note in our conventions, a note in the Manual of Style, and widespread awareness among mathematics editors may be enough to stamp out the problem.

I also go after a few other issues as I see them. I've mentioned "ditto" previously. Others are the Latin abbreviations "i.e." (id est, "that is") and "e.g." (exempli gratia, "for example"). Although I know what they mean and am perfectly comfortable with them, I think they pose an unnecessary barrier to many readers; and since the English glosses are perfectly good substitutes, I see no reason to use the abbreviations here. The list goes on, but that's enough for today. --KSmrq^T 23:40, 21 June 2006 (UTC)

So what is the proper rewrite for "a triangle is right if and only if its sides satisfy a² + b² = c²"? -lethe ^{talk +} 23:49, 21 June 2006 (UTC)

Depends whether you're defining the term "right" or whether it's been defined previously. Dmharvey 23:55, 21 June 2006 (UTC)

I'm asking KSmrq how to rephrase a theorem whose converse is also true, so assume "right" has been previously defined as, say, "contains a ninety degree angle". -lethe ^{talk +} 01:27, 22 June 2006 (UTC)

I'd need more context to be sure; good writing doesn't happen one sentence at a time. Since this is a theorem asserting an equivalence, I would not object to "if and only if", and perhaps not feel the need to edit it. However, if I were writing this ab initio myself, I might choose different language. For example, if I wanted to highlight the assertion I might write

Theorem. Let a triangle have side lengths a, b, c, with c the longest side. Then the following two statements are equivalent:
1. The triangle is a right triangle.
2. a² + b² = c².

For an inline statement, but still feeling the double implication is important, I might write

For any right triangle with sides a, b, c, the sides satisfy a²+b² = c², where c is the longest side. The converse is also true: any triangle whose sides satisfy the equality is a right triangle.

But it really depends on the topic, the audience, the assertion, and the context. For example, in a larger context where this is a minor point, and the paragraph in which it appears is building a more important concept, I'd try to keep it as short as possible consistent with clarity. Does that answer your question? --KSmrq^T 12:53, 22 June 2006 (UTC)

It does answer my question. But I don't like it. You want to double the length of the assertion so that you can mention the statement and its converse explicitly? I would really much rather stick in an "if and only if". Listing the equivalent conditions is nice when there are three or four equivalent conditions, but rather burdensome for only two. Therefore I cannot support the idea to revise the MSM to suggest that "if and only if" be avoided (for theorems, that is. I'm on board avoiding this turn of phrase for definitions though). -lethe ^{talk +} 03:54, 23 June 2006 (UTC)

Yes, I described two variations that are longer. But the last thing I said was that in certain contexts I'd prefer to keep it as short as possible, so as not to detract from a larger point.

Here's one way to think about it. I have an assertion in mind. It's a nifty little assertion and I quite like it. But my first question is, does it help the article? Is it important either as an end in itself, or as support for a larger goal? Or perhaps as entertainment or enrichment? If it does not help the article, no matter how much I like it I shouldn't use it. OK, I decide it stays. Is it a brief aside, or is it something the reader really should understand? If the latter, then brevity is less important than clarity. Both of the longer versions I offered are predicated on the assumption that each direction of the implication is important for the reader to absorb. If it's that important to say, then spend a few extra words and do it right. If it's not that important to say, then maybe we don't really need it.

Prose that packs five major ideas in one paragraph is not reader-friendly. We tolerate it in mathematics texts if we must, but we don't enjoy learning from it. (I'm reminded of a graduate algebraic geometry class that spent the better part of a term covering the first chapter of the text: Hartshorne, ISBN 978-0-387-90244-9.) That kind of density intimidates mathematics graduate students; surely it is inappropriate for an encyclopedia.

As for the MSM, my proposal was to ward off "iff", not "if and only if". --KSmrq^T 23:03, 23 June 2006 (UTC)

OK, since it seems like no one is opposed to changing iff to if and only if, I'm going to continue. As far as replacing some with just "if", that can be done afterwards. —Mets501 (talk) 01:24, 22 June 2006 (UTC)

I think that's a misreading. Both Paul August and I explicitly objected to making the change in the context of a definition, a view widely supported by others in prior discussion. Is there some reason you can't be careful about that? --KSmrq^T 13:00, 22 June 2006 (UTC)

Basically, what I've gotten out of this discussion is that nobody objects to changing "iff" to "if and only if" (they do mean the same thing), but that you both support removing some of the "if and only if"s and making them just "if"s, or removing them altogether and rephrasing definitions. It will be no harder for you to do that when it says "if and only if" than when it had said just "iff". If you want to go back and do that, well, all the pages that have "if and only if" are now grouped in my most recent contributions. —Mets501 (talk) 13:18, 22 June 2006 (UTC)

I also would like to add that through my going through all the "iff"s I came by very few definitions. —Mets501 (talk) 13:21, 22 June 2006 (UTC)

I don't think this is a big problem. Paul August ☎ 17:54, 22 June 2006 (UTC)

I would point out, however, that this is one of the reasons we have a link for iff; so if someone doesn't understand it, it can be explained.Septentrionalis 00:15, 2 July 2006 (UTC)

Fraction refraction. :-)

I've never poked my head into the Math WikiProject before, but a few months back I did some work on Fraction (mathematics) before I had to take a break to tend to both Real Life and my proper job. Looking around, I can't help feeling there's a lot to be done, and it's not just a matter of the one article:

If Vulgar fraction and fraction (mathematics) are not to be merged, then duplicate material needs to be excised. If they are to be merged, then let's merge 'em!
Fraction (mathematics), while slowly improving, needs cleanup, and needs it badly, but the lengthy material on the arithmetic of fractions really belongs in an article all its own. Or, for that matter, in a Wikibook, but...
the Wikibooks material is scant, sometimes incorrect, and things are often hard to find, or can be found in more than one place. Looking for fraction arithmetic, for instance, I found it under both Algebra/Arithmetic and Applied Math Basics, but not under Beginning Mathematics. Are Wikibooks out of the scope of this WikiProject?
Amongst the mess, there's probably more duplicated material about Egyptian fractions than there needs to be.

I'd keep going, but another task is calling me from my PC. I know that fractions might not be a hip'n'trendy subject, but I work as a tutor at a community college and there are a few math topics that come up a lot, and manipulating fractions is one of them. :) I'd be willing to take the lead on this, as long as I have the support of the Project. --Jay (Histrion) (talk • contribs) 21:09, 21 June 2006 (UTC)

New template

I just created a new template, {{sqrt}}. It basically displays the radical (√) and the the number with an overline. For example, if you enter {{sqrt|x}}, it will produce √x. It works great for all CSS capable browsers, otherwise it just displays a radical sign. I was wondering, should we put this in the mathematics manual of style as a recommendation for all inline square roots? —Mets501 (talk) 01:15, 23 June 2006 (UTC)

otherwise it just displays a radical sign

So what happens if I enter √x+2 in a non-CSS capable browser? Is it going to appear as √x+2? Dysprosia 01:50, 23 June 2006 (UTC)

Yes, I think it will. However, there are so few non-CSS capable broswers that this is not an issue. Or if people here think it is an issue, then don't use this template for polynomials. —Mets501 (talk) 01:56, 23 June 2006 (UTC)

If it's going to fail and effectively look incorrect for any number of users, then it's not a Good Thing. As KSmrq said, √(x+2) is always correct. Dysprosia 03:57, 23 June 2006 (UTC)

I take it the benefit is the vinculum (overline)? Otherwise, √2 produces √2 just fine.

I'm leary of this for a few reasons. One is that a browser that doesn't support CSS properly doesn't have a graceful fallback to show the grouping, so readers can't distinguish √x+2 from √x+2, whereas with √(x+2), √(x+2), they can. The second problem is that the radical sign doesn't stretch up or down, so that something like √^x⁄_y or √x²+y² won't look right. It seems I can't write the fraction using the {{fraction}} template, because there is no nesting; still, I suppose this doesn't come up often. But template use incurs extra server overhead; is it worth it?

My last concern involves the arrival of BlahTeX. Currently the notation <math>\sqrt{x^2+y^2}</math> produces a PNG, $\sqrt{x^2+y^2}$ . BlahTeX can serve this as MathML that renders beautifully inline. However, this creates a predicament for the template. How should the template adapt? Should it be revised to produce the <math> form, or continue to produce the Unicode/CSS form which is now less attractive for many readers?

Your thoughts? --KSmrq^T 03:45, 23 June 2006 (UTC)

On my machine (Firefox on Mac OS) it renders like this:

. Honestly, if I saw something like that in an article, I would change it to <math> straight away. I think it looks awful. I looks like "square root of the conjugate of x+2". It's marginally better in Safari. Dmharvey 11:04, 23 June 2006 (UTC)

I really dislike the idea. Sure, presentation is important for Wikipedia, and we all (or at least some of us) are looking forward to seeing a beautiful print version of wikipedia in the library one day (or just a nicer version on a high-resolution display with large fonts).

However, at least as far as I'm concerned, the real value's in the database being created. I'm already somewhat skeptical of the guideline to avoid using inline math. Templates make it even harder to understand what's going on, are limited in their applications, and I'm not sure they'll ever do exactly what you want with screen readers. Blahtex promises to be a better way out, for now, with MathML salvation on the horizon.

(I don't think Wikipedia should be using TeX-derived syntax forever, though. An advanced language that would allow us to specify not only what our formulas should look like, but also what they mean, and allow wikilinked symbols, might be a good idea when MathML has become accepted).

RandomP 12:08, 23 June 2006 (UTC)

Thanks everyone for your input. I will stop using the {{sqrt}} template (it appears as if that's what everyone above thinks), and have removed the changes to the square root article (the only one which I changed. Oh god, we need BlahTeX! It's so ugly with inline PNG square roots and even uglier with the √ sign. —Mets501 (talk) 12:51, 23 June 2006 (UTC)

While we're on the topic, something else I should mention is that blahtex knows how to get the vertical alignment of a PNG equation correct (thanks to dvipng). That is, it aligns the baseline of the equation with the surrounding text. This is not enabled on the demo wiki, because it requires some (minor) changes to mediawiki's database schema, and we don't want to be pushing our luck yet. It is however enabled on the interactive demo. Things like inline square roots become a lot less uglier when the baseline is correct, especially if the font size is approximately correct. Dmharvey 13:20, 23 June 2006 (UTC)

Yes, I forgot to mention baseline issues as one of the advantages of BlahTeX. MathML display, of course, automatically gets it right without clever hacks. --KSmrq^T 14:21, 23 June 2006 (UTC)

Yes, I've experimented more with the interactive demo, and it does render much better. How long do you guys think it will be before it's implemented? (or is not quite finished yet?) —Mets501 (talk) 17:53, 23 June 2006 (UTC)

Don't know. We're working on it. (In between the real lives that we sometimes pretend to have.) Dmharvey 18:02, 23 June 2006 (UTC)

What, you're not still faking that whole doctoral thing, are you? Or do you mean serious pursuits like sleep and beer? Oh, now I remember; you were planning to spend time celebrating Australia's 6–0 win over Brazil! Ah, well; at least you didn't have to play Ghana. ;-) --KSmrq^T 20:26, 23 June 2006 (UTC)

Category:Degenerate forms up for deletion

Wikipedia:Categories for deletion/Log/2006 June 23#Category:Degenerate forms Oleg Alexandrov (talk) 01:48, 23 June 2006 (UTC)

Need third opinion at Operation (mathematics)

JA: Could use a third opinion at Operation (mathematics), a page that was created as a gloss on the generic concept but is now being converted into "hwk-helper" with material that either belongs or is pretty much already covered at Binary operation and other places.

JA: Looking down the road, in both directions, I am seeing here a more generic issue for the WP math community. For instance, the article in question was categorized as Mathematical Logic, and is now being recategorized as Elementary Mathematics. I think that there needs to be a standard operating procedure for sorting out and coordinating "tutorial" and "standard" articles. I notice that the physics folks already have a template for doing this. Anyway, something to think about. Thanks, Jon Awbrey 17:56, 23 June 2006 (UTC)

As the other editor in this dispute, let me summarize my position. "Operation" is an elementary term in mathematics. Someone helping their kid with his or her homework would likely end up at Operation (mathematics). The term belongs in Category:Elementary mathematics. In editing the article I preserved the full formal definition. The entire article fits on one screen. There is no need in this case (though there certainly may be in others) for "tutorial" and "standard" articles. (I gather by "standard" JA means aimed at specialists.)

No specialist is harmed by having to skip over a dozen or so lines of introductory material to get to a formal definition. If there were a need for a specialized page for the mathematical logic community (and I fail to see why since they are using the ordinary meaning), a proper name for such an article might be "Operation (mathematical logic)." According to Wikipedia policy WP:NAME: "Generally, article naming should give priority to what the majority of English speakers would most easily recognize..."

I agree with JA that a broader discussion would be helpful. I have no problem with highly technical articles that treat their subject rigorously, but where it is possible to do so introductory sections should be included that speak to a wider audience. I have tried to do this in several places and I consider it some of my best work. See homotopy groups of spheres for example. Wikipedia should try to demystify math, not obfuscate it. --agr 17:28, 23 June 2006 (UTC)

My personal opinion that the article requires a general definition as well as examples. In this version, the examples are nicely covered in introduction (one more example: operations on sets and functions, which I have just added). Operations in math logic is just one of the examples, and I think that elementary mathematics is more appropriate. (Igny 19:10, 23 June 2006 (UTC))

In this specific case I see no reason not to combine an elementary treatment with one for the specialist. And let's be honest, a specialist has no need to look up such basic stuff, so actually general understandability is more important. One thing that is not made clear and may be confusing, is that there is no clear distinction in mathematics between the meanings of function, operation, and operator. For example, the article Operation (mathematics) now mentions square root as an example of a unary operation, while the article Square root itself only mentions "function". It is largely a matter of historical convention when which term is used. --Lambiam ^Talk 19:26, 23 June 2006 (UTC)

JA: This is like deja vu of discussions that we had on Function and Relation, and so I'd rather focus on the generic problem, as I'm fresh out of ergs to be caring about this stuff unless others do. I created this article because of a recurring need in other articles — check the "what links here" page — for a quick gloss to a suitably general concept of k-adic operations. And now anybody chasing those links is likely to skip the whole darn thing before getting past the TOC. What we have now is two articles whose front ends are devoted to Binary operations, and so it seems like the whole thing is better dealt with by way of a 1-liner up top like: {{for|an introductory treatment|Binary operation}}. Jon Awbrey 19:48, 23 June 2006 (UTC)

First of all, the present intro to operation (mathematics) does not just deal with binary operations. It also describes unary operations. The common mathematical use of the word "operation" includes both. The binary operation page is not that elementary and goes off to discuss groups, monoids and the like, as it should. The unary operation page devotes a lot of its space to computer programming operations. So there is a need for the current version of "operation." This is an encyclopedia, not a glossary, and specialists can put up with a little intro material. Regarding "what links here," I came to this article in the first place when I was editing exponentiation and wanted to link the word "operation.' What I found when I looked there was totally inappropriate. I suspect other editors of elementary articles have come to the same conclusion.

As for the relation (mathematics) article, it already has a long introductory section. It would take very little editing to make its intro beginner friendly, eliminating the need for an initial redirection. Basically defer the jargon for sentence or two. And that I think is the broader issue here. Where it is possible to do so, editors should be able to add short introductions to articles that make them more accessible to non specialists, without a big battle each time. Long tutorials deserve their own article, of course. But an average reader landing on a basic mathematical topic should get an initial explanation they can understand before being redirected.--agr 21:44, 23 June 2006 (UTC)

I suggest creating operation (elementary mathematics), function (elementary mathematics) and relation (elementary mathematics) which would have content aimed at the primary-school/secondary-school/high-school level. This might solve the edit-warring over these articles. linas 00:19, 2 July 2006 (UTC)

Span.texhtml

Please see my proposal here. —Mets501 (talk) 22:20, 23 June 2006 (UTC)

Doesn't anyone want to comment? It's very relevent to all math pages on Wikipedia. —Mets501 (talk) 23:49, 24 June 2006 (UTC)

We've seen it before. There's little enthusiasm for a global stylesheet change for two reasons (at least).

For an inline formula using <math> tags that happens to force a PNG, the "x" will appear in a serif font, which is also the way it appears in most displayed equations (since the typical display is a PNG); consistency in this case dictates that the HTML should use a serif font as well.
Anyone who really cares about using a sans-serif font can do so using using their personal stylesheet, just like the users you noted.

No matter which choice is taken, so long as the monobook body text uses sans-serif and TeX PNGs use serif, we have a conflict. Nor is that the end of it; look at the difference in other characters, such as Greek symbols and operators.

This conflict is unlikely to end with the release of the STIX fonts, as suggested by the following statement:

“Most of the glyphs in the STIX Fonts have been designed in Times-compatible style. Times was first designed under Stanley Morison's direction by Victor Lardent at The London Times in 1932. Many variations of this design have been produced since the original.

“In addition to Times-compatible glyphs, some portions of the STIX Fonts include other design styles such as sans serif, monospace, Fraktur, Script, and calligraphic.”

Thrilling; all of the extra styles except sans serif are essential for TeX. So get used to serif mathematics; it looks to be with us for a long time to come. --KSmrq^T 00:27, 25 June 2006 (UTC)

How about "span.texhtml {font-size=14px}"? That will at least get it to be the same line height as the sans serif.

Will it? For which OS, browser, fonts, and settings? This kind of hair-pulling madness is a tiny fraction of the issues Dmharvey and Jitse Niesen have been wrestling with over in BlahTeX-land. --KSmrq^T 22:38, 25 June 2006 (UTC)

he's baaaacccckkkkk..... "made it clear"

[66] Dmharvey 18:35, 24 June 2006 (UTC)

He never seems to tire, does he? Blocked again... -- Fropuff 05:35, 25 June 2006 (UTC)

In defense of our clarificator, there is an apparent contradiction between the Real number article, in which "a [presumably meaning any here] real number can be given by an infinite decimal representation", and the article Decimal representation, which has: "Every real number except zero has a unique infinite decimal representation" (which is true the way things are defined locally). Instead of blocking, it might be better to smooth away the contradiction. --Lambiam ^Talk 10:00, 25 June 2006 (UTC)

I just removed that section in "decimal representation". It was probably also put there by WAREL and missed by others. JRSpriggs 11:00, 25 June 2006 (UTC)

Actually, if you read that paragraph again, you will notice that it is correct. Every positive real number has exactly one decimal expansion which doesn't end with all 0's, and one decimal expansion which doesn't end with all 9's (usually, these two are the same). That paragraph emphasized the first of these - which looks unusual, so I don't object to the removal. -- Meni Rosenfeld (talk) 18:05, 26 June 2006 (UTC)

The first sentence of the removed paragraph said was "Every real number except zero has a unique infinite decimal representation, that is, one in which not all of its digits become zero after a while. ". Although the subordinate clause tries to rescue it, the main clause is false. Some real numbers have more than one infinite decimal representation. It is senseless to discriminate against a terminal string of zeros in favor of a terminal string of nines. If anything, I would do it the other way around. JRSpriggs 10:22, 27 June 2006 (UTC)

The subordinate clause clarifies what was the meaning of "decimal expansion" in the main clause. The main clause would have been false on its own - but it is accompanied by the subordinate clause to form a whole sentence - a correct one. It is the same as saying "every real number a has a unique cube root, that is, a real number b such that b³ = a". The first part could have been seen as false on its own, if we see it in the context of complex numbers - but the second part clarifies that we are only concerned with real numbers. Not much point in arguing about this, though - I do agree that ther article is better off without that section. -- Meni Rosenfeld (talk) 10:35, 27 June 2006 (UTC)

It is more like saying "Every positive real number has a unique square root, i.e. a negative number which when multiplied by itself gives the positive number.". He is treating the abnormal case as the normal. JRSpriggs 11:01, 27 June 2006 (UTC)

That is something I certainly agree with. -- Meni Rosenfeld (talk) 11:28, 27 June 2006 (UTC)

I would agree with all this, but I have to say that I do recall situations in proofs, where it is more convenient to use the version of a real number which ends in a string of 9's (it means that every strictly positive real has a non-terminating decimal representation) - but in this instance, I agree that he is advocating the 'abnormal'. Madmath789 11:48, 27 June 2006 (UTC)

Here is an attempt to say something that is (a) true, and (b) not a manifent consequence of what is already in the article:

Every non-negative real number has an infinite decimal representation. It is unique, except for those positive real numbers that also have a finite decimal representation: these have two infinite representations. For example, the number 5/4 = 1.25 has the two infinite decimal representations 1.24999… and 1.25000….

Is it worth adding this? --Lambiam ^Talk 17:23, 28 June 2006 (UTC)

If you do add it, add it to the existing section "Multiple decimal representations" rather than making a new section. JRSpriggs 04:55, 29 June 2006 (UTC)

Request from non-mathematician

When I do "random article" I occasionally come across mathematical formulae (and sometimes with general science books etc). It would be useful for those of us who are not mathematically informed if there was a "basic explanation" as to use and purpose.

See the examples I put on Wikipedia:Requests for expansion for what I mean. Jackiespeel 16:54, 26 June 2006 (UTC)

In reference to boolean-valued function, boolean domain, and finitary boolean function. Those are pretty short stubs. They need lots of work (or perhaps even to be merged somewhere). In response to your general query: yes, I will try to make every math article I write have explanations, examples, context, and everything else that makes for brilliant writing. Sometimes a stub is better than nothing though. -lethe ^{talk +} 17:37, 26 June 2006 (UTC)

On the request for expansion page, you wrote:

Finitary boolean function, Boolean domain and Boolean-valued function and some of the links thereof - can someone give an explanation in "ordinary English" as to what these functions are. I can see that they are complex mathematical functions - but "what are they"? Perhaps a brief standard text could be added. "This mathematical function is used in xxx, and does yyy." (add more detail as required) Jackiespeel 23:14, 24 June 2006 (UTC)

The article "finitary boolean function" describes a simple generalization of a boolean function. There's not much else to write. Perhaps that article needs to be merged into the "boolean-valued function" article. The article "boolean domain" is just a definition, and is already marked as a stub. The article "boolean-valued function" gives what you ask for: it describes the function and gives several fields where it's used. Could you explain why that doesn't meet what you want? Lunch 18:32, 26 June 2006 (UTC)

Finitary boolean function is not a generalization but a specialization of boolean function. The situation is a bit messy. There is also the article Boolean function, which never defines what a boolean function is. Is there a difference between the concepts of "boolean function" and "boolean-valued function"? What is sorely missing here are examples. There is further an article Logical connective, which treats operators like AND and NOR, the redirect page Boolean operator redirecting to Logical connective, and the redirect pages Boolean operation, Logical operator and Logical operation, which instead redirect to Boolean function. --Lambiam ^Talk 20:03, 26 June 2006 (UTC)

Conventions in graph theory : strongly regular graph

I was busy trying to make a Strongly regular graph separate article, and I was wondering : what will we agree on the conventions.

Graph theory can really be annoying when you really want to do it right. For instance my syllabus agreed on not including disconnected graphs and their complements, which in turn implied $v - 1 > k > μ > 0$ .

The spectrum also changes when you allow disconnectedness: the degree of disconnected graphs becomes an eigenvalue with more than dimension one.

What is your opinion?

Evilbu 18:22, 26 June 2006 (UTC)

My advice would be to have a look at the other graph theory articles to see if their conventions seem reasonable, and try to follow those if so. You can of course use your own conventions too — the most important part right now is to write the article; we can discuss your conventions later. Just be sure to explain what your conventions are in the article. - Gauge 02:39, 28 June 2006 (UTC)

Research first, write afterwards. Halmos, a widely respected mathematics author, says:

"A good, consistent notation can be a tremendous help… Bad notation can make good exposition bad and bad exposition worse; ad hoc decisions about notation, made mid-sentence in the heat of composition, are almost certain to result in bad notation."

Try to conform to standard conventions. But especially, be explicit about what conventions you choose; don't leave the reader guessing. This is essential within Wikipedia, where readers and editors come from different disciplines, different schools, different continents, and different levels of experience.

Graph theory is mathematics applied to many tasks, and the conventions that are helpful for one may be an impediment for another. Since we cannot know why someone is reading an article, we cannot assume that for their purposes all graphs are connected. However, it is fair to introduce a discussion by saying something like, "Here we restrict attention to connected graphs." That's not only good for the reader, it also makes it easier for another editor to come along, see the restriction, and expand the coverage.

You will find this done throughout the mathematics articles. In fact, it can help to start an article that includes both introductory material for a general audience as well as much more abstract material for an advanced audience. First give the accessible and common cases to build intuition, then later remove restrictions.

Specifically with regard to strongly regular graph (and note: don't capitalize the first word just because it's linked!), nothing in the definition of regular graph implies or depends on having a connected graph. If some of the results you want to state only apply with that restriction, say so.

A fine point of TeX usage is that it is incorrect to write

$srg(v,k,\lambda,\mu) . \,\!$

TeX typesets this as if s, r, and g are three single-letter variables being multiplied. I mention this here instead of on the article talk page because it's a common mistake. Instead, try

$\operatorname{srg}(v,k,\lambda,\mu) . \,\!$

The special notation here, "\operatorname{srg}", does several good things; use it. This is not highlighted at Help:Formula, but many other helpful suggestions are; read it. Especially note the trick (which I've used here) to force displayed equations to use a PNG image (which is large and uniform) instead of an approximation in HTML.

I'll also use this opportunity to point out that since there is no reason to capitalize the first letter of a link, there is also no reason to write, say, "[[Adjacency matrix|adjacency matrix]]" instead of merely "[[adjacency matrix]]". The MediaWiki software also performs other background magic, such as simplifying plurals like "[[complete graph]]s", which comes out looking like "complete graphs". Something that often proves handy in mathematics articles is that trailing parentheses in a link, needed for disambiguation, can be automatically removed by using the "pipe" character, "|". Thus we can write "[[graph (mathematics)|]]s" to get the word "graphs" with a disambiguated link, like this: "graphs". --KSmrq^T 04:27, 28 June 2006 (UTC)

Okay, well first of all, I checked my syllabus and found that followig THOSE conditions works out eventually. But I don't want to get into any trouble with my own University for copying very explicitly. The problem is that the University of Ghent is such a big 'player' in the field of incidence geometry, that a lot on the internet (and that is assuming you find something) comes from their sites I bet you also disapprove then of my pg(s,t,\alpha) notation in the partial geometry article? I read that Formula page and even applied one of the guidelines on Paley graph. But I am totally confused with HTML/Tex/PNG, especially since I was instructed very recently to switch my Preferences to 'Always render PNG'. Evilbu 13:09, 28 June 2006 (UTC)

Explicit copying is a bad idea anyway, because this is an encyclopedia, and written for a much wider audience. It's not enough that you understand what you write, or that a university lecturer understands; the goal is that anyone in the world with an interest in the topic (and sufficient background or determination to learn) can understand. We have a mathematics style manual that is helpful. Much more could be said. My personal guidelines remind me to try to include, among other things,

intuition
examples
counterexamples
connections
pictures
humor

Although it is helpful to have an article that is little more than a definition or theorem, it is much more helpful to explain in what area of study the definition is used, why it may be useful or plausible, and to show it in action either directly or with links. And since this is an encyclopædia, we also like to cite at least one academic source (something more reliable and permanent than lecture notes or online course material).

Looking at the partial geometry article, I see again the need to use "\operatorname{pg}" instead of "pg", but I also see two other problems. (And, again, I discuss this here for the benefit of everyone, not just one editor and one article.) The first sentence looks like this:

"An incidence structure S=(P,B,I) is a (finite) partial geometry …"
"An [[incidence structure]] ''S=(P,B,I)'' is a ([[finite]]) partial geometry …"

The italics are misused; only the variables should be italicized, not the equality and not the parentheses. While we're at it, we'd like the equation to have a little breathing room but not a bad line break. Here's a way to do all that.

"An incidence structure, S = (P,B,I), is a (finite) partial geometry …"
"An [[incidence structure]], ''S'' = (''P'',''B'',''I''), is a ([[finite]]) partial geometry …"

The wiki markup is a nuisance, and we eagerly look to the day when BlahTeX will rescue us; but, for now, that's it.

The second issue has to do with your HTML/TeX/PNG confusion. The sad fact is that mathematics markup is confusing. Again we look to BlahTeX, which will simplify this as well. Switching your preferences affects you alone; most of your readers will not be using the "PNG always" preference. For example, I don't. Many of us do not like to see big PNG images jutting out in our inline text. We do our best to confine the PNG to displayed equations, and there we always want to see it.

This leads to a highly annoying dual writing technique: hard-to-edit wiki notation for inline, and TeX notation for display. Either way, we're taking a leisurely stroll through a minefield. We have a diversity of philosophies about what we're comfortable with inline, with some people using TeX whenever they need a special character and others (including me — see here) using Unicode; but we have a broad consensus that "built-up" material such as "{a \over b}" is undesirable inline. So this is a second thing you should fix in the partial geometry article.

I find that TeX (or LaTeX) has many subtleties that the average mathematics writer overlooks; the typesetting of operator names is but one of them. For example, not many people know the correct way in TeX to write the colon in f: R² → R. (Use "\colon" instead of ":" to get the right spacing; try it!) However, our current situation is even worse, because Wikipedia depends, not on genuine TeX, but on a lame partial imitation, texvc. Again we look to BlahTeX for eventual relief!

I appreciate that there is a lot to learn about writing mathematics for Wikipedia, and I hope you will not be discouraged. We're here to help, and eventually we'll have new software to help as well. --KSmrq^T 19:22, 28 June 2006 (UTC)

Bots and automatic Unicode conversion

I noticed User:Bluebot is automatically converting HTML entities to Unicode on various articles. See e.g. [67]. Does anyone have an opinion on whether such conversion is desirable in mathematics articles? Would it hinder possible future efforts to automatically switch to MathML? - Gauge 05:55, 28 June 2006 (UTC)

First of all, MathML only affects math written in <math> tags, and unicodifying only takes place outside <math> tags, so it would have no effect of MathML. As far as being desireable, it makes it easier to read the article in edit mode, especially for newbies who are not used to used to HTML entities. —Mets501 (talk) 12:44, 28 June 2006 (UTC)

I know the automatic conversion of Blahtex would only apply to math tags; I was thinking instead of possible future efforts to convert inline HTML being used for math into MathML (using blahtex with math tags), once it is widely supported by browsers (likely several years off, but worth discussing now). What if different bots use different Unicode symbols for the same HTML entities? - Gauge 18:38, 28 June 2006 (UTC)

It makes a little more difficult to edit the article, especially with HTML entities such as & nbsp; , but it's probably a good thing. — Arthur Rubin | (talk) 17:25, 28 June 2006 (UTC)

Converting Unicode to MathML should be just as easy as converting HTML to MathML I think, so ∫ --> \int and ∫ --> \int should not be that different. I would be opposed however on such bots (or worse, semiautomatic editors) doing mass unicodification very often, they just obscure watchlists with no good purpose. Oleg Alexandrov (talk) 19:02, 28 June 2006 (UTC)

Somewhere we've had this discussion before. My recollection is that many editors objected to replacing an HTML named entity with Unicode because the HTML name and the TeX name were the same, making consistency easy. That objection does not apply to numerical entities, but those are so unpopular that we rarely see them. MathML can cope with any Unicode (UTF-8) character for a symbol; in fact, it knows special things to do with many more than are supported in TeX. I don't recall exactly how BlahTeX copes, but it either can or will do better than texvc, at least for passing things on to MathML. My personal preference at the moment is to stop the bot, on the grounds of previous rejection and of TeX (not BlahTeX) incompatibility. --KSmrq^T 19:38, 28 June 2006 (UTC)

On a different note, will we deprecate HTML math formulas with the arrival of BlahTeX? —Mets501 (talk) 20:19, 28 June 2006 (UTC)

I think not. Not in the immediate future.

To address KSmrq's question: currently blahtex does not allow non-ASCII characters in math mode material, on the grounds that people would abuse it, and it would lead to the database becoming horribly incompatible with standard tools. People should be using the TeX commands instead. It does allow arbitrary non-ASCII in text mode, which gets passed through to the MathML <mtext> element. I suppose this could lead to the same sort of abuse (like <math>\text{∫}_0^1</math> -- yuck!). It might become desirable to limit the characters that could be used in text mode (e.g. extended latin, and other scripts like japanese, chinese, klingon, etc). Dmharvey 20:49, 28 June 2006 (UTC)

Why wouldn't we deprecate HTML math formulas, though? If we put it in <math> tags, then BlahTeX will render it as HTML, anyway. So there seems to be no reason why we should keep using math formulas written in HTML. In fact, I'm not quite sure why we use inline HTML now for things like variables or "flat" equations that would render (in <math> tags) now as HTML now anyway with texvc. —Mets501 (talk) 01:13, 29 June 2006 (UTC)

The main reason to use HTML now instead of texvc for inline stuff is that the texvc conversion of TeX to HTML on "simple formulas" is so pitiful. Blahtex would generate MathML output for math tags for people who want it, but I think it still falls back to the old texvc HTML conversion for people not using MathML. Also, there are certain things that texvc will tend to encode as PNG rather than HTML (any sort of spacing, for example), so one might be forced to use HTML for the desired result anyway. - Gauge 19:59, 29 June 2006 (UTC)

In response to KSmrq's comment about prior discussions involving unicode in mathematics article, on this page, there have been at least three:

Unicode in math articles (Sep 24 2005)
Mathematical characters usage (Oct 18 2005)
IE compatibility (Mar 28 2006)

Paul August ☎ 21:37, 28 June 2006 (UTC)

Thanks Paul. I found this quote by Dysprosia that I thought was worth repeating here:

The difference is that the Unicode alpha is just another character in the text, like "t", or "q". The HTML entity is the string "α". All good computer systems should support ASCII, and the HTML entity consists of only ASCII characters, so no matter if you use a computer that supports Unicode or if you don't, the string will be unchanged. However, some browsers that don't support Unicode simply ignore the Unicode characters, so if someone edits with one of those browsers, it will look like all the Unicode characters in the article have suddenly disappeared. If the browser chooses to render "α" with a Unicode character, that's fine, but it doesn't mean that that Unicode character is somehow equivalent to the HTML entity -- they aren't. Hope that explains things a bit better...

I think this is reason enough to discourage proactively converting HTML entities to Unicode. Let the browser decide which symbol to use instead of forcing a particular Unicode symbol. Also, what is the state of screen reader support for Unicode as of about 5 years ago? It seems reasonable to give handicapped users some time to upgrade their software if Unicode is going to be proactively deployed. I don't mind if people use Unicode in articles, but they shouldn't be converting HTML entities to Unicode wholesale without some discussion. - Gauge 22:53, 29 June 2006 (UTC)

\mathscr anyone?

Are people interested in having the \mathscr command available? (Provided by \usepackage{mathrsfs}.) Here's what it looks like:

The top one is \mathscr, the bottom is \mathcal (which is what we have now). I've noticed that \mathscr (or something similar) is quite popular in certain fields. I've noticed it especially in functional analysis.

There wouldn't be any difference in MathML because MathML only defines a single "mathvariant=script".

Opinions welcome. Dmharvey 19:25, 28 June 2006 (UTC)

It's also popular in algebraic geometry, for denoting sheaves and sheaf-y versions of various things like functors. I've once or twice wished I could use it. It's not essential, but I guess I would say that I'm interested in having it. Ryan Reich 21:11, 28 June 2006 (UTC)

Do we get one or the other, or can we have both? Personally, I find \mathcal very useful at times, and wouldn't want to lose it. If we can have \mathscr for those that want it, without losing \mathcal, then that would be great. Madmath789 21:21, 28 June 2006 (UTC)

You get to have both. Unless you're viewing with MathML, in which case they look the same. This would only become a problem in articles that use the same letter in the two fonts to mean different things. It would be possible to disable MathML for \mathscr if that's what people wanted, in which case it would fall back on PNGs. Dmharvey 21:50, 28 June 2006 (UTC)

MathML is only part of the obstruction. Unicode itself has no font variation facility to handle this (that I know of). There is a code point for "B" (U+0042) and "b" (U+0062), and for "Б" (U+0411) and "б" (U+0431), and for "ב" (U+05d1), and for "𝔅 (U1d505) and "𝔟" (U1d51f), and for "𝔹 (U1d539) and "𝕓" (U1d553), and for "ℬ" (U+212c) and "𝒷" (U1d4b7). The idea seems that be that these variations of "B" are in separate alphabets (Latin, Cyrillic, Hebrew, Fraktur, double-struck, and script), not separate fonts. (The difference between uppercase and lowercase is an anomaly, retained for historical reasons even though it's somewhat inconsistent.) So an argument would have to be made to the Unicode committee that there is an essential semantic difference between the calligraphic alphabet and the script alphabet. I'm guessing it would be a hard sell; we all know mathematicians have a boundless appetite for new alphabets and new characters. (We need this alphabet for the space, and that one for the structure over the space, and the other one for the mapping of the structure over the space, and so on.) I think we already have enough distinctions to tough it out if we must! In fact, any author who wants to make a semantic or type distinction between script and calligraphy is already unkind to readers. For those who are still not persuaded, MathML accepts CSS styling, so it's possible to use a Latin code point and ask for a different font-family. --KSmrq^T 01:18, 29 June 2006 (UTC)

All very true. In fact, there are a few more: for example there's also 𝖡 (U1d5a1) which is "MATHEMATICAL SANS-SERIF CAPITAL B" ([68]). Interestingly, the reference glyphs for script letters given on the mathml site ([69]) appear to be the same as the \mathscr above, even though the fonts that I got from the Mozilla site render more like \mathcal. I wonder what the STIX ones will look like. Dmharvey 01:42, 29 June 2006 (UTC)

Is anyone aware of any sources that use both a mathscr-like font and a mathcal-like font, with different semantics? There's a thread on the www-math mailing list discussing this now. If anyone could build a case, we might well get two different font variants in MathML 3.0 (which is on the drawing board). Dmharvey 18:39, 5 July 2006 (UTC)

he he he

You know how we all put something like "\,\!" at the end of <math> blocks to force the output as PNG? Well I was just doing some database work and happened to be trying things out on the hebrew wikipedia, and discovered that they all put "\ " at the beginning of the equation! (e.g. [70]) Or is it the end of the equation? I don't even know... the </math> comes before the <math>... Dmharvey 22:02, 28 June 2006 (UTC)

The LaTeX equation itself runs from left to right. In this equation the "\ " is at the beginning. If we think of the eqn as an atom in a right-to-left context, then to the reader the blank space appears to appear to the left of and therefore after the atom (instead of being part of the atom). --Lambiam ^Talk 22:50, 28 June 2006 (UTC)

interesting statistics

More database work.... last time I checked around the beginning of March, the 13 largest wikipedias had 208,000 distinct equations altogether. Now (as of about mid-June) there are about 289,000. That works out at about a 10% growth rate per month. Pretty amazing. Dmharvey 02:06, 29 June 2006 (UTC)

You should write a paper about it. When it gets published, I can write a Wikipedia article about the paper. Ryan Reich 02:53, 29 June 2006 (UTC)

And make sure in the Wikipedia article that you use more formulas :-) —Mets501 (talk) 03:15, 29 June 2006 (UTC)

Help wanted

The "proof that 0.999... equals 1" article is once more under attack — from the inside. And for the n-th time, Melchoir is involved. I'm sick of dealing with him and (now) Supadawg. If anyone is interested, please get involved in whatever way you see fit. As for me, it's come down to a revert war or walking away.

Some of you may be aware I completely stopped editing Wikipedia articles awhile back, except for really minor things like typos. I confined my contributions to talk pages, because I had no more stomach for seeing articles obstinately trashed by editors with inadequate subject knowledge, horrible writing skills, and no social skills. That worked for me, though not so well for the articles I abandoned. In the current instance, I can't see wasting more time debating with someone who pretends a proof using Dedekind cuts and the Archimedean property is original research, and who doesn't see a problem in beginning a sentence with a decimal point, but who knows exactly how the article should be rewritten.

However, if you long for abuse or have a desperate yearning to save the world (or both!), here's your opportunity. You'll need to act quickly, for the Mongol hordes are invading as we speak. They have already insisted that an article devoted to a proof should not be so named, nor should state that in the opening sentence. ("It's unencyclopedic!") Next on their agenda is a complete rewrite. It boggles the mind.

OK, so saving this article probably won't save the world. Still, I'll bet it gets more page views than the snake lemma and the hairy ball theorem put together (no disrespect intended). Please stop by the talk page, or help revert. (This version works for me, tolerably.)

Just for fun:

Question at job interview: "What is one third plus two thirds?"

Mathematician: "It's one."
Engineer (using calculator): "It's 0.999… ."
Accountant (winking slyly): "What do you want it to be?"

Thanks, all. --KSmrq^T 06:42, 29 June 2006 (UTC)

I must say that I find the article unconvincing, also in its earlier incarnations. Surely, it is intended for people who, in a Zeno-like way, feel queasy with the identity. Most of what is in there is completely above their heads. If I was not mathematically educated, and I saw something that needed so many different proofs for its validity to be demonstrated, I would start to doubt the claim made! Can't we just have two proofs:

A solid one from first principles, basically saying (sketch): (1) By definition, 0.999... stands for the limit of the sequence 0.9, 0.99, 0.999, ... (2) That limit is, by definition of limit, equal to one when the elements of the sequence |0.9-1|, |0.99-1|, |0.999-1|, ... eventually become less than any positive number ε you care to state. (3) And indeed, it does: if the decimal representation of 1/ε has n digits before the decimal point, then the n+1st and subsequent elements are all less than ε.
The informal argument: 10x = 9.999...; subtract x giving 9x = 9.000... and therefore x = 1.000..., remarking that this, in fact, informally presents an actually valid mathematical argument.

More is not always better. --Lambiam ^Talk 09:23, 29 June 2006 (UTC)

First of all, thanks for your imput Lambiam, but I'm afraid that's a no (from me at least). It doesn't need so many proofs to prove its validity. The many proofs are to present alternate methods of prooving this "theorem". Any one of those proofs would serve to prove that 0.999…=0.

Second, KSmrq, I think that you're actions were not appropriate above. We don't have a consensus yet either way, and you're already assembling a revert army, or so it seems from your statement above. Also you did not provide a link to the infinite geometric series proof, and only to your version of the article, without the proof. If we do achieve consensus to delete the section, I will let it be deleted (although personally I would rather it stay – perhaps you remember when I added the proof on April 1 of this year, and you swiftly removed it), but until we have that consensus, it will stay in the article. —Mets501 (talk) 13:00, 29 June 2006 (UTC)

Please direct all follow-ups to the article talk page. They will properly be associated with the article history, and won't annoy the vast majority of mathematicians who don't long for abuse. Thanks. --KSmrq^T 15:44, 29 June 2006 (UTC)

I'm happy to join the corps of reverters for that article, but I cannot in good conscience revert to the version you link, which is buried behind over a hundred edits already. The best I can do is add the article to my watchlist and revert future changes. -lethe ^{talk +} 15:37, 29 June 2006 (UTC)

Not a problem. I had a hard time picking through all the debris to find a good target, with all the additions and reversions that have been happening lately, so I went back further to be safe. Thanks for anything you feel comfortable doing to help. --KSmrq^T 15:44, 29 June 2006 (UTC)

Redirect question

Is there a way to have a redirect focus the point on a specific section of the article? Specifically, I have in mind the redirect from Koszul connection to covariant derivative, which reads

# REDIRECT [[covariant derivative#Koszul connection]]

If you follow the link explicitly, by clicking the above link, then the point focuses on the relevant section. But if you follow the link Koszul connection, then you are taken to covariant derivative without the change in focus. Any thoughts or advice? Silly rabbit 17:32, 29 June 2006 (UTC)

See Help:Link#Redirects_with_section_links. I recall reading a different document that explicitly said that they had no intention of ever allowing section links within redirects, but I don't know where that went (the "Help" is not always very much help here; they make it very hard to find the detailed manual and I always forget how). Ryan Reich 18:05, 29 June 2006 (UTC)

Hehehe... I just found some related results, and was about to come here and answer my own question: Meta:Help:Redirect#A redirect to an anchor and bugzilla:218. It's kind of annoying that this seems to be impossible. Any stylistic pointers on how to handle a merger of this sort? Silly rabbit 18:13, 29 June 2006 (UTC)

Redirect to the top of the page. If the article is well-written then the appropriate section header will be in the TOC and clearly visible (i.e. the preamble won't take up much space). If not, well-rewrite it. In any case, if you have a page that used to link to Koszul connection, you could just put a pipe in that link and avoid the redirect entirely. Ryan Reich 18:45, 29 June 2006 (UTC)

Split of List of mathematicians

Sorry if I startled you, the WikiProject, but I boldly separated the List of Mathematicians article into eight smaller articles. Prior to this, the article was giant: it ranked in the Top 50 on Special:Longpages. Seeing as this is problematic, since not all of our users have the patience to load a page that is hundreds of kilobytes in size, I took the liberty to divide it into smaller pieces. I'm sorry if it's unacceptable to the WikiProject, but I was doing what I felt was good for the list. —THIS IS MESSED OCKER (TALK) 02:50, 30 June 2006 (UTC)

Relax. :) As I told you on your talk page, the big problem is that you did not realize a bot is used to update that page, and it will just happily overwrite your changes, or worse, will get confused by it and then the page will be messed up.

The list of mathematicians is 164 kilobytes. Time to split? Should it be split modeling the list of mathematics articles, that is, separate lists for each letter, or should there be a grouping into bigger lists, say A-C, D-F, etc.? Oleg Alexandrov (talk) 02:55, 30 June 2006 (UTC)

Yes a split seems a good idea. I would go for one list per letter. I can't really see an an advantage of A-C lists etc. I suspect most people who use the list will be looking for a specific person and so it will be easy enough for them to click on a specific letter. Further, the number of mathematicians per letter is already quite long for about half the letters. --Salix alba (talk) 08:41, 1 July 2006 (UTC)

I thought of the same thing. I will work on it when I find time. Oleg Alexandrov (talk) 16:56, 1 July 2006 (UTC)

Done. Oleg Alexandrov (talk) 03:52, 15 July 2006 (UTC)

Geostatistics

This article is extremely POV, particularly considering the open criticism of Geostatistics within the main page. I was hoping that someone with more experience could build some equations and expand on the evolution of geostatistics. Considering how widely geostatistics is used for the natural sciences, environmental planning, climate studies, oceanic studies, military analysis, urban planning, and Geographic Information Systems, this topic warrants some attention from math experts. SCmurky 03:56, 30 June 2006 (UTC)

JanWMerks is at it again. He's been editing geostatistics, semivariance, spatial dependence, variogram, sampling variogram, kriging, junk science, consensus science, Tolstoy syndrome, and Bre-X; I may have missed some. He's been admonished in the past for his crusading; see his talk page and his list of "contributions". It might be nice if more people added these pages to their watch lists to undo his edits. (BTW, SCmurky, why did you delete my previous comment?) Lunch 17:50, 30 June 2006 (UTC)

Maybe it is time to take more serious action Wikipedia:Resolving disputes posibly a request for mediation. --Salix alba (talk) 20:03, 30 June 2006 (UTC)

Jul 2006

This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

Serre conjecture vs Serre's conjecture

Do we need a disambiguation page for these? Dmharvey 21:56, 1 July 2006 (UTC)

It would suffice to put a disambiguation link at the top of Serre conjecture, the Quillen-Suslin theorem being the only likely ambiguity. Having "Serre conjecture" and "Serre's conjecture" mean different things is asking for trouble. --KSmrq^T 22:48, 1 July 2006 (UTC)

Done. Septentrionalis 00:24, 2 July 2006 (UTC)

OK for the present, but Serre has dozens of conjectures, I believe. --Charles Matthews 10:58, 5 July 2006 (UTC)

Rogue wikibots

This unicodification stuff made me realize that as just one editor I have very little control over what people decide to do with their bots on wikipedia. I asked the guy running User:Bluebot politely to stop proactively converting HTML entities to Unicode in math articles (and am waiting for a response), but if he doesn't comply what recourse do I have before all of the articles are converted anyway? Apparently he already refused Dysprosia's request.

It seems to me that bots could do a lot of damage in a very short amount of time (shorter than it would take to get the hosting user banned, for instance), and the damage might also be difficult to fix, probably requiring someone to write up a new bot just to fix the mess that the former bot created. How long will it be until someone truly malicious tries to write a bot that trashes (or worse, subtly introduces sign errors, for instance) in hundreds or thousands of articles? Are there any measures in place to prevent this sort of thing from happening? - Gauge 23:38, 1 July 2006 (UTC)

As a bot owner, whose bot has, on occasions, gone rogue, I can say that it does not take long for somebody to notice something odd and notify the bot owner and/or block the bot. Bots are fifth class citizens (in order: Jimbo/bureaucrats/admins/users/anons/bots), they are shown no mercy. :) Oleg Alexandrov (talk) 00:04, 2 July 2006 (UTC)

If an ordinary user can block a bot, how is this done? When should one do it? JRSpriggs 10:09, 2 July 2006 (UTC)

Blocking a bot, like any user, requires an admin. (There are several in this project: Oleg Alexandrov, Jitse Niesen, Lethe, Charles Matthews, Mindspillage, Fropuff, Michael Hardy, Mikkalai, Toby Bartels, The Anome, Isomorphic, Charles Stewart — did I miss anybody? — and me.) Paul August ☎ 15:58, 2 July 2006 (UTC)

TeX tips

While working through many pages with equations listed as acceptable to texvc but incorrect according to BlahTeX's parsing, the single most common issue seems to be a construction like

<math>x^\sqrt{2}</math>,

which must be changed to

<math>x^{\sqrt{2}}</math>.

This often arises with a subscript like

<math>x_\mbox{kind}</math>,

which must be changed to

<math>x_{\operatorname{kind}}</math>.

The corrected appearance is as follows.

$x^{\sqrt{2}}$

$x_{\operatorname{kind}}$

It would be helpful to keep this in mind when editing: Use the braces. --KSmrq^T 02:16, 5 July 2006 (UTC)

Since TeX rightly rejects x^\sqrt{2}, so texvc should also, hence texvc is being Bad. Dysprosia 02:26, 5 July 2006 (UTC)

I am currently rewriting blahtex in python. Along the way I am reworking the parser. As a result it detects even more TeX incompatibilities than the current blahtex version. Dmharvey 02:38, 5 July 2006 (UTC)

You mean texvc problems? Dysprosia 02:42, 5 July 2006 (UTC)

Yes. I mean that the new version of blahtex will produce error messages for certain inputs that texvc accepts and that the current version of blahtex accepts but for which TeX produces an error. Dmharvey 03:13, 5 July 2006 (UTC)

I'm sure the BlahTeX developers are aware of this, but I want to point it out before people go out and mangle the TeX code in articles. The current BlahTeX sandbox seems to support <math>x_{\mbox{kind}}</math> as well, which has the semantic advantage that the word kind should get set as text. The MathML output seems to put operatorname into <mi> and mbox into <mtext>. I don't know the MathML standard, but I doubt these are guaranteed to be the same font. I think operatorname should be reserved for operators. According to the sandbox, BlahTeX also supports the AMS \text command for putting text into math formulas. CMummert 02:44, 5 July 2006 (UTC)

Here's what I can tell you about blahtex's behaviour. The \mbox command is treated very similarly to \text. Pretty much the only difference is some fiddly stuff to do with text sizes. So in x_{\mbox y}, the "y" is the same size as the "x", but in x_{\text y}, the size of "y" is what you would expect a subscript to be. The arguments of \mbox and \text are both treated as text mode material; so for example whitespace is significant, and you can't use mathematical symbols. (This is also why <mtext> is used.) On the other hand, \operatorname takes a math mode argument; it's supposed to be used for things like \operatorname{sin} when you don't have a shortcut like \sin. Using \operatorname has spacing implications too. Compare the output of \operatorname{lim sup} X, \mbox{lim sup} X and \operatorname{lim\,sup} X. It's still got some bugs, for example \operatorname{sin}\limits_2 doesn't do the right thing, for reasons I don't yet completely understand. Dmharvey 03:13, 5 July 2006 (UTC)

Assuming folks are reading this with the typical PNG output, here's a comparison of subscript options (with a deliberate error message):

input		output
<math>x_{\mbox{Hello world}}</math>		$x_{\mbox{Hello world}}\,\!$
<math>x_{\text{Hello world}}</math>		$x_{\text{Hello world}}\,\!$
<math>x_{\operatorname{Hello world}}</math>		$x_{\operatorname{Hello world}}\,\!$
<math>x_{\operatorname{Hello\ world}}</math>		$x_{\operatorname{Hello\ world}}\,\!$
<math>x_{\mathrm{Hello\ world}}</math>		$x_{\mathrm{Hello\ world}}\,\!$

It should be obvious why I suggest "\operatorname"! (Or perhaps "\mathrm".)

Also keep in mind that the design of MathML mixes "presentation" and "semantics" in peculiar fashion. The distinction between <mi> and <mo> is named "identifier" versus "operator", but it's hard to know what that really means. --KSmrq^T 04:16, 5 July 2006 (UTC)

Possibly <math>x_{\mathrm{Hello\ world}}</math>, which gives $x_{\mathrm{Hello\ world}}$ would be acceptable too.--LutzL 10:08, 5 July 2006 (UTC) || other possibilities: bold face $x_{\mathbf{Hello\ world}}$ , sans serif $x_{\mathsf{Hello\ world}}$ , italics $x_{\mathit{Hello\ world}}$ --LutzL 06:54, 6 July 2006 (UTC)

Worth noting. I've added it to the table. --KSmrq^T 19:24, 5 July 2006 (UTC)

The problem is that neither \operatorname nor \mathrm is the right font for textual identifiers; it is a shame that texvc only accepts operatorname. It looks like there is nothing that can be done until if and when BlahTeX is implemented. Then <math>x_{\text{Hello world}}</math> will work. CMummert 12:10, 5 July 2006 (UTC)

I'm not sure what you're hoping for as the "right font". Within MathML I believe it could be inherited from the surrounding document, giving a sans-serif font like Arial. Within TeX, that's not going to happen. And even if that's fixed, we already have a mix of fonts for variables, serif within TeX and sans serif in wiki markup.

I remind you that, although it does not choke BlahTeX, usage like

<math>x_{Hello world}</math>, producing $x_{Hello world}\,\!$

is still rampant. --KSmrq^T 19:24, 5 July 2006 (UTC)

Boy do I hate that, using words and text in variable-mode. I see

D i f f (M)

a lot for diffeomorphism group,

h o m (a, b)

for hom-sets, etc. -lethe ^{talk +} 18:38, 6 July 2006 (UTC)

Mathematics Templates

I'm not that good at creating/organizing templates, but I'd like to throw out the idea that using templates in mathematics-related articles would be quite helpful/unifying. There could be an overall Template:Mathematics which includes every topic from elementary algebra to knot theory; we could also make individual topic-related templates such as Template:Calculus. So far as I can see, there are currently very few mathematics templates, with apparently only one in Category:Mathematics templates and a handful in Category:Mathematics navigational boxes. 66.229.182.113 09:03, 6 July 2006 (UTC)

For my part, I don't like linkfests or find them helpful; we had some a while ago, and deleted them after consideration as random collections of articles. Septentrionalis 18:39, 6 July 2006 (UTC)

The template Template:mathematics-footer may already provide what you're looking for. -lethe ^{talk +} 18:48, 6 July 2006 (UTC)

I agree with Septentrionalis, one should keep templates small and use them very sparingly. Templates can be distracting linkfarms in many cases. Oleg Alexandrov (talk) 18:55, 6 July 2006 (UTC)

I am not sure but I think it may be useful to have infoboxes for theorems, inequalities, conjectures, lemmas, mathematicians. (Igny 21:12, 6 July 2006 (UTC))

I would strongly disagree with any of that. I don't quite understand what you mean by infoboxes, but from what I can tell they will just amount to more clutter. Oleg Alexandrov (talk) 22:08, 6 July 2006 (UTC)

I just would like to say that many people have infoboxes, see Abraham Lincoln, Isaac Newton, Friedrich Nietzsche (note the nice infobox the philosophers have), Blaise Pascal; but not so many mathematicians are with infoboxes, see Friedrich Bessel, Andrey Kolmogorov, Henri Poincare, Fermat etc. (Igny 02:56, 7 July 2006 (UTC))

I see. I thought infoboxes are some kind of glorified templates allowed to be transcluded on hundreds of pages. I agree now that they could be useful, although the danger of creating unnecessary clutter is still there. Oleg Alexandrov (talk) 03:20, 7 July 2006 (UTC)

Additive Group

Can someone look at Additive group and clean it up. It's marked as a disambiguation page. --Usgnus 18:20, 6 July 2006 (UTC)

And so it ought to be: it is a disambiguation page. It links to three different articles which are in three different branches of mathematics, and all of which could be the topic for additive group. If you mean Abelian group, written additively, go there. Septentrionalis 18:37, 6 July 2006 (UTC)

It's marked for disambiguation cleanup. --Usgnus 18:41, 6 July 2006 (UTC)

Oh, so that means it doesn't conform to Wikipedia's disambiguation page norms. Well I'm not sure what those norms are. Perhaps this request should go to Wikipedia talk:WikiProject Disambiguation instead, seems like more their cup of tea. -lethe ^{talk +} 18:46, 6 July 2006 (UTC)

(Edit conflict) Yeah, I'm not sure what the problem is. I don't see a need for an article about additive groups. On the other hand, I might support redirecting additive group to abelian group, so long as the latter article had a segment about underlying additive groups and other additive group functors. -lethe ^{talk +} 18:43, 6 July 2006 (UTC)

I'm asking for help here because the last time I tried to clean up a mathematics-related "disambiguation" page, I was scolded. --Usgnus 18:55, 6 July 2006 (UTC)

Ha! Asking mathematicians to disambiguate is asking the fox to guard the chickens. We even have a little ritual phrase, "by abuse of notation", to cover some — but by no means all — of our wanton ways. Anyway, since you don't want to offend anyone who is passionate about one of the meanings as being "the right one", asking for participation in such edits is wise. --KSmrq^T 20:38, 6 July 2006 (UTC)

The {{disambig-cleanup}} tags are an unnecessary evil, a policing of format by editors who often don't understand the subject matter. The complaint here seems to be that each line of a dab page should link to an article for that meaning, if one exists, and ideally there should be no other links. I have revised the format; I trust that will do. Septentrionalis 20:22, 6 July 2006 (UTC)

Huh? Did you miss to save your edit? It's still in the unwanted many-links-per-line format. --Pjacobi 21:03, 6 July 2006 (UTC)

No, I intentionally left some links, because those terms may not be clear to the dabber. I see the link to addition has been restored, which is probably unnecessary. Septentrionalis 02:19, 7 July 2006 (UTC)

Thanks for your help, Septentrionalis. --Usgnus 21:11, 6 July 2006 (UTC)

I'm confused about these definitions, and currently none of the links point to anything about the first term additive in the definition. So from the article I can know that an additive group can be a group, ring, field, or functor, but nothing about additive apart from its and addititive group if we choose to call it such.

Consider a deliberately perverse example. Take the multiplicative group of non zero integers. Instead of writing × for the symbol write +. Now by the first line this staisfies the definition for an additive group, even though it has a very different structure.

The mathworld article has a stricter definition for the first line, (identity must be called zero and the inverse written as -a) and is much more extensive. I'd suggest making the page a real article rather than a disambig. Either that or just redirect to group. --Salix alba (talk) 19:16, 7 July 2006 (UTC)

Point of detail: in your example, do you mean the integers, or the rationals? (The details of the answer will be different if the group is {-1,1} or the non-zero rationals). But the gist is the same: yes, I'd call that perverse; but I'd also call it an additive group. Septentrionalis 19:28, 7 July 2006 (UTC)

I would support a redirect (but to abelian group, not to group). In fact, it used to be one. Charles Matthews changed it to a disambig. Maybe he can offer some arguments why we need that disambig. As for making it an article in its own right, I don't support that. There's nothing to say about additive groups that isn't actually a statement about abelian groups, right? -lethe ^{talk +} 19:41, 7 July 2006 (UTC)

Probably my fault for scolding User:Usgnus. There have been cases where editors, who are not very good at math, have been marking various pages as needing merges or splits or disambiguation, etc. These show up on cleanup project pages, whereupon other editors, who know nothing at all about math, attempt to do a good deed, and perform the recommended split/merge. And make a mess, because the article should not have been tagged in the first place. I caught one such in progress and pseudoscalar, and posted some nastygrams recommending that this project be contacted first .. which is what Usgnus did. linas 03:43, 9 July 2006 (UTC)

new article: algebraic equation

I'm not sure the definition given is that widespread. Seems a bit too restrictive. Author gives Mathworld as a source. Please comment at Talk:Algebraic_equation. Dmharvey 20:16, 6 July 2006 (UTC)

Nice double arrows

I just figured out how to do nice looking double arrows in texvc exact sequences. Here is a demo:

${\mathcal F}(U)\rightarrow\prod_i{\mathcal F}(U_i){{{} \atop \longrightarrow}\atop{\longrightarrow \atop {}}}\prod_{i,j}{\mathcal F}(U_i\cap U_j).$

The point is to put some phantoms above the top arrow and below the bottom arrow which apparently forces the arrows to space more closely together. I also did a native TeX diagram for splitting lemma this way, using names for the arrows. I hope someone finds this useful. - Gauge 00:26, 7 July 2006 (UTC)

Of course what you really want is this... Dmharvey 01:24, 7 July 2006 (UTC)

I noticed that the character ⇉ looks too short and stubby in MathML compared to the png output. It doesn't rescale when I change the text size either. Maybe it's because I'm missing the Symbol font? I still haven't found a reasonable explanation of how to get Symbol to work on my Gentoo box. I successfully installed all of the others required for MathML. Running Firefox 1.5.0.4, of course. - Gauge 04:11, 7 July 2006 (UTC)

It sounds like a font thing, but it might also be a problem with Firefox's scaling code. It knows how to stretch some operators but not all. Dmharvey 22:04, 7 July 2006 (UTC)

Regular number up for deletion

Please comment at Wikipedia:Articles for deletion/Regular number. --Trovatore 16:52, 7 July 2006 (UTC)

That article was deleted, but there is a genuine (and different) concept here; so I wrote a new one. Weissstein got it wrong. If anyone insists on AfD'ing the new article, fine; we can discuss it there. Septentrionalis 21:42, 13 July 2006 (UTC)

I think this one should be fine; I made a mistake in my MathSciNet search the first time and missed a few references to sexagesimal numbers, Babylonians, etc. There appear to be six articles (with only one by Sachs), which while not overwhelming, is probably more than enough, going by the usual standard. There are more or less the same number of hits for other definitions of regular numbers though, in number theory, group theory, etc. So it may be best to create a disambig page for "regular number". --Chan-Ho (Talk) 23:11, 13 July 2006 (UTC)

The Bernouilli-number definition I would put at regular prime; what are the others? But it may be simpler if we write Regular number (disambiguation) and then decide on what goes where. Septentrionalis 02:26, 14 July 2006 (UTC)

A regular number can refer to the order of a regular element of a finite reflection group; Springer is apparently the name here. Actually, looking up "Springer" and "Regular element" brings up a lot more hits; I imagine regular number is mentioned much more often in the actual articles, rather than in the MathSciNet reviews. Springer's 1974 article "Regular elements of finite reflection groups" already defines regular number in that context. There are also k-regular number fields; here, the usage may be different, but is similar enough to require some disambiguation in my opinion. There's also several other usages that appear in a MathSciNet search for "regular number", but it's hard to tell how common they are (as it shows up only if it's in the title or review). So it looks like there is some work to be done here. --Chan-Ho (Talk) 16:16, 14 July 2006 (UTC)

Scalars

A proposal to merge Scalar has turned into a protracted discussion of whether or not the term 'scalar' means the same thing in different disciplines. See Talk:Scalar. --Smack (talk) 05:13, 10 July 2006 (UTC)

Gosh Numbers

(copied from Portal talk:Mathematics)

Wikimathematicians, if you are interested, please help determine this afd discussion about Gosh Numbers. Thanks! Bwithh 04:40, 10 July 2006 (UTC)

AFD listings

The following articles have been listed at AFD and not picked up by the current activity 'bot:

Basic matrix (mathematics) (AfD discussion)

Please contribute to the discussions. Uncle G 23:18, 10 July 2006 (UTC) The following articles have been listed at AFD and not picked up by the current activity 'bot:

Maths A (AfD discussion) (including Maths B and Maths C)

Please contribute to the discussions. Uncle G 13:17, 18 July 2006 (UTC)

sextic equation

A microstub of dubious utility. AfD? -lethe ^{talk +} 06:19, 12 July 2006 (UTC)

It was already (correctly IMO) changed to a redirect. However, alternatively, we could snatch [71] from PlanetMath if anyone can confirm the veridicity of the information. AdamSmithee 07:53, 12 July 2006 (UTC)

Arthur Rubin for admin

I nominated one of us, Arthur Rubin, for administrator. If you are familiar with Arthur's contributions, and would like to vote, see Wikipedia:Requests for adminship/Arthur Rubin. Oleg Alexandrov (talk) 04:38, 13 July 2006 (UTC)

I definitely will. RfA is the biggest popularity contest these days and it seems that scientists and mathematicians aren't very popular amongst the general public. See Wikipedia:Requests for adminship/Edgar181 to see what I mean - some people who do 2000 small edits and write 1 article get twice as many votes. Blnguyen | rant-line 04:45, 13 July 2006 (UTC)

I disagree about scientists and mathematicians. It seems to me that most of them sail through RfA without hardly a sideways glance. -lethe ^{talk +} 22:44, 18 July 2006 (UTC)

In any event, Arthur Rubin was promoted to administrator a few minutes ago with a 99/2/3 final tally. CMummert 02:40, 20 July 2006 (UTC)

User:Tokker and ...illions of redirects

He's created approximately 200 redirects from names of large numbers to Jonathan Bowers. Any chance a mathematically inclined admit could delete these, or at least automate the RfD script.... — Arthur Rubin | (talk) 05:17, 14 July 2006 (UTC)

It looks to me like the page Jonathan Bowers is a candidate for deletion:

It has a lot of unsourced material which I doubt is verifiable
It is a biography of a non-notable person.

Also Bowers style acronym looks like original research. CMummert 12:49, 14 July 2006 (UTC)

Good idea. I've alraedy summarily deleted the names of the large numbers and the notations for creating large numbers from the article, as naming things and re-creating notations are not notable unless the new notation catches on. I'm investigating whether the Polychoron family should be deleted as well, as being a neologism, not used in professional mathematics. (15 of the first 20 examples of the netscape search for "polychora" are Wikipedia, Bowers' site, or MathWorld. The other 5 may be from one of the other members of the Uniform Polychora Project. I've contacted a professional recreational mathematician named in one of the articles for further information.) — Arthur Rubin | (talk) 14:44, 14 July 2006 (UTC)

The word "polychoron" would not appear in classic Coxeter because it is more recent. We use 4-dimensional polytopes often enough that it is helpful to give them their own name. Both Johnson (of Johnson solids) and Olshevsky were students of Coxeter, which lends a certain amount of credibility to what they say. Here's the story of the name, as reported by Olshevsky on his web site:

POLYCHORON (plural: polychora) is my term for a four-dimensional polytope, analogous to polygon in two dimensions and polyhedron in three. The only other names for such a figure that I had seen in the literature, “polyhedroid” and “hypersolid,” seem uninspired and inappropriate, because they’re too close to terms for three-dimensional polytopes; the ending -oid connotes similarity or resemblance; and the prefix hyper- is badly overused. A four-dimensional polytope resembles a polyhedron no more than a polyhedron resembles a polygon, so it should have a similarly distinctive root following the poly-. The Greek root choros means “room,” “place,” or “space,” describing the three-dimensional polytopes, or cells, that make up the polychoron. In early versions of this website, I called such a figure a polychorema (plural: polychoremata), but Norman W. Johnson persuaded me of the benefits of the shortened form, and I changed this document everywhere accordingly.

Therefore "polychoron" is relatively new, but that doesn't mean it isn't also respectable. Remember that “polytope” itself was a neologism of Alicia Boole Stott before it was popularized by Coxeter. A possible contact to assess academic acceptance of the name might be computational geometry expert David Eppstein, a professor at UC Irvine famous for his Geometry Junkyard pages. Another academic contact might be Brown University professor Tom Banchoff, well known for his interest in things four-dimensional.

My impression is that although neologisms are rampant among enthusiasts, this term has gained traction and has been around long enough that it will probably persist. --KSmrq^T 20:01, 14 July 2006 (UTC)

Our article says that Coxeter uses polytope; unless there is some differentiation for polychoron, there is probably consensus against it. The images and facts should probably be salvaged. Septentrionalis 16:39, 14 July 2006 (UTC)

If polychoron is strictly dimension 4, that is the required difference. Septentrionalis 21:59, 14 July 2006 (UTC)

Even if I were an admin (see the above nomination), I'd need help keeping up with these. Someone is creating separate articles for the sections I deleted from Jonathan Bowers, and creating more pieces. (Is there something I could put in my .js which would, with a single click, add an {{rfd}} to the above redirect, and add it to a list in a user subpage so I could copy the list to WP:RfD. This is would be tiring.) — Arthur Rubin | (talk) 17:02, 14 July 2006 (UTC)

I don't think those redirects are actually that bad. Having them makes it less likely that someone will create stub entries on those numbers. It's kind of like the redirects we have at names of large numbers, which otherwise people would create stub articles on those numbers. Voortle 17:26, 14 July 2006 (UTC)

If those redirects are original research, they should be deleted also. Oleg Alexandrov (talk) 17:31, 14 July 2006 (UTC)

Dear Lord [72]. I suggest a massive speedy delete campain. Any comments on that? Oleg Alexandrov (talk) 17:27, 14 July 2006 (UTC)

Wikipedia:Articles for deletion/Other names of large numbers dealt with this issue, and the decision was to delete back them. Oleg Alexandrov (talk) 17:29, 14 July 2006 (UTC)

Yeah, redirects to other names of large numbers should be deleted, as that page doesn't exist. However, redirects from -illion names are not bad, because they prevent someone from creating stub articles on these numbers. Voortle 17:32, 14 July 2006 (UTC)

Redirects to other names of large numbers should be deleted, as that page shouldn't exist. Redirects to Bowers' names of large numbers are just as bad. — Arthur Rubin | (talk) 17:41, 14 July 2006 (UTC)

I don't think it would be any great loss to delete all of these. Paul August ☎ 17:52, 14 July 2006 (UTC)

Nominate for deletion all Jonathan Bowers related pages?

Is Jonathan Bowers that important a person? To me he appears to be a crank, and not even notable at that. How about nominating for deletion his page and all his other stuff? Oleg Alexandrov (talk) 17:37, 14 July 2006 (UTC)

Anyone got a script? I think we need to delete most of the Polychoron pages, and the other people linked from Uniform Polychora Project. — Arthur Rubin | (talk) 17:41, 14 July 2006 (UTC)

I would agree with deleting the whole lot. I don't believe they enhance wikipedia at all. Madmath789 17:44, 14 July 2006 (UTC)

Note that Oh Crap (talk · contribs · logs · block user · block log) has created a malformed AfD for Jonathan Bowers and L. Craig Schoonmaker. Is there any way to separate them. (The issues are not related.) — Arthur Rubin | (talk) 18:05, 14 July 2006 (UTC)

See Wikipedia:Articles for deletion/Jonathan Bowers. Oleg Alexandrov (talk) 18:07, 14 July 2006 (UTC)

STOP! First off lets look at the members of the Uniform Polychora Project among them was the late Norman Johnson a student of Coxeter, and perhaphs one of the most important recient figures in the field of polyhedra, having created the Johnson solids, and also the nicest way of classifying the uniform polyhedra List of uniform polyhedra by vertex figure (Johnson, N. W. Uniform Polytopes. Cambridge, England: Cambridge University Press, 2000). So Johnson then went onto study the four dimensional polyhedra and enlists the help of various amature mathematicians, Bowers being one of them. Bowers is responsible for discovering most of the uniform 4D polyhedra and as discoverer probably gets the naming rights. Bowers names are probably becoming the defacto standard for 4D uniform polyhedra, considerably more pratically useful than the long names (First due to Coxeter, modified by Wenninger and later by Johnson). So we have a group resposible for discovering most of the uniform 4D polytopes. So its run by amatures who don't bother to publish in maths journals. Well the whole field of polyhedra is very much dominated by the amature, the most read book on the subject is Wenninger polyhedra models and Wenninger is in an order of Monks, not a professional mathematician.

As for the array notation. I'm not sure but I think is is capable of representing larger numbers than the closest contender Conway chained arrow notation. In my book thats worth a page, published or not. This stuff is important as it has close links to transfinite cardinals, helps us get a feel for the true emensity of natural numbers and is also a good way to bring people into apreciating mathematics, a natural extension of the game of naming bigger and bigger numbers we all played as kids.

I'm less bother about the names of large numbers, although the largest finite number so far conceive by man, seems to be of some interest. Here I'd take a pragmatic approach, we will always be getting people adding these very large names. Theres two options, spend our lives reverting Names of large numbers or keep a seperate out of the way page for these numbers to appear.

To sum up Wikipedia isn't great because it's like the Britannica. The Britannica is great at being authoritative, edited, expensive, and monolithic. Wikipedia is great at being free, brawling, universal, and instantaneous. — Cory Doctorow --Salix alba (talk) 18:11, 14 July 2006 (UTC)

I strongly object to wholesale deletion without closer scrutiny. As I noted above, the name "polychoron" was created jointly by Olshevsky and Johnson, both of whom worked and studied with Coxeter, and both of whom were involved in creating the Uniform Polychora Project. Partly we are confronting a problem of volume and organization: there are too many of these beasts! They can hardly all be well-known, it's a pain to enumerate them, it's a pain to name them, names are still in flux, and so on. Frankly, I doubt many people can name the convex regular polytopes in four-dimensional Euclidean space, or even recall how many there are — and these are surely notable. Or how about the Archimedean solids? Our page lists 13 of them, over half with more than two names! Please, ease off on that trigger finger; don't shoot first and ask questions later. I'd suggest that few polychora deserve a page of their own, and that we surely don't want to duplicate the content of the project; but don't throw out the baby with the bathwater. I'd also suggest it would be absurd to delete the page on Norman Johnson. --KSmrq^T 20:29, 14 July 2006 (UTC)

I'm not in a hurry to delete the polychora; I'm still researching. Mr. Bower and his pet names are not notable. Messers. Olsehvsky and Johnson may be more notable. — Arthur Rubin | (talk) 22:19, 14 July 2006 (UTC)

First, Norman Johnson is not late. He is alive and well.

About Jonathan Bowers and polychora, I am familiar with his work and have met him at a conference. I am also acquainted with Olshevsky, and know Wenninger and Johnson fairly well. Jonathan Bowers would be classified as an amateur mathematician, but has an astounding ability to work with four-dimenionsal figures. He can sketch three-dimensional cross-sections of polychora as easily as I might sketch, say, an equilateral triangle.... He is in close contact with Johnson, and Johnson is trying to incorporate Bowers's work into an upcoming book to be published by Cambridge University Press.

User Tom Ruen is also working on the Wikipedia pages on polychora.

This group is at the forefront of work on polychora. The project is to enumerate all uniform polychora in four dimensions. The problem of enumerating the 75 uniform polyhedra in three dimensions was solved only in the 20th century and has an interesting history. I think it is reasonable to assume that any work done in the area (in 4D) will be known to this group.

I only recently read about Bowers's work on naming large numbers. I think that subject should be discussed independently of his work on polychora.

I would argue that Jonathan's work is legitimate, even though he doesn't have appropriate 'credentials.' You might not wish his work in the Wikipedia for other reasons, but it is certainly not spurious. Vince Matsko 21:10, 9 August 2006 (UTC)

The work is legitimate. The classification theory seems notable enough; however his naming conventions (both for large numbers and for polytopes), any of the individual names that have articles, and the term "polychoron" may need to be removed, unless some legitimate geometer publishes those names. — Arthur Rubin | (talk) 00:55, 10 August 2006 (UTC)

Evolution of an article!

I am still fairly new to wikipedia, and I would really appreciate a view from a more experienced wikipedian about the evolution of the article Homogeneity. I have looked at the history of this article over the last year or so, and it seems to have 'evolved' in an extremely strange way. Please take a look at the Revision as of 07:02, 10 February 2006, and compare with the Revision as of 08:34, 10 July 2005. What on earth is going on here??? I am totally baffled by the latest incarnations of this article, but if more experienced editors tell me it is OK, I will accept their wisdom ... Madmath789 22:47, 14 July 2006 (UTC)

It looks like an editor decided that there is basically only one meaning for "homogeneity", i.e. its use in statistics, and then proceeded accordingly. --Chan-Ho (Talk) 10:50, 15 July 2006 (UTC)

Yes, indeed, but I can't make much sense of the article as it stands, despite being a reasonably competent mathematician with a fair knowledge of probability and statistics! I am also a little suspicious of the possibility of OR here, as much of the editing of Homogeneity and a linked article Reliability (statistics) seems to have been done by David Cruise or by Cruise, and a couple of external links from Reliability (statistics) point to 'visualstatistics.net (e.g. The problem of negative reliabilities ) which seems to be authored by David J. Krus / Cruise scientific. I might be off-beam, but I am very suspicious of these articles. Madmath789 11:37, 15 July 2006 (UTC)

Yes I agree the article does look very out of ballance. Go ahead and bring it back into line. --Salix alba (talk) 11:53, 15 July 2006 (UTC)

Apart from the present article being whacky, I also think that Homogeneity (instead of Homogeneous) should be a disambiguation page, with Homogeneous a plain redirect to Homogeneity, and the statistical concept being handled at Homogeneity (statistics), which now redirects to Homoscedasticity, a different concept in statistics. --Lambiam ^Talk 12:34, 15 July 2006 (UTC)

Whacky indeed! I have spent some time trying to decide if this article homogeneity is genuine or totally off-the-wall. Can I make a plea: if anyone here knows more than I do about this sort of statistics, could you please advise as to the validity of this weird-looking stuff? Madmath789 16:56, 16 July 2006 (UTC)

Greek letter proposal

Please see my proposal for Greek letters at Wikipedia talk:WikiProject Mathematics/Conventions CMummert 23:27, 15 July 2006 (UTC)

Computability Articles

JA: User:CMummert is making a mass of what appear to be improper page moves, renames, and reorgs to computability related articles. Could somebody please sort all that out and makes sure it's by the book? Thanks, Jon Awbrey 15:58, 16 July 2006 (UTC)

What I've seen looks legit to me. --CSTAR 16:23, 16 July 2006 (UTC)

I would be glad to explain, if anyone asked me; one the other hand, I am an expert in the area. For a while, there have been two articles: Computable function and Recursive function. These titles are synonyms in the current vernacular, and having them as separate articles is confusing. I have moved Recursive function to Mu-recursive function which is the consensus on what that article is actually about. I made Recursive function into a disambiguation page, which is important because there is a CS meaning for the term that was not reflected on the previous page. Then I chased almost all the things that linked to Recursive function. Many of them actually wanted to link to Recursion or Recursion (computer science); the previous page had no relation to the material in articles that were linking to it! So I fixed many of the links to Recursive function to point to a more helpful location. I also made a start towards fixing Mu-recursive function. CMummert 16:35, 16 July 2006 (UTC)

STIX Fonts update

Many of us have been eagerly awaiting the culmination of the STIX font project. A major milestone was recently announced.

On 10 July, the STI Pub group received the final delivery of requested glyphs for the STIX Fonts Project. This final set is being reviewed by the STI Pub Technical Review Committee, and packaging instructions for the beta test of the fonts are being prepared. Tables of STIX glyphs will begin to appear on this website within the next few weeks, and the beta font set will begin to be constructed.

So far every deadline has been overly optimistic; still, progress has been real. It appears the race is on, between universal adoption of the STIX mathematics glyphs and Wikipedia adoption of BlahTeX! Regardless of which tortoise crosses the line first, we all win. Huzzah! --KSmrq^T 09:47, 17 July 2006 (UTC)

Fleiss' kappa

I don't know if this is the right place to ask about this, but I've been working on Fleiss' kappa, and I'd like to get someone who actually knows what they are talking about to look over it. I have the paper here, but I worked out what is what by trial-and-error because I am pretty much maths illiterate. I'd appreciate it if anyone could look over it, and add {{accuracy}} or something if I've made a mistake. Thanks - FrancisTyers · 16:01, 17 July 2006 (UTC)

See my comments on the talk page of Fleiss' kappa. VectorPosse 22:44, 17 July 2006 (UTC)

Discussion at Category talk:Mathematics user templates

Hi all,

Just wanted some of the editors opinion on a discussion I started at Category talk:Mathematics user templates. The discussion is about userboxes, a bit technical, but not serious. I don't want to advertize, but the fact is that in most cases, category pages are usually watched by the creators only, and probably even worse in this case, only be the sysop who moved the category. Thanks, — Ambuj Saxena (talk) 17:17, 18 July 2006 (UTC)

Homogeneity

The 'whacky' article Homogeneity is up for deletion - please take a look and comment at Homogeneity. I think it really needs looking at by a statistician. Madmath789 06:33, 20 July 2006 (UTC)

Following some moves by Michael Hardy, the AfD seems to have vanished, and the material I was worried about now lives at homogeneity (statistics) - does anyone see a good reason for not having an AfD discussion about this stuff? Madmath789 15:11, 20 July 2006 (UTC)

I've now listed a new AfD at Wikipedia:Articles for deletion/Homogeneity (statistics) and voted speedy keep on Homogeneity, previous votes have been copied across. --Salix alba (talk) 16:22, 20 July 2006 (UTC)

User:David Cruise

I would like someone with experience look at edits made by User:David Cruise, User:Cruise, and also IP 65.39.86.104 ([73]) to the mathematical articles, in particular, Supermatrix, matrix addition, matrix subtraction, canonical analysis, homogeneity (statistics) (this article is currently listed at AfD and this actually triggered my interest in the user Cruise) and probably many other articles as well. Note references to Krus' publications and links to Cruise Scientific ([74]), also note many links from Cruise Scientific (see for example, [75]) to the Wikipedia articles in question. I would like someone to sort out contributions with scientific value from original research. (Igny 18:21, 21 July 2006 (UTC))

I have only looked at the article on matrix addition, but it certainly has all the earmarks by being hijacked. Alterations include non-standard definitions and notation, as well as self-promoting links. --KSmrq^T 19:41, 21 July 2006 (UTC)

I think I am responsible for bringing this to peoples attention, but I have "trodden carefully" as a comparative newcomer to WP (but a comparative 'old-comer' to maths!). I have been looking at the things mentioned above for a few days, and have to say that I believe that most of the content of the articles Homogeneity (statistics) and Canonical analysis are mathematical gibberish, and the matrix stuff is probably nonsense (I have seen many examples of such over the last 4 decades, but these examples are quite staggering!). I do not wish to appear to be waging a vendetta against any contributor to WP, but I have to say that I cannot find anything worth keeping in the previously mentioned articles, and feel that trying to rewrite them would best be done by deleting everything and starting from scratch. Madmath789 20:54, 21 July 2006 (UTC)

I don't think the material at canonical analysis is nonsense, but it is not clearly explained in a manner that makes it comprehensible to mathematicians in general. Similarly at homegeneity (statistics). Michael Hardy 22:29, 22 July 2006 (UTC)

Our discussions here may become academic, as User:David Cruise seems to be trying to blank contributions he has made - see for example: Canonical analysis. I know I have been a harsh critic of some of his contributions, but I am unsure if this is the right way to proceed. What do others think? Madmath789 16:56, 23 July 2006 (UTC)

Ones contributions are an irrevokable gift (if they are not an infringment of someone else's copyright). So we are free to resurrect them by reverting his deletions. Also we should take care that he does not also delete the contributions of other people. But perhaps any such corrections should be done only after he has been blocked so that he will not commit more such vandalism. JRSpriggs 03:16, 24 July 2006 (UTC)

Blatant spam is of course not needed. But as for 'nonstandard stuff', I don't take stock in nonstandard stuff, because doing stuff in a non-standard way can lead to new ideas. As for matrix addition and matrix subtraction, I reverted one of the articles back to the way it was with his changes, and later removed some spam-like stuff from references and external links. I ask someone who knows more than the textbook definition of matrix addition/subtraction that I do to look over whatever new matrial he put in, save actual methodology that works and is substationally useful. I'm not so sure such a lengthy section is needed on a particular application of matrix subtraction, for example, involving variance. Kevin_b_er 04:45, 24 July 2006 (UTC)

David Cruise's additions to matrix addition and matrix subtraction are probably correct (though they are badly explained, so I can't be sure of that). However, his definitions are not used in the field of matrix theory. They may well be used in statistics or social sciences, but all we have are some papers written by D. Crus in nonmathematical journals. In contrast, the standard definitions are in every linear algebra textbook. I do not think that "doing stuff in a non-standard way can lead to new ideas" is a good reason for including nonstandard definitions in an encyclopaedia. I think that the nonstandard material to these two articles should be removed, or at least greatly reduced, unless somebody tells us that these definitions have found widespread use in some disciplines. -- Jitse Niesen (talk) 05:13, 24 July 2006 (UTC)

I noticed that David Cruise just vandalized two sections of this very talk page. From the history:

11:52, 25 July 2006 Gandalf61 (Talk | contribs) (rv blanking)

11:48, 25 July 2006 David Cruise (Talk | contribs) (entries containing libellous statements)

Fortunately, Gandalf61 reverted the vandalism. I think that the first administrator who reads this should immediately block David. JRSpriggs 06:02, 26 July 2006 (UTC)

I was considering asking an admin to look at this myself, in view of his blanking of parts of this page, and also his removal of the AfD notice (and other stuff) from Homogeneity (statistics). I am aware, though, that he has also made contributions from another account User:Cruise (not active since 17th April) and might use that one while blocked. I will keep an eye on it. Madmath789 08:13, 26 July 2006 (UTC)

I haven't been around much, so I don't know the details, but a single blanking at this page, while unacceptable, is probably not sufficient to block. I've placed a warning on his talk page. If his behavior continues, a block can certainly be considered. By the way, if we do decide to block, using sockpuppets is grounds for blocking the second account, so that's not a problem. -lethe ^{talk +} 08:18, 26 July 2006 (UTC)

As I understand things, he has already been given a one week block by User:IanManka. Madmath789 08:27, 26 July 2006 (UTC)

Terminology clarification and first use references: "Hypercomplex Number"

Hello,

I'm currently trying to clarify the use of the term "hypercomplex number" over the years and to-date. The goal is to update the hypercomplex number article. Since this may result in a rewrite, it would be great if any ideas or comments could be posted in talk:hypercomplex number, so the reasoning behind a potential rewrite would remain with the article.

Thanks, Jens Koeplinger 21:27, 22 July 2006 (UTC)

PS - It may be that the term "hypercomplex number" is to-date a rather freely used term, like "numbers with 2 or more dimensions and at least one non-real axis". If so, I'll scratch together what I can find in some common places (here, mathworld) and rewrite hypercomplex number in a fashion that puts different systems into different categories (like Cayley-Dickson, split-complex, etc). Thanks, Jens Koeplinger 13:28, 24 July 2006 (UTC)

I've just posted a rewrite of the hypercomplex number article. While I tried to carry over all previously existing information and statements into the new version, it now contains much more detail and categorization. I would appreciate any comment or help. Thanks, Jens Koeplinger 22:29, 31 July 2006 (UTC)

Hello; I haven't received much feedback yet about the hypercomplex number rewrite, so I figure it can't be too bad. There are two obvious weeknesses: "The term hypercomplex number has been used over the years rather freely ..." - if anyone knows about references to be added, please do so. I've seen two more book titles mentioned in the internet, but I'm reluctant to referring to books or titles I didn't read. Without references, my statement has no support within the article.

The second weakness is that I'm writing about "Arguably the most common use of the term hypercomplex number [...]" and only provide links to some other numbers. I'm comfortable with this wording, but to the least I'd like to add a section that groups together these 'arguably not so common uses' of the term "hypercomplex number" (surreal, hyperreal, transfinite, superreal nubers, and - as I recently learned - Mark Burgin's hypernumbers which appear not to have an article in Wikipedia yet).

Maybe we could tailor the "hypercomplex number" article into an overview over all number systems that somehow go beyond or extend the reals. This might help to have the current number article focus on commonly used systems (from natural to complex numbers), and clean-up references to other less frequently applied numbers.

But first I'd like to put the "hypercomplex number" article on better feet, and remove the 'stub' notice once done. Any comment is greatly appreaciated. Thanks, Jens Koeplinger 12:40, 8 August 2006 (UTC)

Good articles

While trying to expand the list of important articles in Wikipedia:WikiProject Mathematics/Wikipedia 1.0, I've come across a few articles I feel are close to Wikipedia:Good articles status and nominated them appropriately. of these Euclidean geometry, Georg Cantor and David Hilbert has reached GA status. Pi, Fractal, Gottfried Leibniz, Ronald Fisher have failed. Fractal needs someone to check recent additions made by reviewer, Leibniz needs some work organising the references and Pi and Fisher needs more extensive work. If anyone would like to have a look at these articles it should not take much to gain GA status. --Salix alba (talk) 09:47, 23 July 2006 (UTC)

84.40.138.111 (talk • contribs • WHOIS • RDNS • RBLs • block user • block log) and -http://www.apronus.com/provenmath/ links

We've got a new IP address adding external links to the above mentioned web site. I'm tempted to revert en mass, but I'd like a second opinion. — Arthur Rubin | (talk) 17:52, 24 July 2006 (UTC)

I had just noticed this too, and I agree the links don't belong here. Dmharvey 18:36, 24 July 2006 (UTC)

Yes, noticed them earlier, and find them hard to read (but they may well be valid) - the notation used on that website is 'tedious' to read - see [76] I agree they don't belong here. Madmath789 21:19, 24 July 2006 (UTC)

If I read this page correctly, they claim to have their own proof of the equivalence of Zorn's Lemma and the Axiom of Choice; I hope I'm being unfair, but... What next, the Pythagorean Theorem? Septentrionalis 23:03, 24 July 2006 (UTC)

Proving induction

Please take a look to the article proof of mathematical induction. As a consequence of a remark of mine [77] an editor made some addition to the hypothesis of the proof to make it work. I would like to understand if this proof is "standard" (it should be other wise would be original research) and what is his original form (in particular which hypothesis should we require). What do you think?--Pokipsy76 15:41, 23 July 2006 (UTC)

The concept of "proving" induction is strange. Typically we use an axiom scheme that explicitly states that induction works. A quick glance at this leaves me feeling that it's a bad article. --KSmrq^T 19:02, 23 July 2006 (UTC)

The concept of proving the principle of mathematical induction is certainly not strange - it is a well-known part of mathematical logic and the development of the number system logically. The article might need a bit of work, but the idea is good. Madmath789 19:15, 23 July 2006 (UTC)

I'm not quite sure what you mean by "proving". For example, here's a quote from Peano axioms:

Informally, the Peano axioms may be stated as follows:

0 is a natural number.
Every natural number a has a successor, denoted by Sa or $a'$ .
No natural number has 0 as its successor.
Distinct natural numbers have distinct successors: a = b if and only if Sa = Sb.
If a property holds for 0, and holds for the successor of every natural number for which it holds, then the property holds for all natural numbers. This axiom of induction legitimizes the proof method known as mathematical induction (induction over the naturals).

I draw your attention to the last item. Essentially it says we "build in" induction; we don't deduce it. Although there are many ways to approach foundations, I don't think we can avoid something along these lines; natural numbers and induction are inseparable. If natural numbers are defined per Peano this whole proof article is silly. If not, the article is confusing; it's not clear where we're beginning, nor exactly what is being accomplished.

If we are going to discuss the article further, we should do so on its talk page. --KSmrq^T 23:19, 23 July 2006 (UTC)

Proving just means deduction from axioms. Clearly, in PA, mathematical induction is an axiom, but in developing maths from ZFC, it is not an axiom, so it needs to be proved from the axioms. Madmath789 06:51, 24 July 2006 (UTC)

I have to agree with both KSmrq and Madmath: The idea of proving the induction principle is not "strange" in itself, and yet the article in question is a bad article (and I have my doubts that any article with that title would be good). Induction is not assumed explicitly in, say, the usual formulations of ZFC, and can be proved once you've defined the naturals. But there's less here than meets the eye; it's a boring technical detail rather than something particularly significant, and having an article about it might give the misimpression that there's something fundamental being done. The existing article is worse than that; it starts with the assumption that the naturals are wellordered. From there the induction principle really is a triviality. --Trovatore 19:56, 23 July 2006 (UTC)

It's not clear to me in which sense can we be supposed to prove induction principle from the well ordering assumption: the well ordering itself is useless unless we have some extra assumption to work with (for example the assumption that x#0→x=y+1)--Pokipsy76 20:04, 23 July 2006 (UTC)

I gave that article a prod. -lethe ^{talk +} 20:37, 23 July 2006 (UTC)

Maybe you could have waited a little bit to let us discuss about it before going to vote.--Pokipsy76 20:55, 23 July 2006 (UTC)

Prodding does not involve a voting process. We have ample time to discuss this. --Lambiam ^Talk 00:39, 24 July 2006 (UTC)

Are you sure? Look here.--Pokipsy76 20:59, 24 July 2006 (UTC)

The PROD, which involves no voting and can be halted in an instant, was forced into AfD, which requires voting and admin participation. The official decision was no consensus. My unofficial summary of the comments: the article needs improving, and probably the proof should be merged into the parent article. It would be nice for one of the "keep" voters (Pokipsy76?, Ryan Reich?) to volunteer. --KSmrq^T 00:18, 1 August 2006 (UTC)

Done. I "morally" merged the article; the actual material in it was sort of long-winded. I also put in the stuff on transfinite induction and included a reference to Kolmogorov and Fomin. The original proof article remains, with a {{merging}} tempate added. Ryan Reich 02:23, 1 August 2006 (UTC)

Thanks, that's much better. --KSmrq^T 09:56, 6 August 2006 (UTC)

Good. I've changed the old article to a redirect now. Ryan Reich 15:25, 6 August 2006 (UTC)

Articles listed at Articles for deletion

The following articles have been listed at Articles for deletion but not caught by the 'bot:

Wilkinson's polynomial (AfD discussion)

Uncle G 11:54, 25 July 2006 (UTC)

it is now. Septentrionalis 21:25, 26 July 2006 (UTC)

The decision on Wilkinson's polynomial was keep, after a number of editors worked on cleaning it up and clarifying its significance. --KSmrq^T 00:15, 31 July 2006 (UTC)

The following articles have been listed at Articles for deletion but not caught by the 'bot:

Imaginary logarithm (AfD discussion)

Uncle G 17:24, 28 July 2006 (UTC)

The bot runs once a day; it may be preferable either to wait a day and see if it is picked up, or add this to the list by hand. Septentrionalis 22:49, 28 July 2006 (UTC)

The decision on imaginary logarithm was redirect to complex logarithm, agreed unanimously. --KSmrq^T 09:54, 6 August 2006 (UTC)

article variational number theory is back

User_talk:Karl-H has recreated the page. He's also made edits to calculus of variations and number theory among others. Somebody familiar with the subjects and the original RfD might want to take a look. Lunch 19:09, 26 July 2006 (UTC)

Integral equations has been edited too. Lunch 19:14, 26 July 2006 (UTC)

Reverted all of those. — Arthur Rubin | (talk) 21:18, 26 July 2006 (UTC)

Removing the redlinks in the list of mathematicians

Currently the list of mathematicians has a certain number of redlinks. I would argue that that was a good thing when Wikipedia was new and plenty of famous people did not have articles and when there was no bot to maintain that list.

I would think that now we would be better off having the list of mathematicians list articles which actually exist, with redlinks (requests for new articles) going to Wikipedia:Requested articles/Mathematics instead. Removing the redlinks from the list of mathematicians would also make it easier to see what mathematician articles got created/deleted by inspecting the Current activity.

In short, how about removing all the redlinks from the list of mathematicians? Oleg Alexandrov (talk) 20:32, 29 July 2006 (UTC)

I think that's a good idea. Can I also encourage people to add to the requested mathematician list? As a grad student, I'm hesitant to create articles for mathematicians that work at my school. I'd feel more comfortable if they were on the requested list. Thanks. Originalbigj 19:45, 30 July 2006 (UTC)

The bot now removes redlinks from the list of mathematicians (log). Oleg Alexandrov (talk) 23:53, 31 July 2006 (UTC)

It appears that you removed the redlink to Thomas Jech from the list of mathematicians, but did not add it to the list of requested articles on mathematicians. If a redlink is removed from one, I think that it should be added to the other (if not already there). And what if someone destroys the article or moves it to another name? JRSpriggs 03:10, 1 August 2006 (UTC)

Update. I just created a stub for Thomas Jech. I did not see the redlink removal in the log. But I remember creating a redlink for him a month or two back. JRSpriggs 03:27, 1 August 2006 (UTC)

I did not add the redlinks to Wikipedia:Requested articles/Mathematics on purpose, it is not clear if those redlinks are indeed "Wanted" articles.

If an article gets deleted (which only administrators can do) my bot will remove it from the list of mathematicians. If an article gets renamed, the bot will reflect the rename in the list. Oleg Alexandrov (talk) 04:55, 1 August 2006 (UTC)

Oyam's Pyramid

The article Oyam's Pyramid is currently proposed for deletion. It seems to me that it would be likely to be covered by some area of mathematics rather than being a complete hoax, but I've been unable to track down any evidence for its existence with this title. Could somebody take a look and see if a) it's a valid but wrongly-titled article, b)it needs merging or redirecting to some other concept, or c) it's complete garbage. Thanks Yomangani 10:46, 31 July 2006 (UTC)

Since there are no Google hits for any of this (except to Wikipedia), it is definitely made up. In my opinion it doesn't make much practical sense if you actually mean to build a pyramid. (Disclaimer: I have no actual experience in pyramid construction.) Mathematically it seems to be a pointless triviality. --Lambiam ^Talk 23:00, 31 July 2006 (UTC)

Piotr Blass

I was wondering what people thought of the article Piotr Blass and the anon User: 69.163.189.9 who has created it and spent some time inserting the name of Piotr Blass into the articles of several distinguished mathematicians, e.g. Hassler Whitney and Heisuke Hironaka. I spy several dubious claims to fame in the Blass article, e.g. inventing the World Wibe Web. There's also a very interesting assertion that he's the student of a number of famous mathematicians (such as the ones I mentioned prior). Blass is apparently enough of a famous mathematician that the statement that Whitney taught "mathematics education" to Blass is an important thing to include into Whitney's article.

Blass' publication list looks fairly average and is bolstered by a number of publications to a journal that he founded and that I've never heard of. To be fair, I noticed that Zariski surface exists and was created by User:r.e.b.; it appears that Blass named Zariski surfaces and has some papers on them in respectable journals. So I wouldn't advocate a deletion of the Blass article. But it seems there's a lot of what might be called "tooting one's own horn" (if the anon is indeed Blass). --Chan-Ho (Talk) 17:14, 31 July 2006 (UTC)

A quick google reveals Blass was given Grothendieck's prenotes for EGA 5. [78] So he certainly knew some influential people. There also seem to be proof of editorship of journal [79], standing in elections as a write in candidate (lots of links). Slashdot (that most relaible of sorces) mentions hims in conection with some dubious compression algorithm work with ZeoSync [80]. --Salix alba (talk) 19:35, 31 July 2006 (UTC)

And another quick look at Google Schoolar shows 24 publications mentioning his name, including some on Zariski surfaces. Google Print also gives few hits. On the other hand, the article needs copyedit and other claims ('one of the fathers of the Internet) seem more dubious.--_{Piotr Konieczny aka Prokonsul Piotrus | talk} 02:53, 2 August 2006 (UTC)

I removed links to his name from several well known mathematicians. Math Genealogy lists two advisors: James Milne and Melvin Hochster. Others may have taught him some undergrad classes but anyway this is not notable. Using ip trace I found a clear evidence that he is trying to promote himself and is using WP for political purposes. I actually don't mind (and don't care) whatever is on the page on him but find inappropriate the insertion of his name averywhere. Inventor of WWW is simply laughable (he does give half the credit to Sir. Tim Berners-Lee). Mhym 14:36, 2 August 2006 (UTC)

15 of his 33 publications are in the Ulam Quarterly, which he founded. This journal was founded in 1987; before going defunct in 1997, it published a whopping 10 issues, each of which contains at least one (sometimes two) articles co-authored by Piotr Blass. This journal is, according the journal website, also the first electronic mathematics journal and is apparently the basis for Blass' claim of being inventor of the WWW.

It's not just the WWW claim that is dubious. A number of his achievements listed are suspect. Simply knowing and interacting with famous people is not an achievement. In fact, a number of people do this...that goes hand-in-hand with being famous (a lot of people know and talk to you). Organizing seminars at IAS is not an achievement. Being a member (even visiting), would be.

Blass' claim to fame is doing some of the early work on Zariski surface and naming it. I'm not sure if he's even as notable as Norman Johnson. But like I said, his bio should probably stay, but it needs to be heavily edited by people other than Blass. --Chan-Ho (Talk) 16:51, 2 August 2006 (UTC)

I got the founding date of 1987 for the journal from the anon/Blass edit, but apparently the first issue came out in 1992 according to the journal website (see contents of first issue) and MathSciNet. I don't suppose this really matters or adds anything except to give a more accurate context for Blass' WWW claim. --Chan-Ho (Talk) 17:29, 2 August 2006 (UTC)

There is some wonderful dirt on Blass [81]

[82] I don't quite understand it all but it seems to involve a company called CyberNet, 5 Star Trust Bank, kids in abusive treatment center, Diebold. Seems like Blass had evidence of defects in Diabold voting machines, being hacked by kind from Bay Point School correction facility (where he taught), but he withheld information due to ties with an atoney with connections to the republican party (the attony helped Blass get his son out of another correction facility).

So to add to inventing the WWW, we might add Blass was responsible for Bush getting into the whitehouse in 2000. --Salix alba (talk) 18:19, 2 August 2006 (UTC)

AfD it is Wikipedia:Articles for deletion/Piotr Blass. --Salix alba (talk) 19:11, 2 August 2006 (UTC)

Aug 2006

This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

Prerequisites

I was reading an amusing interchange on the talk page for Lie groups just now. (Sorry, I don't know how to link to the specific section in the talk page. Maybe someone can help me with that.) Anyway, a user who clearly didn't understand the complexity of Lie group theory was trying to suggest that the page was worthless. This user suggested that the complexity of the article meant that the uninitiated could not follow it and the initiated didn't need it since they knew it already.

While I vehemently disagree with these sentiments, the discussion did lead me to think that maybe we need some system by which we can communicate prerequisites to those seeking information on a topic for the first time. No textbook would ever discuss Lie groups without either mentioning in the preface the need for a solid background in smooth manifolds, or else providing a reasonably comprehensive introduction to the subject in the book itself. I fully realize that Wikipedia is an encyclopedia and not a textbook. Nevertheless, a newcomer to Lie groups should know first thing that they ought to be comfortable with smooth manifolds (and probably some group theory too) before attempting to read (let alone criticize) an article on Lie groups. (I am thinking about this for all math topics, not just Lie groups, of course.)

What do y'all think? VectorPosse 05:58, 6 August 2006 (UTC)

The link you want is to Talk:Lie group#is this useful?. I am not familiar with templates, but perhaps we need a template for pointing to another article containing the prerequisites for reading the current article. JRSpriggs 06:44, 6 August 2006 (UTC)

I strongly disagree with putting any list of prerequisites on top of articles.

First, if a user never heard of differential geometry before, and complains that Lie group is hard to read, he/she has only himself/herself to blame. Reminds me of somebody who complained that logarithm is a useless article, because that person could not find a motivation for that article to exist.

Second, a well-written article should have a good introduction, and relevant links to other subjects should be embedded in context. That's encyclopedic.

All in all, while I strongly agree that articles should be accessible, boxes of prerequisites are not the solution. Oleg Alexandrov (talk) 07:07, 6 August 2006 (UTC)

An encyclopedia article is not a textbook, nor even a chapter of a textbook. Also, the web of knowledge admits no simple linear ordering. We get complaints about mathematics articles being opaque on a regular basis. The appropriate response depends on the state of the article, and on the topic.

People can arrive at an article in many ways. Perhaps they were searching the web for a word or phrase. Perhaps they were reading another article that thought this would be a useful link, either for background or enrichment. Maybe someone overheard the topic in a conversation and wanted to get a feel for what it's about. Or maybe someone has a text that is less than clear to them and thought Wikipedia could help. (We wish!)

Sound like a challenge? It is. A good mathematics article on a popular topic is especially hard. If that topic includes a modicum of technical difficulty, look out. If lots of people think they know something about it, the editing can get controversial.

Unfortunately, "Lie group" should be a major service article. It needs an introduction that a high school student can handle, but also needs to touch on material that can occupy months of graduate study.

We never want to say "if you haven't studied group theory and differentiable manifolds, go away". And what about matrices, since many of our examples occur as subgroups of GL(n,R)? No, prerequisites are unacceptable.

What might be more helpful is a "related topics" box. We would want to indicate something about the nature of the relationship, and we would need to avoid the temptation to link everything to everything. But I think it could be a major project to begin augmenting our articles in this way, and I'm not sure who would do it. Meanwhile, we do have a "Categories" area at the bottom of the page, which means it is often overlooked. --KSmrq^T 09:48, 6 August 2006 (UTC)

I initiated the discussion without any preconceived notion of what might be a "good" or "bad" way to approach the idea, but now that I've seen some of the discussion, I would tend to agree with Oleg Alexandrov. A well-written introduction can and should refer to the subjects that are required without causing any great disruption to the thousands of pages that already exist. (Having said that, many such pages probably do need better introductions. The more abstruse pages seem very far removed from their basic categories.)

I do not think that prerequisites suggest "go away". If presented correctly, they should come across as helpful. Those who are curious about an advanced topic will try to read the article anyway (and this is a good thing), but at least they are informed as to why the article is confusing to them and where they can go for more basic information. I think there are unintimidating ways of writing an introduction that communicate the essence of a topic, but at the same time point the reader toward articles which may be more appropriate for their level. I would guess that this is an ideal that we can all get behind. VectorPosse 21:30, 6 August 2006 (UTC)

This might be a good time to mention that we do have a Manual of Style specifically for mathematics, and that the first piece of advice offered is:

"Probably the hardest part of writing a mathematical article (actually, any article) is the difficulty of addressing the level of mathematical knowledge on the part of the reader. For example, when writing about a field, do we assume that the reader already knows group theory? A general approach is to start simple, then move toward more abstract and technical statements as the article proceeds."

In my experience, the advice is accurate, but no substitute for experience! Anyway, perhaps that article will help. --KSmrq^T 23:27, 6 August 2006 (UTC)

Proposed merge: "Bicomplex number" into "Tessarine"

Hello. I recently came across the article bicomplex number, which appear isomorphic to tessarines. The latter appear the first use of this arithmetic, and all properties listed in "bicomplex number" are already contained in "tessarine". Another complication is that when Hamilton's quaternions were still new, some also referred to them as "bicomplex number" (but I have not seen this term used for quaternions in articles in the past 100 years). See also talk:bicomplex number.

As a suggestion, we could have bicomplex number redirect to tessarine, and add the isomorphism (with the one reference) there. The tessarine article itself needs some minor work, e.g. to list its algebraic properties first and then refer to isomorphic numbers (I acknowledge having contributed to this disorder while working on rewriting hypercomplex number; sorry for that, I simply haven't gotten to clean up "tessarine" yet).

Any comment, concern, or help is appreciated. Thanks, Jens Koeplinger 13:17, 8 August 2006 (UTC)

After finding at least four different uses of the term "bicomplex number" within just a few hours, we may be looking at (yet another) term that appears to have been used freely in mathematics, where each use was apparently clear within the context of the particular program where it was used. Similar to the use of "hypercomplex number". Well that's just great. I hope for the future that the internet, and in particular establishments like Wikipedia and full-text search, will give authors better tools to research existing terminology when scoping out naming for something they deem "new". Therefore, maybe we should rather make the "bicomplex number" article in a way that disambiguates all these uses. A simple disambiguation may not be enough, because one may want to write a few sentences for each section. Oh well. Thanks for any comment or additional information (see also talk:bicomplex number. Jens Koeplinger 17:18, 8 August 2006 (UTC)

Looks like the current version of the bicomplex number article stub refers to a special type of the multicomplex number program, and appears to be widely used. Therefore, I've added a new multicomplex number stub, with some barebone description, and updated some references and isomorphisms. So the bicomplex number article is really for keepers, but we must also provide reference to the other uses. One use (synonym to quaternions) is outdated and can be referenced as such, another use is actually from a compound term "variational bicomplex" and we can provide a link to this different area (which doesn't exist yet in Wikipedia). I'll follow-up on the one remaining use (appears to be initiated by Aristophanes Dimakis and Folkert Müller-Hoissen about 6 years ago), as name for an algebra program. - - - Thanks for your patience in reading my monologues here; though I'd always be glad for *any* kind of feedback. Thanks, Jens Koeplinger 01:42, 9 August 2006 (UTC)

I noticed that the article Hypernumber (redirected from Conic quaternion) states the following: "Conic quaternions are isomorphic to tessarines". I have to confess ignorance as to the proper terminology in this area, but this should be taken into account if true, or corrected if wrong. --Lambiam ^Talk 01:53, 9 August 2006 (UTC)

Agreed, just updated, thanks for letting me know. For reference on the term "conic quaternion" see e.g. the preprint http://www.kevincarmody.com/math/sedenions1.pdf . Thanks, Jens Koeplinger

Hypernumbers crackpottery

From the immediately preceding discussion I stumbled upon the article on hypernumbers which is, at best, incomprehensible (to me being a mathematician) and probably plain crackpottery. Nowhere does the article state what hypernumbers actually are (presumably certain finite-dimensional algebras over the real numbers, but what properties are sought of them is left entirely unstated), nor is the linked site http://www.kevincarmody.com/math/hypernumbers.html any clearer. (On the other hand, it does contain such ridiculous statements as "New kinds of number [sic] will likewise give rise to new areas of science." or "This enables great advances in consciousness and matter." (page 15 of http://www.kevincarmody.com/math/hypernumberreference.pdf — which claims to be a reference but still does not explain what hypernumbers are).)

The only reference we are given are the papers of a certain Charles A. Musès, all published in Appl. Math. Comput., so I looked them up in MathSciNet and the reviews are eloquent enough (indeed, most reviewers flatly decline to comment, or seem to have found them hilariously funny); in fact, such sentences from the articles are quoted as: "How can any mathematician doubt where the source of new creativity in mathematics lies? […] We suggest that hypernumbers in our unrestricted sense are the key to a coming and deeper nuclear mathematics; that their explanation and delineation will mark as great a step as did the implications of nuclear structure in modern physics." (this is from "Hypernumbers II. Further concepts and computational applications", Appl. Math. Comput. 4 (1978), 45–66). Obviously C. Musès found the editors or referees of Appl. Math. Comput. sympathetic to his kind of crackpottery.

It would be nice to have the Wikipedia article deleted, but as it is nearly impossible to suppress an article, I guess we should just put up a banner of some kind. Ideally, the article would be reduced to a sentence such as: "Hypernumbers are a 16-dimensional non-associative algebra over the real numbers (or certain subalgebras thereof) which was studied by Charles A. Musès who believed in their application to physics, biology and engineering." Perhaps with a description of the generators and relations of the algebra, if anybody can make sense out of them.

(I don't have time to fight this battle or to argue with crackpots, so I'm just writing to make sure other participants are aware of this.) --Gro-Tsen 11:25, 9 August 2006 (UTC)

Your last sentence is remarkable. I thought I had filtered the properties of certain hypernumber types from all of the rest Musès wrote. The filter I applied was that at least two people had published about it (C. Musès and K. Carmody), and that I could understand and confirm it from defining relations. I find Mr. Carmody's works on hypernumber arithmetic clear, sound, and well written. I find the focus on multiplicative modulus of a number interesting, do believe they qualify as their own number system, and do not believe that deletion of the article is an improvement. How do we deal with a situation where the person who discovered something gives ridiculous and even derogatory statements, throws out statements and "proofs" that don't work? I do not find Musès' articles funny, I am actually frequently offended by them. To my knowledge, though, it was him who found the real powers and logarithm of $\varepsilon$ (the non-real root of +1 that is also part of split-complex algebra), and it was K. Carmody who found sedenions with a multiplicative modulus. As far as I can see, what's currently on the Wikipedia page "works" ... What do we do? Thanks, Jens Koeplinger 15:25, 9 August 2006 (UTC)

I think for a start, we should define hypernumbers. I don't understand after reading the article what they are, and I followed the link to Carmody's page, and I can't tell from what he has there what they are either. Everything that is written seems to assume that the reader is familiar with the definition. Take the subsection Hypernumber#Epsilon numbers, from which no one could deduce what an epsilon number is, what epsilon itself is, and what it means for them to be the third level in the program. Not to mention that the seemingly fundamedntal idea of "power orbit" is referenced everywhere but never described (I suppose it means "all powers of a number", but the terminology is new to me, and confusing). I have to say that everything in the article strikes me as typical of what crackpot ideas I've seen: a confusing and grandiose compilation of claimed results without clear definitions, consistent notation, or verifiable statements. Of course, that's the way the articles on Carmody's page are written too, so it's not necessarily your fault...but if there doesn't exist a coherent account of this stuff I would say it's the work of a crackpot. However, if it's been published it may be "notable", so at the very least it would then be our duty to figure out what "it" is in the first place. Ryan Reich 20:46, 9 August 2006 (UTC)

Sounds great to me. I recognize that the article is not well structured and lacks clarity, and it would be wonderful if it could be improved. What about adding an "algebra stub" notice on the article, to highlight that the article cannot remain in its current form? Thank you very much for pointing out several weaknesses. While we may have trouble finding a definition of hypernumbers in general (Musès did not provide one ...), we can put the numbers that are currently stated on the page on defining relations. We could say "Musès conceived hypernumbers as [...thisandthat...] Select examples are [...]" and so on. As for the definitions that are missing, epsilon is a non-real base number with $\varepsilon{}^2 = 1$ and is identical to j from split-complex algebra. The "power orbit" of a number b is

b α

with

α

real. Maybe it would make sense to have two sections in the article, the first section focusing on the hypernumber types containing reals, imaginaries, and $\varepsilon$ bases, and then a section that gives a briefer overview over the three other types currently listed. Well, let me put the stub notice out there for now, hopefully we'll get more responses (possibly on talk:hypernumber?). Thanks a lot, Jens Koeplinger 01:18, 10 August 2006 (UTC)

Already the article on split-complex numbers seems of dubious interest to me: most unfortunately it does not mention the (obvious) fact that, by the Chinese remainder theorem, "split-complex numbers" / "epsilon numbers" can be identified with pairs of real numbers with termwise addition and multiplication (I mean, not only are they a two-dimensional algebra over the reals, but actually they are the direct product of two copies of the real numbers), which makes them sort of boring (why bother about the product of two copies of the reals, not arbitrary tuples?); the identification takes the pair

(a, b)

to $\frac{a+b}{2} + \frac{a-b}{2}\varepsilon$ (the number $\varepsilon$ is called

j

in the article on split-complex numbers; and it's a trivial exercise to see that this is indeed an isomorphism). (Also, incidentally, the article is wrong in stating that split-complex numbers have nilpotents: they don't, they have divisors of zero but no nilpotents.) I'm stating all this to refute the idea that the number $\varepsilon$ is an interesting object. As to it's "power orbit", i.e., a one-parameter subgroup, once we have identified split-complex numbers with pairs of real numbers as I explained, and the number $\varepsilon$ with the pair

(1, - 1)

, it is clear that one-parameter subgroups all lie in one connected component (both coordinates positive) of the multiplicative group of invertible split-complex numbers, and $\varepsilon$ is not there, so it does not have a "power orbit" (no more than -1 has in the real numbers). Similarly, trying to add both

i

with

i 2 = - 1

and $\varepsilon$ with $\varepsilon^2=1$ just gives you pairs of complex numbers, again not very interesting. This is all basic algebra and applications of the Chinese remainder theorem. --Gro-Tsen 10:15, 10 August 2006 (UTC)

I can only agree that many articles need improvement (but I am glad that you did respond). If you repost your last message in talk:split-complex number I'd be glad to respond (it's getting very specific now). Or, to save you time, I'd also be glad to cite your last post there ... This will be funny, I'm looking forward for the reactions.

As for the hypernumbers page, I do thank anyone for the attention, and I'm glad to "let go" and answer question on the talk page, from what I can answer. I'm a physicist, with interest on physics on numbers that are not typically used, and I noticed gaps, missing information, and missing links (isomorphisms) in Wikipedia. So I've added some as good as I can, though I'm not native to the field (mathematics). Any review or improvement is, as always, welcome. Thanks again, Jens Koeplinger 12:08, 10 August 2006 (UTC)

Feel free to repost my comment elsewhere if you think it wise. Personally I won't follow the "split-complex numbers" page because I don't think it's interesting in any way (but it's not really crackpot stuff either: it's just entirely boring) and I don't have time to improve it. I just find it laughable if it turns out that nobody noticed that these "split-complex numbers" are just isomorphic to pairs of real numbers (something which should be obvious from the start to anyone with a minimal background in algebra, e.g., having read Lang's book). Btw, "tessarines" / "bicomplex numbers" are similarly isomorphic to pairs of complex numbers. Any (commutative and associative) étale algebra over the real numbers is a product of copies of the real numbers and the complex numbers, anyway. --Gro-Tsen 12:38, 10 August 2006 (UTC)

I looked at this Kevin Carmody's website, the main reference of the hypernumbers page, and I'd like to point out that he's an unmitigated crackpot. Even if this topic were at all standard, we probably shouldn't be using his website as a reference. I will say that it can be very difficult to tell crackpot math from real math, especially if the crackpot in question studied mathematics in earnest before losing their grip, and especially they attract followers. I think this is the situation we have going here. It just has that certain feel - think of John Nash in "A Beautiful Mind" with the newspaper and magazine clippings. Originalbigj 16:55, 10 August 2006 (UTC)

Please see talk:hypernumber for the list of sources from which I directly drew from, and the reasoning behind it. Thanks, Jens Koeplinger 18:03, 10 August 2006 (UTC)

I would like to point out that "epsilon number" already has an established meaning. An epsilon number is an ordinal $\epsilon_\alpha \!$ such that $\epsilon_\alpha = \omega^{\epsilon_\alpha} \!$ . JRSpriggs 02:58, 11 August 2006 (UTC)

This is one of several meanings of ε, ranging from conic sections to calculus. If Carmody and Musès have come up with another one, so be it. Nor are they entirely original; the use of ε for a non-trivial unit is fairly common in the study of rings - outshone, I think, only by ω. Septentrionalis 13:57, 11 August 2006 (UTC)

Adminship requested

I have requested adminship, largely to deal with the backlogs of move and discussion pages. Since Oleg endorses, I think I can mention it here. See Wikipedia:Requests_for_adminship/Pmanderson. Septentrionalis 20:50, 12 August 2006 (UTC)

Am I the main math admin lobby or what? :) Good luck! Oleg Alexandrov (talk) 20:55, 12 August 2006 (UTC)

Ovoids in polar spaces

Hello,

as you can see I am on the list of participants of the Math Project. I'm still not experienced in creating my own articles.

Any quick look at Ovoid (polar space) would be appreciated, also because of the fact that English is not my native language (I do my best though).

And one fundamental question : what to do with these ovoids, they are often only treated in the case of finite polar spaces, while in fact there isn't exactly anything wrong with the definition for infinite polar spaces.

Thanks a lot,

Evilbu 22:32, 12 August 2006 (UTC)

What's lacking most are the references. --Lambiam ^Talk 02:24, 13 August 2006 (UTC)

You could probably say the same about polar space though at least there's a wiki-link to Tits there. Lunch 02:45, 13 August 2006 (UTC)

Okay, I get the message. There should be references. I am willing to accept any suggestion. The problem is that incidence geometry is not well represented on the net, most of the sources would be (online) courses from my own university. It would help me a great deal if I could know which users are into geometry as well. Evilbu 12:24, 13 August 2006 (UTC)

Use Google scholar as a starting point, and the library resources of your university to find good references, usually either a textbook, or the original articles introducing the concepts. Another acceptable source is the Encyclopaedia of Mathematics. Make sure the article agrees with the reference. --Lambiam ^Talk 18:25, 13 August 2006 (UTC)

Our university does have a library... But on a side note : the first professor's article on that Google scholar link, is my own professor, who taught me the definition of polar space... Evilbu 19:05, 13 August 2006 (UTC)

Verifying a reference

An anonymous contributor has edited A. Cohn's irreducibility criterion to claim that the criterion has been proved to hold for the case n=2, whereas the relevant PlanetMath page says that this is a conjecture. The contributor provided the following link to a dvi file as a reference. I cannot read the dvi file, but I think it contains an article by number theorist Ram Murty published in Amer. Math. Monthly, Vol. 109 (2002), no. 5, 452-458. Perhaps someone with a dvi reader, or with access to the journal itself, can verify that this paper does indeed provide a proof for the case n=2 ? Gandalf61 10:25, 14 August 2006 (UTC)

It gives a new proof for the n>2 case, then a long discussion and another lemma claimed to give the n=2 case as well. JPD (talk) 11:20, 14 August 2006 (UTC)

JPD - thank you for the prompt response. Gandalf61 15:54, 14 August 2006 (UTC)

Well, it seems the Planet Math page is very outdated, giving as the only reference Polya and Szego vol 2, which is actually a very old book: the 1998 version is just a reprint of the 1976 English edition which was translated and revised by someone other than the original authors. Furthermore the 1976 German edition (according to Math Reviews reviewer) differs very little from the original 1925 edition. In any case, the Murty paper mentioned above gives as the first reference a 1981 paper which proves Cohn's theorem for any base (Brillhart, John; Filaseta, Michael; Odlyzko, Andrew On an irreducibility theorem of A. Cohn. Canad. J. Math. 33 (1981), no. 5, 1055--1059.) The review for it on MathSciNet notes that the original Cohn theorem was mentioned in Polya and Szego. So it seems this conjecture has been known to be closed for quite a while. --Chan-Ho (Talk) 02:07, 15 August 2006 (UTC)

I updated the article A. Cohn's irreducibility criterion to reflect Brillhart et al's priority for the n=2 case. In a future edit I hope to change the letters used for certain subscripts to agree with the Ram Murty paper, because using 'n' it is easy to confuse the base used with the degree of the polynomial. The other improvement that might be suggested is to change the title to 'Cohn's Irreducibility Criterion', because Wikipedia's search function is too feeble to return this article in the first screen when you type in 'A. Cohn'. EdJohnston 22:04, 18 August 2006 (UTC)

Antiderivative

I wonder if there are any comments on this edit (please write them at talk:derivative). Thanks. Oleg Alexandrov (talk) 16:16, 14 August 2006 (UTC)

Did you mean to say write comments at Talk:Antiderivative? I don't see much need for discussion; the matter was already considered and decided long ago, at the top of the talk page. Are you suggesting it should be reconsidered? (Follow-ups to talk.) --KSmrq^T 03:37, 15 August 2006 (UTC)

Mathematics needed

Please help with adding the various mathematical analyses of the game Fetch (game) to the article. (See the references and further reading given in the article.) Uncle G 10:56, 15 August 2006 (UTC)

The process by which a dog tries to catch a ball may be similar to the way that a fielder in baseball tries to catch a ball which has been hit in his general direction. I know that that has been analyzed mathematically, but I do not remember the details. JRSpriggs 05:10, 16 August 2006 (UTC)

Abel Prize more prestigious than Wolf Prize in Mathematics?

That is what one anon has insisted, but I believe this is unsubstantiated and actually OR. See Talk:Wolf_Prize for my lengthy comment with diffs. Perhaps a personal remark here is in order. When the anon replaced the mention of the Wolf in the intro to Serre's article (saying Wolf is not more prestigious than Abel), I was willing to let it go as I thought at least that the Abel would be more familiar to the lay reader (due to the extensive media coverage); however, a later edit revealed that this person regards the Abel as more prestigious than the Wolf and that would be appear the basis for the first edit. I would appreciate if people could take a look, particularly mathematicians who have been been in the mathematical community for a longer time than me who can gauge this issue with their more extensive experience. I think this is kind of an interesting math cultural issue. --Chan-Ho (Talk) 11:33, 15 August 2006 (UTC)

I take the Wolf Prize to be, de facto, the top lifetime achievement award. That being said, we can't possibly talk about prestige in the abstract (would have to be via quotes). I suggest just removing all loose talk. Charles Matthews 12:19, 15 August 2006 (UTC)

Ditto. Prestige is in the eye of the beholder. Speaking of which, please report all rumors on the talk page of Grigori Perelman! ---CH 07:17, 16 August 2006 (UTC)

That's also how I would rank them, but looking at the winners they seem to be the best of the best for both, so now I wonder, what would actually make one more prestigious than the other? For the Fields Medal, could it play a role that it is only awarded once every four years? And of course you can't be an old geezer, so it does not honour a lifetime of ~~servitude~~ service to mathematics, but specific memorable achievements.

Problem editor

All mathematics editors should be alert to the ongoing behavior of Bo Jacoby (talk). In article after article Bo has tried to use invented (original research) notation. Then Bo lures others into endless discussions on the talk pages, where a host of editors again and again waste their time saying the same thing: "Don't do it." Examples include

A related wrong-headed persistence has been seen at Talk:Wilkinson's polynomial. I do not know the cause nor the intent of this behavior, but we need to find some effective way to deal with it. Patient responses on article talk pages have not been effective. Please be vigilant to catch more abuses, and please do not let Bo turn article talk pages into his own chat room. --KSmrq^T 14:23, 16 August 2006 (UTC)

I would add to that talk:polynomial and talk:formal power series. I believe we are dealing with a person without formal math education, and it takes a long time (and many editors sometimes) to convince him that he is wrong. Oleg Alexandrov (talk) 16:25, 16 August 2006 (UTC)

Aha, I would also add Talk:Lebesgue integration. That explains a lot.--CSTAR 16:53, 16 August 2006 (UTC)

And Talk:Binomial transform. Bo's behaviour, while annoying and disruptive, is minor in comparison to some of the mono-maniacal and outrageous behaviour I've seen recently seen (e.g. my talk page, ughhh). linas 03:49, 17 August 2006 (UTC)

Wikipedia:Lamest where it applies. Charles Matthews 21:12, 17 August 2006 (UTC)

Could someone check out inferential statistics? This is an article that seems to have been largely written by Bo. Statistics is not my field, but some of the technical terms defined in the article, like "deduction distribution function" and "induction distribution function", don't seem to appear anywhere else on the web (at least, not with the same meaning). A closer look by a statistician might be warranted. Another article largely written by him, in which he cites his own publications, is Durand-Kerner method. Again, I have not checked this and make no claim as to whether it is good or bad, but it might be worth a closer look given Bo's past behavior. —Steven G. Johnson 15:45, 21 August 2006 (UTC)

Durand-Kerner is ok, he earlier claimed to be the inventor of the method, since he did not find related information, but changed or allowed to change to the more usual name. The method is, as it seems, not widely known, but (personal communication by prof. Yakoubsohn at Toulose) common knowledge in the root finding community.--LutzL 17:04, 21 August 2006 (UTC)

There's still the vanity link/redirect at Jacoby's method. Lunch 20:38, 23 August 2006 (UTC)

Also, in the article to which this redirect points, Durand-Kerner method, there are two references to Bo Jacoby added by Bo Jacoby. Being relatively new to all of this, I'm not sure if this counts as WP:NOR or not. VectorPosse 22:44, 23 August 2006 (UTC)

See also Talk:Fourier transform. —Steven G. Johnson 16:29, 21 August 2006 (UTC)

Meaning of QED

Should QED be:

a page about the phrase quod erat demonstrandum, with a dablink to QED (disambiguation),
a page about quantum electrodynamics, with a dablink to QED (disambiguation), or
a disambiguation page, with links to both the above and to lesser uses.

My opinion is clearly (3), but come share yours at talk:QED (disambiguation). --Trovatore 20:40, 17 August 2006 (UTC)

You have shown via your question that the term is ambiguous; therefore, it should be a disambiguation page. QED Ryan Reich 20:50, 17 August 2006 (UTC)

The discussion is taking place at talk:QED (disambiguation), not here; this is just a notice. --Trovatore 20:52, 17 August 2006 (UTC)

At least admit that it was good for a chuckle. Ryan Reich 20:57, 17 August 2006 (UTC)

You could have that on your tombstone. Charles Matthews 21:14, 17 August 2006 (UTC)

I'll take mushroom, black olive, and anchovies. --Trovatore 22:53, 17 August 2006 (UTC)

I've had pizza that chewed like marble myself...Septentrionalis 01:53, 19 August 2006 (UTC)

Oppose anchovies. --Chan-Ho (Talk) 04:56, 19 August 2006 (UTC)

Per the ethics of terminology, QED as quod erat demonstrandum has priority by several thousand years over all the New QEDs On The Block. Jon Awbrey 05:26, 19 August 2006 (UTC)
- Well, my feeling is that, if we were to take the intrinsic importance of the subject into account, it would have to swing massively the other direction: quantum electrodynamics is one of the most fundamental attempts to describe nature yet devised by the mind of man, whereas quod erat demonstrandum is just a phrase, a piece of historio-linguistic trivia. (Obviously this is quite distinct from any consideration of the importance of the idea of proof, or even of individual proofs at the end of which Q.E.D. has appeared; those are separate discussions altogether, and the Q.E.D. article isn't about them.) Perhaps more to the point, just from a practical point of view, it's an observed fact that lots of people link to QED from physics articles, which has bad consequences if it's a redirect to the Latin phrase.
- Still, if you want to "vote", this isn't the place to do it; I've given a pointer above to the actual debate. --Trovatore 05:46, 19 August 2006 (UTC)
  - Trovatore, Quantum Electrodynamics is a temporary theory. It is a set of rules, and the theory is not entirely well-defined mathematically. On the other hand proofs are very important, not only in mathematics, but also in theoretical physics.Hillgentleman 03:22, 7 September 2006 (UTC)
    - Luckily, there was no need to judge the relative importance of quantum electrodynamics and proof. Proof is an extremely important topic; quod erat demonstrandum is not. --Trovatore 03:32, 7 September 2006 (UTC)

JA: The just notable difference tends to be relative and shifty from year to year. That's why we have rules like prior use. Of course, this is WP, and the rule is to find the "most illiterate use" and go with that, so why am I not already sleeping, he asks himself. Jon Awbrey 05:52, 19 August 2006 (UTC)

ICM Madrid

Starts 22 August, I believe. It would be good if we geared up for the Fields Medal awards. By which I mean: get ready with a story to offer the Main Page here; have articles ready on Terence Tao and Grigori Perelman who are the hot tips; be prepared to do something quick and dirty for anyone else on the list. Compared to 2002, the world's press are likely to turn to enWP for enlightenment, as soon as the news hits the wires. Charles Matthews 21:18, 17 August 2006 (UTC)

Uh, so who else is on the list? --Chan-Ho (Talk) 05:51, 19 August 2006 (UTC)

So, as part of that, anyone ready with good pictures for Kakeya problem page? Charles Matthews 21:21, 17 August 2006 (UTC)

Update: plenty of excitement as Perelman was a no-show; need work on Andrei Okounkov (I've just mailed Princeton to see if they have a photo), Wendelin Werner. Matter arising from the latter: self-avoiding random walk is surely worth an article. Charles Matthews 12:15, 22 August 2006 (UTC)

A Google Image search turns up photos for everyone, rights status unknown. --KSmrq^T 12:34, 22 August 2006 (UTC)

Perhaps self-avoiding random walk could start as a section of Random walk before being spun off on its own. Michael Kinyon 15:48, 22 August 2006 (UTC)

There is a raw definition somewhere there, true. Quick-and-dirty is to redirect and forget ... given a Fields has been awarded, there might be rather more to it. Also, an article on Charles Loewner would be good (there is a MacTutor article); I just had time to start some of Werner's lecture notes which do hark back to Loewner's work of the 1920s. Charles Matthews 16:10, 22 August 2006 (UTC)

Wikiversity Mathematics School open

I cordially invite the partisipants of this project to the newly founded wikiversity school of Mathematics. We are still working out the policies, but any help is appreciated. --Rayc 23:55, 17 August 2006 (UTC)

Eigenvalue, eigenvector and eigenspace

Eigenvalue, eigenvector and eigenspace is up for a featured article review. Detailed concerns may be found here. Please leave your comments and help us address and maintain this article's featured quality. Sandy 22:04, 18 August 2006 (UTC)

A novice editor has created an article for the Jacobi eigenvalue algorithm; a few fixes there could be a big help as well. --KSmrq^T 12:14, 19 August 2006 (UTC)

It seems like there is a need for some people to do some copyedditing on the article. These been a lot of suggestions on fixes to the article needed to get it to FA status but no one is acting on them. Volunteers welcome! --Salix alba (talk) 07:28, 14 September 2006 (UTC)

Talk:Pi#Move Pi to π, the official discussion!

This move idea has come up again. Please discuss. (I made the point that software limitations mean that the actual move, if this passes, will be to Π.) Septentrionalis 01:59, 19 August 2006 (UTC)

Kerala school?

I copied this message from Portal talk:Mathematics. -- Jitse Niesen (talk) 14:34, 19 August 2006 (UTC)

What do you guys think about the Kerala School article and the possible transmission of mathematics from Kerala to Europe? Should the theory get a mention on our articles about calculus, newton, wallis etc? Frankly, I'm a bit alarmed about the points brought up here. Borisblue 07:51, 19 August 2006 (UTC)

I came here to post a message on Madhava, and saw this... Actually, I remember reading somewhere that several conferences have been convened worldwide to discuss the possible transmission. But none of them, AFAIK, have been able to come to a conclusion. However, the theory has never been discounted, because the people who back it, have a very strong point. IMO, (and this is not because I'm from Kerala), this should be mentioned as a theory that is prevalent. All my attempts at introducing it in some articles failed, (primarily because I happen to be from Kerala). It certainly would be nice if someone would be willing to take initiative in this regard (after a discussion, of course).-- thunderboltz^{a.k.a.Deepu Joseph |TALK}14:44, 23 August 2006 (UTC)

An RFC will be nice. However, I have a lot of difficulty finding academic papers that discuss and critique this issue (can't find any record of conferences either?), I think because this theory is so new. Hence, it will be difficult to satisfy verifiability in a lot of the claims, at least untill a few more historians come up with some peer-reviewed papers. Science and math issues require very reputable sources. Borisblue 04:51, 24 August 2006 (UTC)

Unicode article names

User:CyberSkull moved T1 space to T₁ space, that's on the heels of a move of Mu operator to Μ operator. I believe that these are cheap Unicode tricks and not a solution to the fact that Wikipedia can't represent faithfully some mathematical notation.

T1 space should ideally be "T₁ space". Since that's impossible, I think T1 space is a better name than the T₁ space gimmick. Comments? Oleg Alexandrov (talk) 21:18, 19 August 2006 (UTC)

Unless Unicode tricks can solve all our problems along these lines, I would agree that we would be better sticking with things like T1 space. I think it would be better to be consistent and avoid gimmicks - and hope that some future version of the software will give a more sensible solution. Madmath789 21:32, 19 August 2006 (UTC)

My thanks to Oleg for fixing Mu operator and Mu-recursive function which had been moved inappropriately by User:CyberSkull. I agree that titles of articles and categories should not contain characters other than printable ascii characters. It is hard enough dealing with unusual characters in the text of an article. Having such characters in a title is much worse. One might look in the wrong place in the category listing (as I did for the two I mentioned above). Or one might fail to find them with a search or even be able to enter the correct title into the search box. Or the title might not display correctly depending on one's fonts. JRSpriggs 08:48, 20 August 2006 (UTC)

Fields template

If Grigori Perelman has declined his Fields Medal, how should Template:Fields medalists read? Charles Matthews 15:42, 22 August 2006 (UTC)

How about "Perelman (declined)"? Yes, I realize that if he has declined, then technically he is not a medalist, but there should be some indication that the award was offered to him. Michael Kinyon 15:46, 22 August 2006 (UTC)

According to the New York Times, Sir John M. Ball, president of the International Mathematical Union, said, "He has a say whether he accepts it, but we have awarded it." So maybe Perelman is technically a medalist. Having said that, I believe that Michael's suggestion is adequate. VectorPosse 20:50, 22 August 2006 (UTC)

Now of some urgency, since Template:In the news has the Fields as leading item. Charles Matthews 16:16, 22 August 2006 (UTC)

Since the fact the Perelman declined will be discovered at his article, perhaps it's enough to do nothing special. Or at least postpone a more clever solution. The exact details still seem mysterious, so letting the article explain seems wise. If "(declined)" is included, be sure to use   between it and his name to prevent an awkward break in the future. (Actually, the current breaks are none too appealing.) --KSmrq^T 18:38, 22 August 2006 (UTC)

It seems that he has indeed specifically declined to accept the Fields Medal. I agree with "Perelman (declined)" in the template. ---CH 23:39, 22 August 2006 (UTC)

There's a New Yorker article on Perelman that got slashdotted: rather interesting read, gives insight into why the prize was declined. http://www.newyorker.com/fact/content/articles/060828fa_fact2

BTW: Manifold Destiny (article) --Pjacobi 20:20, 28 August 2006 (UTC)

Grigori Perelman

I've extensively rewritten this twice in the past week to incorporate latest news and clean up "edit creep" (well intentioned edits by inexperience writers--- or thoughtless ones--- which disrupt the flow of ideas, exhibit poor diction, and generally tend to eventually render an article unreadable.) There has been some apparent trolling by editors who want to discuss the Israeli-Palestine conflict, so watch out. Sheesh! ---CH 23:38, 22 August 2006 (UTC)

Madhava of Sangamagrama

Hello! This article is about Madhava, a mathematician who lived during the middle ages. Despite being one of the greatest mathematicians (he is, in fact considered as the founder of mathematical analysis), most of his work has been discredited. The talk page of the article has a large number of unanswered questions. It would be nice if someone well versed in mathematics take a look at them. I am not submitting the article for collaboration, because it fails the nomination criteria. However, it would be wonderful if people would come forward to cleanup all the confusion and chaos on this article. Thanks! -- thunderboltz^{a.k.a.Deepu Joseph |TALK}14:34, 23 August 2006 (UTC)

Articles listed at Articles for deletion

Simplex algorithm method (AfD discussion)

The 'bot hasn't picked this one up, it appears. Uncle G 11:43, 24 August 2006 (UTC)

Request from Non-math Person

I feel certain that this comes up a lot, but as a relatively well-educated and well-read individual who has only a general interest in mathematics, I am consistently stumped by even the simplest of mathematics entries on wikipedia. Granted, some math issues, conjectures, and theories are plain ol' difficult, but it seems like Mathematics entries on wikipedia are by far the least accessible entries (for the average reader who comes to an encyclopedia for general information). The Clay Institute's descriptions of the Millennium Prize problems [83], for example, do a much better job of describing and analogizing the problems for us lay-folk. With so much to work on, this may not be a valid top priority for the Project, but as an outsider I would greatly appreciate if it became a focus. Thanks! aww 18:34, 25 August 2006 (UTC)

Well, it's a known issue. For us here, I suppose, the point of view might be that the mathematics is only about 1% of enWP; but its place in sustaining the reputation and credibility of the project is much greater than that would suggest. We have certainly emphasised getting 'professional' mathematics here. An analogy would be with medicine: no one would want the clinical medicine articles to be accessible only to doctors, but on the other hand if a doctor can say "that's just wrong", that is also not good.

Let's look at the Clay description of one of the problems in detail.

Mathematicians have always been fascinated by the problem of describing all solutions in whole numbers x,y,z to algebraic equations like

x² + y² = z²

Not true. In the eighteenth century this kind of number theory, namely Diophantine equations, was consider a backwater. That attitude prevailed for a long time.

Euclid gave the complete solution for that equation, but for more complicated equations this becomes extremely difficult.

See Pythagorean triples.

Indeed, in 1970 Yu. V. Matiyasevich showed that Hilbert's tenth problem is unsolvable, i.e., there is no general method for determining when such equations have a solution in whole numbers.

True.

But in special cases one can hope to say something. When the solutions are the points of an abelian variety, the Birch and Swinnerton-Dyer conjecture asserts that the size of the group of rational points is related to the behavior of an associated zeta function ζ(s) near the point s=1.

Actually, writing 'abelian variety' rather than elliptic curve is reprehensible here: far too general. If I tried to write down the equations defining an abelian variety, you wouldn't thank me. It would be much better to say cubic curve, in fact. This slurs over the fact that if such a curve has a singular point, we don't call it an 'elliptic curve'; but that case is already done by the Euclid method, anyway.

In particular this amazing conjecture asserts that if ζ(1) is equal to 0, then there are an infinite number of rational points (solutions), and conversely, if ζ(1) is not equal to 0, then there is only a finite number of such points.

We don't use words like 'amazing', naturally. This is OK, and could usefully go in an article here. (Then for experts we have to remark something on the analytic continuation question, supporting the idea that the zeta function is even defined at the actual point.)

Right then, this was an exercise. I would criticise the exposition for not using the proper term (Diophantine equations). Anyone browsing our Category:Diophantine equations should at least be able to pick up what the subject is about.

Charles Matthews 19:09, 25 August 2006 (UTC)

So this Clay write-up was perhaps good in explaining things to the interested layperson, and lousy for professional mathematicians. We have many articles that are lousy in explaining things to the interested layperson, and perhaps good for professionals. We also have some articles that are lousy for both. Why be so defensive about it? Can't we just admit that we'd like to have more articles that do a good job for both? Unfortunately, we don't have that many editors who combine the required background with the necessary writing skills and also have unlimited time to devote to the project. --Lambiam ^Talk 01:34, 26 August 2006 (UTC)

I thought the middle way was found a long time ago. Articles should have a good and easy to read introduction. Moving down an article, things will become more complex, and for good reason.

I don't think Charles was trying to be defensive (he's rather good at writing expositionary articles, without formulas pile-ons :) We have some good articles, and some bad articles. And math articles could be harder to read than say biology articles because we use much more symbolism and abstract concepts, and that for good reason. Oleg Alexandrov (talk) 05:45, 26 August 2006 (UTC)

Well, I was certainly enjoying myself looking at other expositions for change, rather than patching up our own. And I hope I made a point about what the mathematics articles here are good for, at least: we do have a very thorough coverage (23 Hilbert problems you can look up here, not just one). There are plenty of popular mathematical books around that will give you a 'feel' for Fermat's Last Theorem, Riemann Hypothesis, Monster group. What you can find here is one step up from that: the level was defined as undergraduate student, back a couple of years ago. Anyway, let's do it again, for the Hodge conjecture (defined as On a complex algebraic variety, every homology class that could reasonably contain a subvariety does contain a subvariety here). The Clay gves us this:

In the twentieth century mathematicians discovered powerful ways to investigate the shapes of complicated objects. The basic idea is to ask to what extent we can approximate the shape of a given object by gluing together simple geometric building blocks of increasing dimension. This technique turned out to be so useful that it got generalized in many different ways, eventually leading to powerful tools that enabled mathematicians to make great progress in cataloging the variety of objects they encountered in their investigations. Unfortunately, the geometric origins of the procedure became obscured in this generalization. In some sense it was necessary to add pieces that did not have any geometric interpretation. The Hodge conjecture asserts that for particularly nice types of spaces called projective algebraic varieties, the pieces called Hodge cycles are actually (rational linear) combinations of geometric pieces called algebraic cycles.

So they try not even to mention the words manifold and topology. Pieces that did not have any geometric interpretation. Yes and no: de Rham cohomology is fairly geometric. The statement leaves out the technical points that the varieties are over the complex numbers (OK, that's the default), and are non-singular (which one can't really get away with).

Someone writing in the style of the first three sentences here would get them edited to more precision of statement pretty fast. The idea buried in the fourth unfortunately we do not cover well (homology classes represented by actual subspaces - I think there are results by major topologists not here). Saying 'nice' is a lapse into the way mathematicians communicate to each other.

We are really stuck with a world where on Monday we may be having to try to write up what Andrei Okounkov did to deserve a Fields Medal (breaking news) and the next day supposedly trying to find new paraphrases for things like algebraic variety or manifold. I'd like to point out that we also get criticism from the other direction (see for example Talk:Abelian variety for an extreme example).

Charles Matthews 10:02, 26 August 2006 (UTC)

I can certainly see how that would be. It's the problems of wikipedia combined with a less accessible sets of subjects. I have to say, it dawned on my from your examples that the best way to explain a complex problem to a lay person is with analogy and abstraction, which in certain mathematics articles could just as easily translate into "inaccurate" or "wrong." Nonetheless, I would encourage pushing some of the intros even farther, even if they include such vague statements as "while not exactly (thing), it is similar to (thing)." Then again, I'm a lawyer, and this is how we talk about everything, so there you go. Thanks for the good work, and I'll keep reading and trying to learn. aww 13:40, 26 August 2006 (UTC)

To do a good job on a sophisticated mathematics article, an editor must have detailed technical knowledge, the ability to know what's essential versus peripheral, great empathy for the untrained reader (to see through their eyes), a solid command of the English language, exceptional skill in writing, and world-class patience and diplomatic skills.

A one-paragraph introduction may be the shortest part of the article, but is almost always the most difficult to write. The Millennium Prize Problems are singled out because they are connected to a great deal of interesting mathematics, and because they are very difficult to solve. How do you take a problem that the best mathematicians in the world do not yet understand adequately and present it in a few short, accurate, engaging sentences to the general public?

You may be surprised at the extraordinary stuggle behind a basic mathematics article, such as manifold.

Ironically, mathematics today is so broad and so deep that a specialist in one branch may know almost nothing about an advanced topic in another specialty. Therefore we appreciate a good introduction just for ourselves!

Finally, while some in the world are hungry to learn more mathematics and science, others are actively hostile, or indifferent. One consequence is that we continue to struggle to convince the WikiMedia developers to better support our notational needs. Another is that we see lazy outside editors take a quick glance at an article and slap a fixit tag on it, without even doing us the courtesy of leaving a note on the talk page to describe what they see as the problem. Or we see editors reword things they do not understand, which someone must then notice and fix.

And yet, we persist. We mathematicians have a love of beauty and pattern, which draws us in and sometimes leads us to want to share the joy. And to solve difficult problems, we have learned to persist in the face of constant frustration and defeat. Perhaps if it was easier to write a good Wikipedia article, we'd be less interested! ;-) --KSmrq^T 21:26, 26 August 2006 (UTC)

However, we also have introduction to quantum mechanics and introduction to special relativity and why 11 dimensions because there is simply so much to say about these topics at the introductory level, that a single article cannot do justice to both the introductory and the technical aspects of the subject. linas 22:22, 26 August 2006 (UTC)

Department of Injustice

For years I have regarded it as a running joke that named theorems, if they are really important, are almost never named for the "right" person. In funnier, it often turns out that the "wrong" person actually cited the earlier contribution, but nobody listened (or cared)! One can often see that even if famous person F tries to credit obscure person O, the result still usually becomes known for F. Anyway, I invite you to contribute your own examples in List of misnamed theorems, but please be very careful since the syntax is easily munged. If you can't figure out how to do it from the examples in the current version, put your entry in the talk page (with a complete citation if at all possible) and I will move the information to the article. ---CH 05:15, 26 August 2006 (UTC)

Um, isn't this a little bit OR-ish? Granted that lists in general are sometimes given a little rhythm on that point, still this seems especially close to the line, to me. --Trovatore 16:29, 26 August 2006 (UTC)

Surely the many items that cite secondary sources are okay? Melchoir 16:56, 26 August 2006 (UTC)

Its not just theorems. Farey numbers were first noted by Haros in 1802. Care to change the name to Misnamed topics in mathematics?

Its not just theorems and topics: Pell's equation was so named because Lord Brouncker solved it! - How about Misnamed equations? Madmath789 22:35, 26 August 2006 (UTC)

How about misnamed things? Fredrik Johansson 22:39, 26 August 2006 (UTC)

...List of misnomers in mathematics? Melchoir 23:35, 26 August 2006 (UTC)

I'm a little leery of the whole idea. The underlying premise seems to be that something is "misnamed" if named after someone other than the first person to come across it. That is not clear to me. Remember the "Columbus principle": It's not who discovers it first, but who discovers it last; that is, the person who makes the concept permanently available. Not everyone agrees with that idea, which is fine; it's not my purpose to promote it here. I'm just saying that a list that assumes the opposite, for its very existence, strikes me as POV. --Trovatore 17:53, 28 August 2006 (UTC)

Well, maybe there is a way of turning this into more of a history-of-mathematics type article? The few cases that I read about are just that: I read about them because someone else thought it was interesting enough to do some historical research and write about it. Once it is realized that some idea is improperly named, why would people continue to use the improper name? Habit .. laziness . ignorance .. lack of interest. I see no POV problem. FWIW, I recently did a little reading on the principle of least action, the correct attribution of which was littered with denouncemnts and accusations, mediated by councils, and even a kingly decree! At least we don't call it "sos-n-so's principle of least action", but I imagine there are more stories like this. linas 20:15, 28 August 2006 (UTC)

Hm? The POV problem is precisely the claim that such-and-such a name is "improper". --Trovatore 20:19, 28 August 2006 (UTC)

One problem is that many times it is not clear cut who was the "first" to discover something. Usually the modern reformulation is quite different than the original, and then it becomes a long debate whether so-and-so really discovered such-and-such or only a nonimportant special case or whether a later person really added anything essential, etc. Some people go with the "attribute to anyone in the neighborhood" philosophy, e.g. "so-and-so essentially had the idea but didn't know the formalism of the later such-and-such theory" whereas some go with the "attribute to the first person to make that exact statement" philosophy. So there are other reasons besides laziness, ignorance, etc., that somebody may choose to use a particular terminology.

Depending on your particular philosophy, you could argue almost all theorems named after persons are "misnamed". So the list could get quite long and useless. I think, as pointed out by Trovatore, that there are inherent POV issues in this list idea, only some of which have been pointed out. An additional source of concern is that the most reliable sources, say by math historians, will not attempt to assign credit but merely describe what contributions were made. So there's an opportunity here for editors to fall into the OR trap by saying "So-and-so wrote in his book that earlier Bunyakovski did such-and-such. So the theorem is misnamed". --Chan-Ho (Talk) 22:04, 28 August 2006 (UTC)

Yes I agree with Trov and Chan here. Paul August ☎ 22:10, 28 August 2006 (UTC)

A momentous question

OK, here's a poser for you all, and I'm sure you won't want to eat or sleep until it's settled. If you start a sentence with the phrase von Neumann–Bernays–Gödel set theory, should the "v" be capitalized? I say yes, because you would capitalize it if you start a sentence with "von Neumann", and therefore the article does not need the {{lowercase}} template. Arthur thinks otherwise. Please focus your full intellectual powers on this question, as I know you wouldn't want to make a mistake here. --Trovatore 16:16, 26 August 2006 (UTC)

To up the ante, I don't see anyone crying havoc over Von Neumann architecture, Von Neumann probe, Von Neumann algebra, Von Neumann conjecture, or Von Neumann regular ring. And I've always thought that template was silly anyway. Melchoir 16:55, 26 August 2006 (UTC)

To add to the confusion, the "abbreviation" vNBG (at least, as used in my parents' work on logic and set theory) clearly cannot be uppercased at the beginning of a sentence. I'm now uncertain whether the entire expression, if spelled out, should be lowercased at the beginning of a sentence. I don't have time to research it for another few days, although I made the assertion in the appropriate article. — Arthur Rubin | (talk) 17:32, 26 August 2006 (UTC)

Response to Melchior's comment. It appears that, about 48 hours ago, someone went through and removed the lowercase template from all those pages. That person agrees with Trovatore that von Neumann is capitalized at the beginning of a sentence; I do not know whether this is correct, but it is surely a matter of editorial style, not grammar. In some style guides it depends on the original language (Dutch, German, etc) that the von comes from. The style I am used to would never capitalize von Neumann, even at the beginning of a sentence, and so I think the lowercase template is appropriate. Wikipedia is free to have its own style; my guess is that it is already documented somewhere, although a quick glance at WP:NAME didn't show anything. CMummert 17:34, 26 August 2006 (UTC)

Ah; I looked at the talk pages of those articles, but not their edit histories. I am not familiar with the usual treatment of "von Neumann" at the beginning of a sentence, so I'll back out of that particular issue. Melchoir 20:03, 26 August 2006 (UTC)

(responding to Melchor -- edit conflict) Well, I don't think it's silly on the articles where it really belongs, such as e (mathematical constant). We don't want our students deciding that it's sometimes OK to write it E, say if it's the first letter in an equation. And I'm fine with it, also, at eBay or bell hooks, though I don't think it's as important in those cases. But it should really be expunged from all the articles that start with "de" or "von" or "bin" or "ter"; those article titles are, in my view, correctly uppercased. Anyway, this is getting a little non-mathematical; if you want to get in on the whole earthshaking discussion, please see template talk:lowercase#Inappropriate use of this template (even that discussion should maybe go better at the MoS discussion page). --Trovatore 17:42, 26 August 2006 (UTC)

There's a conflating issue with e, though: in good writing one shouldn't be starting a sentence with it at all. Anyway, while it's a worthwhile goal to avoid misleading readers, usually the first, bolded usage of an article's title is where its correct usage is displayed-- and presumably, where the form will have a greater impact on the reader. In fact, if there's a conflict between the displayed title and the first usage, that alone draws the reader's attention, and that the actual usage is the one to imitate seems implicit. We don't have to beat the reader over the head with it. Maybe I should visit that talk page... Melchoir 20:11, 26 August 2006 (UTC)

(replying to the original question) I would capitalize "von Neumann" if it appears at the start of a sentence. That's at least the rule in German, Dutch and French, and it seems strange that English would deviate from it (though of course spelling is not always logical). -- Jitse Niesen (talk) 02:27, 27 August 2006 (UTC)

John von Neumann was so well known that he was often simply called "John von". So clearly the solution is to go thru all articles whose names begin with "von Neumann" or "Von Neumann" and replace those with "John von". Since this should clearly be capitalized, the ambiguity would be avoided. ;-) JRSpriggs 08:38, 27 August 2006 (UTC)

Navigational templates

I know I'm not a regular to this WP, but I'd like to throw out a suggestion: If the table on Portal:Mathematics/MathematicsTopics could be broken up into templates (as well as one large template of all of them), the templates could be placed on the respective articles to the great improvement of mathematics articles. 24.126.199.129 20:17, 26 August 2006 (UTC)

The majority of folks here despise the use of navigation templates, and delete them summarily. For good reason. linas 22:34, 26 August 2006 (UTC)

For those of us who don't see offhand what's wrong (or what's right) with navigational templates, could someone post a link to an earlier discussion where consensus was reached? The "good reason" linas cites are not evident to me. Michael Kinyon 00:42, 27 August 2006 (UTC)

There are long discussions that took place multiple times in the archives. Mostly, the problems were that the navboxes tended to get very large, chew up a lot of screen real-estate, and contain rather bizarre groupings of topics -- typically, obscure topics lumped in with major fields of study, thus giving undue weight to the obscure topic while effectively hiding the wealth of the major areas. Frequently, the navboxes would be skewed towards a college freshman's view of the world -- 23 ways of solving a differential equation and nothing else matters. If an article is well-written and properly linked, you don't need nav-boxes; you need an attention span that is longer than 15 seconds, which is something most of the editors here posses, but most proponents of nav boxes do not. Basically, you ain't gonna learn no math by surfing, and there's not point in encouraging surfing. linas 04:16, 27 August 2006 (UTC)

Ah. I didn't realize that earlier efforts were bloated and skewed toward the elementary and obscure. Looking at the existing mathematics nav-boxes, I see what you mean. The nav-box for convex, regular 4D polytopes seems fine, but someone stuck E7½ in the exceptional Lie groups nav-box. That was obviously inappropriate. The problem is clear: since the nav-boxes can be edited by anyone, of course they would bloat. Michael Kinyon 13:43, 27 August 2006 (UTC)

I am new to this discussion. I actually came here to propose such an idea! lol... I tend to like how the German wiki does it. For example, look at de:Gruppentheorie, "Group theory" (you may not speak German, but you can probably guess what most of the terms in the nav box mean.) It has three boxes, designating what field of math we are in, what is more general than a group, and what is more specific. It makes browsing around more enjoyable. Even if we dont have a sidebox, a box at the bottom of the articles could be nice. Am I redundant to some earlier conversation? - grubber 02:08, 23 September 2006 (UTC)

I tentively support an idea like de:Gruppentheorie. Personally I find the mathematics articles hard to navigate, and we do get ocasional comments from our readers who get lost engaging in a definition chase. Inline links present the reader with an unstructured web, whease a suitable nav box scheme would provide a more structured tree navigation scheme. Further the inline links can make navigation harder, you need to scan the text to find the appropriate links, these links may not always appear in standard places like the lead and see also sections making navigation even harder. A well thought through nav box system could make it easier for readers to find their way around the vast number of mathematics articles. --Salix alba (talk) 08:15, 23 September 2006 (UTC)

Infoboxes

Also: what is the consensus in WP Mathematics on infoboxes? Michael Kinyon 00:45, 27 August 2006 (UTC)

Dunno. Seem pretty enough in those places where they make sense. linas 04:16, 27 August 2006 (UTC)

Announce: Mathematics subject classification template

I created Template:MSC for use on category pages, for those who are into classifying things. I also did a brutal and summary redirect of Mathematics Subject Classification; specialists are encourages to write a blurb on those topics that don't have a blurb.

Speaking of templates, I'd like to remind everyone again about Template:Springer for links to articles in the Springer-Verlag online encyclopaedia of mathematics. —The preceding unsigned comment was added by Linas (talk • contribs).

I undid the redirect as it doesn't make sense. The page on the AMS' Mathematics Subject Classification shouldn't redirect to a page that attempts to list and describe areas of mathematics (using the MSC as a "starting point"). The MSC is an interesting and encyclopedic subject in itself; its article should not only explain the classification scheme, but its differences (from the 2000 and 1991 versions), how it was created, who uses it, etc. --Chan-Ho (Talk) 23:11, 26 August 2006 (UTC)

OK, well, its just was a nasty and brutal little article that threatens to try to duplicate the conetent of areas of mathematics, and I saw no point in encouraging duplication. linas 04:20, 27 August 2006 (UTC)

A little bit of politics

I'm going to ask here for help from native speakers (German particularly needed) in translation my Candidate statement for the Board Elections starting next week.

Putting together two comments above (User:KSmrq on the need for mathematical software support, and my own on the credibility the mathematics coverage disproportionately brings), having a mathematician on the Board might seem a positive step, to some here anyway.

Charles Matthews 14:23, 27 August 2006 (UTC)

Please place a notice here to assist those (like me) who would like to participate in the voting when it begins. I expect Wikipedia mathematicians will be especially interested in learning about a candidate who is a known mathematics editor. --KSmrq^T 20:33, 27 August 2006 (UTC)

meta:Elections for the Board of Trustees of the Wikimedia Foundation, 2006/En. But I spy a link at the top of this and most other pages. Charles Matthews 21:14, 27 August 2006 (UTC)

Update: I've had some very useful translation assistance, and am working on Italian right now. Spanish, Polish, Russian? Voting opens shortly. Charles Matthews 21:25, 30 August 2006 (UTC)

Soap bubble

Soap bubble is up for a featured article review. Detailed concerns may be found here. Please leave your comments and help us address and maintain this article's featured quality. Sandy 17:21, 27 August 2006 (UTC)

Citation templates

Hi all, please use these wherever possible. In particular, when citing an on-line article, please note that very few Wikipedia readers have an academic appointment and are using their office computer to access a journal's website, whereas anyone can download an arXiv eprint for free, so

in the case of published papers which are on-line, please use a link to the arXiv abstract page (not everyone prefers to download a pdf!; postscript is much faster for those with a postscript printer!) rather than a link to the journal website,
in the case of eprints, please use the arXiv citation template.

Here is the tutorial (created for the defuct WikiProject GTR, hence the gtr-related examples):

Book:

*{{cite book | author=Misner, Charles; Thorne, Kip S.; and Wheeler, John Archibald | title=Gravitation | location=San Francisco | publisher= W. H. Freeman | year=1973 | id=ISBN 0-7167-0344-0}}

Article in a research journal:

*{{cite journal | author=Kerr, R. P. | title=Gravitational field of a spinning mass as an example of algebraically special metrics | journal=Phys. Rev. Lett. | year=1963 | volume=11 | pages=237}}

Article in a research journal which was previously an arXiv eprint (check the arXiv abstract page to see if any publication details are noted):

*{{cite journal | author=Bicak, Jiri | title=Selected exact solutions of Einstein's field equations: their role in general relativity and astrophysics | journal=Lect. Notes Phys. | year=2000 | volume=540 | pages=1-126}} [http://www.arxiv.org/abs/gr-qc/0004016 gr-qc/0004016 eprint version]

arXiv eprint (not yet published):

*{{cite arXiv | author=Roberts, M. D. | title=Spacetime Exterior to a Star: Against Asymptotic Flatness | year = 1998 | version=May 16, 2002 | eprint=qr-qc/9811093}}

Article in a book:

*{{cite conference | author=Ehlers, Jürgen; & Kundt, Wolfgang | title=Exact solutions of the gravitational field equations | booktitle=Gravitation: an Introduction to Current Research | year=1962 | pages=49–101}} See ''section 2-5.''

Biography in the MacTutor archive:

{{MacTutor Biography |id=Friedmann|title=Aleksandr Aleksandrovich Friedmann}}

Article at the Living Reviews website:

*{{cite web | author=Gönner, Hubert F. M. | title=On the History of Unified Field Theories | work=Living Reviews in Relativity | url=http://relativity.livingreviews.org/open?pubNo=lrr-2004-2 | accessdate=2005-08-10 }}

These have the following effects:

Misner, Charles; Thorne, Kip S.; and Wheeler, John Archibald (1973). Gravitation. San Francisco: W. H. Freeman. ISBN 0-7167-0344-0.
Kerr, R. P. (1963). "Gravitational field of a spinning mass as an example of algebraically special metrics". Phys. Rev. Lett. 11: 237.
Bicak, Jiri (2000). "Selected exact solutions of Einstein's field equations: their role in general relativity and astrophysics". Lect. Notes Phys. 540: 1-126. gr-qc/0004016 eprint version
Roberts, M. D. (1998). "Spacetime Exterior to a Star: Against Asymptotic Flatness." May 16, 2002.
Ehlers, Jürgen; & Kundt, Wolfgang (1962). "Exact solutions of the gravitational field equations". Gravitation: an Introduction to Current Research: 49–101. See section 2-5.
O'Connor, John J., and Edmund F. Robertson. "Aleksandr Aleksandrovich Friedmann". MacTutor History of Mathematics archive.
Gönner, Hubert F. M.. On the History of Unified Field Theories. Living Reviews in Relativity. Retrieved on 2005-08-10.

Maybe some kind project member can move this tutorial to the appropriate project page? And what about a page called something like "introduction for project newbies" which helps newcomers to editing math-related articles find valuable resources like List of mathematical topics (I like the old name better) and this tutorial? TIA! ---CH 19:17, 28 August 2006 (UTC)

Five points:

These templates are more flexible than shown; more info is available at WP:CITET.
When giving page ranges, please use an en dash (–) rather than a hypen-minus: "49–101", not "49-101".
When giving ISBN data, please be forward-looking and convert to ISBN-13 (with online converter): "ISBN 978-0-7167-0344-0", not "ISBN 0-7167-0344-0". (And, please, do provide a valid ISBN.)
When citing a journal, please provide ISSN data using the {{ISSN}} template: ISSN 0031-9007.
Many online journal publications have a doi link; please use it if available.

A great deal of work has gone into writing these elaborate templates, and for good reason. They can really help the citation process. --KSmrq^T 23:00, 28 August 2006 (UTC)

Thanks for bringing these to my attention. Why should I use them "wherever possible"? What is the "good reason"? Thanks. -- Dominus 10:08, 31 August 2006 (UTC)

Official Wikipedia policy has not yet determined a standard set of templates, nor dictated their use. A journal or print encyclopedia or other formal publication does have standards. For readers, consistency makes references easier to search and easier to understand. For editors, use of templates makes a consistent preferred style easier to achieve.

Fill in the blanks, and the rest happens automatically. Should the author be listed "John Doe" or "Doe, John"? What gets italicized, quoted, bolded? What punctuation goes where? Where does the date go? All these questions and more are avoided, because the template knows what to do. Experienced authors of technical material have long relied on BibTeX databases and automatic formatting. We do not have a Wikipedia-wide database, but we can at least take advantage of templates.

Consider a novice editor who would like to cite Coxeter's classic Introduction to Geometry. Here's the template:

{{cite book | last = Coxeter | first = H. S. M. | authorlink = Harold Scott MacDonald Coxeter | title = Introduction to Geometry | edition = 2/e | publisher = Wiley | date = 1989 | pages = 366–368 | id = ISBN 978-0-471-50458-0 }}

and here's the result:

Coxeter, H. S. M. (1989). Introduction to Geometry, 2/e, Wiley, 366–368. ISBN 978-0-471-50458-0.

A novice might not italicize the title, without the prompting of a template might not include an ISBN, and so on. Journal citations are a still greater challenge. Yet merely populating the slots of a template:

{{cite journal | last = Lawvere | first = F. William | authorlink = William Lawvere | title = Taking categories seriously | journal = Revista Colombiana de Matemáticas | volume = XX | pages = 147–178 | publisher = Sociedad Colombiana de Matemáticas – Universidad Nacional de Colombia (Bogotá) | date = 1986 | url = http://www.tac.mta.ca/tac/reprints/articles/8/tr8.dvi | format = [[DVI (file format)|]] | id = {{ISSN|0034-7426}} }}

produces this lovely citation:

Lawvere, F. William (1986). "Taking categories seriously" (DVI). Revista Colombiana de Matemáticas XX: 147–178. ISSN 0034-7426.

Finally, use of such templates across Wikipedia makes a global change in convention, perhaps for another medium (or a non-English wikipedia), a minor change to implement. For example, we could switch to omitting quotation marks, or to using the typographically preferred curly quotation marks. --KSmrq^T 21:08, 31 August 2006 (UTC)

Have the recommendations, examples and points to remember in this section been posted somewhere more permanent and publicly visible? — merge 13:46, 31 August 2006 (UTC)

The math-specific template examples could be put in a subpage, which could be added to the list of math Project Pages at WP:WPM. EdJohnston 02:12, 1 September 2006 (UTC)

But wait! The WikiProject Mathematics page says there is already a math-specific manual of style: Wikipedia:Manual of Style (mathematics) . How about putting the new template advice in there? For extra visibility, also add the manual of style to the list of math Project Subpages? EdJohnston

One question re arXiv version versus versions published in journals. I would suspect that these will not be exactly the same as the journal version is likely to have gone through a review process before publication. Whats the best way to handle this? --Salix alba (talk) 18:47, 31 August 2006 (UTC)

Retrieved from "http://en.wikipedia.org../../../w/i/k/Wikipedia_talk%7EWikiProject_Mathematics_Archive_Index_8b3a.html"

Category: Wikipedia talk archives

Wikipedia talk:WikiProject Mathematics/Archive Index

From Wikipedia, the free encyclopedia

Contents

Nov 2002 – Dec 2003

Two suggestions

Some ideas

On fine-tuning the appearance

TeX style

bold vectors

Differential d

Cyclic Groups

"Well, Im obviously not getting along with the mathematicians here …"

"I remember the set theory edit wars …"

"I have great sympathy for those who want 'verbose'. …"

"Let's put it this way …"

"Oh and one more thing …"

"The point is …"

"Can all these people who are agreeing …"

Issue of readability and pedagogy

Styles of Mathematics Articles

History of Mathematics

"The beauty of mathematics …"

"Template for pages about probability distributions?"

"… looking for some help with TeX …"

About 'iff'

mathematical markup

New WikiProject, WikiProject Probability

Jan 2004 – Aug 2004

"This article assumes knowledge of" notices

Ring theory pages

MediaWiki Side Tables

Dynamical systems

What to do with references?

Proposal on Chinese surnames

Do we have to begin every article with the word "In"?

Comments on Peter Kwok's concerns

Clarification: I am not one of the founders of Wikipedia

Typesetting of mathematical formulas

Links to surnames of mathematicians are often very bad things

The case for LaTeX

Use of \mbox

TeX/HTML currently incompatible

"Well, the ideal solution would be …"

Crazy idea

A clarification

Editing the articles on set theory.

Notation for the empty set: "{}" vs. ∅

∪ symbol displays as box?

Schaun MacPherson

Sep 2004 – Dec 2004

New Article: The algebra of sets - request for comment.

cdot and times

variable letters

Simple formulas

Upright differential operators

Pages for review

Wikipedia:Math 1.0

Japaridze and Computability Logic

Trace

Zech?

Category:Topological spaces and List of manifolds

Spoof edits alert

User:Jim Slim vandal attack

Current position re User:ExplorerCDT

User:199.248.201.253

Qualculus

White paper

"I am taking this to vfd"

Using images from the St.Andrews Uni. they believe are public domain?

Jan 2005 – Mar 2005

Graph (mathematics) vs Graph theory

joy of tex

Bug in new version

A little note on using purple dotted boxes

Wikipedia:WikiProject Mathematics has this article lost focus?

\pi image in Template:Math-stub

PlanetMath

Where to contribute math articles? Wikipedia or Planet Math?

MathWorld references

Wikipedia:WikiProject Mathematics/PlanetMath Exchange -- version 0.1 -- comments requested (on this page)