Wikipedia talk:WikiProject Mathematics/Archive Index

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< 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

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. —Preceding unsigned comment added by Angela (talk • contribs) 17:09, August 17, 2003

"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.

—Preceding unsigned comment added by 24.145.133.16 (talk • contribs) 19:14, December 27, 2004

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 —Preceding unsigned comment added by 24.145.133.16 (talk • contribs) 06:42, December 28, 2004

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 —Preceding unsigned comment added by 24.145.133.16 (talk • contribs) 06:42, December 28, 2004

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

—Preceding unsigned comment added by 24.145.133.16 (talk • contribs) 06:42, December 28, 2004

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 [209.157.64.200/focus/f-news/838576/posts 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. —Preceding unsigned comment added by 80.168.225.12 (talk • contribs) 18:09, December 28, 2004

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^{believe^{this^is}} the _{correct_behavior^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^{f^s}) 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

Template:SampleWikiProject

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

v • d • e Major fields of mathematics

Logic · Set theory · Category theory · Algebra (elementary – linear – abstract) · Calculus · Discrete mathematics · Number theory · Analysis · Geometry · Trigonometry · 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, machines.html RegisterMachine 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)

Style and formatting
Manual of Style and its subpages
Abbreviations Accessibility Anime & manga articles Biographies Capital letters Chemistry Command-line examples Dates and numbers Disambiguation pages Flags & similar icons Infoboxes Latter Day Saints Legal Links Lists of works Manual of Style, main page Mathematics Medicine Military history guidelines Music Pronunciation Spelling Text formatting Titles Trademarks Writing about fiction
Related policies and guidelines
Categorization Categorization of people Citing sources Explain jargon External links Film guidelines Footnotes Layout Lead section Lists Music samples Naming conventions Overlinking Proper names Stubs Summary style Technical terms Writing better articles Wikimedia sister projects Words to avoid
Other advice, including essays and proposals
Captions Diagrams and maps Glossary How to edit a page Picture tutorial Sections Trivia sections
Related to specific cultures
Arabic-related articles Chinese language Chinese history Ethiopia-related articles France & French-related Hebrew transliteration India-related articles Ireland-related articles Islam-related articles Japan-related articles Korea-related articles Philippines-related articles Portugal-related articles Thailand-related articles Syriac/Assyrian-related articles United Kingdom nationalities U.S. highways

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. Hiding 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/archive1

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)

v • d • e Major fields of mathematics

Logic · Set theory · Category theory · Algebra (elementary – linear – abstract) · Calculus · Discrete mathematics · Number theory · Analysis · Geometry · Trigonometry · 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 topics
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
Recent changes: 0-9 A-C D-F G-I J-L M-O P-R S-U V-Z All
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 | Lists | Basic topics | 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)

Categories: 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)