Wikipedia talk:WikiProject Mathematics/Archive2006

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< Wikipedia talk:WikiProject Mathematics

1 Jan 2006 – Feb 2006
2 Mar 2006
3 Apr 2006
4 May 2006
5 Jun 2006
6 Jul 2006
7 Aug 2006
8 Sep 2006
9 Oct 2006
10 Nov 2006
11 Dec 2006

Jan 2006 – Feb 2006

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

Help with Simple harmonic motion

A newbie, Itzchinoboi, rewrote Simple harmonic motion. The new article is more elementary, which is good. To me both the original version looks good, and the rewritten version looks good, although the latter is full of newbie mistakes. See the diff. Anybody knowledgeble willing to spend some time understanding the changes and see how to deal with all this matter? Note that a plain revert is not an option, it seems that the user spent half a day on that article. Oleg Alexandrov (talk) 22:31, 2 January 2006 (UTC)

Scalar (mathematics)

This newly created page is an abomination. Please help. Michael Hardy 02:41, 3 January 2006 (UTC)

I've had a go. Dysprosia 04:20, 3 January 2006 (UTC)

Nice one, D. This seems to be rather an uphill battle. It would be good to get the thoughts of others regarding the article introduction - see this bit of the talk page. Thanks! — merge 04:14, 12 January 2006 (UTC)

Tensor wars

We may be in for more of the traditional troubles at Tensor. Category:Tensors now has 70 articles. I really think the main tensor article should reflect that (at least - some of the more algebraic pages are in Category:Multilinear algebra or elsewhere).

There is a sub-issue, rank of a tensor, which might be tractable on the basis of some sourced research.

Charles Matthews 17:02, 3 January 2006 (UTC)

Articles listed at Articles for deletion

Set descriptions in colloquial English (AfD discussion)

Uncle G 01:03, 4 January 2006 (UTC)

Wikipedia talk:Stable versions#Certification gang

would you like to create certified articles in mathematics? -- Zondor 03:19, 5 January 2006 (UTC)

Hmmm ... I have major issues with this idea. How do you decide who can join your gang ? You wouldn't want to let just anyone in, would you ? They might start doing stuff that you disagreed with. It sounds awfully like a self-elected technocracy. I would be more worried if I didn't think that the chances of reaching critical mass on this idea are really, really small. Gandalf61 09:46, 5 January 2006 (UTC)

It will start out as a gang but eventually to something professional like a league. -- Zondor 13:35, 5 January 2006 (UTC)

Certification is an interesting idea, but its not yet completely fleshed out. Its primary utility is to handle articles where there have been significant edits wars, or get a lot of inappropriate edits from newbies, or even regular vandalism. This is maybe less than 1% of all math articles. The goal is to certify one particular version of the article, and then let anon hack on it. If one comes back in a month or two and its a horrid mess ... well, so what, at least the certified version is good. This is much better than the battle fatigue of having to defend an article on a daily basis. linas 15:20, 5 January 2006 (UTC)

But if you don't defend an article on a daily basis, then it will get messed up, and after a month or two you won't be able to sort out any good edits from the rubbish, so the only way forward will be to roll back to the "certified" version. In effect, you have frozen the article - no one will bother to make any serious contributions because they will all be lost in the next purge. Gandalf61 16:23, 5 January 2006 (UTC)

Our energy can be spent better in places other than in certifying articles. If you come back to an article months later and it's "messed up", you should take the time to go through the diff and find out what went wrong, and then either revert there or fix it by hand. Reverting to an outdated "stable" version is too crude a tool.

Meekohi 19:05, 5 January 2006 (UTC)

The energy is well spent if creating a Wikipedia:WikiReader project for Mathematics. -- Zondor 15:10, 7 January 2006 (UTC)

Yes, well, these points should be argued there, not here. My take is that I've seen too many good editors get wiki-fatigue and wikistress and have some of them leave, because they were unable to defend thousands of articles on a daily basis. If you can do this, great. Like many other "old-timers" (ok, I've been here a year), I now spend more time watching articles, trying to ward off decay, than I do on actually writing. That is wrong. It should not be a herculean effort to stave off wikirot. (See above, Wikipedia talk:WikiProject Mathematics#Help with Simple harmonic motion for a real-life example. Oleg watches a lot of these kinds articles, and can't keep up with the changes. The old version should have been declared "stable", and stay that way till the new one is done.) linas 21:25, 5 January 2006 (UTC)

This is getting offtopic, but I gave up watching articles by the thousands. After going under 1000 I actually found time to write new stuff every now and then. :) Yes, open acces is the biggest asset but also the biggest disadvantage of Wikipedia. But seems to work so far. :) Oleg Alexandrov (talk) 01:03, 6 January 2006 (UTC)

The single most important thing for stable versions is to have a guarantee of accuracy and reliability otherwise it is no different to the system we already have. So at any given time, we can demand a print edition of Wikipedia 1.0. Whereas, the wiki version serves as the playground for boldness, experimentation and to be cutting edge. Once you have made the published version, you can forget about it and concentrate on the wiki version. Eventually, it becomes better than the previous stable version, you then supplant it after it has been certified for accuracy. -- Zondor 01:02, 6 January 2006 (UTC)

Math Collaboration of the Week

I hope nobody is too opposed to the requets for nominations at the top of the page. I think we need it if we're going to get MCoW up and running again. Meekohi 20:06, 5 January 2006 (UTC)

Nevermind, apparently the big man minds. ;) Meekohi 20:07, 5 January 2006 (UTC)

Uhh, I've never really seen Oleg, but I would bet he's not really that big. Nevertheless as Fropuff suggested below it will get more attention here anyway. Paul August ☎ 03:46, 6 January 2006 (UTC)

What units do you want it in, feet, meters, edits per second? Oleg Alexandrov (talk) 18:59, 6 January 2006 (UTC)

It's alright, many people watch the discussion on this page. For those of you who don't know User:Meekohi is trying to get the Mathematics Collaboration of the Week going again (it has been dead for about four months now). If you are interested in participating please list nominations on that page. -- Fropuff 20:42, 5 January 2006 (UTC)

Perhaps that page should scale back to a less ambitious "Math Collaboration of the Month". Paul August ☎ 17:58, 6 January 2006 (UTC)

Well, is it flogging a dead horse? The discussions have always seemed to show up the way people here have rather disparate interests, within mathematics. We could have Algebra COTM, Geometry COTM etc., running in parallel.Charles Matthews 18:03, 6 January 2006 (UTC)

Honestly I feel it should be the Fortnightly collaboration since that is about how long it takes to get an article up to par, but it wouldn't fit in with all the other Weekly Collaborations we have in other subjects. Meekohi 15:45, 13 January 2006 (UTC)

A new project idea

I have an idea for a new math project that provides a somewhat concrete way of evaluating progress. I call it the "Let's Beat Mathworld" project; its goal is for every topic listed on Mathworld, to write a better article on the same topic. We've already done so for many of them, but I bet we can cover them all. We can make a project page listing all the topics in the Mathworld hierarchy with links. We have to watch out for copyvio, but I think it's a great source of useful topics that we may be failing to touch on or that may currently be stubs. Deco 04:25, 6 January 2006 (UTC)

For all that's worth, the mathworld articles already are listed at Wikipedia:Missing science topics (Math1 through Math7). Whoever did that seems to to have avoided copyvio by shuffling things and possibly mixing with entries from other places. Oleg Alexandrov (talk) 04:47, 6 January 2006 (UTC)

I was unaware of those lists. I've now added a link to them in the "Things to do" table on the main project page. (By the way Oleg, just how big are you?) Paul August ☎ 05:06, 6 January 2006 (UTC)

~~If you are asking how I got to know about that project, then the answer is that there was an announcement on this page a while ago, and actually Linas and Rick Norwood got there long before me. :)~~

Answered above. Oleg Alexandrov (talk) 04:17, 7 January 2006 (UTC)

By the way, there is also a User:Mathbot/List of mathematical redlinks, which I made at Fropuff's suggestion, containing 11,000 redlinks found in existing math articles. Oleg Alexandrov (talk) 07:38, 6 January 2006 (UTC)

Wow, 11k links. I wonder if it would be helpful to somehow categorize those missing links/ topics. I mean missing theorems, lemmas, formulas, problems, scientists... (Igny 14:45, 6 January 2006 (UTC))

A good chuck of those are nonmathematical. You would need artificial intelligence to sort out theorems from problems and from scientists. Yeah, I don't know how helpful that list is, but it exists. :) Oleg Alexandrov (talk) 15:01, 6 January 2006 (UTC)

Many of those 11K links are now blue. Oleg, do you plan on updating this list anytime? I don't know about other people, but I find it useful. Thanks again for doing it. -- Fropuff 15:26, 6 January 2006 (UTC)

I updated them now, and will do every couple of weeks or so. Oleg Alexandrov (talk) 04:17, 7 January 2006 (UTC)

I asked permission to used those list a few months ago, but received this reply

Rudy, Thank you for your mail. We appreciate your effort to secure proper permission before using our material. Our lists *do* represent original works of authorship and, as such, enjoy copyright protection. Further, the value of our editorial work is evidenced by your desire to incorporate the material into your project. We understand your need for such a list, and we would very much like to support Wikipedia -- as I am sure you would like to support the continued development of MathWorld. It is worth noting the relative dearth of links to Mathworld from Wikipedia. Regardless, it isn't obvious how reproducing MathWorld (which already offers unfettered, free access) furthers the goals of Wikipedia. Are there other areas of mathematics/science that are in greater need of free web-based exposure that we could help Wikipedia develop? Benson Dastrup Wolfram Research, Inc.

—Ruud 10:02, 6 January 2006 (UTC)

I really think we can set our own agenda now. Why not lead rather than follow? This is more likely to attract active research workers. Charles Matthews 15:22, 6 January 2006 (UTC)

I second Charles' opinion. MathWorld should be asking for our lists. If you see an article on MathWorld that doesn't have good coverage here, just post a request on Wikipedia:Requested articles/Mathematics. -- Fropuff 15:29, 6 January 2006 (UTC)

Well, that's if it's actually worth covering here. MathWorld's topic selection can be, to put it kindly, quirky (cf the Somer-Lucas pseudoprime article, which along with Somer pseudoprime probably ought to be deleted). --Trovatore 15:49, 6 January 2006 (UTC)

Trovatore, I don't understand you at all. Why would any article with substantiated content be deleted? Why would any topic not be worth covering? As for beating Mathworld, I do believe we already did, but in any case I think it will be much more efficient if every Math Wikipedian will, once in a while (or multiple times in a while), go to "random entry" in Mathworld, and make sure that Wikipedia has a better coverage of the encountered topic. If not, improve it or put a request for it. While this could create a little duplicate effort, it will solve many of the aforementioned problems (copyright issues, alleged statement that we are not as good as Mathworld, manageability of large lists of topics) as well as guarantee that changes to Mathworld will not be overlooked. --Meni Rosenfeld 17:01, 6 January 2006 (UTC)

Okay, perhaps those articles aren't as substantiated as I thought at first. Stil, I think the direction should be attempting to substantiate such articles, rather than delete them. --Meni Rosenfeld 19:50, 6 January 2006 (UTC)

I've noticed that while in many cases, we have better articles than mathworld, their articles will have a much larger section of raw often obscure formulas and identities. Those can detract from the quality of an article, as they're not very readable, but they're still important and useful, for any reference work. And remember, we're a reference, not a textbook. -lethe ^talk 04:25, 7 January 2006 (UTC)

The emphasis on formulas at MathWorld is surely to do with the Wolfram connection in the site's origins. Anyway I like classical formulae myself, but a more wordy style is indeed better for WP. Charles Matthews 08:01, 7 January 2006 (UTC)

It would probably be best to include such formulae, perhaps placing the less important ones near the end of the article so as not to be a distraction. --Meni Rosenfeld 15:09, 7 January 2006 (UTC)

While on one hand I agree that attempting to merely reproduce Mathworld's extensive quality entries might seem silly, on the other hand as the above e-mail demonstrates, their articles are not libre: we need to make the same information available to everyone to use, and update, in any way they please. Also, for the sake of our reputation, it would be neat to say that we unequivocably have even better coverage than a site as well-known as Mathworld. Deco 06:56, 10 January 2006 (UTC)

Mathematics Portal

I've been doing some work on the Mathematics Portal recently. It has been in fairly poor shape for most of the last year as very few people have bothered to maintain it. If you have any suggestions for improvement please mention them on Portal talk:Mathematics. I do need suggestions for future featured content. You can list these at Portal:Mathematics/Suggestions. Thanks. -- Fropuff 17:32, 6 January 2006 (UTC)

I think the new portal looks great. Paul August ☎ 17:45, 6 January 2006 (UTC)

Multivariable calculus help

If someone who remains div, grad, curl better than me would have a look at the van Hove singularity article I've just written, I'd be pleased. I can't recall the name of the series expansion $\mathrm{f(x) = f(0) + f'(0)x + 1/2f''(0)x^2 + \ldots}$ . Probably there's a math article on this expansion that I could point to. Also, I have a feeling that the change of variable I'm doing where I go from a volume integral over k to a surface integral over E is the result of one of those fundamental theorems, (Gauss? Stokes? Green?) but I'm not sure which one. Perhaps in addition I have made an egregious notational faux pas. Thanks for any suggestions you have. Alison Chaiken 18:58, 8 January 2006 (UTC)

The series expansion you mentioned is the Taylor series. Unfortunately I don't remember multivariable calculus well enough to offer any additional help. --Meni Rosenfeld 19:28, 8 January 2006 (UTC)

The change of variable may have a more specific name, but "generalized Stokes theorem" would suffice. --KSmrq^T 20:31, 8 January 2006 (UTC)

Well, looks to me like this is about pushing forward a measure/density, and the only difficulty indeed would be at a critical point (mathematics). Not that that page is a great help. The thing about the square-root singularity comes out of the Morse lemma, and so is only generically true (true in practice ...)? That anyway is why you only get cases like the quadratic form cases to worry about. (Sorry Alison, this is hardly helpful, talking amongst ourselves here.) Charles Matthews 20:46, 8 January 2006 (UTC)]]

Thanks Charles for your editing. I added a link in the van Hove singularity article to critical point (mathematics) in the hope that it will improve eventually. I'm contemplating a link to the Morse lemma or Stokes theorem articles but need to think about it more. Alison Chaiken 03:23, 9 January 2006 (UTC)

The above expansion is, to be more specific, the Maclaurin series (the Taylor series about zero). Same article though. Deco 06:57, 10 January 2006 (UTC)

Formal calculation

During my studies, I have encountered the concept of a "formal calculation", in the sense of, roughly, a calculation for which the steps are not completely substantiated, and yet the result can give us insight about the true answer to the problem in question. I want to write an article about that concept, but I haven't found any references to it on the web, so I'm not sure how widely it is used and whether I understand the concept properly. Any ideas? --Meni Rosenfeld 18:34, 12 January 2006 (UTC)

On the contrary, I think of a "formal calculation" specifically as a calculation in which every step is very clear and verifiable. I'm not sure I know a name for what you're referring to. Meekohi 20:43, 12 January 2006 (UTC)

I think I know roughly what Meni is trying to say. I would have thought you might find it at heuristic or heuristic argument or something similar, but they seem to be run by philosophers. Dmharvey 20:47, 12 January 2006 (UTC)

A formal argument is when you just follow what the syntax seems to suggest your reasoning, without proving the reasoning is sound. Like when you prove that, in a ring, if (1+ab) is invertible, then so is (1+ba) by using power series. Power series don't exist in a ring, but but you can still make formal arguments using them. -lethe ^talk 21:58, 12 January 2006 (UTC)

Lethe's example is what I would call a heuristic inference. It seems very strange to me to call this "formal": it's good because of informal gut feeling experience, not in virtue of the formal structure of the problem. --- Charles Stewart 22:02, 12 January 2006 (UTC)

Lethe's reply coincides with my experience. I suspect that it may be hard to find good references, but I remember reading about it recently. Bear with me … -- Jitse Niesen (talk) 22:05, 12 January 2006 (UTC)

Here we are. Stuart S. Antman, Nonlinear Problems of Elasticity, Applied Mathematical Sciences vol. 107, Springer-Verlag, 1995. Page 1 contains the paragraph: "I follow the somewhat ambiguous mathematical usage of the adjective formal, which here means systematic, but without rigorous justification. A common exception to this usage is formal proof, which is not employed in this book because it smacks of redundancy." (his emphasis). -- Jitse Niesen (talk) 22:28, 12 January 2006 (UTC)

I think the term systematic calculation would be far more fitting nomenclature, but that doesn't really carry the connotation of being subtly incorrect that we're looking for. Meekohi 02:02, 13 January 2006 (UTC)

I wouldn't call it incorrect: it is, after all, an excellent heuristic. I'd rather say it was non-well-founded. --- Charles Stewart 02:13, 13 January 2006 (UTC)

Are all in favor of creating a stub, bearing the title "Formal calculation", based on the definition Jitse found, and beating it around until we reach something we can agree upon? --Meni Rosenfeld 13:40, 13 January 2006 (UTC)

I don't know, personally I'm fairly opposed. To me the term Formal Calculation distinctly implies that it is rigorously correct. The reference Jitse gave doesn't really give much support in my mind, seeing as he points out this is ambigous usage. If we are going to make an article on it, I think the main article should describe what it means to be rigorous/systematic, and then there should be a short section pointing out that it is possible to be apparently systematic, but still incorrect. Meekohi 14:05, 13 January 2006 (UTC)

I know that "formal calculation" seems to imply a rigorous one, and actually that did confuse me the first times I encountered the concept. But I got the impression that, while perhaps ambiguous, it is usually used in the sense I described - Much like in the probably more common term formal power series. In this sense, "formal" actually means of form, namely, the form of the objects matter and not their underlying meaning - making the calculation perhaps systematic, but not really rigorous because we are using properties without any justification to why these properties should hold. We could always delete the article later if we can't seem to rich any consensus. --Meni Rosenfeld 14:59, 13 January 2006 (UTC)

Formal power series are just sequences over a ring with convolution as multiplication. Since all sums involved are finite, this is a rigerous mathematical topic. Convergent power series is a different topic requiring the ring to be a Banach algebra. In france there is a state wide research association called "Calcul formel", which would probably translate as symbolic calculus or even symbolic algebra. The research and design of computer algebra systems is part of that.--LutzL 15:09, 13 January 2006 (UTC)

Of course formal power series are ultimately defined in a rigorous way, but the inspiration for this definition comes from a non-rigorous application of properties of convergent power series to arbitary power series. That's where the term "formal" comes from. --Meni Rosenfeld 15:12, 13 January 2006 (UTC)

I think the originally-proposed topic is a 'derivation', universal in (say) theoretical physics. It's not a particularly good topic for an article, though. Charles Matthews 16:20, 13 January 2006 (UTC)

I think that this is a good topic for an article, and it may well prove useful for my planned article on Boole's algebraic logic (to be carefully distinguished from Boolean algebra, since Boole's system allows terms that do not have set-valued denotations). They can be seen to be similar to the status of polynomials prior to the discovery of complex numbers: onbe can know the sum and product of the roots of a quadratic and know furthermore that those roots don't exist. If we are to resort to neologism, why not optimistic calculation? --- Charles Stewart^(talk) 16:29, 13 January 2006 (UTC)

I think "formal" in "formal calculation" has the same meaning as in "formal power series". In my experience, it is often used in the following context (for instance, in a talk on Kolmogorov-Arnold-Moser theory which I just attended): We want to prove that a function f_epsilon with a certain property exists for epsilon sufficiently small. We know f_0, so we expand f_epsilon in a power series in epsilon. If this is possible (i.e., if we can find all the coefficients in the power series), we have a "formal solution". To prove that this is actually a solution, we have to show that the power series has a positive radius of convergence.

So, formal is not just optimistic. And I don't think "formal" in this meaning is a neologism either, as Meni, Lethe and I have all heard of "formal" in this meaning. -- Jitse Niesen (talk) 18:08, 13 January 2006 (UTC)

Another example: formal group law. Dmharvey 21:16, 13 January 2006 (UTC)

It appears that the phrase is used in the proposed sense. It also appears to be understood in other ways, and it appears that some folks feel that the proposed sense is not a good sense. For an inclusionist (not necessarily me), Wikipedia should have an article. The article should note the opposition and provide disambiguation. However, a major unresolved question is: What is the primary meaning of "formal calculation"? The answer to that I do not know, but I'm inclined to think it's the "rigorous" sense, not the proposed sense. --KSmrq^T 01:23, 14 January 2006 (UTC)

I believe the phrase is commonly used in physics in the sense of "we know this can't possibly be right, but by shoving symbols around on a page, here's what you can come up with". For example, "formally", one has 1+2+3+...=-1/12, which is clearly both "right" and "wrong" in various deep ways. That is, its ambiguous without further clarification about how in the world this could possibly be a valid manipulation; but in physics, further clarification is often too hard to provide. A formal calculation is one step up from handwaving. linas 06:01, 14 January 2006 (UTC)

In a nutshell, I think my original proposition of creating a stub and beating it around is fair. I'll do that now. Be sure to check it out for any flaws\omissions\whatever as I am an inexperienced editor. Formal calculation. --Meni Rosenfeld 15:20, 15 January 2006 (UTC)

Yeah it seems that there is enough support for the idea now that we should have an article, even though I still don't like the terminology ;) Meekohi 15:28, 15 January 2006 (UTC)

Red links

Is there a handy way, given a red link, to figure out what articles link to it? Some of the red links we have seem like they just need to be reworded to link to something more appropriate. Meekohi 15:41, 13 January 2006 (UTC)

To find all articles linking to Magnus series, for instance, follow the red link and then click on "What links here". -- Jitse Niesen (talk) 15:59, 13 January 2006 (UTC)

Ha ha, hiding from me in the toolbox all this time. Thanks! Meekohi 18:29, 13 January 2006 (UTC)

70.22.128.220

Could an admin keep an eye on this IP? I've reverted two of their edits. They obviously know a little about the material they are editing, but are still make some pretty serious false claims and mistakes. I've put the details up on the Talk page. Meekohi 16:10, 13 January 2006 (UTC)

Well, you'd better explain your concern some more. Apart from the deletion of one reference, which is not explained, this looks like a technically proficient editor. Charles Matthews 16:16, 13 January 2006 (UTC)

For Scale-free networks he deleted the entire formal definition from the page, and for Complex networks he made claims that preferential attachment was the first generative model for power-law distribution graphs, which is false (and was stated as false in the article already). I'm not saying he's not technically proficient, but he's altering articles for the worst. Meekohi 16:35, 13 January 2006 (UTC)

The more you can document these points on the Talk pages of the articles, the easier it is for others to follow the changes, and contribute to the discussion. Charles Matthews 17:14, 13 January 2006 (UTC)

Math Will Rock Your World

Seems that math made it as the cover image at businessweek.com. See article. Admittedly this is not a Wikipedia related post, however, I found it interesting. The article ends with "Yes, it's a magnificent time to know math.". Oleg Alexandrov (talk) 20:05, 13 January 2006 (UTC)

That head is some kind of scary ;) Meekohi 20:22, 13 January 2006 (UTC)

History of Science WikiProject being formed

ragesoss is trying to start up a History of Science Wikiproject; add your name here and help him get started. linas 05:50, 14 January 2006 (UTC)

proof of impossibility

Someone's just started proof of impossibility, which seems like it could end up being quite nice. I've created a redirect from impossibility proof, which I think is a more common term. Perhaps we should move the original? Dmharvey 02:19, 15 January 2006 (UTC)

I chose the name. Either is fine for me. Deco 08:43, 15 January 2006 (UTC)

List of decimal expansions

Is there an article "List of decimal expansions of mathematical constants"?

If so, where is it located?
If not, does anyone think it would be a good idea to create one? Where should it be placed?

--Meni Rosenfeld 16:17, 15 January 2006 (UTC)

If you mean a list of mathematical constants sorted by magnitude, with 50 or so decimal places given, then sure, it would be a good idea. I started a Swedish such list a while back. Fredrik Johansson - talk - contribs 16:23, 15 January 2006 (UTC)

That seems like a potentially useful list, although I'm not sure if it's encyclopedic enough to be added. It would be better if rather than listing them bby magnitude (which is fairly meaningless) you catagorized them in some sensible way. Meekohi 16:58, 15 January 2006 (UTC)

Maybe I'll sort them by order of popularity or something like that. I'll try to see what I can put up... --Meni Rosenfeld 17:02, 15 January 2006 (UTC)

The page mathematical constant already provides such a list (for some definition of "popularity"...) Fredrik Johansson - talk - contribs 17:14, 15 January 2006 (UTC)

Well, this page will have to do for now - Although I do think a list with more digits per constant, perhaps without all the additional information, could be interesting. Perhaps we could also add binary expansions and factorial base expansions (which could be argued to be less arbitary than decimal). Maybe I'll try to compose something over the course of time. --Meni Rosenfeld 17:22, 15 January 2006 (UTC)

Decimal expansions of constants and other tables of numbers should go to Wikisource (see [1]). Samohyl Jan 18:42, 15 January 2006 (UTC)

Areas of mathematics article

To quote from the start of the article, "The aim of this page is to list all areas of modern mathematics, with a brief explanation about their scope and links to other parts of this encyclopedia, set out in a systematic way." Although this has been done for some areas, others are most definately lacking. (All the Analysis, Non-physical sciences and General sections, plus about half the Algebra and Physical sciences sections). Due to the wide ranging nature of the topics in question, this needs contributions from plenty of people. Even if you are only able to expand on a bullet point or two, that would be a definate help. Tompw 11:38, 16 January 2006 (UTC)

Subset notation

As far as I can tell, the conventional notation for "subset" in most of mathematics and in WP is $\subseteq$ . However, it has been argued that in probabilty theory the notation $\subset$ is used. Which one of the symbols should be used in the article shattering, which deals with a topic in probability theory? --Meni Rosenfeld 19:39, 16 January 2006 (UTC)

I believe that $\subset$ refers to a proper subset, while $\subseteq$ does not necessarily refer to a proper subset. NatusRoma 19:55, 16 January 2006 (UTC)

Unless the article specifically states that ⊂ may refer to nonproper subsets it seems wise to use ⊆ for the general case and ⊂ for proper subsets. I don't see why this should be any different in probability theory. -- Fropuff 20:16, 16 January 2006 (UTC)

To NatusRoma: Yes, that is the common convention - However it seems that in probability theory, a different convention is used, where $\subset$ means a not necessarily proper subset.

To Fropuff: That is what I also think, but it has been argued that probabilitists will be confused when they read an article in their field which uses a different convention than they. I would like to hear more opinions to make sure we have consensus on using ⊆. --Meni Rosenfeld 20:22, 16 January 2006 (UTC)

Probabilists use $\subset$ (⊂), to mean subset -- however they seem never to use $\subseteq$ (⊆), so the mathematically correct usage shouldn't confuse them. Arthur Rubin | (talk) 22:21, 16 January 2006 (UTC)

I have proposed a convention regarding this issue. Discuss it here. --Meni Rosenfeld 09:41, 17 January 2006 (UTC)

Chaos theory needs help

The Chaos theory page needs help. There is a Wikipedia user that insists in inserting comments about biotic motion into the page. Several contributers have tried to point out the problems with biotic motion to the contentious user, but to no avail. What should be done about this?

The long discussion in the Chaos theory talk page has brought up a series of difficulties with the published work in bios theory: lack of mathematical definitions, one common author in all the six papers in citation indices, no reference to a century of work in dynamical systems, simple analytical arguments not made, etc.

Despite the results being published, I find it hard to see how a topic that has failed to attract attention for seven years should be included as a major idea in the Chaos theory article.

XaosBits 03:08, 18 January 2006 (UTC)

Editors need help at function (mathematics)

There is a dispute going on at function (mathematics), where substantial rewriting (with reverts) has been going on, with the two editors unable yet to agree on how the article should be rewritten. Rich Norwood is requesting other editor's views. Please help out. (I will be away for a few days but I will try to lend a hand when I get back.) Thanks all. Paul August ☎ 15:20, 18 January 2006 (UTC)

Mathie

I nominated this for deletion. Votes (either way) welcome. :) Oleg Alexandrov (talk) 01:57, 19 January 2006 (UTC)

Shape or set?

I am having a dispute with Patrick over at shape. Here's the relevant diff to Patrick's version. I would argue that Patrick is a bit pedantic insisting on the word "set" instead of "object" and that it makes the article less clear for the general public. Patrick's explanation is in the edit summary to that edit, stating "object is undefined; e.g., there is unclarity about color". I would like some comments, on this page, which I will later move to talk:shape. Oleg Alexandrov (talk) 01:03, 21 January 2006 (UTC)

Yeah, it should be object. To talk about shape, there's already an implicit assumption made that the set has a metric. There's also an implcit assumption that there's a space so that rotations, translations, etc. are defined. By contrast, true "sets" don't have metrics and can't be rotated or translated. So insisting on "set" is kinda goofy. linas 01:25, 21 January 2006 (UTC)

Maybe we should use the word "object", and add a comment like "object here is taken to mean a subset of a metric space"? This will make it more or less accurate, while maintaining readability. -- Meni Rosenfeld (talk) 06:40, 21 January 2006 (UTC)

Real projective line

Hi everyone.

It seems that currently the only reference in Wikipedia on the real projective line ( $\mathbb{R}\cup\{\infty\}$ ) is this 3-line subsection. I believe there is much more to be said about it, elegantly extending analytical properties of reals to it. The problem is that I've never really read about such definitions (I'm not very proficient in the mathematical literature), but it seems natural to me that these are things that should be defined. Examples are to say that $\lim_{x \to a} {f(x)} = \infty$ iff for every M > 0 there is ε > 0 such that $| f (x) | > M$ for every |x - a| < ε. In this way, $\lim_{x \to 0} {\frac{1}{x^2}}$ , $\lim_{x \to 0} {\frac{1}{x}}$ and even $\lim_{x \to 0} {\frac{1}{x sin{1/x}}}$ are all equal to $\infty$ . Since we don't want to use signed infinities, classical limits like $\lim_{x \to +\infty} {f(x)}$ and $\lim_{x \to -\infty} {f(x)}$ become $\lim_{x \to \infty{-}} {f(x)}$ and $\lim_{x \to \infty{+}} {f(x)}$ (approaching the point at infinity either from the left, through increasingly positive numbers, or from the right, through increasingly negative numbers). The concept of continuous function can be extended. The notion of intervals can be extended, for example if a > b, we define the open interval $(a, b) = (a, +\infty) \cup\{\infty\}\cup (-\infty, b)$ . This way, we have for example the nice propety: The image of the interval (a, b), under the funtion $f(x) = \frac{1}{x}$ , is $(\frac{1}{b}, \frac{1}{a})$ , no matter what the values of a and b are.

I want to write an article on these topics (more specifically, turn real projective line from a redirect to an article). The questions are these:

Is there a place in WP where these concepts already appear?
Does anyone know a reference where these definitions appear, to make sure I'm not inventing anything?
Does anyone think this is not a good topic for an article?

I'll be grateful for any comments. -- Meni Rosenfeld (talk) 15:24, 22 January 2006 (UTC)

There are three more lines in a more abstract setting at compactification (mathematics) (look for the one-point compactification). It seems to me a good topic for an article if you can find some references and I expect these references to exist. -- Jitse Niesen (talk) 15:40, 22 January 2006 (UTC)

Have you heard about these concepts? That would be a good start. Unfortunately I do not know of any references. Would it be okay to create the article now, and add references as we find them? -- Meni Rosenfeld (talk) 16:11, 22 January 2006 (UTC)

No. I think you shouldn't write an article without consulting references. Personally, I even make mistakes if I know the stuff very well unless I have a book lying next to me. -- Jitse Niesen (talk) 00:50, 23 January 2006 (UTC)

It wasn't clear to me from your answer whether you have heard about these definitions. It is important to me to know, because if not I will have a mind to put this matter to rest. In either case, is there anyone who has heard about it, and preferrably, know of a reference to it? -- Meni Rosenfeld (talk) 06:34, 23 January 2006 (UTC)

Oh, and I've just found this. It doesn't address all of the above ideas, but it's a good start, no? Is it enough for starting an article with just what is mentioned there? But please do tell me if you've heard about the limits thing. -- Meni Rosenfeld (talk) 08:34, 23 January 2006 (UTC)

I have no definite recollection of the limit thing. On the other hand, I doubt I would remember it if I had read it somewhere as it seems quite natural to me and a consequence of general topology.

I'm quite sure I've seen the thing of how division of intervals might result in an interval containing infinity in a paper on interval arithmetic. This is also mentioned in the MathWorld link. -- Jitse Niesen (talk) 11:42, 23 January 2006 (UTC)

Yeah, I figured this is a special case of more general topologic spaces. But the reason I think these explicit definitions are of notable interest is because they are an elegant extension of the good old real numbers, a structure we all know and love. Also I don't know much topology so I'm not proficient in all the structures that exist.

I think we have sufficient grounds to at least start an article, which I will begin working on now. It will be called Real projective line. Everyone be sure to check back in a few hours and leave some feedback. -- Meni Rosenfeld (talk) 09:08, 24 January 2006 (UTC)

Hmm I don't like that name so much. Mostly because it's not a name that anyone uses. The space you're talking about is called (in my experience) the real projective line or else the one point compactification of the real line. -lethe ^talk 09:15, 24 January 2006 (UTC)

Okay, I thought it would be a good idea to call it this way because that's how it's called in Mathworld, but if you say it's uncommon I'll change that. -- Meni Rosenfeld (talk) 09:22, 24 January 2006 (UTC)

While we're at it, what is the most common notation for this space? -- Meni Rosenfeld (talk) 09:30, 24 January 2006 (UTC)

$\mathbf P^1(\mathbf R)$ perhaps. Double-struck if you prefer. Dmharvey 13:33, 24 January 2006 (UTC)

Hmmm not so sure now. You seem to be talking about a set with certain arithmetic operations, and the notation I suggested doesn't really cover that. Dmharvey 13:48, 24 January 2006 (UTC)

Functions, partial, pre-, proto-, total, etc.

JA: I'll be introducing some language under the heading of Relation (mathematics) to cover these cases and more, as they arise within the setting of relations in general. Stay tomed. Jon Awbrey 15:48, 22 January 2006 (UTC)

Notation for positive infinity

Another question on a loosely related subject: Is there a notational convention in WP regarding positive infinity? I think it is most commonly denoted $+\infty$ in the literature, but I've seen places in WP where it is denoted just $\infty$ . Should the + sign be added for consistency and clarity? -- Meni Rosenfeld (talk) 16:40, 22 January 2006 (UTC)

As a rule the plus sign is used only if it is necessary to distinguish a positive infinity from a negative one. Also, some contexts require other ways of denoting infinities, such as ω or ℵ₀. --KSmrq^T 18:39, 22 January 2006 (UTC)

My experience is that it's referred to as $+\infty$ only where it is necessary to distinguish it explicitly from negative infinity, such as in the limit of some real-valued functions. In some contexts such as complex numbers there are an uncountable number of different kinds of infinity. Generally I think just $\infty$ is fine for most purposes. Deco 18:43, 22 January 2006 (UTC)

Maybe this example will clarify the question... Don't you agree that the + sign should be used there? These are statements about plain real numbers, not a projected line, a Riemann sphere, cardinalities, non-standard analysis and all the other stuff (which are all very nice but have little to do with my question). -- Meni Rosenfeld (talk) 18:47, 22 January 2006 (UTC)

I don't agree. For the same reason we don't need to write +1 to distinguish it from –1, we don't need +∞ to distinguish it from –∞. -lethe ^talk 00:15, 23 January 2006 (UTC)

I don't see any harm in using +∞, except that it seems maybe a little pedantic. It does serve a colorable purpose in distinguishing +∞, not from –∞, but from "unsigned infinity". --Trovatore 00:18, 23 January 2006 (UTC)

I like +&infinity;, especially when writing down an integral or sum. Also helps to distinguish from unsigned or complex infinity. —Ruud 00:28, 23 January 2006 (UTC)

I once thought like lethe, but have since come to realize that, like Trovatore and Ruud said, you don't need to distinguish +1 from an "unsigned one", but you do need to distinguish $+\infty$ from unsigned infinity. So what do you say? Should we use $+\infty$ consistently for this purpose? -- Meni Rosenfeld (talk) 06:30, 23 January 2006 (UTC)

OK, the point that infinity can be signed or unsigned while finite numbers are not is well-taken. I'm still not sure of the absolute necessity for adherence to this convention here. Seems to me that it will always be clear in context which is meant. In short, I think it's OK for you to use this convention, but I don't believe it's necessary to ask that everyone use it everywhere in the project. -lethe ^talk 06:40, 23 January 2006 (UTC)

I agree that no harm is done by not following such a convention, but I do believe that it can only improve things. I have proposed the convention, discuss it here. -- Meni Rosenfeld (talk) 07:54, 24 January 2006 (UTC)

Division by zero

I am having a dispute with Rick Norwood regarding division by zero. The problem is that I want to write about structures where division by zero is possible, while he systematically tries to prove that defining division by zero is "wrong" and that you mustn't do it, because it leads to problems. I will appreciate your comments (either way) on the issue.

And while you're at it, I would also like to hear your opinions regarding the size of inline fractions in the article. -- Meni Rosenfeld (talk) 06:41, 23 January 2006 (UTC)

Technically, you can come up with you own theory, which defines division by zero through axioms somehow. However, I think you will have a difficulty proving consistency of your theory. (Igny 13:36, 23 January 2006 (UTC))

We already have wheel theory, which purports to be such a theory. But such things are better structured as 'see alsos' to the main article. Charles Matthews 13:47, 23 January 2006 (UTC)

If I had to invent such a theory myself, I probably would have encountered difficulties formulating it; Fortunately, the theories are well developed and it is well known what is or is not true. About the wheel theory, I don't know much about it, but I think it may indeed be too advanced to be discussed thoroughly in this article. But things like the Riemann sphere are certainly more than mere curiosities, and should be discussed in such an article. -- Meni Rosenfeld (talk) 20:04, 23 January 2006 (UTC)

Not really. There are places like birational geometry, rational map and so on, where it can better be put into context. Charles Matthews 13:45, 24 January 2006 (UTC)

Sets of sets

A new but promising editor, User:MathStatWoman, has written an article called sets of sets, apparently in response to some talk-page discussion that I can't really remember where to locate at the moment. I think the article has two major problems. First, it seems to be more a personal essay than a verifiable encyclopedia article. Second, I don't think it's really correct: It claims, essentially, that locutions like "collection of sets" are preferred over "set of sets" because of the Russell paradox. I don't think that's the reason at all; when people discuss sets of reals and collections of sets of reals, the Russell paradox is not remotely in the same time zone as the objects being discussed, which can all be coded in V_ω+2. The reason for preferring the word "collection" is that it helps to keep the types straight in the reader's mind (and for that matter, in the author's mind).

I really think the article should go to AfD, hopefully without any prejudice to MathStatWoman. Any thoughts on the matter, or alternative suggestions? --Trovatore 04:36, 24 January 2006 (UTC)

AfD for sure -lethe ^talk 07:59, 24 January 2006 (UTC)

I agree that, at least in some contexts (possibly most), "collection of sets" is used for clarity rather than for accuracy. But I can't see why it looks to you like a personal essay. In any case, call me an inclusionist, but I think it's worth having an article with this name. Perhaps some of the content should be removed, some can be disambiguated (something like "'collection' is sometimes used for clarity, and sometimes because it really isn't a set"), and perhaps some words about the simple fact that an element of a set can be itself a set, a concept that is difficult for some first-year students. -- Meni Rosenfeld (talk) 08:03, 24 January 2006 (UTC)

The article is problematic. I saw the it late last night just before I went to bed, and was too tired to do anything about it then. I had planned to contact User:MathStatWoman and discuss it with her this morning. I don't really think we need such an article and as it stands it is misleading and inaccurate — but I had really hoped to avoid AfD. I hope we don't end up alienating the author. Paul August ☎ 13:22, 24 January 2006 (UTC)

No offense taken; no, you have not alienated the author. :-) But indeed there is a reason for not declaring certain collections sets. Some groups of things are not sets. Agreed, there are some sets of sets that are ok, when logical inconsistencies or incompleteness does not come into play. But we probabilists often run headlong into difficulties with certain particular peculiar collections, classes, or families of sets (and with AoC, and with measurability problems, too, by the way) My suggestion: let's keep the article sets of sets for now, discuss the issue, and clean it up together. with references and examples. Seem ok to all of you? Thanks for the input. I like a good debate like this one. You were all polite and kind, and I appreciate that. MathStatWoman 15:37, 24 January 2006 (UTC)

You said:

we probabilists often run headlong into difficulties with certain particular peculiar collections, classes, or families of sets

What are these problems, and how does this article address or resolve the problems? linas 16:23, 24 January 2006 (UTC)

First, please let me preface the answer: The article on empirical processes is under development; anyone else who works in this field is welcome to contribute, of course; that would be excellent, in fact. But I am struggling with the markup language, so it takes me a very long time to add very little information. Now the answer: Anyway, once the article is expanded,it will be evident that the study of empirical processes involves classes of sets, and also collections of functions related to those sets. It is well known that functions are related to families of subsets, since a particular function, (e.g. indicator functions, important in empirical processes and statistics), often can be viewed as a subset; hence we would end up using sets that could contain themselves, or not contain themselves; hence a paradox unless we use terminology such as families, collections, or classes of sets. See, for example, Vapnik and Chervonenkis, Pollard's, Wellner's, R. M. Dudley's, and R.S. Wenocur's works in V-C theory, empirical processes, and learning theory...they always use terms "classes of sets or collections of sets or functions to avoid these paradoxes. In some cases, a class" of sets cannot be a set itself, or we have inconsistency. Hope that clarifies the issue a bit for now. I would like us all to work more on the article sets of sets rather than delete it. I can add references soon, if that would help. MathStatWoman 17:00, 24 January 2006 (UTC)

MathStatWoman, I'm going to have to call you on this claim that the Russell paradox is relevant to anything that comes up in probability theory. I just don't see it happening. The Russell paradox fundamentally arises from a confusion between the intensional and extensional notions of set; no doubt one could code that confusion into probabilistic language, but only in an attempt to turn probability theory into foundations, and I've never heard that probabilists were into that. If you're going to stick to this claim, please find a minimal example and explain it here. --Trovatore 17:28, 24 January 2006 (UTC)

I have to go to work/schoool now, so just a few quick words; no time for markup language; please forgive my using plain typesetting here. Please understand that this is not a joke; it is serious mathematics; I am not trying to play games here. In probability theory, the probability space Omega and the sample space X can be anything; its elements can be sets (or, equivalently, functions, which can be viewed as sets, e.g. all functions from set Y to {0.1) is equivalent to the collection of all subsets of Y, i.e. its power set 2^Y. We use indicator functions in empirical processes. To show that we need to restrict sets under consideration to V-C classes of sets, or uniform Donsker classes of sets, or P-Glivenko-Cantelli sets, etc...we need counterexamples that involve e.g. X being the class of all sets. Cantor's Paradox and Von Neumann-Bernays-Gödel set theory (in which we do not speak of sets of sets apply here. When empirical process article develops, all this will become apparent. Let's just make the sets of sets article better, or, as an alternative put it (cleaned up and referenced) into Von Neumann-Bernays-Gödel set theory, how does that seem? Talk to you later. gtg now MathStatWoman 17:58, 24 January 2006 (UTC)

The notion of proper class is discussed in several places, I think; I don't see any need for a new article
If you really meant to say that NBG doesn't use sets of sets, that's wrong. In fact all sets in an interpretation of NBG are sets of sets. Yes, NBG also has collections of sets that are not themselves sets.
I'm still extremely skeptical that you're going to be able to show us how the Russell paradox attaches to VC theory or probability theory. Please give a minimal example. --Trovatore 21:33, 24 January 2006 (UTC)

I believe that this article should be deleted. If something needs to be said about sets and classes it should be said in proper class or class (mathematics) (the considerations here are too elementary for NBG, I think). "Set of sets" is the wrong title, because sets of sets per se are ubiquitous and unproblematic. There might be some issues here which should be moved to proper class or class (mathematics), though -- after being clarified; the existing text is confusing. Randall Holmes 03:59, 27 January 2006 (UTC)

On looking at these articles, I think the proper context for a discussion of these issues would as I said be class (set theory) (which is the same article as proper class, class (mathematics)); adding some informal examples with explanation to this article would be the right way to achieve the author's apparent purpose. There are some technical points: in most mathematics, a finite set which is one of its own members (used in one of the examples) will not arise; in the standard set theory ZFC, no set is an element of itself. And in the standard set theory ZFC all sets without exception are sets of sets; sets of sets is not the right title. Like Trovatore, I would be very interested in seeing any relevance of this topic to probability theory (though I wouldn't be surprised if there were some; mathematicians are ingenious :-) Randall Holmes 04:11, 27 January 2006 (UTC)

I should also add, lest I seem too encouraging, that the only real content in the article sets of sets seems to be a discussion of Russell's paradox, on which there is already an article. I do notice that class (set theory) might (or might not) benefit from an informal summary of reasons why certain classes (the Russell class, the class of all ordinals) actually are proper classes, and this might do what is wanted in sets of sets. If there are specific applications of the set/class distinction in probability theory, these might make a subject for an article. Randall Holmes 04:17, 27 January 2006 (UTC)

another point: the mere possibility of having sets which are elements of themselves does not in itself imply any danger of paradox. Aczel's theory of non-well-founded sets has this kind of circularity (and I suspect this may be all that is needed in the theory of empirical processes) and doesn't come anywhere near needing proper classes or risking Russell's paradox. Applications of hypersets may be the issue here. Randall Holmes 04:19, 27 January 2006 (UTC)

Lethe for admin

In case some of you don't follow Wikipedia:Requests for adminship, I nominated one uf us, Lethe, for administrator, which, in my opinion, was long overdue. If you are familiar enough with Lethe's work, you can vote at Wikipedia:Requests for adminship/Lethe. Oleg Alexandrov (talk) 17:06, 24 January 2006 (UTC)

Mediation needed in big dispute at relation (mathematics)

There is a big argument at talk:relation (mathematics), with Arthur Rubin and Randall Holmes on one side, and Jon Awbrey on the other side. I did not study the matter in a lot of detail (and am not an expert in the matter), but it seems that Jon Awbrey is making things more complicated than necessary and is rather pushy at enforcing his version (judging from the edit history. Anyway, help would be very much appreciated. Oleg Alexandrov (talk) 18:57, 24 January 2006 (UTC)

Proposed changes to mathematics

I've proposed some changes to the "Major themes in mathematics" section of the mathematics article, see: Talk:Mathematics#Proposed changes to "Major themes in mathematics" section. Paul August ☎ 21:35, 24 January 2006 (UTC)

Question about bases

Hi all, Base (mathematics) gets very little (if any) traffic so I'd like to ask this here. The question is on Talk:Base (mathematics), at the bottom, about integers vs. numbers (please respond there as I'm not watching this page). I'm not a mathematician, just an enthusiast, so this is me asking experts for (knowledge and) advice with the article (be warned, it is unreferenced and possibly inaccurate). Thanks :-) Neonumbers 10:02, 25 January 2006 (UTC)

another problematic article

The article SuperLeibniz law seems to be complete nonsense. I would have put it on AfD, but a search makes it look like a superLeibniz law might be something real (see e.g. Poisson superalgebra). However all the hits seem to be Wikipedia reflections, and Poisson superalgebra doesn't give any clue as to a definition for SuperLeibniz law. Poisson superalgebra was written by User:Phys, who hasn't been around since November. Unless someone knows what a SuperLeibniz law is supposed to be, I still think AfD is where it's headed. --Trovatore 03:30, 26 January 2006 (UTC)

Oh, I should amend the claim that Poisson superalgebra doesn't give any clue as to a definition; it does in fact give an example. But it's not clear whether it's the only example, nor what would characterize any others. --Trovatore 03:32, 26 January 2006 (UTC)

I see a red link for the article you mention, and searching didn't turn it up either. Did someone speedy delete it already? -lethe ^talk 03:41, 26 January 2006 (UTC)

Ooops, I've found it SuperLeibniz Law here. -lethe ^talk 03:45, 26 January 2006 (UTC)

Ahhh, the thing that is mentioned in Poisson superalgebra is what I know as a graded derivation or an antiderivation. It's defined in derivation (abstract algebra). The stuff in SuperLeibniz Law is, as you suggest, patent nonsense. The question is whether we want to redirect or just delete. Is that name attested anywhere? -lethe ^talk 03:47, 26 January 2006 (UTC)

The notion of a super Leibniz law is a valid one, although what was SuperLeibniz Law was patent nonsense. The concept usually goes by the name of superderivation or graded derivation. If V is a superalgebra and D is a (graded) linear operator on V, then D satisfies the "super Leibniz law" if

$D(ab) = (Da)b + (-1)^{|a||D|}a(Db).\,$

I'll will amend these articles shortly. -- Fropuff 04:50, 26 January 2006 (UTC)

Yep, that's it. The Lie derivative, exterior derivative, and inner derivative satisfy that equation with degrees 0, 1, and –1 respectively. I've not heard it called a superderivation before, but it sounds like a reasonable enough name. -lethe ^talk 05:01, 26 January 2006 (UTC)

I added a section to derivation (abstract algebra). -lethe ^talk 05:16, 26 January 2006 (UTC)

I think the name graded derivation is a more general term applying to Z-graded algebras, whereas the name superderivation means a graded derivation of superalgebras. Maybe a separate article at graded derivation would be best, but I'm fine with a redirect to derivation for now. -- Fropuff 05:48, 26 January 2006 (UTC)

Isn't a superalgebra just a Z₂ graded algebra? -lethe ^talk 05:54, 26 January 2006 (UTC)

Yes it is, but one can have graded derivations on algebras with a more refined grading than just Z₂; e.g. the exterior algebra. It is not common to refer to the exterior algebra as a superalgebra (although it is one). More importantly, it is important to keep track of the more refined grading for linear maps. As you say, the exterior derivative and the interior product have grades +1 and −1 respectively, but as maps of superalgebras I would say they both have grade 1 (i.e. they are both odd). -- Fropuff 06:05, 26 January 2006 (UTC)

Right, right. I think I thought you made a complaint that you didn't actually make, now that I reread your complaint. I added graded derivation to that article, when really what we wanted was superderivation, which is a special case. And I didn't mention it the term at all.. Antiderivation is already there, which is pretty close, but not it. As for whether it should get its own article, I'm not opposed to the idea, but I'm not going to do it. I've got to think about dual spaces some more. -lethe ^talk 06:25, 26 January 2006 (UTC)

I think I thought you made a complaint that you didn't actually make. That's got to be the quote of the day ;) -- Fropuff 06:29, 26 January 2006 (UTC)

Appeal to clean up the page on "list of paradoxes"

There are so many items in the list of paradoxes that are not paradoxes. I commented on just a few examples on that page's discussion page. Could we please collaborate to clean up that page and remove what does not belong? MathStatWoman 09:05, 27 January 2006 (UTC)

No genuine paradoxes in mathematics. So we should just cut the maths? Actually it is OK by me for list of paradoxes to list things called a paradox, and then annotate/comment in individual articles as to the aptness of the name. Lists are mostly a navigational tool; 'added value' in terms of comment is good, but judge them mainly by the help they can give in fiding what you were looking for. In that sense, Category:Paradoxes might need to be more rigorous. Charles Matthews 10:30, 27 January 2006 (UTC)

So there are two ways of understanding the word paradox and people often talk past each other until they notice that they're using the word differently. Both of you seem to be using it to mean simply "contradiction". In my usage a paradox is an apparent contradiction. Paradoxes are much more interesting than contradictions. A contradiction just tells you that one of your assumptions is wrong, which is commonplace. A paradox tells you that something about your intuition is wrong, and that your intuitions need to be reconstructed to fit the facts. --Trovatore 15:21, 27 January 2006 (UTC)

W.V.O. Quine says the same thing in an essay on paradoxes. He identifies "veridical" paradoxes, which are arguments that prove apparently absurd results that are nevertheless correct, such as the Banach-Tarski paradox, and "falsidical" paradoxes, which are apparently-correct arguments that nevertheless prove false results, such as Zeno's paradoxes. -- Dominus 17:06, 27 January 2006 (UTC)

I'm not quite so ignorant. For example Smale's paradox is really Smale's counterintuitive result? But Bertrand's paradox is really a verbal trick about 'uniform'? There is a bit of history on this, monster barring and so on. Charles Matthews 16:43, 27 January 2006 (UTC)

I didn't mean to imply you were ignorant. But what can it mean to say there are no genuine paradoxes in mathematics? (As I said on Talk:List of paradoxes, "genuine paradox" puts me in mind of "genuine faux pearls", a bonus offered on TV ads for those who call now.) --Trovatore 16:50, 27 January 2006 (UTC)

No contradictions in a consistent formal system. But 'paradox' actually connotes only semi-formalised reasoning. Charles Matthews 08:29, 28 January 2006 (UTC)

Article intro text

I'm sure this has come up before, but I'd like to ask - what thought has been given to how "technical" the first paragraph of maths articles should be. I'm of the opinion that the introduction should try only to explain what an interested non-mathematician would understand and find useful - what it is, why it's important, and what it's used for, all in non-technical terms. The detailed technical information can follow later. What do you think? --Khendon 21:10, 28 January 2006 (UTC)

Non-technical is always a great goal. But it may be a challenge. It took an hour of rewrites to get the first line of the dynamical systems article. And I am not sure how useful it is. It is very tempting to say: a dynamical systems is a tuple [M, f, T] where M is ... There are many technical reviews available on the WWW, but I feel there is a lack of non-technical reviews. The reader I try to keep in mind (but often loose) is the college freshman. XaosBits 23:52, 28 January 2006 (UTC)

Right. It is good for the intro to be motivational. See also the math style manual. Oleg Alexandrov (talk) 23:55, 28 January 2006 (UTC)

One should not try and "dumb down" articles too much. It is important to make sure the article explains everything following from the article (such as any further definitions, concepts, etc that need to be made), but the article should not spend time trying to teach concepts that a reader should already be familiar with. Motivational explanations and examples are a Big Plus. Dysprosia 08:26, 29 January 2006 (UTC)

I agree that the article as a whole should not be "dumbed down". However, I think there are two readers of maths articles - the casual reader who's heard the word "topology" and wants to know what it means, and the mathematician. I think we should cater to both --Khendon 09:41, 29 January 2006 (UTC)

It's important to cater for both sure, but we shouldn't sacrifice "encyclopediality" (to coin a phrase) to do so. Dysprosia 13:01, 29 January 2006 (UTC)

Does the Wikipedia model really work for mathematics?

I am developing a fundamental doubt after spending time watching relation (mathematics) and function (mathematics). I don't see how we can possibly have sensible articles on core concepts on whose definition everything else depends unless someone competent writes them and they are then frozen and edited (by a manager or by a limited class) after consultation only. This doesn't apply to all topics, but these two articles (for example) are about ideas about which many people have ill-informed, strongly held ideas and about which other people, perhaps not so ill-informed, have ideas based on philosophical or pedagogical ideas which deviate too far from the norm for easy accommodation. It was interesting to be able to write an article on New Foundations for people to read -- this is unlikely to attract the attention of too many people of the categories mentioned; articles about obviously technical subjects are not usually subject to this kind of problem, and seem to look pretty good. But central ideas of mathematics (especially ones about which silly statements are prevalent in low-level textbooks or in the popular literature) must require a constant painstaking watch which in the end may not be a sensible use of the time of competent people. (Jon Awbrey should not necessarily assume that I am referring to him). Maybe this does work out in the long run, but I'm certainly finding a watch on these articles to be much less productive and much more frustrating than watching technical articles in set theory... Randall Holmes 02:33, 29 January 2006 (UTC)

Welcome to the real world. :) Randall, both you and Jon are rather new, and I believe that's part of the problem (I remeber my bitter fights with Linas a year ago :) Yeah, the Wikipedia model has its advantages and disadvantages, takes a while to get used to it, and yes indeed, constant watch and occasional frustrations are part of the game. Sorry I can't say something more meaningful, hopefully others will have better insights. Oleg Alexandrov (talk) 06:57, 29 January 2006 (UTC)

Yes, well, Randall none-the-less does bring up a valid point. My response has been to ignore articles on pop topics, but this is not really a "good" answer. I don't know the answer, but direct interested parties to Wikipedia:Stable versions linas 17:06, 29 January 2006 (UTC)

Mirabile dictu, both articles which are bothering me are looking mostly correct today, though the text is becoming increasingly dense and qualified... Randall Holmes 21:57, 29 January 2006 (UTC)

GSL GFDL Copvio problem.

Please see discrete Hankel transform. The article incorporates text taken from GSL, which is GFDL'ed. However, the GSL license has "invariant front and back-cover texts" which the copy did not preserve, resulting in a copyvio dispute. Surely WP has a GFDL sources policy? I don't understand that policy, but links to where it is explained would be handy. linas 17:11, 29 January 2006 (UTC)

Another small step towards MathML support in MediaWiki

Jitse and I have been making progress with MathML support in MediaWiki.

Try out the test wiki.

See also the announcement at the village pump, and our page on Meta.

Please direct all discussion to the talk page on Meta.

Dmharvey 01:50, 30 January 2006 (UTC)

You da' man, David! Major kudos for working on this. I really hope blahtex makes it into MediaWiki someday soon. I'm happy to help out testing. -- Fropuff 02:17, 30 January 2006 (UTC)

I am looking forward to the day when math on Wikipedia will look good, when we won't worry about \, vs \! to PNGfy things, when html and TeX live in peace and harmony, blah, blah, blah... Oleg Alexandrov (talk) 03:41, 30 January 2006 (UTC)

Oleg, given your comments on MathML in the past, I'll take that to be your way of trying to sound encouraging :-) Dmharvey 04:14, 30 January 2006 (UTC)

I never had anything gainst BlahTeX or MathML. It is just I was (and still am) very skeptical about the pace of introduction of MathML and the timing of when we won't need to worry about PNG and HTML and all that. My skepticism is based on my past experiences with other (cool!) things. But you are doing great work, and I hope things will work better/sooner than I think. :) Oleg Alexandrov (talk) 21:16, 30 January 2006 (UTC)

Scepticism is good, action is better. -- Jitse Niesen (talk) 22:10, 30 January 2006 (UTC)

You've got to admit that at least we look a bit better than PlanetMath... Dysprosia 10:48, 30 January 2006 (UTC)

I'm still holding my breath for Safari to implement MathML before I get excited. -lethe ^talk 11:20, 30 January 2006 (UTC)

Me too. Paul August ☎ 19:38, 30 January 2006 (UTC)

That's true. At least HTML/PNG is compatible on nearly *all* browsers. Dysprosia 11:53, 30 January 2006 (UTC)

Don't get me wrong. I'm looking forward to being excited about it. I was even toying with the idea of trying to pitch in to MathML implementation in Safari. I think one day a lot of browsers will have it. -lethe ^talk 12:26, 30 January 2006 (UTC)

I didn't really mean it like that; the fact that MathML isn't supported in Safari highlights the problems a lot of people may have if we eventually switch to MathML. I tend to use Lynx or w3m a lot sometimes in browsing things, and MathML would be unreadable in those circumstances. Dysprosia 00:35, 31 January 2006 (UTC)

I'm of the opinion that we should push for MathML implementation in MediaWiki as soon as possible, regardless of whether or not major browsers such as IE or Safari have native MathML implementations (the PNG/HTML option will still be available to those users). In fact, I think having a high profile site like Wikipedia making heavy use of MathML will be a major motivation for browser developers to implement MathML in their browsers (lest everyone switch to Firefox/Mozilla). -- Fropuff 19:55, 30 January 2006 (UTC)

I like this argument a lot. -lethe ^talk 23:51, 30 January 2006 (UTC)

In fact, the process that Fropuff is alluding to has already started happening (sort of). At the time I released the previous version of blahtex (August 2005), MathML development in gecko (i.e. mozilla/firefox) had been close to moribund for a few years. But as soon as they heard that wikipedia was planning MathML support, a few developers there started fixing all kinds of bugs, and indeed fixed the majority of the really nasty ones that I specifically pointed out to them. I haven't yet seen any evidence of other browsers getting their act together, but maybe with a working demo wiki now available, they'll take more notice. Dmharvey 21:14, 30 January 2006 (UTC)

Thats encouraging. Maybe wikipedia will be the killer app which makes maths on the web finally happen. Its been do-able for at least 10 years now (since the geometry center folks were developing WebEQ) but its never been a priority and never got that critical mass. I'm all for a push for MathML in MediaWiki, might be able to help with coding. There is a MathML (if possible) option in 'my preferences', don't know if it has any functionality. --Salix alba (talk) 22:09, 30 January 2006 (UTC)

The "MathML (experimental)" option presently only produces MathML for the very simplest things like "x + y = 2". Give it a superscript and it stares back blankly at you. But that's besides the point: it is also necessary to deliver the entire document as XHTML, get the browser recognising the MIME types, and a few other things, without breaking browsers that don't understand any of that. Currently MediaWiki doesn't do these things. Dmharvey 22:39, 30 January 2006 (UTC)

BlahTex now work in Internet Explorer (Win) with the MathPlayer plugin. I've also created a page meta:Blahtex/Compatibility to list how well it works with different browsers. Testing of the blahtex wiki welcome. --Salix alba (talk) 15:22, 5 February 2006 (UTC)

Definition of "computational mathematics"

The term "computational mathematics" turns up over half a million Google hits; most seem to come from names of institutions or courses. I've thought of starting a stub, but I'm not sure how to define the term and relate the field (if there is one) to others. My intuitive understanding is that, roughly speaking, computational mathematics is to mathematics what computational science is to science; i.e. it comprises the study and/or use of algorithms for the purposes of mathematics (including discrete and symbolic mathematics, in addition to numerical analysis). Is this correct? Fredrik Johansson - talk - contribs 19:09, 30 January 2006 (UTC)

Good luck with coming up with a definition. I'd say that it's the study of algorithms for mathematical problems, regardless whether the ultimate application is in mathematics or without. My list of fields which can be considered part of computational mathematics: obviously numerical analysis (including optimization and approximation theory), symbolic mathematics, computational number theory, learning theory, computational geometry, image processing, and some complexity theory. But generally it is very hard to define a research discipline, especially one of these fashionable multidisciplinary ones. -- Jitse Niesen (talk) 20:13, 30 January 2006 (UTC)

Springers journal has a nice def [2]

Foundations of Computational Mathematics (FoCM) publishes research and survey papers of the highest quality, which further the understanding of the connections between mathematics and computation, including the interfaces between pure and applied mathematics, numerical analysis and computer science.

a non copyvio rewrite of that could be a good place to start. --Salix alba (talk) 20:40, 30 January 2006 (UTC)

Don't bother rewriting it - just quote it in the intro. I think this will make a great high-level topic for linking lots of more specialised areas - it might even be a good idea to link it directly from Mathematics. Deco 00:39, 31 January 2006 (UTC)

Yes please; cf Talk:Mathematics#Request for link to mathematical computing. Hv 16:53, 31 January 2006 (UTC)

I'am a bit confused by this discussion. Fredrik, you said above, that you understand it similarly to computational science, so, by this analogy, do you mean application of computational methods to mathematics itself (like experimental mathematics and automated theorem proving)? But then, what other people said, it seems that they mean study of computational methods mathematically, regardless of the application field. So which one of these two possibilities is "computational mathematics"? Samohyl Jan 19:21, 1 February 2006 (UTC)

I mean the former. I don't think "study of computational methods mathematically" would be correct; nor does this phrase, as far as I can tell, agree with what others here have suggested. Fredrik Johansson - talk - contribs 23:14, 1 February 2006 (UTC)

Actually, I meant the second of the possibilities that Samohyl mentioned. On rereading my comment, I still agree with myself ;) -- Jitse Niesen (talk) 23:20, 1 February 2006 (UTC)

And now I'm confused ;-) I'm reading "study of computational methods mathematically" as "mathematical study of algorithms", which seems to be the opposite of "algorithms for mathematical problems" as you said first. Fredrik Johansson - talk - contribs 23:29, 1 February 2006 (UTC)

Sorry, let me try to explain using an example. For weather forecasting, you need to make a mathematical model of the atmosphere (basically a PDE), gather the initial data, solve the PDE, and interpret the result — apologies to the people involved for the huge simplifications. The step of solving the PDE is part of computational mathematics, in my interpretation of the term. The problem you are solving is mathematical on one level (a differential equation), but physical on another level (forecasting the weather). On the other hand, I'm not so sure that automated theorem proving is computational mathematics, because there is no computation involved.

I think the definition from JFoCM is a good start, especially since it is verifiable and does not involve the comments of random Wikipedians. -- Jitse Niesen (talk) 16:15, 2 February 2006 (UTC)

I think the best way to view it is in the context of computational modeling:

Step One- Model Setup/Knowledge of the Problem: Engineer/Scientist. Requires thorough knowledge of the physics etc (i.e. can fluid flow be treated as potential flow or not = engineer not mathematician). Sets up the basic equations to be solved.

Step Two- Formulation of the numerical scheme and method of solution (espicially method of solving large matrix equations): Mathematician. This is, in my mind, the biggest aspect of Computational Mathematics. Usually, mathematicians design this part and Engineers/Scientists scan the literature and use those methods developed (ex GMRES, SOR, etc).

Step Three- Implementation of the numerical scheme: Computer Scientist. Here is the science of actually writing the code on the computer, implementing massively parallel computations, etc. Best done in the hands of a computer scientist.

Step Four- Data Analysis/Insight: Engineer/Scientist. Running the simulations, coming up with conclusions, verification of data.

Of course sometimes, one person does everything, but in the "ideal world" that would be how the process works and explains the specific role/ability each type of scientist can bring to the table.

Differentiation of functions of matrices with respect to matrix

Moved to talk:Matrix calculus'. 09:34, 2 February 2006 (UTC)

Functions of matrices

Do we have an article on functions of matrices? I can see some specific cases like Matrix exponential but not a general discussion. Also (and this question overlaps) what about convergence of series of matrices (such as the theorem that a pwoer series of matrices converges if it converges for all of the eigenvalues of the matrix)? Thanks. --Zero 03:58, 2 February 2006 (UTC)

I'm glad to see that you volunteer to write an article on functions of matrices ;) The closest we have is holomorphic functional calculus, but that's probably too abstract. Look at matrix logarithm, somewhere near the bottom, for how it applies in concrete situations. -- Jitse Niesen (talk) 13:21, 2 February 2006 (UTC)

The power series thing is holomorphic functional calculus, but is also clear enough from Jordan normal form, I guess. Charles Matthews 14:08, 2 February 2006 (UTC)

History of manifold

Hey, if there are any experts reading this talk page, it would be great to see the Manifold#History section fleshed out. Thanks. –Joke 04:24, 2 February 2006 (UTC)

It's not so bad now. Query what Weyl actually did in his book on Riemann surfaces, though. Charles Matthews 14:15, 2 February 2006 (UTC)

Surely it is possible to say more about it than that Riemann and Weyl contributed? What about its influence on other branches of mathematics, and vice versa? What about the relationship to physics? What about the development of modern differential geometry, the contributions of Sophus Lie, etc...? –Joke 15:22, 2 February 2006 (UTC)

Yes, always more to say. However the story about the basic, underlying manifold idea is not the same as that of the history of differential geometry, or of Lie groups. (In a strange way, the technical development of manifolds lagged behind.) Charles Matthews 15:32, 2 February 2006 (UTC)

I agree, but the manifold did not develop in a vacuum. Well, maybe if you believe in the Hartle-Hawking state it did. The page differential geometry and topology has no reference to any history either. My point is that saying Riemann did this, then Poincaré conjectured, then Weyl made it abstract seems a little haphazard. Maybe I should try and do some research. –Joke 16:03, 2 February 2006 (UTC)

Template for deletion

Template:Axiom

Seems pretty useless to me. - Gauge 23:41, 4 February 2006 (UTC)

I would think it would be a nice template if it weren't so goddamn ugly. All math books have demarcation for theorems, axioms, definitions, etc. Unfortunately, I don't see how this can be accomplished with current wiki markup. Maybe someday, but not today; this one's gotta go. -lethe ^{talk +} 00:35, 5 February 2006 (UTC)

What appearance would you like? Wiki markup is not the only option; CSS is more powerful. --KSmrq^T 01:24, 5 February 2006 (UTC)

CSS or not, adopting those boxes in any way will make Wikipedia look like American calculus books; with each theorem, lemma, definition, and important formula, in its own shiny box, with different colors for each and so on. Gosh, I hope we don't get there. Oleg Alexandrov (talk) 02:03, 5 February 2006 (UTC)

Agree with Oleg; American calc textbooks are very ugly in their presentation. I don't think we want to be emulating that. If you have lots of axioms, having boxes around each would get out of hand really quickly. I don't see any compelling need to have such a template. - Gauge 06:34, 6 February 2006 (UTC)

If we had something, it would have to be at most an indentation with a boldfaced Theorem inline heading, as is common in textbooks. Putting things in boxes is just ugly (and this particular box is uglier than most). -lethe ^{talk +} 02:42, 5 February 2006 (UTC)

I think it's quite a pretty box. All those purple dots. Look:

Template:Axiom Dmharvey 02:52, 5 February 2006 (UTC)

The template takes only one argument at present, which would have to change if the axiom name is to be bolded automatically. But indentation (left and right), bold, and italics should be possible otherwise.

Axiom 3 (Composition): Given f:a→b and g:b→c, the composition g○f:a→c exists.

This is merely an example. Styling details can be tweaked per taste. --KSmrq^T 04:30, 5 February 2006 (UTC)

I don't think colored text is a good idea. Simply indenting an axiom and making italic should be enough I would guess. Oleg Alexandrov (talk) 04:55, 5 February 2006 (UTC)

I'm not recommending color, only presenting it as an option for people who like purple dots. ;-)

Also, the style can do more than indent. Observe a longer "axiom":

Axiom 9 (Greek): Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.

Notice the "indentation" of the right margin as well as the left; again, an option. --KSmrq^T 07:52, 5 February 2006 (UTC)

I think all axioms in boxes should be stated in Latin as above ;-) - Gauge 06:34, 6 February 2006 (UTC)

This is my little typographers' joke. The text of the "axiom" is explained at lorem ipsum. And "greeking" means either "to display text as abstract dots and lines in order to give a preview of layout without actually being legible", or to fill with meaningless text like "lorem ipsum". Of course, I would never actually use the florid style in the example, with its ugly and distracting background color and small caps. --KSmrq^T 16:34, 6 February 2006 (UTC)

What, pray tell, is wrong with a simple bullet point? Dysprosia 08:16, 5 February 2006 (UTC)

For one thing, you can't put math tagged equations in a bulleted item without resorting to HTML. -lethe ^{talk +} 10:00, 5 February 2006 (UTC)

$\cos{x}+3\,$

Looks like you can? Dysprosia 10:25, 5 February 2006 (UTC)

That's fine for a list of formulas, but doesn't work for a theorem or axiom. See this:

Theorem 1: A right triangle with sides a, b and c obeys

$a 2 + b 2 = c 2$ where c is the hypotenuse and a and b are the legs.

or with the usual indentation for math tags:

Theorem 1: A right triangle with sides a, b and c obeys

a 2 + b 2 = c 2

where c is the hypotenuse and a and b are the legs.

It sucks. When I want to make things like this, I resort to HTML tags. And as Jitse will tell you, I often forget to close them. But you get this:

Theorem 1: A right triangle with sides a, b and c obeys

$a 2 + b 2 = c 2$

where c is the hypotenuse and a and b are the legs.

If there were a template that would give some indentation like that, but without the bullet point, and put theorem, definition, axiom according to an argument, I would consider using it. -lethe ^{talk +} 11:17, 5 February 2006 (UTC)

Theorem 1: A right triangle with sides a, b and c obeys $a 2 + b 2 = c 2$ where c is the hypotenuse and a and b are the legs.

This looks like it works fine. One doesn't have to always indent with math tags unless it's supposed to be displayed. And if there is content that needs to be displayed, it shouldn't be in the one line.

Theorem 1: A right triangle with sides a, b and c obeys

$a^2+b^2=c^2\,$

where c is the hypotenuse and a and b are the legs.

In the second case, observe that using another colon to indent appears to solve the indenting problem. However, there appears to be a minor spacing issue there...

The template option sounds like a good idea, by the way. Dysprosia 11:25, 5 February 2006 (UTC)

your first case is not so great because it has the math png inline. The second one is a bit awkward, but it would serve if nothing else were available. But the html tags are available and do better in my opinion. Anyway, a nice template might be nice. -lethe ^{talk +} 12:13, 5 February 2006 (UTC)

That's if you use the PNG always option. I don't. Dysprosia 12:19, 5 February 2006 (UTC)

To play with the concept I created a template Template:Pfafrich/Axiom which has a configurable style option so the look can be changed.

no style same as a blockquote

Theorem 1: A right triangle with sides a, b and c obeys

$a^2+b^2=c^2\,$

where c is the hypotenuse and a and b are the legs.

user defined style

Theorem 1: A right triangle with sides a, b and c obeys

$a^2+b^2=c^2\,$

where c is the hypotenuse and a and b are the legs.

default style

Theorem 1: A right triangle with sides a, b and c obeys

$a^2+b^2=c^2\,$

where c is the hypotenuse and a and b are the legs.

It turns out the axiom box fails when used with * its just that TfD notice hides this. So in a wiki * bullet point we have

Theorem 1: A right triangle with sides a, b and c obeys

$a^2+b^2=c^2\,$

where c is the hypotenuse and a and b are the legs.

The green box should surrond the whole theorem. It fails because MediaWiki does template substitution before interpreting the * bullet syntax. MediaWikis does the simplest thing when it finds a * - it just puts li tags at beginning and end of line, closing whats necessary. The upshot is that its imposible for a template to box multiline theorems in a * bullet point. Using html <li> will work.

Theorem 1: A right triangle with sides a, b and c obeys

$a^2+b^2=c^2\,$

where c is the hypotenuse and a and b are the legs.

--Salix alba (talk) 23:28, 6 February 2006 (UTC)

I find all the frameboxes, regardless of how they look, to be not so pleasing. In my opinion, they give an unprofessional/naive appearance to the Wikipedia pages, while not helping in understanding the concepts. Neither mathworld nor planetmath use them, nor any books or math publications (as far as I am aware), save again for American calculus and college algebra books. If one really wants an axiom to stand out, I would think indenting it would do a better job. Oleg Alexandrov (talk) 03:49, 7 February 2006 (UTC)

I agree with Oleg that outlined boxes are terrible. Why are you making us look at them? Oleg is right, indentation should be enough. But of course a template might be a nice way to accomplish an indentation (because of the math tags issue). Your first one, the one with no outline, I might consider using that. Maybe I should change the axiom template and then change my vote. -lethe ^{talk +} 04:12, 7 February 2006 (UTC)

Lethe is right, why are you making us look at them? Oleg Alexandrov (talk) 04:21, 7 February 2006 (UTC)

I agree with the both of you. A bullet point suffices. Dysprosia 11:17, 10 February 2006 (UTC)

Copula (statistics)

Can someone take a look at this article, specifically the value of theta at the end of the Archimedean copula subsection? A couple of months back, it said theta=+1. I looked there, and though I don't know the topic, it seemed to me it had to be -1. I changed it and marked it as uncertain. Today I noticed that an anon with no other edits has changed it to theta=0. Once again, I think that's likely wrong, but I don't have the knowledge or time to fully think it through. Can someone check? I want to be sure we don't have some sneaky vandalism happening. Martinp 19:06, 7 February 2006 (UTC) (a lapsed mathematician)

0 it is.

$\lim_{\theta \to 0}(a^\theta+b^\theta-1)^{1/\theta} = a \cdot b$

Arthur Rubin | (talk) 19:57, 7 February 2006 (UTC)

Good. Thanks. That's an interesting limit, btw. Would make a good exam question... Martinp 15:40, 8 February 2006 (UTC)

New stub cat (topology)

Following prescribed discussion, I've created a new stub category, {{topology-stub}}. Assistance in populating it would be appreciated (a lot of articles marked with {{geometry-stub}} are really topology, and there are many articles marked with just {{math-stub}} that are topology). --Trovatore 19:29, 7 February 2006 (UTC)

Proofs and derivations

In many of the pages on wikipedia, articles go over proofs and derivations of forumlae and other such things. Most of the time I don't need a proof, and in some cases the proof obscures the end formula. I think a very clean and elegant way to include proofs would be to link to a separate page that goes through a proof or derivation. This way, an article can be kept uncluttered and clean, while being complete and non-mysterious. (btw, is this the wrong place for this suggestion?). I'd like to know if anyone feels the same way I do. Fresheneesz 22:01, 7 February 2006 (UTC)

We've had previous discussion on this. Basically proofs should only be here if they have some merit or interest. Charles Matthews 22:07, 7 February 2006 (UTC)

See Wikipedia:WikiProject Mathematics/Proofs for discussion, and the Math_style_manual#Proofs for the policy. Oleg Alexandrov (talk) 22:51, 7 February 2006 (UTC)

Here are a few examples like what you suggested: Proofs of Fermat's little theorem, Proofs of Fermat's theorem on sums of two squares, Proofs of quadratic reciprocity. I'm sure there are plenty of others. Dmharvey 03:54, 8 February 2006 (UTC)

Dmharvey references the very finest proofs, those that are well-enough written to be deserving of real articles. By contrast, the dirty, ugly ones that got ripped out of articles can be found in Category:Article proofs. This is, I believe, what you are talking about. linas 04:26, 8 February 2006 (UTC)

So would it be ok if I randomly snatch proofs from articles, and put them in their own page, if I think the page they're on would be more readable with just a link to the proof? Fresheneesz 21:29, 8 February 2006 (UTC)

If you think it improves readability, be bold! Dmharvey 22:27, 8 February 2006 (UTC)

I think I have nothing to do here

I was hoping to help in the areas that I like (not abstract algebra), but all of these are full. Only abstract algebra articles are available to give a respectable edit, the problem is: I'm really not interested in abstract algebra but I want to contribute here, what should I do. juan andrés 03:32, 8 February 2006 (UTC)

I hardly think any area is "full"! However you would be a pretty unusual sixteen-year-old if you could just pick mathematical topics at random that you know well, and easily find important subjects that don't already have articles. Why don't you start by looking at some stub articles, and seeing if you can expand them? You don't necessarily need to already know the material you'll be adding; looking it up is considered better procedure anyway, and as a byproduct you'll learn some interesting things.

Look at Wikipedia:WikiProject Stub sorting/Stub_types#Mathematics to see the various stub categories listed, pick something that looks interesting, and have fun! --Trovatore 03:41, 8 February 2006 (UTC)

There are 300+ articles in Category:Elementary mathematics and its subcategories, and almost all are in poor condition, are poorly explained, are missing details, etc. Do not be mislead by the word "elementary": while all of these topics can be first taught/introduced at an elementary level, many also can lead to very sophisticated mathematics. My favorite example is the torus, which appears in many many places, including leading edge research. If you can take some elementary topic, and fill it out so that it connects with higher math, that would be excellent. linas 04:20, 8 February 2006 (UTC)

Per linas's comment, also don't forget that "elementary mathematics" doesn't mean the same thing as "mathematics that is easy to explain". I should spend some more time around there some day. Dmharvey 05:09, 8 February 2006 (UTC)

Thank you. That's what I was talking about. Sorry if I could not answer but I was very busy with school homework. I know is very difficult to explain because you have to go back to the basics. juan andrés 20:21, 18 February 2006 (UTC)

blahtex 0.4.1 released

No bug fixes today, but one very nice new feature: correct vertical alignment of PNGs. This is something that PlanetMath has that I think is very cool (actually it's their underlying converter LaTeX2html that does it), but I'm using a different, somewhat experimental strategy. :-)

Try it out on the interactive demo, and also have a look at what it does with the equations from Wikipedia (which I've just updated from some more recent database dumps).

It's not enabled yet on Jitse's test wiki. It might be some time before it gets enabled, not because it's technically difficult, but for other semi-technical reasons that might be discussed another day...

Also, the blahtex manual is now online in HTML format, should make it easier to read.

Enjoy, Dmharvey 04:06, 9 February 2006 (UTC)

This is totally awesome. Deco 04:16, 9 February 2006 (UTC)

Blahtex Compatibility Project — seeking volunteers

Hi math(s) people,

As you all know, Jitse and I are working on developing some MathML support for Wikipedia/Mediawiki. For this to actually happen, a lot of things have to go right simultaneously.

One of the issues we need to deal with eventually is that blahtex's input syntax is ever-so-slightly different from texvc (i.e. the current input syntax on wikipedia). In fact, blahtex's input parsing is much closer to TeX's parsing than texvc is. Here are some examples of where they differ:

The characters $ (enter/leave math mode) and % (denoting comments) are illegal in blahtex, but texvc treats them as literally the $ sign and the % sign. The correct TeX for these is \$ and \%.
You can leave out curly braces in texvc sometimes, where TeX wouldn't allow it. For example: "\hat\overrightarrow x" is OK on wikipedia now, but not cool in TeX or blahtex; it should be "\hat{\overrightarrow x}". Similarly "x^\left( y \right)" is legal in texvc but not in blahtex or TeX.
Because of the way TeX handles macros, certain constructs like "x^\cong" are illegal in TeX (needs to be "x^{\cong}), even though other ones like "x^=" are ok.

These differences between blahtex and texvc are entirely deliberate. The idea is that we should make it as easy as possible to translate wikitext into other formats, using standard tools. The closer we are to TeX, the easier it is to do this.

So the question is: if and when we ever switch over to using blahtex for MathML support, what will happen to all the existing equations on Wikipedia that break under blahtex?

The good news is that only about 1,000 out of 180,000 equations on Wikipedia (this data includes the ten largest language versions) have problems, and of those, most of them fall into easily defined categories, like the $ and % sign issues described above. A complete list can be found on the blahtex website (http://blahtex.org) under the "Wikipedia samples" section.

I propose that we fix these equations, one by one, over the next few months, or however long it takes, and I would like to ask people here to volunteer to help out with the effort. Probably some of it can be automated (it's easy to change $ into \$) but some of it probably requires some human attentiveness.

This is not an entirely trivial task, and I think it would be best if someone volunteers to organise the effort. I don't have time myself to organise it right now; besides real life, I have code to write! This "Director of Blahtex Compatibility" might consider doing the following: setting up a page where people can volunteer to fix up "blocks", based on (say) the md5 of the equation. If you need the list of equations in a different format, I can provide that; I have code that can extract it from the Wikipedia database dumps fairly easily. Also they might want to write a page explaining what this is about, so that people can use a link to the explanation page in their edit summary. And they might want to find someone willing to write a bot to handle the automate-able parts of the project.

Please put up your hand if you're willing to organise this. And of course please speak out if you think this is a really stupid idea. Dmharvey 18:05, 9 February 2006 (UTC)

I'm willing to take responsibility for dewiki.--gwaihir 00:11, 10 February 2006 (UTC)

The other major problem is malformed html tags written directly in (i.e. not using MediaWiki code). For example

<ul>
<li>line one
<li>line two
</ul>

this is legal html but not legal xhtml, and it breaks the BlahTex wiki. It might be possible to integrate HTML-Tidy into the code so that we get pure xhtml out, but its going to be a major problem. Malformed html abounds for example Help:Formula had an extra </table> tag (now fixed on meta).

I might be up for helping with compatibility (director sounds too grand).

Testing on various platforms also appreciated. --Salix alba (talk) 00:31, 10 February 2006 (UTC)

Thanks Gwaihir.

The issue raised by Pfafrich (Salix Alba) concerning malformed HTML is an important one (a *very* important one), but not on topic :-). Here I'm only talking about the stuff inside <math> tags. Dmharvey 00:51, 10 February 2006 (UTC)

I suppose I can answer Pfafrich's point a little better here. HTML tidy is already integrated into mediawiki. But it's switched off on blahtexwiki at the moment, because HTML tidy doesn't like math tags. Jitse is working on a clean solution to this. So it's not as big a problem as it sounds. Not easy, but not insurmountable. Dmharvey 01:10, 10 February 2006 (UTC)

Fixed occureces of $ in main article namespace (a few left in Talk and old ref desk) see User:Pfafrich/BlaxTex $ bugs for all occurences . A possible earier way round the problem is to search for malformed latex from the database dumps, a relatively simple grep and sed found all the $'s. --Salix alba (talk) 03:50, 10 February 2006 (UTC)

Pfarich, nice work. We need that done on the other languages too :-) I'm concentrating on the ten largest ones: en, de, ja, fr, it, es, pt, pl, sv, nl. Maybe this will help: I've put up a list of all the problem equations (i.e. all the ones I have listed at blahtex.org) in a simple text format at http://blahtex.org/errors-20060203.txt. Be careful: if you feed the data to a machine, keep in mind that some entries have more than one web address listed; use the "-----" line to work out where. Let me know if a different format would be more convenient. Dmharvey 14:01, 10 February 2006 (UTC)

Is this the right place to ask specific questions (like: what's wrong with $x\not\subset y$ ? Error message given here reads: "No negative version of the symbol(s) following "\not" is available"; but TeX doesn't complain).--gwaihir 10:55, 10 February 2006 (UTC)

Yes it is the right place to ask. The answer is: that's a bug in blahtex, and it's on my list to fix. Don't worry about those ones for now. Thanks. Dmharvey 14:01, 10 February 2006 (UTC)

Update: I've corrected this behaviour for blahtex 0.4.2. This particular one (\not\subset) will be translated correctly now, and I've also added all the others that have specific MathML characters associated to them. If you try one that blahtex doesn't know (like "\not\partial" which occurs in fr:Matrice de Dirac), it will now only give up on the MathML output, and will still succeed for PNG output. A similar issue is errors like "The symbol "1" is not available in the font "bb"", which should give you $\mathbb{1}$ . The updated behaviour is that it gives up on the MathML output but still does the PNG output. This is not ideal, but it's something I will revisit later. Dmharvey 22:44, 10 February 2006 (UTC)

Well, \mathbb1 is nothing more than a dirty hack for some missing macro/mathchardef. It should not work. If this symbol is needed, a corresponding command should be made available.--gwaihir 23:34, 10 February 2006 (UTC)

Well said. This is why it's not a priority. Soon I will expand coverage of symbols to get as much as possible of LaTeX and AMS-LaTeX. Dmharvey 23:39, 10 February 2006 (UTC)

My own view would be to have BlahTex be as compatible with texvc as possible, and introducing the feature which allows it to be more compatible with TeX (and less wtih texvc) later. That because having MathML be accepted and working on Wikipedia would already be hard enough, thus, worrying about slight incompatibilities with the existing system would be an unnecessary distraction. Oleg Alexandrov (talk) 20:08, 10 February 2006 (UTC)

I agree, but it's a fine line to be walking. The earlier versions of blahtex (0.2.1... or perhaps even earlier ones that I never released) were in fact more compatible with texvc, because they used a yacc-based parser, as texvc does. But I discovered that to be able to do more interesting things, this approach had to be abandoned. On the other hand, blahtex has a command line option "--texvc-compatible-commands" which enables use of all of the texvc commands which are not standard TeX/LaTeX/AMS-LaTeX. This is enabled on Jitse's wiki, and I expect it to be enabled if blahtex ever gets deployed on the real thing. Here's the list of commands, i.e. commands that work on wikipedia but in no latex installation that I know of: \R \Reals \reals \Z \N \natnums \Complex \cnums \alefsym \alef \larr \rarr \Larr \lArr \Rarr \rArr \uarr \uArr \Uarr \darr \dArr \Darr \lrarr \harr \Lrarr \Harr \lrArr \hAar \sub \supe \sube \infin \lang \rang \real \image \bull \weierp \isin \plusmn \Dagger \exist \sect \clubs \spades \hearts \diamonds \sdot \ang \thetasym \Alpha \Beta \Epsilon \Zeta \Eta \Iota \Kappa \Mu \Nu \Rho \Tau \Chi \arcsec \arccsc \arccot \sgn. These ones could of course be easily simulated by means of macro definitions (and that's in fact how I implement them in blahtex :-)). In contrast, the real problems (the ones I mentioned above) are the ones that *cannot* be solved by adding a few macros. For a while I even tried writing *two* parsers that could live side-by-side.... but it was too much trouble. I spent quite a while analysing how much of a burden this would be, and the net result is that 1000 equations --- across ten different languages --- is actually not so bad. I decided it was worth making a clean break. I can assure you that compatibility has been uppermost in my mind, but compromises had to be made. I think this is the least bad solution. Anyway, it was a good chance to fix tons of other things in texvc which are partly a consequence of its parsing strategy. For example, it's annoying that \mathop{\rightarrow}^f doesn't put the "f" above the rightarrow, like it should: $A \mathop{\rightarrow}^f B$ . (And the spacing's wrong there too.) Actually, given what pfafrich has been up to, I wouldn't be surprised if we were already down to 900, and with a few more helping hands, the issue will pretty much disappear before we get around to considering deployment... Dmharvey 20:35, 10 February 2006 (UTC)

A short comment, hope it's not too much of a nonsequitur as I don't know much about how you're implementing blahtex: why don't you resort to standard TeX to get certain "difficult" things done instead of falling back on LaTeX and nothing deeper? For example, won't the AMS \buildrel do what you need instead of \mathop (which I gather is a LaTeXism)? Dysprosia 05:24, 13 February 2006 (UTC)

I don't completely understand your question, but I can make two comments: (1) I don't know AMS-LaTeX nearly as well as I should, so for example, I've never used \buildrel, and (2) \mathop is buried even deeper than LaTeX, it's a TeX thing. Any advice you have is appreciated. (Hmmm... wikipedia is very broken today... can't seem to log in.... so this is Dmharvey, 15:35, 13 February 2006 (UTC))

LaTeX is built on TeX. TeX is not the evil twin of LaTeX ;) I don't know what you're doing in the backend of blahtex, but if you're interfacing with LaTeX, presumably you can include plain TeX commands. So, if you figure out how to do something in plain TeX, why not give the plain TeX code to LaTeX and get it to do what you like? If you don't want to use the entire complement of AMSTeX or AMSLaTeX, you can always just snip out the bits you want from the AMS code. Sorry I'm not more precise on this. If you'd like me to attempt something specific, let me know and I can give it a shot. Dysprosia 06:15, 22 February 2006 (UTC)

Carathéodory theorem

I found out that there is no real entry on Carathéodory theorem in wikipedia. The article Carathéodory's theorem (measure theory) links back to outer measures, and you cannot find the definition of Carathéodory theorem for extension of measures on algebra. I don't know what you think, but the article is really not clear about what the theorem is, and I would consider this theorem fundamental in measure theory. Ashigabou 11:29, 10 February 2006 (UTC)

Are you talking about Carathéodory's theorem (convex hull)? Probably renaming the article is in order. (Igny 13:51, 10 February 2006 (UTC))

Oh, you meant absence of the Caratheodory extension theorem as defined in [3].(Igny 14:01, 10 February 2006 (UTC))

exactly. I know the theorem myself, but I am not that familiar with other "abstract theories", as I studied it recently in the theoritical fundations of probability; I wouldn't be able to link it to other fields. I created a stub, but I am not sure that semi-ring is the standard naming convention (subset S of the power set of X, closed under finite union, and difference can be written as a finite union of elements of S). Ashigabou 15:32, 10 February 2006 (UTC)

#REDIRECT Carathéodory's theorem -- linas 23:52, 10 February 2006 (UTC)

Why is it Carathéodory's theorem but Cauchy theorem (as opposed to Cauchy's), which is also a dab page? Should we standardise? —Blotwell 01:57, 11 February 2006 (UTC)

Kramers-Kronig relation

Hello, up until a few minutes ago there were two different articles Kramers-Kronig relations and Kramers-Krönig relation. Having determined that Ralph Kronig spelled his name with o, not ö, I merged both articles to one named Kramers-Kronig relation. However, since I know nothing at all about math and physics, it would be very good if someone who actually understands the text could look at the new article and make any necessary changes. Thanks! Angr/talk 18:16, 12 February 2006 (UTC)

blahtex 0.4.2

Now can do every symbol from LaTeX/AMS-LaTeX. (Well, almost all of them.) Results may vary depending on the fonts you have installed. At the very least you should be able to see them as PNGs. Dmharvey 02:37, 13 February 2006 (UTC)

Cool! But won't this break texvc when blahtex is incorporated? That is, texvc will choke on a symbol that blahtex accepts. (Of course, the correct thing to do is fix texvc not handicap blahtex.) -- Fropuff 04:59, 13 February 2006 (UTC)

Um, yes texvc will of course choke on symbols that blahtex accepts, but I don't really that this is a problem. Right now on blahtexwiki, Jitse has set it up (hope I've got this right) so that both texvc and blahtex are attempted, texvc's output is used wherever it succeeds, and blahtex is used for anything else. This means that (1) all MathML output is generated by blahtex, (2) PNG output is generated by texvc whenever texvc can manage it, otherwise blahtex does the PNG output, (3) all HTML output is handled by texvc, because blahtex doesn't do any HTML at all. By the way, I started this whole project trying to "fix texvc", but I soon gave up on that, and started again from scratch. Hence, blahtex. (-- Dmharvey, who can't log in now, some time on Feb 13.)

What, every? Almost every. --Trovatore 05:02, 13 February 2006 (UTC)

That's what I said. Almost every. Soon, with everyone's eagle eyes, we'll hopefully be able to substitute "every". (-- Dmharvey, who can't log in now, some time on Feb 13.)

AfD: Foundational status of arithmetic

Up for deletion: Foundational status of arithmetic - an interesting if slightly unusual article on the history of arithmetic. Contains some non-standard views, but maybe it can be cleaned up? 17:42, 13 February 2006 (UTC)

Maybe. Looks like a chore, though. Could be tagged with NPOV in the meantime. It points to arithmetization of analysis, which seems equally problematic; it seems to take the astonishing view that analysis has been mapped into the arithmetic of the natural numbers. (It's just possible that it means this has been done in higher-order logic, which is arguably true.) --Trovatore 17:48, 13 February 2006 (UTC)

By inspection

I am rather unhappy with this article, both the name and the content. I would think that the best thing to do would be to have it deleted, but maybe there are ways of renaming it and rewording it to make it an acceptable mathematics encyclopedia article. Comments? Oleg Alexandrov (talk) 02:52, 14 February 2006 (UTC)

I wrote this little thing after using the phrase in another article, Evaluating sums, which I thought had potentially a naive enough audience that they would appreciate seeing an explanation of this piece of mathematical jargon. I was uncomfortable writing about jargon, but it's not strictly a dictionary definition so I thought it would be excusable. There's more to say than I felt comfortable shoehorning into mathematical jargon, though, so I gave it its own article; however, it is by far the least substantial of the jargons linked to from that page. I don't know if there's much more to say than what I and Charles Matthews have already written; perhaps it can just be put into mathematical jargon anyway.

However, that only addresses one aspect of it being a bad article. What is unacceptable about it to you? For example, aliter and one and only one are analogously brief; what do you think of them? Ryan Reich 03:07, 14 February 2006 (UTC)

OK then, what I don't like is the name. Maybe something like method of inspection or something, or indeed part of the mathematical jargon. Don't know. :) Oleg Alexandrov (talk) 04:09, 14 February 2006 (UTC)

The name is one thing I don't really dislike. However, some other jargons, like arbitrary and canonical, have solved the naming problem by merging into a much larger article on the word taken in all its contexts. There is an article inspection; should I perhaps insert the contents of by inspection there? Ryan Reich 04:21, 14 February 2006 (UTC)

Trigonometric and hyperbolic functions: create separate articles?

Our article trigonometric function lacks much information, but is huge and difficult to expand as is. I think it would make sense to create a separate page for each function (cosine, inverse cosine ...). MathWorld has very rich pages on the individual functions, which are much more useful than Wikipedia's overview for someone with a good basic understanding of the topic. Of course, the main article should be kept as an overview. Same thoughts go for the hyperbolic functions. - Fredrik Johansson - talk - contribs 03:33, 14 February 2006 (UTC)

I am not convinced. Sine and cosine overlap too much as it is. Septentrionalis 05:53, 15 February 2006 (UTC)

I have long thought that the inverse trigonometric functions, at least, needed their own page. I started a draft at User:Fropuff/Draft 5 but I didn't get very far. I'm ambivalent as to whether we should have separate article for each function. -- Fropuff 07:50, 15 February 2006 (UTC)

A separate page for the inverses would help. Fredrik Johansson - talk - contribs 16:10, 15 February 2006 (UTC)

Rather than a split by type of fnction, I's suggest a split by topic (which mirrors the current topics covered in the article): so, for example, there could be Trigonometric function history, and Trigonometric function series and Trigonometric function identities, and so on. linas 22:39, 15 February 2006 (UTC)

Well, we already have the long article on trigonometric identities. I don't think we really need a separate article on the history; it fits in quite nicely in the main article. -- Fropuff 01:40, 16 February 2006 (UTC)

Multi-variable articles

I am still not satisfied with multi variable calculus articles (some of them only). Jacobian and gradient are not developped enough in my opinion. My main point, I guess, is we should have an article which generalizes derivative in one dimension for many practical cases (domain, codomain being vector spaces , with a special treatment for matrix spaces); we have an article on Frechet derivative, but it emphasize the genral case (infinite dimension). I think that in finite dimension, having a good article on derivative with several variables in the context of Frechet is necessary: it has all the good properties we expect from the scalar case (composition rule, inverse rule, differentiability imply continuity, etc...) that partial derivative do not have, and could explain the gradient and Jacobian definition, and some really common rules (for example the multi variable change in integrals). Some people disagree with me on this view, but I started to really understand gradient, jacobian and matrix calculus only once I studied Frechet derivative, and this view is adopted in at least two different documents, one being a reference, I think (I am not a mathematician, so I may be wrong though; the book I am talking about being Analysis on manifolds, from Munkres). As I studied this point recently quite heavily, I am willing to write the article, but I am not sure about the title, and how to link it to other article in multi-variable calculus. Ashigabou 01:54, 15 February 2006 (UTC)

I am not sure what exactly you want, but I think it would be more useful to expand the articles we currently have. So, develop the article on Jacobi matrix and mention that it satisfies

$f(x+h) = f(x) + J_f(x) \, h + o(|h|) \qquad(*)$

and thus it is a Frechet derivative. If the "some people" refers to me, then I'm afraid I didn't express myself clearly. The property (*) is essential for understanding multivariate calculus. What I meant to say is that most people will encounter the Jacobi matrix before they have heard of Frechet derivatives, and therefore you cannot motivate the Jacobi matrix by saying that it's simply a Frechet derivative, but you can (and probably should) refer to property (*) in the motivation.

The article on chain rule (what you called "composition rule") mentions the rule with Jacobi matrices and Frechet derivatives, inverse function theorem has the rule for inverse function, etc. If you want to write a high-level overview, you can add some paragraphs to multivariate calculus (if it gets too long, you can always split of a part to, say, multivariate differential calculus). All these articles can be improved, and I suggest you concentrate on that rather than writing a new article. Don't be afraid of changing existing articles. This goes in particular for matrix calculus (I'll comment on your remarks there).

I don't know Munkres' book, but from what I've heard it's pretty good, but more of a text book than a reference work. However, Munkres has a more general setting in mind: calculus on manifolds, rather than calculus in Rⁿ. -- Jitse Niesen (talk) 12:03, 15 February 2006 (UTC)

Agree with Jitse. Do not confuse the Jacobean with the Frechet derivative: although similar, most calculus books are built on the Jacobean, not Frechet. Personally, I'd already had plenty of classes in "calculus on manifolds"; I'd known a half-dozen different concepts of derivatives, long before I'd ever seen the words "Frechet derivative". Focus on Jacobean, which does what you want for finite-dimensional spaces, and leave Frechet for the infinite-dimensional stuff, for which it was invented. linas 22:52, 15 February 2006 (UTC)

I agree that most calculus books are built on the Jacobian; whether it is a good thing or not is a different matter; I personnally think it is a mistake, because you cannot really understand matrix calculus. I agree that talking about Jacobian with an emphasize on the linear map it represents would be in the right direction (from my POV :) ), but how do you explains derivative of matrix with respect to matrix ? You both seem to think that Frechet is really useful for infinite dimension only, and I don't understand that (I am open to explanations, though, of course). I think taking a maybe somewhat original approach to multi variable calculus would be interesting. At least, I was never satisfied with the standard approach (using partial derivative only) during my undergraduate courses. Ashigabou 00:14, 16 February 2006 (UTC)

I will rephrase my point differently: when I wanted to understand multi variable differentiability, I was interested in a concept which generalized all the 'good' properties of the derivative in 1 dimension, that is differentiability implies continuity, etc... Wether calling it Frechet or not, I don't care, that's not really the point. I feel like an article about how to extend derivability in several dimensions while keeping most good properties would be good; something more than partial derivative. If you think this can be done without Frechet, then I would be glad to hear how. Ashigabou 00:26, 16 February 2006 (UTC)

I'm having great difficulties understanding what you mean, and why you think that you need the Frechet derivative. Si tu veux, tu peux écrire français. Is your point that a function may have partial differentials and thus a Jacobi matrix, without being Frechet differentiable? -- Jitse Niesen (talk) 14:00, 16 February 2006 (UTC)

I don't feel like the difficulty is coming from my English, but anyway: en scalaire, on apprends la definition de la derivée, et pas mal de théorèmes fondamentaux qui sont liés; derivabilité implique continuité, valeur intermédiaire, théorème de Taylor, dérivée de la fonction inverse, etc... Je trouve que ce serait intéressant d'avoir un article qui généralise ces concepts en plusieurs dimensions. In English: in undergraduate, we learn that if f has a derivative at the point a, f is continuous at the point a, that if f has derivative on [a, b], there is c in [a, b] such as f(b)-f(a) = f^'(c)(b-a), that if f is Cⁿ, f has a Taylor expansion of degree n, etc... When I had some courses about multi-variable calculus, we were told the concept of partial derivative, and that was about it, and on wiki, this is the same: gradient, jacobi, defined as vector of partial derivative; partial derivative are a bit strange, because even when they exist, f may not be continuous. I wondered for a long time how can you have a generalization of the derivative for multi variable functions with all the nice properties of the scalar, and the approximation of f(x+h)-f(x) by a linear map with respect to h is the natural extension. This is again related to my remarks in matrix calculus: for now, all the formula are said to be notations, and I think this is plain wrong, that all those matrices and tensor represent linear map which correspond to Frechet derivative (at least in the C¹ case). . When Linas says that Frechet is one of the derivative generalization, I don't agree; I think this is *the* natural generalization for 'nice enough' spaces (Banach spaces). I have some nice examples how to use the definition in Frechet context to find most formula in matrix calculus, but I am told this is different, this is just a notation, and I really don't agree, at least not with some more explanations (you know, those stubborn Frenchs :)... ). Thank you for your interest ! Ashigabou 00:55, 17 February 2006 (UTC)

Hi Ashigabou—I agree with your point that approaching the derivative through the concepts of linear maps and best local linear approximations is the way to go. As usual many undergraduate-level courses and texts are lacking here. There is no reason why this approach must be more difficult than focusing on matrix computations and partial derivatives; quite the contrary. I wonder if you'd like to take a look at a very remarkable book on these topics called (very modestly) Advanced Calculus by Shlomo Sternberg and Lynn Loomis. This is without question the finest treatment of this area of mathematics I've ever encountered. Is the approach to the derivative used in this book the sort of thing you had in mind? — merge 10:28, 18 February 2006 (UTC)

I'm not actually sure what this discussion is about. We can and should have multiple approaches to an area like multi-variable calculus, for which there are superficially-different approaches well documented in the literature. If Fréchet derivative is somewhat too abstract, we can take a more 'gradualist' approach there, or in some other article. Charles Matthews 10:50, 18 February 2006 (UTC)

Ashigabou, I still don't quite know what you want, but I think I mostly agree with you, except for some details. The only advice I can give you now is just to do what you think is best. Once we see what you've written, it will be clear where you want to go. Based on what I've read, I expect that it will be generally okay and it will fill a gap in our coverage of multivariate calculus. I agree that Frechet is the most natural generalization of derivatives in R^n. -- Jitse Niesen (talk) 15:13, 18 February 2006 (UTC)

PROD (Proposed deletion): Empty Summation Equations

I proposed Empty Summation Equations for deletion, using the new Wikipedia:Proposed deletion process. Since this process is only being tested, I thought it would be fair to let you know. I didn't follow the debate, but my interpretation is that Proposed Deletion is for those articles that fail the criteria for speedy deletion, but for which it is still obvious that they should be deleted. -- Jitse Niesen (talk) 14:05, 16 February 2006 (UTC)

Can the /Current activity bot be modified to include this new type of activity? Arthur Rubin | (talk) 14:53, 16 February 2006 (UTC)

Yes. With a bit of luck, the article will appear on Current activity tonight. -- Jitse Niesen (talk) 19:15, 16 February 2006 (UTC)

Revert war at Real number

See for yourself [4]. Comments? Oleg Alexandrov (talk) 19:39, 16 February 2006 (UTC)

It is clear that what DYLAN LENNON has been repeatedly adding is not appropriate for this article. I can understand this happening once due to a lack of knowledge about what is noteworthy, but the repetition makes this unwelcome, and knowingly disruptive. Elroch 20:40, 16 February 2006 (UTC)

Possibly not notable articles

I nominated Colloquium (College of Engineering, Guindy) and Ramanujan Rolling Shield for deletion, as as they appear nonnotable. Comments and votes welcome. Oleg Alexandrov (talk) 04:07, 17 February 2006 (UTC)

I nominated (yesterday) Hiroshi Haruki, and I nominated a couple of DYLAN LENNON's creations for speedies. Comments and votes welcome. (I also removed a number of his lines

"The easiest proof" of (this theory) is due to Name that I never heard of.

Arthur Rubin | (talk) 20:22, 17 February 2006 (UTC)

DYLAN is surely a problem user. Some anon wrote on his talk page a while ago that he was banned from the Japanese wikipedia for trolling. Wouldn't surprise me. Oleg Alexandrov (talk) 21:08, 17 February 2006 (UTC)

Although DYLAN is a problem, it now appears (from the comments made in the AfD) that Haruki is adequately notable, although the article surely doesn't reflect it. Is there a {{sub-stub}} tag? Arthur Rubin | (talk) 00:13, 18 February 2006 (UTC)

Believe it or not, but {{substub}} has been deleted. Six times. I'm sure it has been discussed extensively, and I don't want to know how many edit wars had been going on about whether some article was a stub or a substub. -- Jitse Niesen (talk) 02:22, 18 February 2006 (UTC)

Some of MR LENNON'S links to ja appear to be incorrect or misleading. Then again, some of them seem to be right. We need someone who knows a bit of japanese to review them. Dmharvey 17:45, 18 February 2006 (UTC)

Good articles list

If you look at Wikipedia:Good articles, you'll see that only four articles are listed. I am pretty sure that there are far more than four good mathematics aricles on Wikipedia. So, I would like t orequest that if anyone knows of any other articles that fulfill the required criteria, could they please list them. Tompw 13:22, 18 February 2006 (UTC)

You can usually get a hollow laugh out of mathematicians with lines like should not omit any major facets of the topic. We really don't do completeness, except in some classifications. What would it take, to say that of an article like homology theory or Lie group or partial differential equation? So those guidelines are not written for us. Charles Matthews 14:00, 18 February 2006 (UTC)

Where does it say that? The requiremnts given for a good article are that it:

Be well written
Be factually accurate (which means error-free for a maths articles)
Use a neutral point of view (generally get this one for free :-) )
Be stable
Be reference (which isn't always needed for maths articles)
Wherever possible, contain images to illustrate it. The images should all be appropriately tagged.

Anyway, actions speak louder than words... so will try and seek some out. Tompw 19:50, 18 February 2006 (UTC)

Right after your point 6, it says:

Good articles may not be as thorough and detailed as our featured articles, but should not omit any major facets of the topic.

Now I don't think that necessarily excludes math articles, even ones like homology theory. I would interpret it as meaning something like "any subfield of homology theory accounting for (say) ten percent of the total research effort in that field should get at least a mention". It's not reasonable to read it as meaning that we have to track down the content of every PhD thesis written in the area. --Trovatore 20:01, 18 February 2006 (UTC)

OK, I saw and was editing my reply, but you got in first. However, I agree with you that we have to interpret "major facet" in our own way. Tompw 20:08, 18 February 2006 (UTC)

ALthough the Wikipedia:Good articles process is "sub-optimal" (if not broken) in a variety of ways, it is "well intentioned". From what I can tell, "someday", there will be a print version of WP, and thus, the articles suitable for inclusion in a print version must be identified. There are now many wikiprojects trying to categorize all of thier articles into "good bad and ugly". Seperately, there is a debate at Wikipedia:Stable versions about mechanisms by which the correctness and authority of an article can be atested to. A "good bad ugly" classification will probably feed into that process. I'm not convinced that now is the time to launch into the busywork of classifying math articles, but now is the time to get famliar with the issues. linas 00:53, 22 February 2006 (UTC)

Wikipedia:Articles for deletion/Safe sex makespan

Despite the name, this is a combinatorics / operations research article. It could probably need some sources and a new name, but it's a somewhat interesting problem. If somebody here knows this problem (known as "Glove problem" on Mathworld), please comment at the AfD. Kusma (討論) 00:01, 19 February 2006 (UTC)

can't remember the name of something

I'm not sure, but I think we might be missing an article on something. Unfortunately I can't remember its name, but I can describe it. It should be related to articles like bifurcation diagram, Feigenbaum's constant, chaos theory, dynamical system etc. If you look at the bifurcation diagram, and list the periods of the stable orbits from left to right (including the "islands of stability"), you get some ordering on the positive integers, which starts out 1, 2, 4, 8, ... but then does funny things in a non-well-ordered way. The picture is confusing me a bit (especially since it looks like 6 shows up twice, which is not suppoed to happen !!!), but I'm sure this has a name, it's called "so-and-so's ordering", but I can't remember who. And I seem to remember that the same sequence crops up no matter which dynamical system you choose, kind of like feigenbaum's constant, well at least for some reasonable class of systems. Anyone know about this? Dmharvey 15:30, 20 February 2006 (UTC)

ok, got it now: Sarkovskii's_theorem Dmharvey 15:34, 20 February 2006 (UTC)

blahtex compatibility update

Thanks to the efforts of Pfafrich on en, and of gwaihir and LutzL on de, and possibly others too, the blahtex compatibility project has been making substantial progress. Here's a table showing the number of problem equations on each wiki. The first column is the numbers before they got started, and the second column shows the counts for today's dumps. ("Today's dumps" means "today" for en, de and ja, but is still lagging by about two or three weeks for the other languages.)

      BEFORE   AFTER
en      342     287
de      372      68
fr      103      92
it       81      69
pl       57      49
es       37      32
pt       35      35
nl       34      16
ja       28      32
sv       10       9

TOTAL  1099     689

So already almost 40% of problems have been dealt with.

(Note: some proportion of the decrease -- not sure exactly how much -- is attributable to changes in blahtex. In particular it is now more permissive about using font commands in strange ways like $\mathcal{a}$ , so these aren't reported in the second column.)

An updated list of errors is available at http://blahtex.org/errors-20060220.html.

I encourage anyone who feels like helping us to jump in! Dmharvey 23:00, 20 February 2006 (UTC)

I should add that the samples on http://blahtex.org/ have not been updated with the new dumps, and they won't be updated for a little while yet. Dmharvey 23:08, 20 February 2006 (UTC)

If people are interested in helping on en-wiki I've created a set of pages detailing some of the imcompatabilities User:Pfafrich/Blahtex en.wikipedia fixup, and listing their status. So far all the errors are very minor using % rather than \%. People are welcome to fix bugs listed there, about 100 articles. --Salix alba (talk) 16:42, 21 February 2006 (UTC)

Real, again

OK, it seems we indeed have a problem user, the same DYLAN LENNON, recently reincarnated as WAREL. See the last 100 entries in the history of real number. [5] He was also inserting things at Proof that 0.999... equals 1 and other places. Seems to know math, but has unreliable edits, and is very perseverent. I would like to ask some of you to put real number on your watchlist. So far, it was mostly Jitse and me (with Zundark and an anon) who tried to keep this user at bay. Don't quite know what to do about this. Oleg Alexandrov (talk) 17:02, 21 February 2006 (UTC)

Applying WP:3RR should at least alleviate the problem; I see it's been tried. Septentrionalis 05:57, 22 February 2006 (UTC)

Frivolous articles on little-used geometric terms

See ana (mathematics), kata (mathematics), and spissitude. I don't mind these being merged and redirected to some sensible place, but giving them individual articles tends to give the false impression that the terminology has some currency.

The articles fourth dimension and fifth dimension have related problems. From fourth dimension:

The cardinal directions in the three known dimensions are called up/down (altitude), north/south (longitude), and east/west (latitude).

Well, come on, no they're not, not in general. These articles all seem to take for granted that there's some sort of preferred coordinate system with respect to which we can name directions. I think fourth dimension and fifth dimension should be moved to four-dimensional space and five-dimensional space, respectively, and substantially rewritten to address this problem. --Trovatore 20:12, 21 February 2006 (UTC)

Those articles on ana and kata and spissitude are unlikely to get any bigger than the stubs they are now so they should be indeed combined in a single article describing the terminology.

About moving fourth dimension to four-dimensional space, that may be more complicated. That article is rather big, and is partially about the four dimensional space, but it has sections devoted exclusively to the fourth dimension. Food for thought. Oleg Alexandrov (talk)

I remember debating "the fourth dimension" with grade-school playmates; this is a valid topic for anyone who has no math education beyond addition and multiplication. It should be dealt with at that level. (I also remember hearing about "the fifth dimension" in some movie, or an Outer Limits episode maybe, and thinking "that script-writer got it all wrong, there ain't no such thing") linas 01:34, 22 February 2006 (UTC)

So what exactly can we sensibly and accurately say to such a person about "the" fourth dimension? Which fourth dimension? I think the article as it stands is just wrong; there is no sensible ordering of dimensions (though of course in GR spacetime there's a timelike dimension that can be distinguished from the other three spacelike ones). --Trovatore 03:33, 22 February 2006 (UTC)

Presumably, the fourth dimension would be one orthogonal to the 3-dimensional space we live in (whether it be a timelike dimension or a spacelike one). Whether or not such a dimension exists is debatable, but we can at least ascribe some meaning to the term. -- Fropuff 05:20, 22 February 2006 (UTC)

There isn't any unique 3-dimensional space we live in; there are various spacelike slices. Which one do you pick? --Trovatore 05:32, 22 February 2006 (UTC)

All of them, if you wish. Look, I'm not trying to say the term has a precise definition, but rather loosely binds some related ideas that people like to think about. The article doesn't fall completely within the scope of mathematics (or even physics) and shouldn't be treated as such. -- Fropuff 05:37, 22 February 2006 (UTC)

I'm not sure what's stated in the article has any clear meaning at all, mathematical or otherwise. That's my objection to it. --Trovatore 05:41, 22 February 2006 (UTC)

Well, I agree with you there. I'd say it could do with a complete rewrite (although I'm not volunteering). -- Fropuff 05:43, 22 February 2006 (UTC)

These are references to fairly notable speculations about a physical/psychological fourth (space-like) dimension; see Charles Howard Hinton or John William Dunne, I forget which. (I presume the reference to Henry More the Platonist is at least half true, however.) Cat as history of mathematics and forget about them. Septentrionalis 06:02, 22 February 2006 (UTC)

I had 4D in fairly good shape last time I had a stab at it. Pity it seems to have gone south from there... Dysprosia 06:09, 22 February 2006 (UTC)

Alas, its probably one of those articles which takes constant vigilence to keep the nonsense at bay. Sometimes I think the whole stable versions idea isn't half bad. -- Fropuff 06:21, 22 February 2006 (UTC)

Lists of PRNGs

I see that list of pseudorandom number generators ran into copyright trouble, and was deleted about a week ago . This really needs recreation, with more care to avoid whatever caused the trouble (something about the GNU manual, some eejit copying in too much). I can get back the old text, if someone wants to work on this. Charles Matthews 12:11, 22 February 2006 (UTC)

Just wrote a new stub. Dysprosia 12:21, 22 February 2006 (UTC)

Found the old text from the database dump, see talk page. Is it fair use to have copyvio material on talk page for discussion? --Salix alba (talk) 13:46, 22 February 2006 (UTC)

Better really not to have it back on the site, in the history. It is very likely still on some mirror sites, but perhaps with corrupt formulae and so on. I'll email the text to anyone who needs it. Charles Matthews 15:49, 22 February 2006 (UTC)

If this is GSL-related, then I want someone to explain to me why copying GFDL'ed material from a Gnu/FSF GPL'ed software is considered to be a copyvio. (I ask because there are a few other WP articles that have gotten take-down notices from the GSL authors, which were mostly ignored). linas 17:21, 22 February 2006 (UTC)

From what I can tell Wikipedia:Cleanup Taskforce/List of pseudorandom number generators it was not copyvio which led to its deletion, more just a case of list cruft, not meeting wikipedia standards for an article. Looking at the licence it is OK to include GFDL material, as long as its source is acknowledged. It might be better to take your Q to Wikipedia talk:Copyrights where they will know more on such issues. --Salix alba (talk) 20:15, 22 February 2006 (UTC)

According to the deletion log

22:30, 14 February 2006 Splash deleted "List of pseudorandom number generators" (GFDL article, but with front- and back-cover texts which WP does not permit per Wikipedia:Copyrights)

so I don't think the cruftiness is why it was deleted. It is a good argument against recreating it as it was, though; the stuff on the talk page does not look like a good article. I don't actually know what is meant by "front- and back-cover texts".) --Trovatore 00:58, 24 February 2006 (UTC)

"front- and back-cover texts" is a reference to an optional part of the GFDL, see http://www.gnu.org/licenses/fdl.txt. Dmharvey 01:08, 24 February 2006 (UTC)

A question about differential equations

Hi everyone. This is probably not the best place for this request, but seeing that no-one has replied to a question I have posted in the reference desk, I was wondering if anyone here would be so kind as to help me with a problem that has been troubling me for eons, thus earning my undying gratitude. -- Meni Rosenfeld (talk) 20:20, 23 February 2006 (UTC)

combined set theory

This, according to the author of the page Avrill, is a bit of original research, and Arthur Rubin and Trovatore agree, see here and here. So I prodded the article. After which Avril blanked the page (thereby removing the "prod" tag), meaning it is technically no longer a valid candidate for an uncontested deletion. However, I'm inclined to interpret Avril's blanking of the page as a request for deletion, but since I was the one who added the "prod" tag, I don't think I should be the one to delete it. Would some other admin please take a look and delete it if you think it is appropriate? Thanks. Paul August ☎ 23:56, 24 February 2006 (UTC)

You're being overly process minded. Blanking a page is a nonadmin way of marking a page for deletion, as is recognised in the speedy deletion policy. It's obviously the right thing to do, so just go ahead and do it. --- Charles Stewart(talk) 16:11, 25 February 2006 (UTC)

blahtex 0.4.3

is now available at http://blahtex.org/. The main changes are: now supports \color, support for \not is cleaned up a lot, and a few other bugfixes. The new version hasn't been installed on the test wiki yet (http://wiki.blahtex.org/) because Jitse is out of town for a while.

Also, the sample pages have been updated with the more recent dumps. I'm throwing in russian, chinese and hebrew now (ru, zh, he) as well.

Compatibility project update

More progress has been made with blahtex compatibility on Wikipedia. We are now down to 463 errors across 13 wikipedias. I know there's a few people working on this in the background; I'm starting to tackle some of the smaller wikis myself. It's a bit frustrating that the wikipedia dumps are updated so infrequently (most of them are almost a month old now), making it hard to locate equations that haven't already been dealt with. Therefore, for the convenience of people working on this project, I've written a script that pulls down (via CURL and Special:Export) a live copy of all equations which were broken in the most recent dump, runs blahtex on them, and produces an up-to-date list of errors. So this list will miss any brand new errors that showed up since the last wikipedia dumps, but I expect the number of these to be miniscule. I will try to run this script every few days, and the results will be kept at http://blahtex.org/errors.html, so we can monitor progress. Many thanks to those who have been helping with this. Dmharvey 22:05, 25 February 2006 (UTC)

341 and counting.... and it looks like both de.wikipedia and fr.wikipedia are finished. Good stuff folks! Dmharvey 13:46, 26 February 2006 (UTC)

Ruud for admin

Luck has it that we mathematicians are a close-knit bunch who do good work. :) I nominated another one of us (Lethe was promoted serveral weeks ago), for admin, namely Ruud. If you are familiar with Ruud's work, you can vote at Wikipedia:Requests for adminship/R.Koot. Oleg Alexandrov (talk) 04:00, 26 February 2006 (UTC)

what's happened to planetmath?

When I go to planetmath.org, I see a weird "coming soon" message and a link to a mysterious wiki. Does anyone know what's going on with that? -lethe ^{talk +} 08:01, 28 February 2006 (UTC)

Worksforme. Dysprosia 08:05, 28 February 2006 (UTC)

Weird. It's still not working for me this morning. -lethe ^{talk +} 14:47, 28 February 2006 (UTC)

Works fine now. Oleg Alexandrov (talk) 16:12, 28 February 2006 (UTC)

Mar 2006

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

recategorizing recreational mathematics

I've been being WP:BOLD with the subcategories of Category:Recreational mathematics. In particular I've emptied its rather ill-defined subcategory Category:Mathematical recreations and puzzles; a lot of its articles have found much better homes, but those that really did want to be somewhere under both Category:Recreational mathematics and Category:Puzzles I've put in one of a few joint subcategories such as Category:Mechanical puzzles. (Putting "puzzles" as a subcat of "recreational mathematics", as suggested on one talk page, isn't really an option: there are a lot of puzzles there that really aren't mathematical.)

While I was at it I also emptied Category:Puzzle games, which had an identity crisis as some people thought it was Category:Puzzle computer and video games while others couldn't tell it from Category:Puzzles.

Anyway, I expect I've offended innumerable people one way or another. If I've put your favourite article somewhere you don't think it belongs, please don't hesitate to move it (hopefully not into the categories I've carefully emptied). If you dislike the entire new categorization, please don't hesitate to argue with me about it. Though I can't imagine I've made things worse, since everything was categorized more or less at random to begin with. —Blotwell 14:35, 1 March 2006 (UTC)

Category:Mathematicians by religion

Category:Mathematicians by religion has a single subcategory, Category:Jewish mathematicians. I would think that being Jewish does not necessarily mean being religious. And do we actually need to categorize mathematicians on whether they were relegious, and if yes, what relegion they were practicing? Oleg Alexandrov (talk) 23:48, 1 March 2006 (UTC)

Being a jew does not, of course, make one religious, any more than being a christian makes one religious. So the categories' names do not imply that the mathematicians in question are religious - They just state to which religion they belong. And I think such categories are useful, in the same way that categories of mathematicians by nationality are useful. But obviously, additional categories for other religions, not just judaism, are in order for it to be meaningful. -- Meni Rosenfeld (talk) 07:19, 2 March 2006 (UTC)

I note that Category:Christians in science is applied both to Blaise Pascal, a Christian writer, and Bernhard Riemann, where as far as I can see it does little. I didn't much like like classifying mathematicians by nationality, when it came in; but it was inevitable with the growth, and the issue of several nationalities has the solution of including all of them. There are problems with all such classifications, and I'm not keen on them. Charles Matthews 09:05, 2 March 2006 (UTC)

Hmm, I wonder if Voltaire belongs in the Category:Christians in science, as, like me, his parents were Christian? I don't like this kind of categorization either; I think its basically some subtle political POV-pushing. May I suggest one possible cure: IF the person preached a religion (other than math) at one point in thier life, or published articles on faith (in newspapers, as letters to the editor, etc), THEN they may be classified by faith. However, if they had the bad luck of having Christian, or Jewish parents, that alone is not a reason to classify. I would insist on proof of religious activity before allowing classification. linas 14:49, 6 March 2006 (UTC)

french spelling

Um, I don't actually know french, but I thought only the first "e" in "etale" had an acute accent. So is this edit incorrect? Dmharvey 03:11, 2 March 2006 (UTC)

I think in this context, it's correct: the term in Hartshorne is "éspace étalé". Ryan Reich 03:30, 2 March 2006 (UTC)

So how do you know when it's étale and when it's étalé? Dmharvey 03:36, 2 March 2006 (UTC)

As far as I can tell, it's étalé here, and étale for morphisms. "éspace étalé" means roughly "slackened space", or "stretched-out space", which is reasonable given what it is, while an "étale morphism" is simply a "slack morphism". The metaphor is roughly the same, in that the slackness refers to a space constructed from layers laid out flat, and the grammatical difference distinguishes the "slackened space" constructed from something which was not, of itself, slack, from the "slack morphism", which is inherently so. Of course, "éspace étalé" is not used much anyway. Ryan Reich 03:56, 2 March 2006 (UTC)

It is certainly espace (not *éspace) étalé in French, but this leaves open the question of what the English translation of this expression is. I had been under the impression that it was called the étale space nevertheless, but Google seems to support both usages. —Blotwell 05:12, 2 March 2006 (UTC)

Étaler being a verb, étalé is the past participle (has been spread out, roughly). My MicroRobert says étale, adjective, can be applied to the sea as 'calm', when the tide is about to turn. We have been using sheaf space for espace étalé, which is not so common in English. HTH. Charles Matthews 09:13, 2 March 2006 (UTC)

Please continue with sheaf space. Septentrionalis 21:08, 6 March 2006 (UTC)

After a check in the "Annales de l'Ecole Normale Supérieure", the good term is "espace étalé". --pom 11:18, 2 March 2006 (UTC)

Location of "elementary function" article

I think Elementary function (differential algebra) should be moved to Elementary function, currently a disambiguation page with little value. Despite the title, said article covers the concept of elementary functions in the general sense. Fredrik Johansson 23:50, 2 March 2006 (UTC)

I think it would simplify a few links and a line could be added to the article pointing to the list of common functions. When Elementary function (differential algebra) was created what is currently List of mathematical functions was in an article called Elementary functions, so I had to create something else. XaosBits 02:10, 3 March 2006 (UTC)

Could someone execute the move? Fredrik Johansson 04:56, 6 March 2006 (UTC)

Definition of General Linear Group

Charles Matthews and I are having a discussion about the correct definition of general linear group. It might be useful to have more input. The question is whether it should be defined initially in terms of rings or fields. Talk:General_linear_group A5 22:19, 4 March 2006 (UTC)

LaTeX

I have created a template to tag articles in need of LaTeX formatting. My concern is that it uses the LaTeX logo, which may or may not be a problem. The image was created using LaTeX, and using LaTeX to create images like $\frac{q}{2}$ doesn't seem to be a problem; yet, the image is still a logo with questionable copyright status. I was wondering what everyone else thought? Isopropyl 00:04, 5 March 2006 (UTC)

I would like to note that per the math style manual html formulas are perfectly acceptable (unless they look awful, like Σ_i=1ⁿ). It is also advised that one not modify somebody else's formulas by converting them from HTML to LaTeX or viceversa.

In fact, formulas which become PNG images may actually be preferrable in HTML, as then they show up as text, and look better on the page, also per the math style manual.

All in all, I don't see any pressing need for putting the {{LaTeX}} template on articles which are properly formatted, but only in HTML. Of course, one may use this template for articles which have no formatting whatsoever, like people writiting x_2 or x2 without bothering to use proper markup or math tags. That's what I would think.Oleg Alexandrov (talk) 23:37, 5 March 2006 (UTC)

Thanks for your input! I'll keep it in mind in the future. What is your opinion on the logo used in the tag? Isopropyl 23:42, 5 March 2006 (UTC)

Should a page use a combination of LaTeX and HTML formatting, or should its use be consistent throughout an entire article? I have tagged sections with {{LaTeX}} when the section in question deviated from the precendent set by the rest of the article. Isopropyl 23:45, 5 March 2006 (UTC)

I don't quite know, and for myself I would be fine with a mix. But if you find it stylistically ugly to have html mixed with LaTeX, then a better solution would be maybe to just convert the html to LaTeX right away, rather than put a "work needed" template on it and hoping that a kind soul would do it some time. There is a huge amount of articles needing serious work, as listed at Wikipedia:Pages needing attention/Mathematics, and I think that labeling an article as needing work because of TeX/HTML inconsistency would be probably not good. Cheers, Oleg Alexandrov (talk) 23:57, 5 March 2006 (UTC)

I agree with Oleg. Paul August ☎ 01:48, 6 March 2006 (UTC)

Most linked to and least linked to maths articles

I've been playing around with the database dumps and extracted the most links and least linked mathematics articles.

The top linked articles might be useful for directing our efforts as these are probably most visited pages. The orphaned articles and redirects could help with some housekeeping. For example there is Squircle which seems quite dubious, and there are several highly linked redirects which indicate a need for some topics to be expanded. --Salix alba (talk) 13:54, 6 March 2006 (UTC)

Heh. Pi has 314 links... Ryan Reich 14:15, 6 March 2006 (UTC)

No way.... Dmharvey 14:33, 6 March 2006 (UTC)

And it holds slot 77 which is almost pi/4. linas 15:31, 6 March 2006 (UTC)

I wonder about the correctness of these lists. I was browsing the "orphaned" list and I was very surprised to see Stone–Weierstrass theorem, which of course is linked to from many articles. Paul August ☎ 17:15, 6 March 2006 (UTC)

It is quite a tricky job, especially where redirects are concerned. For Stone–Weierstrass theorem the only pages which link directly to it are 6 redirect pages [6]. For some technical reason, I've not included redirects in the count of articles. So these lists are the bests my little scripts can produce at the moment. If people feel the need, I'll try to update them to get closer to a real number. In the case of Stone–Weierstrass, I'd actually say the appearence in the list is a good thing. Looking closely, the hyphen in the article name is an odd unicode character (0xE28093) rather than a regular ascii hyphen (0x2D). I'd say this would be a good case for the article to be moved to the name with the ascii hyphen. --Salix alba (talk) 18:31, 6 March 2006 (UTC)

Ok I see. Yes I noticed the odd name. I think I will move the article. Paul August ☎ 19:51, 6 March 2006 (UTC)

JA: I thought we were standardizing the use of ndashes, not hyphens, for conjoining names of distinct people, as distinguished from hyphenated names of one person. Jon Awbrey 20:04, 6 March 2006 (UTC)

Were we? I missed that. Why would we want to do that? Paul August ☎ 20:12, 6 March 2006 (UTC)

JA: I'm sure I was directed to do that by some WikiPundit or other -- I just assumed it was to mark an obvious logical distinction for the sake of better hyper-indexing or sumting. Jon Awbrey 20:25, 6 March 2006 (UTC)
- Somebody likes m-dashes and n-dashes, hardcoded by use of — and – and goes through substituting them. I'm not sure why; portability, maybe? Septentrionalis 21:13, 6 March 2006 (UTC)
  - I think I would strongly oppose that policy, on ground of human nature. Most editors will use the ascii hyphen, never get to see the policy on ndashes, leading to the same redirecting problems we have seen on Stone–Weierstrass. --Salix alba (talk) 21:31, 6 March 2006 (UTC)
    - Well, I haven't seen these improvements in article names; only in text. But there does seem to be a tendency to avoid hyphenated article titles: loan word not loan-word. Septentrionalis 23:26, 6 March 2006 (UTC)

JA: YARTIW (yet another reason to ignore wikipundits). Jon Awbrey 21:40, 6 March 2006 (UTC)
dear reader, for a more complete view of the status of the discussion, please do have a look at User_talk:Jon_Awbrey#En-Dash_Protocol_Reigning_Over_Polynominal_Titles_.28EDPROPT.29

Endashes

I knew we'd have to discuss this one eventually. The arguments for the A-endash-B theorem if A and B are two people are (a) it parses uniquely if you don't happen to be able to recognise double-barrelled names, and (b) it is a more professional piece of format. I would, however, always recommend creating [[A-hyphen-B]]'' first, as a precaution, so as to pick up any hungry red links; and only then move to the endash version. Charles Matthews 21:58, 6 March 2006 (UTC)

Yeah, I didn't like it at first, but after thinking about it (and looking at typeset documents) I have to agree. Not so much for the unique parsing, which is a good argument in principle but not so much in practice (you can't reliably conclude that Burali-Forti is a single person just because the article is at Burali-Forti paradox, even assuming you do notice the difference in the length of the dash/hyphen, which I wouldn't have if it hadn't been pointed out). But the endashes really do make the title look more like typeset documents and less like Usenet.

Maybe someone could send a bot around to look for article names that are duplicates except for the hyphen-endash distinction (these should always redirect to the same place), and for articles with endashes with no corresponding hyphen redirects (redirects should be provided). --Trovatore 22:24, 6 March 2006 (UTC)

Agreed. Some folks care as much about typographical niceties as mathematicians care about proof validity, or musicians care about pitch correctness. Lack of personal interest or awareness of these subtleties is no good excuse for hostility toward the interests of those who do care. Accents and quotation marks are another common battleground. With redirection, there is no need to fight. The hypen-redirects-to-dash idea seems like a reasonable compromise. --KSmrq^T 22:26, 6 March 2006 (UTC)

dear reader, for a more complete view of the status of the discussion, please do have a look at User_talk:Jon_Awbrey#En-Dash_Protocol_Reigning_Over_Polynominal_Titles_.28EDPROPT.29

Three forms of mathematical induction

This article was intended to be comprehensible to all mathematicians.

It was not intended to teach mathematical induction. It was not intended to explain what mathematical induction is, nor how to use it.

It was nominated for deletion by those who did not understand it. To some extent, they did not understand it because it was a stub and failed to explain what audience it was intended for and what its purpose was.

A bunch of (mostly) non-mathematicians looking at the stub form in which the article appeared when it was nominated from deletion saw that

It was not comprehensible to ordinary non-mathematicians who know what mathematical induction is, and

The article titled mathematical induction is comprehensible to ordinary non-mathematicians, even those who know --- say --- secondary-school algebra, but have never heard of mathematical induction,

...and voted to delete.

And so I have now expanded the article far beyond the stub stage, including

Substantial expansion and organization of the introductory section.

Two examples of part of the article that is probably hardest to understand to those who haven't seen these ideas.

An prefatory statement right at the top, saying that this article is NOT the appropriate place to try to learn what mathematical induction is or how to use it, with a link to the appropriate article for that. It explains that you need to know mathematical induction before you can read this article.

Therefore, I have invited those who voted to delete before I did these recent de-stubbing edits, to reconsider their votes in light of the current form of the article.

I also ask others here to vote on it by clicking here.

(Nothing like nomination for deletion to get you to work on a long-neglected stub article!) Michael Hardy 23:42, 6 March 2006 (UTC)

WAREL

My assumption of good faith in User:WAREL (formerly User:DYLAN LENNON) is being sorely tested. I know I'm not the only one who has wasted a lot of time over the past few weeks dealing with him/her. I'm wondering whether anyone else here has any thoughts about how to deal with WAREL, short of deploying an automatic WAREL-edit-reverting-bot. Dmharvey 18:00, 7 March 2006 (UTC)

For context, see the following article histories Decimal representation, Real number, Twin prime conjecture, as well as User talk:WAREL (Link to today's version, as WAREL likes to delete things he does not like. See especially the bottom section.) Oleg Alexandrov (talk) 19:47, 7 March 2006 (UTC)

I left a comment at Wikipedia:Administrators' noticeboard/Incidents#Disruptive_contributor to_mathematics articles. Oleg Alexandrov (talk) 05:47, 9 March 2006 (UTC)

al-Khwarizmi

This isn't about mathematics, but it is about a mathematician. Anybody who has spare time and is willing to read a long talk page is kindly request to comment on the dispute regarding al-Khwarizmi's etnicity at Talk:al-Khwarizmi. Cheers, —Ruud 14:49, 9 March 2006 (UTC)

How about showing the whole lot of them the way to Wikinfo, which wants editors like that? ;-> Septentrionalis 19:24, 9 March 2006 (UTC)

Somehow I doubt that most persons involved are interested in updating his biography beyond the first two sentences. —Ruud 19:30, 9 March 2006 (UTC)

Articles for the Wikipedia 1.0 project

Discussion moved to Wikipedia:WikiProject_Mathematics/Wikipedia_1.0 Tompw 16:40, 13 April 2006 (UTC)

Wikipedia talk:Scientific peer review

Notice: interested contributors may wish to participate in the Wikipedia talk:Scientific peer reviews by working scientists.

--Ancheta Wis 17:10, 11 March 2006 (UTC)

Can you guys have a look

Gallagher Index is a Political Science article and subject. But currently it could probably do with a mathematicans eye (alongside a few more things as well). Essentially, is there a neater or nicer way of doing the table at the bottom as an example of how the index is generated? Cheers, --Midnighttonight 08:47, 13 March 2006 (UTC)

Categorizing articles

On my suggestion, Salix alba made a list of Wikipedia articles which are not categorized, but which are linked from a math article. That list has a bunch of false positives, but also articles which are math and are not categorized. I suggest we start a cat wiki-pet (short for a Categorizing Wikiproject), going through those articles and categorizing them.

I split the list into 47 sections of 50 articles each. One may choose a section to work on, and sign at the bottom when done. I did the first three, and found roughly 3-5 articles out of 50 which may need categorizing. See the list at User:Salix alba/maths/uncategorised maths. Oleg Alexandrov (talk) 20:14, 14 March 2006 (UTC)

I don't know much about the category system, but if I just tag relevant articles with Category:Mathematics, is that enough to get them on the radar? (i.e. should I mark a section as "done" if I do this?) Dmharvey 03:03, 15 March 2006 (UTC)

I'd shoot for at least one level more specific than Category:Mathematics. The names of the big categories are pretty intuitive: Category:Algebra, Category:Mathematical analysis, Category:Mathematical logic, Category:Geometry, Category:Topology, Category:Number theory. Just make sure to remember the "mathematical" before "analysis" or "logic". --Trovatore 03:16, 15 March 2006 (UTC)

Sometimes one can pick the right category by looking at the articles going from the current one. But yes, putting them in Category:Mathematics is a good first option. Then my bot will list them to the list of mathematics articles, so more people will see them and may refine the categorization further. So yes, marking a section as done if the articles there are listed in some category is good, thanks. Oleg Alexandrov (talk) 03:18, 15 March 2006 (UTC)

ok guys thanks Dmharvey 03:27, 15 March 2006 (UTC)

I made the sections be 20 items rather than 50, as those were too big I think. To continue with the note at the top of this section, the person who does most work will get a cat as a wiki-pet (the Wikipet which anybody can touch (and edit)). Oleg Alexandrov (talk) 05:08, 15 March 2006 (UTC)

Oleg, you are SO going to award it to yourself. That is, like, so totally not fair. Dmharvey 19:48, 15 March 2006 (UTC)

Not all is lost, the race is still fully open! By the way, if you look at my bot's changes page, you will see a good harvest of math articles for March 15. Awesome work! Oleg Alexandrov (talk) 03:37, 16 March 2006 (UTC)

Now, I eager to get the wiki-pet, reviewed a section, categorized around 10 of the 20 there, felt good of myself, and when I got to editing the section to say "done", I see the section was done already! Dmharvey, now that's unfair. :) Oleg Alexandrov (talk) 04:55, 16 March 2006 (UTC)

Perhaps people should mark their territory -- in a nice way -- at the top of the score of items when they start work on it? Jon Awbrey 05:00, 16 March 2006 (UTC)

I doubt it is worth it; I meant it to be a silly joke rather than a complaint. Oleg Alexandrov (talk) 05:01, 16 March 2006 (UTC)

$''\!$ Jon Awbrey 05:32, 16 March 2006 (UTC)

Cheaters!!!! Hey, I noticed that some of the "finished" sections are still contain uncategorized articles. Even if the article is not about math, please do make an effort to put it into some category, somewhere!!! linas 01:08, 18 March 2006 (UTC)

Be my guest, my friend. :) Oleg Alexandrov (talk) 02:10, 24 March 2006 (UTC)

History of human knowledge about pi

This is the new title of History of pi. Even I think this is pædantry, so it may be over the top. Can we discuss this here, away from the Pi day crowds? Septentrionalis 00:48, 15 March 2006 (UTC)

"History of pi" deserves an article. To think that a table of the history of numerical computation of pi is the same thing as a history of pi is very silly. I've moved the table to another article, and labeled this article a stub. Michael Hardy 01:40, 16 March 2006 (UTC)

Agree w/Michael. I remember reading, as a young student, of plenty of interesting snippets about Egyptians knotting strings, silly legislation in kansas about pi=3, and what not. It deserves an article. linas 22:26, 17 March 2006 (UTC)

LOL... I remember adding that to (what is now called) Chronology of computation of pi (see under 1897), except the reference I have is for Indiana not Kansas. Dmharvey 22:34, 17 March 2006 (UTC)

MathWorld

Hi guys,

I was wondering why I can find so many maths-related articles here that do not reference relevant pages from MathWorld. I'm not sure what their license model is, but I can only assume that this is the reason why it's not popular around here? Please let me know if you think including their articles as references is a desirable thing. I'm watching this page, so do reply here. - Samsara (talk • contribs) 13:18, 15 March 2006 (UTC)

Obviously, we can't include relevant sections of MathWorld articles, as that would be a copyright violation. The reason for not referencing MathWorld articles is probably the uneven quality (yes, even by our standards) and the presence of clear errors (possible copyright traps) and probable neologisms. (I don't think the neologism being published as part of Mathematica makes it any less a neologism.) — Arthur Rubin | (talk) 13:56, 15 March 2006 (UTC)

I agree with Arthur and the reasons he provides. A policy of providing links to mathworld just doesn't make sense for us. However, if you come across a particular article where they have a much stronger version, then certainly linking to theirs would be useful (even better: bring ours up to snuff). -lethe ^{talk +} 15:30, 15 March 2006 (UTC)

Yeah, making it a policy to link to mathworld does not make sense, but I would think we should be encouraged in making external links to mathwolrd on case-by-case basis when those links are relevant (not necessarily much stronger than ours :) Oleg Alexandrov (talk) 16:11, 15 March 2006 (UTC)

Just to clear up a possible misunderstanding: I was referring to the license model because Planet Math is more frequently linked to. Is quality really so divergent between the two? I'm not trained as a mathematician, so I admit my judgement is poor. - Samsara (talk • contribs) 16:17, 15 March 2006 (UTC)

We actually copy planetmath articles, see WP:PMEX, that's why we must refer to the original versions, per their site license. Oleg Alexandrov (talk) 16:21, 15 March 2006 (UTC)

I second Arthur's comments. Just in the past month or so, I've had to remove several external links to MathWorld because when I checked them out, I found out they contained major errors. Sometimes these MathWorld articles can be good, but other times, it looks like a real hack job. So it's definitely not good to just unilaterally add the MathWorld links. I think it best for editors working on particular articles in their area of knowledge to add the links they actually found the most useful. --C S (Talk) 10:20, 10 April 2006 (UTC)

Please vote on this proposed deletion

at Wikipedia:Articles_for_deletion/Proof_that_22_over_7_exceeds_π#.5B.5BProof_that_22_over_7_exceeds_.CF.80.5D.5D.

The delete votes seem to be from non-mathematicians who erroneously think they understand the article. The main idea is this:

$0<\int_0^1\frac{x^4(1-x)^4}{1+x^2}\,dx=\frac{22}{7}-\pi.$

Therefore 22/7 > π.

But the article also includes exposition, discussion, and mention of the appearance of this problem in the Putnam Competition.

One "delete"-voter says this is no more significant than, for example, a proof that π > 3.14159 or the like. The fact that 22/7 is a convergent in the continued fraction expansion of π seems to mean nothing to that person or to escape his notice altogether. The fact that this particular integral is so simple and has a neat pattern also seems to escape them. Another shows signs of thinking that all articles on π-related topics should get merged into one article (see list of topics related to pi). Michael Hardy 02:22, 16 March 2006 (UTC)

arXiv

So what's the deal with linking to the arxiv? This has come up quite a number of times in the last little while. Someone has gone trigger-happy recently on some papers there by Diego Saá, and it took a lot of convincing to get User:WAREL to stop linking there. (Or maybe he/she is still at it.) I would think generally such papers do not qualify for linking from Wikipedia, unless there are very good reasons to the contrary. Somehow a link to the arXiv has an air of respectability that you don't get from your home page on geocities etc, but it's not deserved, and we shouldn't be misleading people into thinking that the arXiv is a reliable resource. Dmharvey 02:16, 17 March 2006 (UTC)

I agree. One should only use references to books and peer-reviewed journals. Oleg Alexandrov (talk) 02:54, 17 March 2006 (UTC)

That's not how it works in mathematics research, and I see no reason why Wikipedia should adopt stricter rules for citations in its mathematics articles than most of the mathematics community itself. Wikipedia would only be shooting itself in the foot. --C S (Talk) 05:08, 25 March 2006 (UTC)

Well, we should prefer refereed references. Of course for journal references that are also on the arxiv, we should provide an arxiv link (not everyone has access to an academic library). Furthermore, there are worthwhile things on the arxiv which don't get published in journals. A lot of times, Witten, for example, publishes a lot of his papers only through the arxiv, he doesn't feel that journal referees are qualified to vet his papers. And there are précis on the arxiv which are very good resources but not original work, and therefore not appropriate for journals. But of course, there is also crackpottism on the arxiv, so care is certainly required. -lethe ^{talk +} 04:07, 17 March 2006 (UTC)

You definitely need a lot of care when citing papers by a guy who "doesn't feel that journal referees are qualified to vet his papers". :) Oleg Alexandrov (talk) 15:49, 17 March 2006 (UTC)

That is a dangerous attitude; but in the case of Witten I suspect many of the referees would agree, and are probably relieved that they do not have to try to keep up! --KSmrq^T 16:17, 17 March 2006 (UTC)

Off-topic: but Alexander Grothendieck stopped publishing in journals as well. linas 23:32, 17 March 2006 (UTC)

The arXiv is mostly reliable, except for the general mathematics (GM) section which is where the crank articles seem to get listed. I removed all the links to Diego Saá's papers that I could find; they were added by User:Diegueins, who claims to be his son. R.e.b. 05:57, 17 March 2006 (UTC)

In the last six months, I have found there a paper proving P=NP and another proving P $\neq$ NP. No comments... pom 16:18, 18 March 2006 (UTC)

Please sign up on the participants list!

If you have this talk page on your watchlist, then you should add your name, field(s) of expertise and interests to the Wikipedia:WikiProject Mathematics/Participants page! I know there are some newcomers who haven't yet signed up, and I suspect there are some old-timers as well. linas 22:15, 17 March 2006 (UTC)

I meant to sign up at some point, but I glanced over the list and, frankly, many of you guys seem to be so good that it's kind of scary (I'm only an undergrad student) :-) - only half joking. But now, if you say so... AdamSmithee 00:20, 18 March 2006 (UTC) And after signing up, I see that my nick and the alphabetical ordering puts me on top of the list :-D AdamSmithee 00:28, 18 March 2006 (UTC)

I would join but you see, I'm on vacation. Good luck to you all. -- 127.*.*.1 01:17, 18 March 2006 (UTC)

Let me also add, feel free not to add yourself to that list or any others, for any reason. I myself don't see what purpose the list serves, and don't like adding myself to lists like that, though I did so eventually. -lethe ^{talk +} 03:41, 18 March 2006 (UTC)

Obviously the list doesn't have any kind of official status, but it does create a kind of community, as well as crystallizing one's own role in the Mathematics project in one's own mind. Mostly it seems sort of like the ritual of everyone gathering in a circle and placing hands one above another to seal a pact. And I'd encourage AdamSmithee to put his name on the list simply because he feels out of place; doing so will put him correctly in place :) Ryan Reich 06:18, 18 March 2006 (UTC)

Actually, I got into a discussion recently about how many particle physicists there are working in WP; looking at the participants list help put a lower bound on the number. This is a lot like any department directory or phonebook or census: rarely looked at, but terribly useful when its really needed. That, and indeed, the community feeling of the historical "I was here" thing. In 20 years, the list may be interesting to review: "I remember old so-n-so." linas 02:58, 19 March 2006 (UTC)

Statistics on User:WAREL

I submit the following statistics as an argument to block WAREL for, I suppose, a few days.

User:WAREL was born 17th Feb 2006. He/she has a total of 242 edits since then. The following survey includes 99 of those edits (41%), plus a few of User:DYLAN LENNON's edits (WAREL is a reincarnation of DYLAN LENNON).

Perfect number: 23 edits. At least 13 immediately reverted. Many prior edits by DYLAN LENNON going back to July 2005 -- generally not reverted
Twin prime conjecture: 17 edits, all reverted
Real number: 12 edits, 11 reverted (As DYLAN LENNON: 14 edits, 10 reverted)
Decimal representation: 11 edits. 10 reverted.
Zeta constants: 6 edits, 3 reverted
Finite field: 6 edits, 3 reverted, the other 3 self-reverted
Proof that 0.999... equals 1: 5 edits, all reverted
Decidability (logic): 5 edits, all reverted
Riemann hypothesis: 5 edits, 1 reverted
Chen prime: 4 edits, 2 reverted
Decimal: 3 edits, all reverted
Halting problem: 2 edits, both reverted.
Fermat's last theorem: 1 edit, reverted
Soliton: 2 edits, both reverted
Wiener's tauberian theorem: 1 edit, reverted
Cousin prime: 1 edit, reverted
List of real analysis topics: 1 edit, reverted

Of these 113 edits, there are at least 88 reversions, which is 78% of the edits listed above, or 36% of all edits logged.

He/she was even reverted twice on his/her own talk page.

WAREL has been reverted by at least 17 distinct editors: User:Jitse Niesen, User:JoshuaZ, User:Dmharvey, User:EJ, User:Schildt.a, User:Arthur Rubin, User:ANTI-WAREL, User:Oleg Alexandrov, User:Elroch, User:Mfc, User:Trovatore, User:Zundark, User:Fropuff, User:Fredrik, User:Paul August, User:KSmrq, User:Melchoir, many of whom you will recognise as being respected contributors to mathematics articles.

On the other hand, I note that WAREL has also made several nontrivial, non-reverted contributions to several mathematics articles: Riemann hypothesis, Perfect number, Hilbert's fifth problem, Perfect power, Proof that the sum of the reciprocals of the primes diverges. He/she also makes plenty of edits to articles in which I am not competent, especially relating to Japanese mathematicians and musicians. Therefore, in my opinion, a permanent block is not (yet) warranted, even given the fact that he/she was permanently blocked on the Japanese wikipedia.

Dmharvey 01:23, 20 March 2006 (UTC)

I wrote a note on his talk page a few days ago about his revertions at decimal representation, and Jitse wrote one today about perfect number (see User talk:WAREL).

I have a silly suggestion. How about writing a petition on his user talk page, telling him that if he engages in any disruptive activity again, at any article, he will be blocked for 12 hours? Then we could all sign it, and then, should he disrupt again, any of us administrators would be able to block him with a clear heart. Wonder what you think. Oleg Alexandrov (talk) 06:53, 20 March 2006 (UTC)

Your suggestion is not silly. I think it would be important to emphasise in this petition that although some of his/her contributions have been appreciated, his/her almost complete disregard for other editors' opinions is not. I've spent enough time on this now; if someone else writes it, I will sign it. Dmharvey 13:11, 20 March 2006 (UTC)

<math> rendering bug

Just noticed at perfect number (at the bottom of the section on odd perfect numbers), this math tag:

 <math>2^{4^{n}}</math>

is getting rendered as this html:

 <span class="texhtml">2<sup>4</sup><i>n</i></span>

to appear as:

  $24 n$

.. which is clearly wrong.

I wasted some time tracking down the paper to check the clearly wrong result before realising that it was the rendering rather than the text that was at fault. I don't know if this is a well known bug, but a brief search on Mediazilla didn't throw up any candidates. I have reported it to the Wikitech-l mailing list mailing list. Hv 16:12, 20 March 2006 (UTC)

I've noticed this before. It's actually not a bug in the LaTeX => HTML converter. It has to do with HTML tidy, which is a program that processes the HTML after the converter is done with it. The correct translation would be something like 24n. I think what happens is that HTML tidy sees the second and assumes that the author forgot the slash. So it inserts an extra slash producing 24n. Then it sees the next and can't find a matching so it kills that one too. Finally the last dies. This is just a theory, but I'm pretty sure that texvc gets the conversion right in the first place. Dmharvey 18:30, 20 March 2006 (UTC)

See for example http://bugzilla.wikimedia.org/show_bug.cgi?id=108. Dmharvey 18:35, 20 March 2006 (UTC)

Thanks for the pointer. Is this HTML Tidy we're talking about? Because if so I'm surprised there's no mention there that it is being used on WP. (I also had a quick browse of the HTML Tidy bugs database, and saw no related item there.) If not, can you point me at some details of the HTML tidy you mean? I'd like to track this problem further ... Hv 19:52, 20 March 2006 (UTC)

Yes, that's the Tidy I mean. There is a flag $wgUseTidy in the mediawiki source which enables use of HTML Tidy. I'm pretty sure they use it on WP itself. You could try asking User:Jitse Niesen, I know he's at least one person who's been thinking about Tidy recently :-) Dmharvey 20:16, 20 March 2006 (UTC)

Indeed, I do know about it. This is fixed in the current version of HTML Tidy, but that is not yet installed on the MediaWiki servers. Details are in mediazilla:599. I haven't yet seen your post to the mailing list (perhaps it's help up in a queue), but the solution is to upgrade HTML Tidy. -- Jitse Niesen (talk) 23:16, 20 March 2006 (UTC)

Cool, I even managed to find the changelog that fixed it ([7]) but I guess that's redundant now. (I also followed up with a "never mind" to my wikitech mail, so it may never get through to the list.) I look forward to the new version. Hv 23:23, 20 March 2006 (UTC)

Decimal representation or decimal expansion?

There is a discussion on which name is more appropriate at talk:decimal representation. Comments welcome. Oleg Alexandrov (talk) 03:39, 21 March 2006 (UTC)

Problem at transfinite number

There is an editor, User:Jagged 85, whom you may recognize as being interested in the contribution of Indian mathematicians. At transfinite number he has been making edits that attribute the concept to certain ancient Jaina mathematicians/philosophers. The evidence presented is, in my estimation, of the sort that would be accepted only by someone who either has an agenda, or who does not really understand the contemporary concept. I'd appreciate it if some interested folks would drop by and take a look. --Trovatore 21:46, 22 March 2006 (UTC)

I fully agree with your assessment. In fact, I'll go further: this is obvious crackpotism. Various ancient philosophers have made dubious or meaningless claims about infinity (I had found a quote by Aristotle stating that the number of grains of sands on a beach was "infinite"), but none of them corresponds to what we now view as transfinite numbers; and Indian mathematicians were so proud of their invention of the decimal system that they had fun writing very large numbers as cosmic cycles, and sometimes they confused them with infinity, but obviously this has nothing to do with the modern concept. I support any move toward removing the incriminated section. --Gro-Tsen 22:04, 22 March 2006 (UTC)

It is no more (and no less) nonsense than Galileo's work on infinite numbers, in which he found that the natural numbers were equinumerous with a subset (the set of squares) and recoiled in horror. It is not the transfinites. Septentrionalis 22:41, 22 March 2006 (UTC)

Well, if it could be documented that the Jaina had the notion of equinumerosity (as witnessed by one-one matching), that would already be a step in the right direction, though I still don't think it would be enough to use the word "transfinite". As I understand it the historical context is that Cantor didn't want to use the word "infinite" because he was talking about things that were not absolutely infinite. They were trans-finite, beyond a limit, but not in-finite, without limit. That last sentence may be a bit of retrospective etymology on my part, but I think it really is the basic idea, whether or not Cantor had that specific etymological reasoning in mind. --Trovatore 22:46, 22 March 2006 (UTC)

A section reviewing the general history of eastern and western ideas about infinity, including Aristotle's ideas, as well as Gaileo's shock, would not be out of place somwhere on WP. We do, after all, have Category:History of mathematics and the topic of infinity, just like the question "what is four dimensions", was a legit intellectual excercise over the millenia. No doubt Immanuel Kant had some pronouncemnts as well. linas 00:54, 25 March 2006 (UTC)

Never mind. That article exists, its called infinity, and the Indian stuff should be moved there. linas 01:02, 25 March 2006 (UTC)

Another tedious orthography question

Vladimir Arnold or Arnol'd? Vladimir Drinfel'd or Drinfeld? We should be consistent: and preferably across all references to them in WP. (In both cases we currently use the apostrophe sometimes, but far from consistently.) —Blotwell 06:46, 24 March 2006 (UTC)

For Арнольд, we may as well defer to the way it appears on his books and web page, "Arnold". --KSmrq^T 02:02, 25 March 2006 (UTC)

Transliteration of the soft sign ("ь")—which does not so much represent a sound as a modification—is problematic, and conventions vary. But for names, it appears that in a context like this, appearing before a consonant, it would typically be omitted. Wikipedia allows us to choose that one as primary, for the article name, and use redirects for the variants. --KSmrq^T 18:35, 25 March 2006 (UTC)

Springer Encyclopaedia of Mathematics

I just stumbled across the Springer Online Encyclopaedia of Mathematics it claims to be

the most up-to-date and comprehensive English-language graduate-level reference work in the field of mathematics today. This online edition comprises more than 8,000 entries and illuminates nearly 50,000 notions in mathematics

and seems to live up to its description. It seems like this could be a useful resouces for many articles. --Salix alba (talk) 00:14, 25 March 2006 (UTC)

Yes, and its pretty good too, at least for the 3-4 articles I looked at. I created a template fr this, which may be usd as the following (for example:) {{springer|id=f/f041440|title=Fredholm kernel|author=B.V. Khvedelidze, G.L. Litvinov}} which results in

B.V. Khvedelidze, G.L. Litvinov (2001), “Fredholm kernel”, in Hazewinkel, Michiel, Encyclopaedia of Mathematics, Kluwer Academic Publishers, ISBN 978-1556080104

linas 00:47, 25 March 2006 (UTC)

Would be a good idea to add those entries to Wikipedia:Missing science topics. I will try to look into that these days. Oleg Alexandrov (talk) 06:45, 25 March 2006 (UTC)

First article I hit was the normal distribution [8] I was quite disappointed in that it doesn't have a single graph of it. That said, it'd be worth copying the index into a new article or added to the missing science topics. Cburnett 06:56, 25 March 2006 (UTC)

No, you can't do that; this came up before with MathWorld. It's a copyright violation.

The Springer encyclopedia seems pretty weak in set theory. --Trovatore 07:29, 25 March 2006 (UTC)

Also compare the article on Self-adjoint operator in WP to the one in Springer. Tell me which one is better.--CSTAR 14:45, 25 March 2006 (UTC)

Ours is definitely more self-adjoint:

C^*=C.

Oleg Alexandrov (talk) 19:30, 25 March 2006 (UTC)

Is it worth an article SpringerLink Online Encyclopaedia of Mathematics? --Salix alba (talk) 20:21, 25 March 2006 (UTC)

I would think it's probably worth an article (I never heard of it before this discussion, but we're not talking about something put up by some random hobbyist; this is Springer). The issue is how to write a neutral review that's not original research. That's a problem to which I have not thought of any good answer (it's why I slapped my own article on Kunen's book, Set Theory: An Introduction to Independence Proofs, with an OR tag). --Trovatore 20:53, 25 March 2006 (UTC)

See what reviews it has in the scholarly press. Scholar.google.com should have something (this should solve the Set Theory problem, anyway.) If that fails, it can be put in WP space, as a resource. Septentrionalis 21:26, 25 March 2006 (UTC)

They have a lot of great articles. They're beating us in a lot of areas, and already kick the crap out of mathworld (soon it'll be time to put mathworld out of its misery). However, have you seen their diagrams? Complete garbage! -lethe ^{talk +} 17:23, 26 March 2006 (UTC)

I have merged their lists of entries into the Wikipedia:Missing science topics. I highly doubt that this is a copyright violation in any way, as while their lists may be copyrighted (the order of entries I guess :), individual items in the list are not, and after merging together the mathworld links and the springer links and removing the bluelinks, little if any resemblance is left to their orginal lists.

By the way, I brought some order in that Wikipedia:Missing science topics by completing incomplete entries (mathworld had those), putting things in lowercase, regularly removing the bluelinks, and providing links to google search and google books for each entry. Those lists can be rather good at suggesting new redirects, new articles, or judging where we are lacking. Oleg Alexandrov (talk) 21:28, 26 March 2006 (UTC)

Actually, I will send Springer an email asking if they mind using their list as a resource for our redlinks list. Just to be safe. :) Oleg Alexandrov (talk) 00:19, 27 March 2006 (UTC)

I've looked things up in the library's copy one or two times; good to see I don't have to go all the way there now... :-) Anyone know if the online edition differs significantly from the one in print? Fredrik Johansson 00:32, 27 March 2006 (UTC)

none of the springer links seems to work. how does one get to it from the springer website? thanks. Mct mht 07:15, 5 April 2006 (UTC)

The Springer server is down every now and then. Will come back eventually. Oleg Alexandrov (talk) 02:36, 6 April 2006 (UTC)

blahtex 0.4.4 released

Major changes since 0.4.3 are:

support for Japanese and Cyrillic in PNGs
much faster PNG output, because we're using dvipng rather than dvips/imagemagick

Useful links:

test wiki at http://wiki.blahtex.org (recently got attacked by spammers :-))
page illustrating blahtex's features
blahtex home page
updated error list (currently 337 errors)

Dmharvey 14:10, 26 March 2006 (UTC)

The dx in \int f(x) dx doesn't look right in the MathML output (it's rendered "d x"). Fredrik Johansson 14:45, 26 March 2006 (UTC)

Which browser+version are you using? This was a known problem with earlier versions of Firefox. Dmharvey 14:48, 26 March 2006 (UTC)

Firefox 1.5.0.1. Fredrik Johansson 14:58, 26 March 2006 (UTC)

Hmmm... does the same thing happen at all font sizes? Dmharvey 20:54, 28 March 2006 (UTC)

Normal, no style, enlarged.

Essentially. Increasing the text size a few times doesn't change the absolute width (it stays at 3 pixels); it looks normal if I use an obscenely large font. By the way, the space gets one pixel narrower if I disable the page CSS style (but still looks too wide, though this could be in my imagination). See image. Fredrik Johansson 21:28, 28 March 2006 (UTC)

That's a bummer. Thanks for pointing this out. I looks like Firefox is interpreting the "d" and "x" as belonging in separate "frames" and doesn't want to overlap them; therefore because the "d" is italicised and tall, it pushes the "x" to the right. I'm not totally sure about this, especially since there's a one pixel overlap in your second example, but that could just be some rendering thing that happens after the frames have been positioned. I will put it on my list of bugs to pursue; it's probably something that the Firefox folks will need to deal with. Dmharvey 03:39, 2 April 2006 (UTC)

gradient issues

There is some disagreement on what to include in the gradient article. It is argued by some parties that it should be a disambig. Comments welcome at talk:gradient#Should gradient be a disambigutation page? Oleg Alexandrov (talk) 17:20, 26 March 2006 (UTC)

Programs for linear algebra illustrations

What programs would people around here recommend for making images to illustrate geometry and linear algebra concepts (and the like)? I'd like to manually input coordinates for vector arrows, line segments, points, etc., choose colors and line styles, and output the result to SVG. Eukleides looks good, but it doesn't do 3D and I need that. Fredrik Johansson 23:45, 26 March 2006 (UTC)

Matlab gives you complete control, 3D, and output to color EPS. Here is a (free) program which it seems outputs to svg [9]. May be more. Of course, Matlab costs money, but should be available at any university, if you are in academia. Here are some pictures I made with it. Oleg Alexandrov (talk) 00:16, 27 March 2006 (UTC)

Yeah, I have access to Matlab, but not at home (not conveniently, anyway). Fredrik Johansson 00:22, 27 March 2006 (UTC)

You could learn a scripting language and roll your own tool. It shouldn't be that difficult. Dysprosia 02:41, 27 March 2006 (UTC)

Next thing you build your own rocket in your backyard, and could as well write your own encyclopedia. :) Oleg Alexandrov (talk) 04:03, 27 March 2006 (UTC)

Been there done that SingSurf, good for algebraic surfaces. It relies on JavaView which is quite good for 3D maths and is free as in beer but not speach. Also see Interactive geometry software for others. --Salix alba (talk) 12:04, 28 March 2006 (UTC)

IE compatibility

I wonder what people think of a policy of changing unicode html tokens to tex tags in order to ensure compatibility with Internet explorer browsers which apparently have problems with some unicode symbols. I guess compatibility with IE takes precedence over our own MoS guidelines, right? What do you folks say? -lethe ^{talk +} 11:53, 28 March 2006 (UTC)

We shouldn't use Unicode gratuitously in articles anyway. Unicode is far from being a ubiquitous standard, and when someone tries to edit in something that isn't Unicode capable, it screws up the entire article. That's not good behaviour. Dysprosia 11:57, 28 March 2006 (UTC)

When I work on my Windows laptop I don't see some Unicode characters on Wikipedia, even though I use Firefox and not IE. I guess it is a problem of missing fonts more than browser.

Changing unicode to LaTeX may be a huge amount of work, and may yield expressions which are a mix of both html and TeX. It would be fine I think if people do it on a case by case basis, but I would not be sure about making that a policy.

To comment on Dysprosia's comment, Unicode is a fact of life on Wikipedia given interlanguage links and foreign names/words. Luckily not that many browsers screw Unicode anymore, maybe just Lynx or really old browsers. Oleg Alexandrov (talk) 18:52, 28 March 2006 (UTC)

Well, I happen to use Lynx some times when I don't have access to a graphical browser, or (less often for me), when I use other operating systems I may use a browser that may not support Unicode. I'm not saying that Unicode should be completely removed from articles, it just shouldn't be used when there are other more portable equivalents out there that won't be mangled if someone edits with something that's not Unicode compatible. For example, one shouldn't just use a Unicode alpha when an α will be just as suitable. Dysprosia 22:55, 28 March 2006 (UTC)

I don't understand your example. Isn't that a unicode alpha that you've displayed? We shouldn't use unicode when unicode will suffice? -lethe ^{talk +} 23:04, 28 March 2006 (UTC)

No, it's a HTML entity, edit the section and have a look: α renders as α. Dysprosia 23:08, 28 March 2006 (UTC)

Oh, I see. But uh, don't the web browsers render the HTML tokens with unicode? I thought they did, and so therefore HTML tokens and UTF-8 text are equivalent (for viewing purposes). Or am I mistaken? -lethe ^{talk +} 23:11, 28 March 2006 (UTC)

The difference is that the Unicode alpha is just another character in the text, like "t", or "q". The HTML entity is the string "α". All good computer systems should support ASCII, and the HTML entity consists of only ASCII characters, so no matter if you use a computer that supports Unicode or if you don't, the string will be unchanged. However, some browsers that don't support Unicode simply ignore the Unicode characters, so if someone edits with one of those browsers, it will look like all the Unicode characters in the article have suddenly disappeared. If the browser chooses to render "α" with a Unicode character, that's fine, but it doesn't mean that that Unicode character is somehow equivalent to the HTML entity -- they aren't. Hope that explains things a bit better... Dysprosia 23:16, 28 March 2006 (UTC)

Yes, I understand now. UTF-8 text will get lost in the edit box by some browsers, even though it renders the same. Thank you for explaining. -lethe ^{talk +} 06:58, 29 March 2006 (UTC)

Replacing Unicode would be bad policy. This question was already decided when the wiki software switched over to UTF-8 as a standard. The world has gone Unicode, and that includes even standards-flouting Microsoft. To the best of my knowledge, all contemporary browsers can display Unicode characters if configured with adequate fonts. Usually Code 2000 will suffice. --KSmrq^T 21:29, 28 March 2006 (UTC)

I brought this up because some user went on a crusade to replace all instances of ℵ with $\aleph$ inline and display mode alike. I didn't like it, but apparently IE doesn't display ℵ correctly even if you have a font for it (which we learned because it displays if he changes web browser). -lethe ^{talk +} 23:08, 28 March 2006 (UTC)

PNG shouldn't be used inline. Dysprosia 23:10, 28 March 2006 (UTC)

That is also my opinion, but do we not have an obligation to lower our standards to support IE? Some might say we do. -lethe ^{talk +} 23:16, 28 March 2006 (UTC)

The HTML entity ℵ looks like it works... Dysprosia 23:25, 28 March 2006 (UTC)

Are you saying that ℵ displays differently from ℵ in IE? Septentrionalis told me once that he couldn't see ℵ correctly (I don't know for sure what setup he was using). --Trovatore 23:33, 28 March 2006 (UTC)

Doesn't work for me, either. I certainly prefer ℵ, regardless, as it's difficult to distinguish ℵ from the Hebrew letter by inspection if they were in Unicode, and those may display differently on different browsers. — Arthur Rubin | (talk) 23:36, 28 March 2006 (UTC)

I'm saying that ℵ should work on IE, that is, it should actually display. It shouldn't matter that much that it "looks different". I don't have IE so I can't check this. Dysprosia 23:56, 28 March 2006 (UTC)

I do not see the point of distinguishing ℵ from the Hebrew letter. Next we will be wanting an α different from alpha. I'm using a computer in the same cluster; both ℵ and ℵ now display well (and almost identically) in this IE set-up, but the second is a little square box in the edit window. Septentrionalis 00:08, 29 March 2006 (UTC)

alefsym definitely looks better alongside roman text than a Hewbrew aleph. The Hebrew aleph is too big. Do you not also find it so? -lethe ^{talk +} 07:05, 29 March 2006 (UTC)

I don't understand what you're talking about. If you want an aleph, you have ℵ, which actually does work. Dysprosia 00:10, 29 March 2006 (UTC)

OK, when I reboot into Windows to look at this in IE, I just see a square for the ℵ character. This is in IE 6.0.2900.someothernumbers, SP2, WinXP Home Edition, Version 2002, SP2. I suppose to really figure out what's going on I should say what fonts I have installed, but there are too many to conveniently list. --Trovatore 00:43, 29 March 2006 (UTC)

It's probably not a font issue, since if you try another browser on the same system, it will display. It's an IE issue. Now the question is, do we want to replace inline HTML token/UTF-8 with tex to support IE? -lethe ^{talk +} 07:05, 29 March 2006 (UTC)

I am the "user [who] went on a crusade to replace all instances of ℵ with $\aleph$ ". I was just replacing characters which I could not read with IE in those articles which I was trying to clean up for other reasons. alefsym causes the same problem as "ℵ" in IE. Also there is an element symbol which does not display correctly; and a proves symbol. Although these are rare. Oddly, I think that the actual Hebrew letter aleph works (at least I see the Hebrew letters OK in Google when I switch languages). JRSpriggs 05:24, 29 March 2006 (UTC)

Why do novices constantly "fix" things that obviously are not broken for most people? If the Unicode characters are in the article, there is nothing wrong with the characters for the author, and presumably for most readers. Adjust your own browser, your fonts, your configuration. Common sense and common courtesy suggest you at least ask before launching an ill-conceived massive alteration campaign—especially if you haven't been editing long enough to create a User page!

Suggestion: Look at this page and adjust the things under your control so you see as few missing characters as possible. (Note: For me, none are missing. Again, I highly recommend Code 2000.) This is a page in my personal user space; do not edit it! --KSmrq^T 07:07, 29 March 2006 (UTC)

I have been editing here for about two months. I did not create a user page because I have no interest in talking about myself for the public. I have a User-talk page to communicate about our shared work here. You are wrong to say that these characters are "obviously are not broken for most people". Most people use Internet Explorer 6.02 or earlier. So most of our readers will not be able to read the characters in question. And remember, this is an encyclopedia for the general public, not a private domain for you and the other authors to glory in their own words. Do not worry, I will not edit your user pages. JRSpriggs 07:33, 29 March 2006 (UTC)

Don't get defensive. KSmrq has a good point. We have a community here with established conventions. You can do whatever you like, make whatever decisions you want, decide what's the best format to use in articles, but we have the same rights, and in order to keep from devolving into continual revert wars, we try to respect consensus and community guidelines. When you've been here a while, you get a stronger feeling for that. Now, obviously you feel that wikipedia has to conform to IE's capabilities. Maybe you should try to win people over to your view instead of fighting with them. At the moment, I'm on the fence, but about to fall on the other side. -lethe ^{talk +} 07:43, 29 March 2006 (UTC)

Several distinct issues are at play. One is the recurring integration of novices into the community, with the usual exuberant misstep and jaded correction. A second is the display of the rich panoply of Unicode characters, whether mathematical or otherwise, in articles as viewed with a diversity of browers and fonts. Almost always the problem is with the fonts and browser settings. The Unicode characters are here to stay, especially when BlahTeX generates MathML for Wikipedia. A third issue is what appears in edit windows. The wiki software could be conservative and convert non-ASCII characters to named or numeric entities, but a browser that can display a page with Unicode characters can probably edit them as well.

But my point is none of these. I'm genuinely puzzled by the hubris of editors who assume that the article is broken because their view of it shows missing characters, especially when the same character appears in many articles. Do they think everyone else is stupid or blind? I don't know the statistics for Wikipedia readers, but one browser watch site shows slightly over 50% IE6 users, so it would seem reasonable to assume that many people had viewed any given Wikipedia article in IE6 without complaint. Yet these editors inexplicably fail to draw that conclusion.

Which leads to a design question: Is there anything we can do to head off these edits before they occur? The insert menu already shows a large assortment of non-ASCII characters, but obviously that's not enough of a hint to some editors. Should every article page have a prominent link to help with missing characters? --KSmrq^T 09:10, 29 March 2006 (UTC)

I know what we need. Here pages that use indic fonts include a template which indicates that they're being used and that if you want to view the page, you have to make sure your system is ready. If we want to use stuff in a math article which doesn't have widespread support, we could have a template like that one. That would probably keep new editors from changing font stuff, right? -lethe ^{talk +} 12:26, 29 March 2006 (UTC)

This page contains Indic text. Without rendering support, you may see irregular vowel positioning and a lack of conjuncts. More...

What about the difference between ''x''² x² and ''x''2 x²? I'd say the latter looks better on my screen. --Salix alba (talk) 23:39, 29 March 2006 (UTC)

Only a few superscript characters have Unicode points, so consistency weighs in favor of the tags. For example, look at x²x³ = x⁵ versus x²x³ = x⁵. Similarly, a few special fractions have Unicode points, while most do not. For example, compare ¾ (entity frac34) to ³⁄₇ (using entity frasl, and tags and ). --KSmrq^T 01:21, 30 March 2006 (UTC)

Move of "Ruler-and-compass constructions" to "compass and straightedge"

John Reid moved the article "Ruler-and-compass constructions" to "Compass and straightedge". As the article currently stands, I think there are problems with the new name. I intended to move the article back to its original name, until we can reach a consensus, but I inadvertently left out the hyphens and moved it instead to Ruler and compass constructions. Please share your views on any of this at Talk:Ruler and compass constructions. I will volunteer to make any necessary changes after we arrive at a consensus about what to do. Thanks — Paul August ☎ 17:58, 28 March 2006 (UTC)

Poll on "ruler" vs "straightedge"

Some of us can't agree on how to properly call the article Ruler and compass constructions, with the other option being Compass and straightedge. "Votes" at Talk:Ruler and compass constructions are solicited. :) Oleg Alexandrov (talk) 21:49, 29 March 2006 (UTC)

Neusis

Please see Jim Loy's angle trisection page. He shows a few methods using forbidden tools; I call your attention to the so-called tomahawk and to the movable, marked carpenter's square. Is the use of these tools not equivalent to neusis? John Reid 18:33, 31 March 2006 (UTC)

Please! Neusis? Yes? No? John Reid 19:59, 7 April 2006 (UTC)

Apr 2006

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

Parametric coords

Hi all. I saw there wasn't any article on parametric coords. I am willing to create one, if needed. However, since it might be the same thing as curvilinear coordinates, I've just put in a redirect for now. I've asked the question on Talk:Curvilinear coordinates, but so far nobody can tell me if they are identical, or just related, topics. Please take a look and post your conclusions at that talk page. StuRat 21:24, 1 April 2006 (UTC)

If someone does write the article, please don't use that name, but spell "coordinates" out in full. Ryan Reich 22:14, 1 April 2006 (UTC)

Absolutely. I do like to add redirects from short names to full names, though. This allows users to enter shorter words like "coords", "lab", "gym", etc., which are both more convenient and less likely to contain spelling errors. StuRat 02:31, 2 April 2006 (UTC)

Parametric coordinates really require a parameterisation, for example a parameterised curve or surface. For that reason I've now made parametric coords redirect to parametric equation. --Salix alba (talk) 09:40, 2 April 2006 (UTC)

Yes, but not all parametric equations describe a parametric curve or surface. Therefore I feel that an article specific to this application of parametric equations is justified. StuRat 02:29, 3 April 2006 (UTC)

Direct logic

Could someone take a look at Direct logic? I see some potential problems with this, given who the author is. —Ruud 16:01, 2 April 2006 (UTC)

IMHO, it looks like this is original research and doesn't belong. How does one tag an article to indicate as much?Lunch 18:42, 3 April 2006 (UTC)

Petition on WAREL's talk page

For background, see Wikipedia talk:WikiProject Mathematics#Statistics on User:WAREL several sections above.

Fresh out of his most recent 48 hours block, WAREL/DYLAN has been engaging in edit wars at field (mathematics) and division ring, moving, incorrectly, interwiki links from the former to the latter, see WAREL's contribs and DYLAN's contribs.

I wrote a petition on the top of his talk page asking him to stop revert wars, as this has been going for too long. If you are familiar with WAREL's edit warrior activity, and think that it's a bad thing, you may help by signing the petition. I doubt WAREL/DYLAN will learn anything from it, but it may give more legitimacy to future attempts at blocking him for disruption. Oleg Alexandrov (talk) 17:46, 3 April 2006 (UTC)

I've tried to figure out what this editor's motivation could possibly be, and my current working hypothesis is that he's engaged in a "destructive testing" experiment to figure out exactly how much it's possible to get away with before drawing blocks/RfC/permanent ban. Otherwise it's hard to understand why he keeps pushing just inside the edge of written rules, trying to get trivial changes kept, ones it's hard to believe he thinks would make any real difference.

Is it time to think about bringing the experiment to a successful conclusion? --Trovatore 21:06, 3 April 2006 (UTC)

Guys, make it an RfC. It's what that is for. Charles Matthews 21:35, 3 April 2006 (UTC)

I am currently editing Wikipedia:Requests for comment/WAREL -lethe ^{talk +} 22:30, 3 April 2006 (UTC)

I guess the RfC has to be certified by other people, so anyone who cares to, certify it. -lethe ^{talk +} 22:55, 3 April 2006 (UTC)

Great, thanks! I guess the RfC has been certified, I see a lot of names there. I now unblocked WAREL so that he can comment in the RfC. Oleg Alexandrov (talk) 00:04, 4 April 2006 (UTC)

DYLAN and finite fields

While I am not sure on what to do about the current dispute at field (mathematics), which is centered on the use of "field" at the Japanese Wikipedia, DYLAN LENNON now claims that a finite division ring is not the same as a finite field, and removed the interwiki link from our "finite field" to the Japanese "finite division ring". Comments welcome at talk:finite field. Oleg Alexandrov (talk) 18:57, 6 April 2006 (UTC)

My Muddle

I have frequently had an unpleasant experience when looking up mathematical terms in Wpedia. I go to the article I want and, reading the definition of the term, I encounter another term I don't understand. If there is a link connected to the term I open a new tab to find the definition of the second term. In reading the second definition I find the need to look up a third, then a forth, fifth, sixth. I am soon swamped by "hanging" definitions. But, not infrequently, a term is used without any attempt to define it. Do mathematicians write these articles only to communicate with other mathematicians? Surely an encyclopedia is meant to educate people about things they don't already know. Too Old 00:19, 7 April 2006 (UTC)

This is more or less of a problem depending on the topic in question and how much effort has been spent on writing it. If you mention it here, or on the discussion page of the relevant article, it's more likely to get fixed. Dmharvey 00:25, 7 April 2006 (UTC)

Hmm...I sometimes find that some calculus-related articles make more sense on Wikipedia than Wikibooks — Ilyan e p (Talk) 00:38, 7 April 2006 (UTC)

Wikipedia is not meant to teach you the background knowledge you need. Wikipedia is an encyclopedia, not a collection of tutorials. If you want that, try Wikibooks. Dysprosia 00:40, 7 April 2006 (UTC)

Yes, it is good to keep things accessible, that means having relevant links to all concepts encountered. That of course does not mean it is Wikipedia's fault if you start reading an article about a term you don't know only to run into links to other terms you don't know. Wikipedia is (and should be) after all a loose collection of essays, not a course (and even for a course, you have prerequisites :) Oleg Alexandrov (talk) 01:08, 7 April 2006 (UTC)

An encyclopedia should not be of use only to a specialist, like a physician's medical database. An encyclopedia is, IMHO, meant to be a resource for the generally well-educated layperson, who might need the occasional definition, but definitely should not need a tutorial to understand an article. The background you speak of should not have to be extensive prior knowledge of the subject. When I consult, for example, the article on steel, I find an extensive treatment of the subject, occasionally having to find a definition, but not having to undertake a course in metallurgy in order to understand the article. When I go to look up a definition in that article, I need not go further and further afield in order to understand the definition. Too Old 01:37, 7 April 2006 (UTC)

An encyclopedia is a reference work, a collection of facts that are explained well and do not attempt to excessively mollycoddle the reader. You are comparing apples and oranges with your example of steel there -- mathematics, as well as certain other fields, are necessarily reliant on your accumulation of prior knowledge. A more apt analogy is expecting to understand an article on quantum spin. That article does not and should not teach you the basics of physics before launching into the actual article content, but it can give some motivation and make some simple insightful analogies. Dysprosia 01:52, 7 April 2006 (UTC)

I would like to dispute you on one point without arguing with the intent. The argument that "math is special" because it is more structured (or more rigorous, or constantly evolving, or any other argument I've seen used at various times) is very silly and I don't think it's good here. There are a lot of topics that can be covered with only elementary background. What do I mean by elementary? Well, read steel carefully and see what it assumes: right off the bat it talks about alloys, various chemical elements, technical ideas like "ductility" and "tensile strength", and the notion of atoms. All fundamental ideas in chemistry and physics. Too Old seems to have had no problem with these, yet I don't feel that this corpus of prerequisites is any larger than asking people to know calculus or Euclidean geometry. But I don't know that this was his problem, since he never said which articles he's found too technical.

I guess my point is that I feel like "math is hard" pulls too much weight around here even (especially!) when spoken by mathematicians. A reasonable article should assume the reader's knowledge of terms which form a language of discourse for the subject, so that each sentence need not be interrupted with definitions and qualifications, but anything that (in the context of the discursive standard) could be taken as technical should be explained. Rather than telling Too Old to go off and get an education, we should at least extract some productive information from his complaints and see what sort of stylistic changes might be needed around here. Ryan Reich 03:03, 7 April 2006 (UTC)

The companion matrix article, for instance, assumes you know what a polynomial is (and knowing what a polynomial is requires its prerequisites), knowing what a matrix is and the necessary basic matrix algebra necessary, plus a little more advanced matrix theory such as the characteristic polynomial is, diagonalizability, plus if you'd like to get through the rest of the article, assumes you know some basic field theory and linear algebra. There are articles and areas of mathematics with much worse prerequisites than that -- there are a lot of extremely deep areas, just pick something that is right near the bottom of that "depth". Mathematics does build on prior knowledge and decreeing this fact as "silly" doesn't quite make much sense.

No one is telling Too Old to "go off and get an education", though one should not blame the article for one's gaps in knowledge. Of course, a bad article can and does exist where it explains the concepts in an illucid way, and that of course should be fixed, but an article should not aim to teach the reader prior knowledge -- that responsibility is up to the reader, not the reference work. Dysprosia 03:43, 7 April 2006 (UTC)

My complaint was that the claim that math has special depths of prerequisites is silly. Go look at any science; they're just as bad. In particular, the use of this claim in this context, namely in response to someone who was almost certainly referring to articles that an amateur might be interested in reading, is silly, since such articles can without doubt be disposed of without using advanced concepts (of course, later in the article advanced ideas may arise. That has never been part of this discussion, though). In particular, I was not claiming that all math can be done at an elementary level (actually, I think I made allowances for the opposite). The example you give simply supports my contention that a common language be established at the start of the article. What might not be a good idea, in this particular case, would be for the article to introduce the theory of companion matrices in the context of modules over a PID, since it can be done more simply. This is the sort of distinction I'm making, yet I'll bet some people (I might be one of them, depending on my mood) will argue that the article should talk about companion matrices this way, since it's "more correct". That argument only works if it doesn't sacrifice clarity. Ryan Reich 04:12, 7 April 2006 (UTC)

I don't understand why you make the claim because I never did claim myself that math has "special depths of prerequisites" -- I said "mathematics, as well as certain other fields", and made special note that physics is just as bad. Otherwise I think we may be in violent agreement. Dysprosia 04:37, 7 April 2006 (UTC)

Oleg, you've absolutely hit the nail on the head. Dysprosia 01:52, 7 April 2006 (UTC)

Two sources of difficulty are obvious: (1) the structure of the subject, and (2) how it's presented. It is a fact of life that knowledge is a web, not linearly structured in dependency. Knowledge of A supports understanding of B, but also knowledge of B supports understanding of A. A writer of a text must work hard to order the presentation linearly, and at best achieve only partial success. Often a text read a second time will make more sense, because the additional context is available. A writer of a web article has no control over order of access. The only option is to include definitions, not just link to them; but taken too far, these intrusions become an obstacle themselves. Instead, some people use popups to get a quick look at a linked definition without opening a tab (or a window, in an antiquated browser). --KSmrq^T 01:24, 7 April 2006 (UTC)

Pop-ups are life savers (well okay time-savers) — Ilyan e p (Talk) 01:31, 7 April 2006 (UTC)

We don't write our articles solely for mathematicians; we endeavor to make them as readable as possible. Accessibility is definitely a consideration for us. But only one of many, so sometimes an article is not as accessible as we might like. If you think the articles need help, then you know what to do. This is a wiki, be bold, edit. Complaining about the quality of some difficult work done for free by volunteers in their spare time is not going to win you any friends. -lethe ^{talk +} 01:57, 7 April 2006 (UTC)

For the record Talk:Hilbert_space#The_Layperson, Talk:Calabi-Yau manifold, Talk:Lie_group#is_this_useful.3F, some more examples of people with the exact same complaint. Happens a lot, I guess. If there were some magical way to easily write mathematics articles that were easy to learn, I would employ it in my writing. -lethe ^{talk +} 04:00, 7 April 2006 (UTC)

Per Ryan Reich, please make the complains specific. There are reasonable complaints, and there are unreasonable ones. :) Oleg Alexandrov (talk) 03:13, 7 April 2006 (UTC)

Well, it seems that I am not alone. But, people, I did not mean to attack your virtue. There was a suggestion that I should "be bold, edit". Were I 30 or 40 years younger, and had the resources, I might take up the serious study of mathematics. I then might find a way to rewrite some of these articles to make them more accessible. But, life is too short... I have had my say. I leave you now to play The Glass Bead Game among yourselves. If you have any thing to say to me I shall be happy to read it on my talk page, or you may email me. Too Old 07:11, 7 April 2006 (UTC)

Sorry, but sciences just aren't for everyone; you have to have a certain basic knowledge to be able to understand more complicated concepts in mathematics, physics, and so on. There's only so much we can do about that. —Nightst a llion (?) ^{Seen this already?} 14:51, 7 April 2006 (UTC)

I think Too Old has a valid criticism, frequently repeated. The coverage of mathematics is often at too high a level, organisation of articles is confusing, core topics like Algebra are woefully inadaquate. Yes we have done good work todate, our coverage is extensive, but there is still a long way to go.

I propose creating Wikipedia:WikiProject Mathematics/Essential articles where we can identify which are the most important mathematics articles, assess then for quality and also mathematical level required. An example we could follow is Wikipedia:WikiProject Computer and video games/Essential articles which nicely organises that fields core material. This would also fit in with the Articles for the Wikipedia 1.0 project discussed above.

Is anyone interested in helping on this? --Salix alba (talk) 23:09, 8 April 2006 (UTC)

WAREL/DYLAN indef blocked

Well, the RfC and all our pleas seem to have no effect on his behavior. I blocked both accounts indefinitely, and wrote a note at Wikipedia:Administrators' noticeboard/Incidents#Indef block of WAREL/DYLAN LENNON.

This will generate serious questioning, as we are talking about an indefinite block, no less, so your comments there are appreciated, to make the case that this is a community-backed decision. Oleg Alexandrov (talk) 17:49, 7 April 2006 (UTC)

formal laurent series

Should formal Laurent series redirect to Laurent series (as it currently does) or to formal power series (my preference)? Dmharvey 18:20, 7 April 2006 (UTC)

I think formal power series is better, especially since the doubly infinite Laurent series cannot be treated formally (with rare exceptions). — Arthur Rubin | (talk) 18:52, 7 April 2006 (UTC)

Maybe the section on formal laurent series in the article Laurent series should be merged into the corresponding section of formal power series. -lethe ^{talk +} 18:54, 7 April 2006 (UTC)

Done. Dmharvey 17:03, 9 April 2006 (UTC)

references: multiple page numbers for same book

I've been trying out the new cite.php tool, i.e. with the <ref> and </references> tags. See for example quasi-finite field. But it looks a bit silly there, because I have two different page numbers for the same book. Does anyone know a slicker way to handle this? Dmharvey 18:22, 7 April 2006 (UTC)

David, I've made an edit at quasi-finite field, to suggest another way of handling your situation. However, I don't really like the look of the cite tool, I prefer the rf/ent templates, so I've also made a second edit using the rf/ent templates, to see if you like the way they look better. Paul August ☎ 21:49, 7 April 2006 (UTC)

I gotta admit I don't like any of the options very much. What I really want is something like LaTeX's \cite command, i.e. each reference gets e.g. a number or sequence of letters, and then you can specify the page number inline. So for example it would read like "according to [Se, p.198] you can do ..., or you can see later on [Se, p.204] suggests blah blah blah", and then in the references it just has one item, "[Se] Serre, Jean-Pierre, Local fields, etc". But it doesn't look like any of the automated mechanisms allow one to do this. Dmharvey 02:27, 8 April 2006 (UTC)

Solicit help organizing topics relating to approximation theory

I have recently created some material in the approximation theory page, relating to polynomial approximations to special functions. This is related to function approximation, Chebyshev polynomials, and polynomial interpolation, but in ways that I'm not clear about. I'm not an expert in the taxonomy of this area of mathematics, only in the specific things about which I wrote. In particular, I know that there is a field of interpolating polynomials through given data points, and that Chebyshev polynomials (and their roots) are involved in this. I can't believe that "approximation theory" is just about Remes' algorithm or use of Fourier/Chebyshev analysis to make optimal polynomials. So this whole area may be somewhat messed up, and my material might be in the wrong place. Would someone who knows his/her way around in this area be willing to take a look and move things around?

William Ackerman 00:40, 8 April 2006 (UTC)

Copies of long essay on multiple talk pages

User:BenCawaling has added apparently identical copies of a 2,500 word essay titled "About the incomplete totality of the infinite set of prime numbers" to the following talk pages:

Talk:Riemann hypothesis

Talk:Gödel's incompleteness theorems

Talk:Cantor's theorem

Talk:Cantor's diagonal argument

Talk:Bijection

Talk:Prime number

Talk:Fermat's last theorem

I don't think that Wikipedia is the right place for this diatribe, and we certainly don't need multiple copies of it - but as it's all on talk pages, I don't know what policy or guideline could be quoted in support of removing it. Does anyone have an opinion on what should be done about this (if anything) ? —Preceding unsigned comment added by Gandalf61 (talk • contribs) 11:41, April 8, 2006

I think we should remove it as a kind of spam. Paul August ☎ 15:36, 8 April 2006 (UTC)

Replace all but one of them with a link to the remaining one? Or replace all with a link to his userspace? -lethe ^{talk +} 15:37, 8 April 2006 (UTC)

I suppose any of these things would be OK, but there's a risk that it would constitute paying him too much attention. At least he's been good enough to confine his ramblings to a single section on each talk page, and as far as I've seen no one's bothered to respond. If it stays that way, maybe he'll get bored and go away, and the screeds will eventually pass harmlessly into archives. Of course if he were to start editing article pages, or injecting irrelevancies into other discussions on talk pages, then action might have to be taken. --Trovatore 18:32, 8 April 2006 (UTC)

You are right about the unnecessary multiple copies of some of my discussion text. I have just downloaded Wikipedia's "How to edit a page" and would make the deletions and links to one in "Prime number" article talk page. For now, you may do as you please with my "contributions".

You are wrong about no one's responding --- countless with positive reactions do in my Yahoo e-Mail address (I intentionally include it because, just like David Petry's last comments "As I see the situation now" in his "Controversy over Cantor's theory" article, the majority of Wikipedian administrators and editors are Cantiorian fanatics who (loking at their user pages (where there are any) are not at all mathematically qualified to discuss these stuff and whose best response is bad-name-calling (just read the next 3 messages) or appeal to their or their idolized "authoritative knowledge" but not actually refuting the arguments proferred even though they cite only elementary mathematics understandable by even honor high school students. The Yahoo e-Mail messages that I received confirms to me that Wikipedia articles are widely read by mostly amateur mathematicians or stidents. I was hoping to give them alternative understanding of the most controversial issues in modern mathematics to discuss with their professors.—Preceding unsigned comment added by BenCawaling (talk • contribs)

A better idea would have been to actually contribute to the creation or update of an article, instead of spamming multiple pages. By the way, thanks for insinuating that we are nothing but name-callers, then accusing us of being "Cantorian fanatics". Isopropyl 03:21, 14 April 2006 (UTC)

Crank spam. Delete. Charles Matthews 18:39, 8 April 2006 (UTC)

Agreed; delete. Talk pages are explicitly devoted to discussions about the article itself. --KSmrq^T 22:05, 8 April 2006 (UTC)

Agreed; crank spam. There is lots of that in talk pages in violation of the stated purpose of talk pages, unfortunately. However, in most cases enforcing this policy is probably a pain. In this case there's so much of it that it should all be deleted. So I guess the message to crank spammers is this: if you have something cranky to say, keep it short.--CSTAR 22:34, 8 April 2006 (UTC)

I have moved this essay to User:BenCawaling/Essay and replaced each copy on an article talk page with a link to its new location. Gandalf61 08:46, 14 April 2006 (UTC)

WAREL is back

This is getting interesting: two socks at the same time: [10] [11]. And an anonymous edit: [12]. Oleg Alexandrov (talk) 19:57, 8 April 2006 (UTC)

How sure do we have to be that these are him before we permban the socks? That's my inclination. -lethe ^{talk +} 20:32, 8 April 2006 (UTC)

I was under the impression that on-sight permabanning of socks was reserved to Willy on Wheels-level offenders. Isopropyl 20:40, 8 April 2006 (UTC)

Oleg, just do it. We'll pick up the pieces later. We can always apologize to anyone blocked by mistake; it's not like any huge permanent damage is done. --Trovatore 20:50, 8 April 2006 (UTC)

Oh, and by the way, this last incident should more than justify restoring the permanent ban on WAREL. --Trovatore 20:52, 8 April 2006 (UTC)

Someone made the comment that WAREL isn't learning anything from these repeated blocks. I think that if we keep unblocking him and he continues along the same path, we're the ones who aren't learning anything. Those who are about to block, we salute you. Isopropyl 21:25, 8 April 2006 (UTC)

I banned 64.213.188.94 (talk · contribs) indefinitely. -lethe ^{talk +} 22:33, 8 April 2006 (UTC)

I asked Lethe to shorten the block for a day, as IP addresses can be shared, unlike user names. On the more general problem, I start thinking that WAREL may actually not only be a highly arrogant user but also have some kind of compulsive disorder. In the worst case scenario he will play a cat and mouse game making new accounts just as we block them. No easy solution in sight. Oleg Alexandrov (talk) 00:25, 9 April 2006 (UTC)

Interesting common line of thought there. I almost posted a comment that when the permanent ban is put into place, a suggestion to seek psychiatric help should be posted on his user page. That would make it clear we have WAREL's interest at heart. On a practical matter, what IP addresses have the named accounts used by WAREL had? Elroch 00:56, 9 April 2006 (UTC)

Looking through the "contributions" of 64.213.188.94, from day one I see lots of silly vandalism and trolling of the worst sort, interspersed by occasional relatively lucid postings on the very mathematics subjects WAREL and DYLAN LENNON like to post, such as Perfect number and Masahiko Fujiwara. I also see some fascination[13][14][15][16] with one Doyle Farr, apparently a black student at Franklin Pierce College. Whether shared IP or not, I can't say that a permanent ban would be a big loss to Wikipedia. Lambiam ^Talk 04:04, 9 April 2006 (UTC)

I don't think this anecdotal evidence makes a very strong case that the next person who tries to edit from that IP won't be a legitimate, good-faith contributor. Let's keep our responses targeted. OTOH I think immediate permanent blocks should be imposed on User:DEWEY and User:KOJIN and future recognizable sockpuppets as they appear. If we make a mistake it can always be corrected. --Trovatore 16:28, 9 April 2006 (UTC)

Length of an "arc" or of a "curve"?

At Talk: Length of an arc I added a comment arguing that the title ought to be Length of a curve (presently a redirect to Length of an arc). Please discuss there if you care (one way or another). Lambiam ^Talk 03:18, 9 April 2006 (UTC)

{numbers}

Number systems in mathematics .
Basic
$\mathbb{N}\sub\mathbb{Z}\sub\mathbb{Q}\sub\mathbb{R}\sub\mathbb{C}$ Natural numbers $\mathbb{N}$ Negative numbers Integers $\mathbb{Z}$ Rational numbers $\mathbb{Q}$ Irrational numbers Real numbers $\mathbb{R}$ Imaginary numbers Complex numbers $\mathbb{C}$ Algebraic numbers Transcendental numbers Transfinite numbers Split-complex numbers $\mathbb{R}^{1,1}$
Complex extensions
Bicomplex numbers Hypercomplex numbers Quaternions $\mathbb{H}$ Octonions Sedenions Superreal numbers Hyperreal numbers Surreal numbers
Others
Nominal numbers Serial numbers Ordinal numbers Cardinal numbers Prime numbers p-adic numbers Constructible numbers Computable numbers Integer sequences Mathematical constants Large numbers Pi π = 3.141592654... e = 2.718281828... Imaginary unit $i 2 = - 1$ Infinity ∞

Here is the {{numbers}} template. Today is the second instance when somebody felt templated to insert it in all the articles linked in there (first time was a while ago). I feel this is the case when being in Category:Numbers is enough for these articles, and the gain given by this template in all articles is not offset by the huge size of the template and the distraction it causes on the page. Comments? Oleg Alexandrov (talk) 04:01, 10 April 2006 (UTC)

The template is certainly sort of obtrusive visually. On the other hand these are all articles aimed at a pretty elementary audience. Maybe it is useful for them to have this reminder of how the various sets of numbers fit together. Could we find some of them to ask? --Trovatore 07:39, 10 April 2006 (UTC)

This is an absurd template. How many times and places do we need to know about, say sedenions? Perhaps if the template limited itself to the basics it might be justifiable. --KSmrq^T 08:41, 10 April 2006 (UTC)

I agree. It's absurd. I'm very skeptical as to its utility even for the "elementary audience" Mike mentions. I would think an appropriately placed link to number systems or whatever would be better; I think we all know how to keep a brower window or tab open :-) --C S (Talk) 08:49, 10 April 2006 (UTC)

This is the sort of thing I made {{otherarticles}} for. Septentrionalis 22:31, 10 April 2006 (UTC)

Neusis again

I'm a bit miffed that my original post on this topic seems to have been blown by without comment. I'm not an expert and I really don't know the answer.

Maybe it's just that no-one here knows the answer. Dmharvey 02:23, 11 April 2006 (UTC)

A curious fact of life in posting to forums like this is the extreme differences in volumes of responses questions can provoke, differences which sometimes seem to be independent of the merit of the questions. The answer to your question requires technical study of the tools in question. The general situation is that we know compass-and-straightedge constructions only allow solutions to linear and quadratic equations; the additional tools allow solutions to broader classes of equations such as cubics. This much every serious mathematician knows. However, it may not be obvious which additional classes any particular tool admits. For example, we know a number of different tools that can be shown sufficient to solve cubics (hence permit trisection); but that does not mean they are equivalent in power. So my short answer to your question is, "I don't know." If everyone who does not know the answer to a question posts a statement to that effect, we are overwhelmed with useless noise; therefore the convention is that only those who know (or, sigh, think they know) post — which in this case may be none of our regular readers. After a respectful amount of time with no response, it is acceptable to ask a followup question. A good followup: "Is there a problem with my question?" :-D --KSmrq^T 03:34, 11 April 2006 (UTC)

I believe the movable square is equivalent to neusis; I think, but am less certain, that the tomahawk is. I have no proof of either right now, which is why I haven't posted. Septentrionalis 03:55, 11 April 2006 (UTC)

(rolling eyes) Oh, that I should have asked mathematicians for opinions! "What color is that tree?" "It might appear to be some shade of green on the side that was visible at the time of obseveration." ;-) It really would be informative to hear a number of expert users say "I don't know."

It's okay. For the immediate, ugly, practical purpose of editing the project, it's enough that I think both are cases of neusis, Pmanderson suspects it, and nobody yet is ready to say they're not. That's enough information for me to proceed with my rounds. If an expert has more information later, well, we'll change it. Thank you. John Reid 18:22, 12 April 2006 (UTC)

Edit war over Jaina "mathematics"

Before I continue the edit war which has developed between "Jagged 85" and myself (with some others), I would like to bring the case to our community. Jagged 85 has been adding (what I consider) irrelevant material to several articles in the "Cardinal numbers" category (and I think elsewhere as well). I removed it once. Now he has put it back. This inspite of the fact that there is an already existing article on Indian mathematics to which he has been adding. See Talk:Cardinal number for more information. In my opinion, he is just cluttering up these articles and making them hard to read. There are no mathematical theorems or hard facts in his writing, just attempts to grab credit for the Jaina. JRSpriggs 03:20, 11 April 2006 (UTC)

Yeah, this is a bit of an ongoing problem, and not just about the Jains, but about ancient Indian mathematics in general. Jag, and maybe a couple of others, repeatedly make "anti-Eurocentric" claims that strike me as having a political axe to grind. See especially Kerala school#Possible transmission of Keralese mathematics to Europe, which consists mostly of speculation that European mathematicians could have learned of these claimed precedents and thus may not really have made their discoveries independently. Now, he does have lots of sources; my guess is that they have a political agenda as well, but that's speculation on my part, given that I haven't seen the sources. --Trovatore 04:03, 11 April 2006 (UTC)

A political agenda won't surprise me. I recall the dispute at Arabic numerals, which was moved to Hindu-Arabic numerals and back in total 12 times hist, and see also Talk:Arabic numerals. That not meaning to say that I have anything against India or its great contributions. Oleg Alexandrov (talk) 04:34, 11 April 2006 (UTC)

Long, long, long, long, LONG "stub" articles!

Please look at:

Template:Algebra-stub

I've deleted the "stub" notice from a few dozen of these. Please help. Click on one. If it's too long to be called a "stub", deleted the {{algebra-stub}} notice. Start at the bottom, since I started from the top, so the ones NOW near the top have been dealt with. Some are AMAZINGLY long articles, and are called "stubs". Others are fairly short and could use more material but are clearly too long to be called stubs.

Then we can go on to "geometry-stub", etc., etc., etc., etc.......... Michael Hardy 03:09, 12 April 2006 (UTC)

I've checked every article in the category [17]. --MarSch 11:59, 12 April 2006 (UTC)

Weisstein reliability (or not)

Debate is getting a bit heated at Wikipedia:Articles for deletion/Radical integer and Wikipedia talk:Articles for deletion/Radical integer, with one contributor arguing that it's not within our purview as editors, even if experts, to judge the reliability of anything written in Weisstein's encyclopedia, unless some other source directly contradicts it.

That idea strikes me as a recipe for disaster. Weisstein's work has so much overlap with our project, and is so full of idiosyncracies, that we have to view with caution any article on which he's the only source. If our hands are tied on this, the quality of WP math articles is at risk. Please come and state your views. --Trovatore 21:34, 13 April 2006 (UTC)

I think you're right, as knowledgable editors, we have to use some discretion about what sources are allowable for original material to be included; otherwise we will have to allow all kinds of crackpot material. However, I don't really see a need to take a hardline stance about Weisstein. We can also use our discretion about what of his meanderings should be allowed, which is why I haven't really entered into that debate. -lethe ^{talk +} 00:12, 14 April 2006 (UTC)

Oh, of course. I'm not saying we should automatically reject material just because it comes from him. I'm just saying it needs extra scrutiny when it comes only from him. More scrutiny than might be required with regard to sole-source material from a recognized specialist in whatever the subject matter is. --Trovatore 01:06, 14 April 2006 (UTC)

Well then we're in complete agreement. -lethe ^{talk +} 01:10, 14 April 2006 (UTC)

Also agree (on both points).--CSTAR 02:23, 14 April 2006 (UTC)

Soni's theorem

Has a trivial subject and I could not find any google hits. Should it stay? Oleg Alexandrov (talk) 04:10, 14 April 2006 (UTC)

I'd say no. --Trovatore 04:14, 14 April 2006 (UTC)

I couldn't find anything about it either --MarSch 11:47, 14 April 2006 (UTC)

I would say this article is a strong keep. It has been refined by another user, and I believe the content is much clearer now. This theorem is not trivial, it is like the Trivial Inequality (I don't know if non-mathematicians will understand that reference, so I will explain). This theorem is useful by itself, and not at all obvious. However, when combined with other things, such as De Moivre's, this can be incredibly useful. It should not be deleted for any reason. perhaps a more experienced mathematician can refine it... Mysmartmouth

I nominated it for deletion using the WP:PROD process. So, if nobody objects in 6 days, it will get speedy deleted. Oleg Alexandrov (talk) 20:42, 14 April 2006 (UTC)

Deprodded by author, listed on AfD by me. --Trovatore 23:01, 14 April 2006 (UTC)

Please add your comments to the AFD page.--C S (Talk) 23:30, 14 April 2006 (UTC)

Help with matrix groups

I've been working on the matrix group page and need some help with the content. In particular I'm trying to summarize the types of classical groups but don't have the necessary background to do so. Some of the changes involve generalizing the definitions on other pages (such as unitary group) to arbitrary fields as well as possibly adding some pages (such as projective special orthogonal group).

I've put a summary of the changes I think would be helpful on Talk:Matrix_group. TooMuchMath 05:00, 14 April 2006 (UTC)

Update: The page is starting to come along, however we now have some redlinks if anyone wants to take a shot at them:

TooMuchMath 17:39, 21 April 2006 (UTC)

Well as you can see the links are no longer red and the classical groups portion of the page is looking pretty good. More contributions are welcome, of course! TooMuchMath 22:52, 24 April 2006 (UTC)

The links have become redirects, but have the target articles added the necessary discussions? For example, "projective special orthogonal group" redirects to "orthogonal group", but that article says nothing specific to support the redirect. --KSmrq^T 23:09, 24 April 2006 (UTC)

references for basic topics

Since we seem to be discussing references/sourcing so much recently.... can I ask what is the deal with references for all of our articles on more basic topics? For example, none of the following articles have any book/journal references: irreducible polynomial, normal subgroup, null space, vector space, affine scheme, group (mathematics), symmetric group, function composition. And there are plenty more, they're very easy to find. For such articles, sourcing would have two primary purposes: (1) historical information about where the concept first appeared, possibly in nascent form (this is hard because it involves genuine historical research), and (2) pedagogical, i.e. "where you can learn more about this idea". The second one is obviously problematic because in some cases there are many thousands of textbooks that cover the relevant material. On the other hand, sometimes I feel like there are some double standards going on in the background: for topics which all of us here know are important and standard, we don't require any sourcing, but things like "radical integer" make sparks fly.... Dmharvey 12:20, 14 April 2006 (UTC)

I certainly think that for basic subjects, referencing one or more modern textbooks on the subject would be really useful. For example, something like "An introduction for Undergraduates is given by 'Algebra' Splodgett and Madeup (Cambridge 2003). A textbook more suitable for postgraduates is 'Introduction to Algebra' Spurious and Fictitious (Springer Verlag 1998)." (I pick on Algebra because I was recently looking at [Elementary Algebra] and that has poor references (though I didn't know of a good one to use myself). There's no way that a wikipedia page, no matter how good, can teach a basic mathematical topic and therefore a textbook reference (and some insight into what level of student it would suit) would be very helpful. I realise this could possibly cause issues with people recommending their own books or particular favourite texts. --Richard Clegg 14:10, 14 April 2006 (UTC)

There are double standards and double standards; I think this double standard is absolutely rational and legitimate. I am unembarrassed to say I think we should have that double standard. Just the same, the point is well taken: While not as essential for topics we know about than those we don't, sourcing is still useful and the article isn't really complete until it's provided. --Trovatore 19:34, 14 April 2006 (UTC)

Well, sure, we should source things properly. If they aren't, then we shouldn't include it. On the other hand, we often give editors the benefit of the doubt. If there are no sources for something, then if the creator of the article is a known, respected contributor, not known for randomly inserting crazy crap into Wikipedia, then we give him/her time to find a source. I think it's perfectly fine to rely on the trust built among known contributors. In this case, it was a respected contributor Henrygb who had created the article, even giving a source. However, in this case, another respected contributor questioned the source, as upon investigation the source cited a mailing list which is not available for view and other searches through the usual methods, Google, MathSciNet, etc., were unable to find the term "radical integer". In this case, it's not applying a double standard to ask, "Should we allow this material?" It's natural and perfectly fine to engage in discussion, even amongst contributors who hold a great deal of trust for each other. Such discussion acts as a "reality check", making sure we don't get carried away and making sure we ultimately uphold the standards.

Even when the editor is an anon, we often give the benefit of the doubt, investigating how common the terminology is and whether the results are mentioned in some well-known resources. I'm even amazed at the lengths people sometimes take to investigate rather dubious-sounding claims, in the interest of completeness and fairness.

So I would say there is no double standard here. We often allow anyone to edit and insert material without citing, as if we didn't, we wouldn't gain a lot of content. On the other hand, to make sure we don't allow the crap to build up, we rely on trust of known contributors and also our expertise, e.g. "hey, this guy says some cubics can't be solved by radicals; that's not what I learned in undergrad algebra!" Eventually, though, we should be adding sources, and indeed some people are clearly going through articles and added citations where needed. So it's not accurate to say we don't require sources for some articles. --C S (Talk) 20:18, 14 April 2006 (UTC)

Let's not mix apples and oranges. Sources for mainstream mathematical content act as enrichment, "See also". The content is not in dispute, perhaps with a few lunatic exceptions. Many of the algebra topics, for example, could cite Mac Lane and Birkhoff's Algebra (ISBN 0023743107), or van der Waerden, Moderne Algebra (ISBN 0387974245), or Artin's Algebra (ISBN 0130047635), or numerous other texts; and they should. In other cases, we have questions of proof, or notation, or history, or who-knows-what. It is not practical to referee every article like a journal paper, and even then many assertions are accepted without proof. We concentrate our demand for references on statements that raise suspicion. In principle, we should be able to defend "1+1=2", but in practice that level of citation would be absurd. --KSmrq^T 22:41, 14 April 2006 (UTC)

I would agree with KSmq. The rules for when a reference is not required (as I remember from high school) is if the information is "widely known" (which in high school meant that it was avaliable in three or more sources). "Moscow is the capital of Russia" would not need a citation for this reason. Even when we do run into problems with conflicting definitions ("St. Petersburg is the capital of Russia" was true for a time) citations aren't strictly required if both definitions are or have been widely used. In fact a discussion of the historical (or motivational) reasons for differing definitions is often more useful than a citation in these cases. A citation is required only when a definition is obscure. Aside from the academic integrity motivations for proper citation, this is particularly important on Wikipedia to ensure the "no original research" policy as well as to weed out the junk science. That said, a good reference or two can enrich the content substatially, so even for widely known topics it would be a good idea to add references. TooMuchMath 18:16, 15 April 2006 (UTC)

That's nicely put. This is the "rational double standard" I was advocating above. However I wouldn't formalize the "three sources" standard; I think the appropriate test is more whether an ordinarily prepared worker in the specialty would know the facts asserted. --Trovatore 19:26, 15 April 2006 (UTC)

OK, I agree with the bulk of what everyone's saying here, certainly I agree with the "rational double standard". I intended my comment to focus more on the educational usefulness of Wikipedia, rather than its veracity. In fact, if I had more time available now, I would consider trying to organise a "let's find book/pagenumber references for all those unreferenced basic topics articles" project, for the sole purpose of assisting those who are using Wikipedia as part of their mathematics studies. It's getting to a point now where an undergraduate and even a graduate student (like myself) can profitably use Wikipedia as their first stop when looking stuff up, and it would be incredibly helpful to have more pointers to denser sources of information. Unfortunately I don't have the time now. (nudge nudge wink wink) Dmharvey 19:47, 15 April 2006 (UTC)

This is a problem I have encountered when ever I nominate maths articles for Good Article status - they very often comment on teh lack of sources. The trouble is that many of the common topics (groups, vectors etc.) are written entirely of own knowledge, which means the source is out own knowledge hence the lack of physical references. That said, I think we should always list *some* references, if only to provide a place for readers to verify the info or find out more. Don't forget it says under any edit box that "Content must not violate any copyright and must be verifiable". Any book which know contains infomation for the article in question is suitable. Putting the article name in Amazon's search box often provides something suitable. (Although the references I list tend to come from the reading list for my uni's maths course). Tompw 20:01, 15 April 2006 (UTC)

PDE Surfaces

Copied from Talk:Mathematics --Salix alba (talk) 14:18, 15 April 2006 (UTC)

This seemed like the best place to get people's attention about the article PDE Surfaces, written by Zer0 cache. I suspect that it's promoting research, but I can't be sure. It would be appreciated if other editors can check this out. I've also left a small query at PDE surfaces talk page. MP (talk) 11:28, 11 April 2006 (UTC)

it seems fully referenced... hmm I guess Salix Alba fixed it already. --MarSch 17:43, 15 April 2006 (UTC)

Hm, what about the naming? I've already downcased it, but it didn't occur to me at the time that it would probably be more standard to move it to PDE surface, assuming there is such a thing as a PDE surface that makes sense in isolation from other PDE surfaces. On the other hand, if it's the description of a method rather than a kind of mathematical object, should it perhaps be method of PDE surfaces? --Trovatore 17:48, 15 April 2006 (UTC)

mathematics for AID

mathematics is curerntly going very well on Wikipedia:Article Improvement Drive. Maybe you want to vote for it --MarSch 18:13, 15 April 2006 (UTC)

debate over external link at Talk: Serge Lang

There's an extremely heated debate going on the talk page for Serge Lang between two editors, User: Revolver and User: Pjacobi. The issue is whether an external link to an article on the AIDS wiki (which was written by Revolver) should be allowed. I've just made my thoughts known there, and I also noticed that an RFC had been filed, but no comments had been made here (which is requested on the RFC page). --C S (Talk) 04:18, 17 April 2006 (UTC)

Theorem 1

I nominated Theorem 1 for deletion. I tried using {{prod}} first but its author disagreed. Comments welcome. Oleg Alexandrov (talk) 03:55, 18 April 2006 (UTC)

Delete. The author says "There is a list, and this is #1." I'm not aware of any cosmic list of theorems. Now it does have something of a place of distinction -- postulate #4 of book 1 of Euclid's elements. But it isn't "theorem #1". Will there be a theorem #2? William Ackerman 17:16, 18 April 2006 (UTC)

There is no point in commenting here. To find the discussion, go to the article in question, and follow the link at the top of the page. --Trovatore 17:17, 18 April 2006 (UTC)

NPOV dispute at geostatistics, kriging, and spatial dependence

There is an NPOV dispute at the above articles: we need expert advice from statistician(s), especially those familiar with spatial statistics.

Briefly: User:JanWMerks claims that geostatistics is a scientific fraud, and has repeatedly edited these related articles to reflect that POV. Myself, User:Antandrus, and others were trying to point out Wikipedia rules, such as WP:NPOV, WP:VERIFY, and WP:NOR. Much edit warring ensued.

Now, the dispute (at spatial dependence) is over whether the F-test is a valid statistical test for spatial dependence. Also: several references (at geostatistics and kriging) are being used to support the claim that kriging is invalid, and I don't have easy access to a good library to check these references.

I hope that someone is willing to research the claims of invalidity better than I can, or perhaps simply provide a third opinion about the dispute.

Please feel free to visit Talk:Geostatistics, Talk:Kriging, and Talk:Spatial dependence to help out. Thanks!

-- hike395 17:40, 22 April 2006 (UTC)

cron vs hedron

I wonder if these two Greek suffixes mean the same or almost the same thing. Then, the following redirects may make sense:

Great dirhombicosidodecacron --------> Great dirhombicosidodecahedron
Great dodecahemicosacron --------> Great dodecahemicosahedron
Great dodecahemidodecacron --------> Great dodecahemidodecahedron
Great icosihemidodecacron --------> Great icosihemidodecahedron
Small dodecahemicosacron --------> Small dodecahemicosahedron
Small dodecahemidodecacron --------> Small dodecahemidodecahedron
Small icosihemidodecacron --------> Small icosihemidodecahedron

I stumbled into them at the Missing science project, and don't know what to do about them. Thanks. Oleg Alexandrov (talk) 18:55, 22 April 2006 (UTC)

I think the ones on the left are duals of the ones on the right or something. They should be given seperate articles. -- 127.*.*.1 20:33, 22 April 2006 (UTC)

Indeed the coverage of dual is week at the moment. I've mentioned this on Talk:Polyhedron. --Salix alba (talk) 22:39, 22 April 2006 (UTC)

Delete "Category:Continuum theory"?

This category called "Category:Continuum theory" is a subcategory of "Set theory" and of "General topology", but it contains no articles. Should it be deleted? How can I propose it for deletion? JRSpriggs 07:20, 26 April 2006 (UTC)

Wikipedia:Categories for deletion explains the deletion process. It might be applicable for speedy deletion. --Salix alba (talk) 07:34, 26 April 2006 (UTC)

Yup, WP:CSD says that empty categories can be speedied. I'm going to do it. This category defines a continuum as a compact connected metric space, which isn't right. The real line is not compact. -lethe ^{talk +} 07:56, 26 April 2006 (UTC)

Continuum has more than one meaning in mathematics. In continuum theory, which is related to dynamical systems, continuum does indeed mean what the category said. Perfectly cromulent articles which would have belonged in this category include pseudo-arc, indecomposable continuum and solenoid (mathematics). —Blotwell 14:49, 26 April 2006 (UTC)

Well, if the category had a correct definition, and also there are articles which could live in it, then the deletion was inappropriate. I will now undelete, and promise to be more careful when speedying things in the future. Thank you. -lethe ^{talk +} 20:34, 26 April 2006 (UTC)

Help requested at hyperbolic 3-manifold

An editor insists on removing red links as "cleanup". I think the participants here realize the importance of red links to this project (and Wikipedia in general). I'm puzzled why anyone would insist on removing them, but this editor has been quite stubborn, insisting that the articles *must* be created before links to them can be included in this article. --C S (Talk) 00:41, 28 April 2006 (UTC)

I've made some comment's at the user's talk page (User talk:PHDrillSergeant); hopefully, this should be enough. --C S (Talk) 01:01, 28 April 2006 (UTC)

Edward R. Dewey

A stock market "analyst" who sold a correspondence course on "cycle analysis".[18] This link includes a table of contents which I think makes clear how trivial Dewey's "system" is; please comment on Wikipedia:Articles for deletion/Edward R. Dewey. Septentrionalis 19:13, 28 April 2006 (UTC)

Should Radical integer be deleted?

A newly created article Radical integer has been listed for deletion. Should it be kept or deleted? Note that the article resolves a long-standing redlink in Algebraic integer listed on Wikipedia:Missing_science_topics/Maths8. Weigh in. Lambiam ^Talk 17:50, 9 April 2006 (UTC)

I'm the one who listed it for deletion, because the given source (MathWorld) looked hinky and in a quick search I couldn't find the term clearly and independently attested. I'm not a number theorist, so if it's not something one of Eric Weisstein's buddies just made up one day, by all means say so. --Trovatore 17:59, 9 April 2006 (UTC)

Someone somewhere has got to have a short name for Algrebraic integer expressible by radicals, but this doesn't seem to be it. Septentrionalis 22:33, 10 April 2006 (UTC)

Radical extension, extension by radicals, or (most common, I think) pure extension is standard, and radical number I think I've seen. Radical integer is logical and has a MathWorld article to go with it, which speaks in its favor. It seems to me that all of this should be discussed somewhere in an article on solvable extensions, but I can't find any such article. Should I write one? I don't want people deleting it if I do. Gene Ward Smith 21:25, 13 May 2006 (UTC)

Let me summarize the history as I see it:

The article radical integer was sourced only to MathWorld and all the Google hits seemed to trace back there. So I nominated it for deletion as one of Eric Weisstein's neologisms (as you'll have gathered, I don't think the existence of a MathWorld article speaks particularly well in favor of it; it's not a strike against it per se, but certainly not enough support for an article by itself).
During the discussion it emerged that there was more than a not-so-interesting definition involved, but rather an actual putative theorem, which (if true) goes as follows: Consider all numbers that can be expressed by starting with the naturals and closing under addition, multiplication, subtraction, division, and extraction of natural-number roots. Intersect that class with the algebraic integers. Then any number in the intersection can be expressed by starting with the naturals and closing under the previous operations, without division.
That theorem, if it is one (which I think it probably is), is very interesting, and clearly justifies the creation of a term for an element of the class. Unfortunately at the current time the theorem cannot be sourced, except to MathWorld, which IMO is not reliable. Moreover I think it's a reasonable principle that sources for putative theorems ought to point the reader to an actual proof, and the MathWorld source does not do that. --Trovatore 17:26, 25 May 2006 (UTC)

It might be posible to get a better source, the theorem was discussed on the math-fun mailing list, which I presume is on the web somewhere. In an email to me Rich Schroeppel said he would try to dig up the archive when the tax season was over. If anyone is interested this would be great to follow through. --Salix alba (talk) 17:35, 25 May 2006 (UTC)

Oh, one more small point: What I said about "sourced only to MathWorld" is not strictly true; I'm including Weisstein's encyclopedia of math as part of MathWorld. With that addendum it's true. --Trovatore 17:35, 25 May 2006 (UTC)

It seems to me if I understand the claim that Schroeppel's theorem is too trivial to use as a reason for an article. If μ is an algebraic integer, then it has a monic polynomial, and expressing it as a root expresses it without division. Expanding on that, the ring of integers in any number field has an integral basis; it can be written as c₁ μ₁ + ... + c_n μ_n, where the c's are ordinary integers and the μs are algebraic integers in the field, so in terms of this basis everything in the ring of integers is precisely everything which can be expressed without division.

So, what exactly is the statement of this theorem? Gene Ward Smith 19:47, 25 May 2006 (UTC)

I think I've already stated it exactly; here's the example that came up as to why it's not trivial. The golden ratio is a root of x²−x−1=0, so it's an algebraic integer. It's also obtainable from the naturals by iterating the operations listed, including division, as

$\frac{1+\sqrt{5}}{2}$

However it's not immediately obvious that you can get it from the naturals by iterating the operations not including division. But you can. It's

$\sqrt[3]{2+\sqrt{5}}$

(Thanks to Lambiam for that representation.) Unless I've misunderstood it, the argument you give does not prove this. --Trovatore 19:55, 25 May 2006 (UTC)

Here's a sketch of an almost-proof. "Almost" because I'm left with a denominator of at most 2.

Let S be those numbers obtainable from the natural numbers by addition, subtraction, multiplication, division, positive integer roots. (I want to call this the maximal radical extension of Q, but I'm slightly concerned about roots of unity. Never mind.) Let R be the "radical integers", i.e those numbers obtainable from naturals by addition, subtraction, multiplication, and positive integer roots (but not allowing division). First I claim that any x in S is of the form y/d for some y in R and some integer d. This is done by induction on the structure of x. Clearly addition, subtraction, multiplication pose no problems. Integer roots also fine (i.e. $(y / d) 1 / n = y 1 / n d (n - 1) / n / d)$ ). Division is slightly more troublesome, you need some kind of "rationalising the denominator" trick.

So now suppose we have x = y/d as above, and suppose further that x is an algebraic integer; we want to prove that x is itself a radical integer. Let K = Q(y), and let O be the ring of integers of K, so x is in O. As Gene pointed out above, O has a finite Z-basis, and the basis elements are polynomials in y with coefficients in Q, so for a large enough integer m we find that mO consists entirely of radical integers. Split m into a product of powers of prime ideals in O, say $m = \prod_P P^{r_P}$ . By looking at the rings $O/P^{r_P}$ , we can find some large integer n such that xⁿ is congruent to either 0 or 1 modulo each $P^{r_P}$ . Then $x 2 n - x n$ is in mO, so is a radical integer, say z. Then we have $x = \left(\frac{1\pm\sqrt z}2\right)^{1/n} = \frac{2^{(n-1)/n}(1+\sqrt z)^{1/n}}2$ , which is a radical integer possibly divided by 2.

Anyone buy that? Getting rid of that last 2 seems a little problematic. Dmharvey 00:26, 26 May 2006 (UTC)

Oh yeah, by the way you can apply that proof to the golden ratio case quite easily. We already have $x = \frac{1+\sqrt5}2$ presented in the right form. Let O be the ring of integers of $\mathbf Q(\sqrt 5)$ . Then the ideal (2) is inert in O because the polynomial

x 2 - x - 1

is irreducible mod 2. So the quotient O/2 is GF(4), so cubes of anything nonzero are congruent to 1. So

x 3 - 1

is in 2O, so is a radical integer. And indeed $\left(\frac{1+\sqrt5}2\right)^3 - 1 = (1 + \sqrt 5)$ is twice an algebraic integer, so must be a radical integer, which is I suppose where Lambian's formula comes from :-) Dmharvey 00:33, 26 May 2006 (UTC)

OK, here's the rest of the proof to handle that annoying factor of 2. You need to treat the residue characteristic 2 a little carefully.

Again suppose x = y/d where x is an algebraic integer. Let $\theta = (1+\sqrt 5)/2$ be the golden ratio. Consider the extension $K = \mathbf Q(y, \theta)$ , let O be its ring of integers. Again we can find some m so that mO consists entirely of radical integers. Consider all prime ideals P of O of residual characteristic 2, suppose their multiplicites in m are given by r_P. Take some high power of x, call it x₂, which is = 0 or 1 modulo each $P^{r_P}$ . Then x₂ + θ is not in any

P

, because θ is not 0 or 1 modulo 2 (i.e. neither θ nor θ−1 is twice an algebraic integer). So some high power of x₂+θ, let's call it x₃, is congruent to 1 modulo every $P^{r_P}$ . Then x₃−1 is = 0 modulo every $P^{r_P}$ . Now consider all the other primes Q of various other residue characteristics, which have multiplicities

r Q

in m. Then some high power of x₃−1, let's call it x₄, is either 0 or 1 modulo each $Q^{r_Q}$ , and is still 0 modulo every $P^{r_P}$ . Now look at x₄+1; it's either 1 or 2 modulo each $Q^{r_Q}$ , and it's 1 modulo each $P^{r_P}$ . Since the residue characteristics of the Q are not 2, some high power of x₄+1, say x₅, is 1 modulo all of the $Q^{r_Q}$ and all of the $P^{r_P}$ . So x₅−1 is in mO, and therefore a radical integer. If you unroll your way through x₅, x₄, x₃, x₂, back to x itself, you get that x is a radical integer. Whew! Dmharvey 02:48, 26 May 2006 (UTC)

Applause. Now get that published in the Journal of Number Theory and we can write an article about it :) --Lambiam ^Talk 16:21, 26 May 2006 (UTC)

Update on the lists of missing math topics

The lists at Wikipedia:Missing science topics#Mathematics now contain entries from MathWorld, Springer Encyclopaedia of Mathematics, Charles Matthews' maths lists (thanks Charles!), St Andrew's, and PlanetMath. There are 15465 redlinks and 9700 bluelinks (in separate lists), which is a progress of 38.55% towards eliminating the redlinks. For many redlinks it is likely that the information exists on Wikipedia but under a different name, so creating redirects is a good way to advance that project forward. The harvest is great and the workmen are few[19] (since it's Easter today :) Oleg Alexandrov (talk) 22:21, 16 April 2006 (UTC)

And I finally got permission from Springer to use their lists in our project. Oleg Alexandrov (talk) 03:25, 25 April 2006 (UTC)

Really? That's very generous of them, I didn't think they would. I think mathworld wasn't willing. Neat! -lethe ^{talk +} 03:32, 25 April 2006 (UTC)

If Mathworld was not willing, how come the Wikipedia:Missing science topics was created to start with? Before I got there, all the math entries from there were copied from MathWorld, all the way to incomplete entries, like Archimedean Spiral Inv.... Oleg Alexandrov (talk) 03:37, 25 April 2006 (UTC)

I seem to recall a discussion here on the wikiproject talk page, where someone created a carbon copy of the mathworld index of topics, and someone emailed them, and they indicated that it was indeed a violation of their copyright. In fact, my recollection is that you were in this converation, though I could be mistaken. Anyway, I don't know where the content of Wikipedia:Missing science topics comes from, but unless I'm misremembering something, to have their index is a copyright violation. I guess I should see if I can find that old conversation. -lethe ^{talk +} 07:37, 1 May 2006 (UTC)

That's really good news. I'm not so surprised though, that Springer was willing but MathWorld not. There are people at Springer that are truly committed to what they're doing and I've seen Springer do things that strictly speaking, they did not need to do. --C S (Talk) 07:27, 1 May 2006 (UTC)

listing variable names after formulas

I wonder what people think of these multiply-indented lists to define all the variables that appear in a formula. An example is found here. It is claimed that this format is somewhat standard here at wikipedia and is found in hundreds of articles, but I've never seen it, and furthermore don't really like it, I prefer instead a regularly indented paragraph of text. What are your opinions of this format? -lethe ^{talk +} 00:52, 22 April 2006 (UTC)

It takes too much space. -- 127.*.*.1 03:26, 22 April 2006 (UTC)

Yes, that is quite an unfortunate presentation style. A simple paragraph of explanation would be much better. — merge 08:07, 22 April 2006 (UTC)

From a dyslexic point of view I have problems parsing large blocks of text and tend to find lists easier to read. I had a play about with a more compact format using tables. Compare

The Schrödinger equation is:	i	the imaginary unit,
	t	time,
$H(t) \left\| \psi (t) \right\rangle = i \hbar {\partial\over\partial t} \left\| \psi (t) \right\rangle\qquad$	${\partial\over\partial t}$	the partial derivative with respect to t,
	$\hbar$	reduced Planck's constant (Planck's constant divided by 2π),
	$ψ(t)$
	H(t)	the Hamiltonian - a self-adjoint operator acting on the state space.

The Schrödinger equation is:

$H(t) \left| \psi (t) \right\rangle = i \hbar {\partial\over\partial t} \left| \psi (t) \right\rangle\qquad$

where i is the imaginary unit, t is time, ${\partial\over\partial t}$ is the partial derivative with respect to t, $\hbar$ is the reduced Planck's constant (Planck's constant divided by 2π),

ψ(t)

is ...., H(t) is the Hamiltonian - a self-adjoint operator acting on the state space.

--Salix alba (talk) 09:27, 22 April 2006 (UTC)

If a list seems necessary, why not use a list?

The Schrödinger equation is:

$H(t) \left| \psi (t) \right\rangle = i \hbar {\partial\over\partial t} \left| \psi (t) \right\rangle\qquad$ ,

where:

i is the imaginary unit
t is time
${\partial\over\partial t}$ is the partial derivative with respect to t
$\hbar$ is the reduced Planck's constant (Planck's constant divided by 2π)
$ψ(t)$ is ....
and H(t) is the Hamiltonian - a self-adjoint operator acting on the state space.

— merge 09:42, 22 April 2006 (UTC)

I wonder if those explanations of the symbols make this equation any more comprehensible to someone not familiar with the notation. If you don't know what the symbol is for partial differentiation then IMO it is very likely that you don't know what partial differentiation is and the same goes for the imaginary unit.--MarSch 09:55, 24 April 2006 (UTC)

I don't think it's necessary to explain certain things, such as the imaginary unit, time, or the partial derivative. Articles assume some basic knowledge, so we should rely on this (however, we should clearly attempt to make the number of assumptions as smallest as sensibly possible). Dysprosia 10:05, 24 April 2006 (UTC)

The Schrödinger equation is:

$H(t) \left| \psi (t) \right\rangle = i \hbar {\partial\over\partial t} \left| \psi (t) \right\rangle\qquad$

where H is the Hamiltonian, ψ is the state and t is time,

but even better is probably

A physical system with Hamiltonian H and initial state vector ψ₀ can be described at time t by the state vector ψ(t) which is a solution of the initial condition ψ(0) = ψ₀ and the differential equation called the Schrodinger equation

$H(t) \psi (t) = i \hbar {\partial\over\partial t} \psi (t)$

--MarSch 10:09, 24 April 2006 (UTC)

I'm in favor of lists for equations. The main reason is that I don't like to read the whole article - and lists of variables show a clear spot where I can find all the information I need. This is of course provided that its written properly. If the variables in the equation are fully clear, then theres no need. However, in the case of the schrodinger equation, almost none of the variables and symbols are familiar to most people. Also, most always, all variables do need description. Leaving out variables leaves the equation incomplete, and even a reader who assumes the right meaning might question himself, and end up having to double check the formula somewhere else. Stuff like simple operators probably don't need explaining, but I've found a good compromise in that respect to define the derivative of something rather than the dervative operator (for example: "dp/dt is the instantaneous rate of change of the momentum").

Another main consideration is consistancy. If equations are written in 5 or more different forms, users will have a harder time sorting through the formats to find what they need. Almost always, variables are written below the equation, and when they're not - I find it difficult to follow. The list format makes it easy to find the perhaps one or two variables you don't know, and refer back to it without losing your place.

We as editors should consider that wikipedia isn't only used by people wanting an in depth overview of a subject, but may also want a quick reference. Articles that distinguish different parts of the article (like equations, subject headers, examples vs generalities) are much easier to read and use. The faster a reader can find the information they are looking for is (in my opinion) far more important than making the page compact. Fresheneesz 07:25, 2 May 2006 (UTC)

AFD - How to get the prime factors of a number

I have nominated How to get the prime factors of a number for deletion. Comments welcome. -- Meni Rosenfeld (talk) 16:46, 26 April 2006 (UTC)

It seems like useful information, although it could be better written. Is this info in some other article? If not, maybe the article should stand. PAR 16:58, 26 April 2006 (UTC)

Please take comments on the merits to the AfD page. --Trovatore 17:04, 26 April 2006 (UTC)

Deleted. -lethe ^{talk +} 05:17, 1 May 2006 (UTC)

May 2006

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

"Tone", pronoun use, etc. in math articles

The other day, I left a pretty extensive comment on Talk:Knot theory, in response to two editors who complained about the article's tone. One specific complaint was the use of pronouns and that the article sounded like a teachger giving a lesson. Now, I just noticed that Braid group has been tagged (by someone else) with a "tone" tag, and the talk page mentions for example, that the use of "we" is bad and that it sounds too much like a "math lesson instead of an encyclopedia".

My thought is that while some of the pronoun use could be favorably excised, I am definitely starting to get the feeling (especially after examining the articles in question) that these particular editors do not understand the conventions in mathematical writing, e.g. "We consider blah as doing blah..." is ok. They also may not understand that sometimes a procedural description should be given, e.g. "take such and such and do such and such...". See my long comment linked above. I would like to know what those who normally work on mathematics articles think about all this, so please drop by those pages and make some comments. --C S (Talk) 03:58, 1 May 2006 (UTC)

We is pretty much mathematical jargon; one is better for the general reader. Charles Matthews 11:45, 1 May 2006 (UTC)

I believe the passive is the preferred thingy. "We consider..." becomes "... is considered". --MarSch 14:08, 1 May 2006 (UTC)

But then... "is considered", er, by whom? By a deity? (Igny 15:33, 1 May 2006 (UTC))

This reflects a certain diference about using We. In a statement like We can deform a knot in 4D it can easily be rewitten as a knot can be deformed in 4D and the prounoun can easily be dropped. However We consider... are subjective statments and in a paper the we is used to indicate the opinion of the authors. In wikipedia such subjective statements need appropriate qualification most mathematicians consider 4D knots to be very boring. --Salix alba (talk) 19:04, 1 May 2006 (UTC)

I've responded where requested; see for details. Passive is not preferred; just the opposite. Overuse of "one" also makes reading drag. Technical writing has a tradition of such conventions, not to its credit. --KSmrq^T 19:15, 1 May 2006 (UTC)

A MIT style guide says to use "we" in the active voice. I see now that I was mistaken in thinking it too personal, and yes, I did not understand mathematical writing conventions as pointed out by Chan. I will try to not be an ignoramus in the future. --Reader12 03:57, 2 May 2006 (UTC)

Well, you live and learn! I tried to carefully explain how the situation appeared to me without being patronizing or rude; I hope you weren't offended. At any rate, I think it's been a very fruitful discussion thus far with a variety of people voicing their thoughts and it's still ongoing! --C S (Talk) 08:08, 2 May 2006 (UTC)

No, no offense taken. This has been very instructive to me. Thanks! --Reader12 21:40, 2 May 2006 (UTC)

I've just come across a great book on Algebraic topology by Allen Hatcher which can be downloaded [20]. To my mind he has a very good writing style, which avoids the problems of overly technical writing, whilst still being technically correct. I fell there is quite a bit which could be learnt by examining how he structures his writing. I think a lot of illustrations help, the sub project /Graphics has reciently been set up to try to improve the illustrations of the maths articles. --Salix alba (talk) 09:21, 2 May 2006 (UTC)

Naming: "fixed-point" vs "fixed point"

Several articles are named inconsistently. I prefer "fixed point". Any opinions? Post here or at Category talk: Fixed points. Staecker 21:18, 1 May 2006 (UTC)

It's my experience that "fixed point" is way more common in the literature, so we should stick with that.--Deville (Talk) 22:25, 1 May 2006 (UTC)

Not so fast; there's a grammatical distinction. As a noun phrase, we would write the "fixed point" of a recursive function, without the hyphen. But as an adjective, we often write "fixed-point" thingy, with the hyphen. In the case of theorem names, the former applies, as in "Brouwer fixed point theorem". And what about "Kleene fixpoint theorem"? It should redirect. --KSmrq^T 22:59, 1 May 2006 (UTC)

I don't mind making the distinction, but I don't think I understand as you've stated it. In "Brouwer FP Theorem," it sounds like an adjective phrase to me (modifying "theorem"). Is this an exception? When would the hyphen be appropriate? Something like "fixed-point set"? That sounds like an adjective phrase to me, but I never write it that way myself. Come to think of it, I don't ever use the dash regardless of context. (Except when I have to link to Lefschetz fixed-point theorem) Staecker 23:19, 1 May 2006 (UTC)

You want me to explain why punctuation conventions make sense?! I wish. I can say that I would never hyphenate in a situation like "Every rotation has a fixed point." The article on hyphen discusses some common rules. So why not "Brouwer fixed-point theorem"? I suppose because it's a ritual thing, with "theorem" doing the modifying. Or it's an example of the general guideline that hyphens are for clarity, and if we don't need them we don't use them. The still more general guideline is to tread carefully in this territory, and don't rush to accuse anyone of doing it wrong just because their choice is not yours. (But you knew that already, yes?) --KSmrq^T 02:47, 2 May 2006 (UTC)

My usage would be like KSmrq's. The underlying reason may be that a "fixed-point set" is a set which consists of fixed points (or is a fixed point, if you're doing category theory); but a "fixed point theorem" is a theorem about fixed points: a more distant relationship, analogous to the difference between mathematics and metamathematics. Septentrionalis 18:58, 5 May 2006 (UTC)

Are you sure there's an inconsistency? A fixed-point theorem (with a hyphen) asserts the existence of a fixed point (with no hyphen), and it is completely appropriate to use a hyphen in one case and not in the other, because of the difference in the way the phrase is being used. That is not an inconsistency. Michael Hardy 20:09, 5 May 2006 (UTC)

hyphens generally

By the traditional conventions concerning hyphens,

A man-eating shark (with a hyphen) scares people away from beaches, whereas
A man eating shark (with no hyphen) is a customer is a seafood restaurant.

The traditional usage is still followed by nearly all newspapers and magazines and in novels, and people are accustomed to seeing it. But many educated people, including many authors of scholarly papers and books no longer follow the traditional rule. I've tended to be conservative about it and I moved the Wikipedia article titled "light emitting diode" (with no hyphen) to light-emitting diode (with a hyphen) and have done the same with various other articles. I think in some cases, the hyphen is a magnificently efficient disambiguation device. Michael Hardy 20:14, 5 May 2006 (UTC)

Nice example, copied from hyphen:

semantic changes caused by the placement of hyphens:

Disease causing poor nutrition, meaning a disease that causes poor nutrition, and
Disease-causing poor nutrition, meaning poor nutrition that causes disease.

Michael Hardy 20:18, 5 May 2006 (UTC)

A fixed point theorem is a point theorem that was found to contain an error, which now has been repaired. Lambiam ^Talk 21:13, 6 May 2006 (UTC)

Blahtex and wikimania

The poster deadline for wikimania is fast approaching. I think it would be really good if we could have some presence there as a step to getting meta:Blahtex integrated into the main encyclopedia sites. Neither User:Dmharvey or myself are able to attend, but posters can be submitted without having a physical presence. Questions: is anyone here planning to go to wikimania Aug 4-6, in Cambridge MA? Anyone happy to spend some time standing next to a Blahtex poster? For those who don't know Blahtex is a extension which converts LaTeX maths into the MathML XML markup which allows for improved rendering of mathematics in MediaWiki with moder browsers. --Salix alba (talk) 10:05, 2 May 2006 (UTC)

Bogus AfD of proof article

Loom91 has been goaded by Melchoir into nominating "Proof that 0.999... equals 1" for deletion, on the grounds that Wikipedia should not contain proofs like this. The archives of sci.math currently show well over a thousand postings related to this topic, which is therefore included in the sci.math FAQ; yet it appears that Wikipedia covers the topic far better. Those who are interested can register an opinion here. Caution: This topic (and perhaps this vote) attracts, um, non-standard thinkers, to put it delicately. (See the talk page archives for examples ad nauseam.) --KSmrq^T 10:31, 5 May 2006 (UTC)

Yeah, I feel bad about that; sorry, everyone! (In my defense, though, I did try to explain why the AfD would fail, after which I didn't think Loom91 would actually go through with it.) Well, at least it's attracting some fresh constructive attention, and it'll be useful to have on record. Melchoir 20:09, 5 May 2006 (UTC)

By the way, in case anyone hasn't seen it yet, the AfD closed with a keep. Melchoir 22:58, 5 May 2006 (UTC)

That's a understatement; it closed with a speedy keep, with overwhelming support and complaints about the nomination as violating WP:POINT. --KSmrq^T 22:31, 6 May 2006 (UTC)

Rewrite of Mode (statistics)

I rewrote the article Mode (statistics). Please review and correct errors, rewrite awkward sentences, simplify, embellish, supply sources, etc. It would further be nice to have some illustrations, both for a continuous density function and a histogram. Lambiam ^Talk 20:40, 5 May 2006 (UTC)

AfD for List of Mathematical Formulas

Should this be kept, deleted, merged, or should there be a category of "mathematical formulas"? (I wonder what the morphisms would be.) Visit Wikipedia:Articles for deletion/List of Mathematical Formulas and contribute your two cents. Lambiam ^Talk 21:04, 6 May 2006 (UTC)

As far as I can see, the chemists don't need Category:Formulas. We might not need it either, though. Charles Matthews 19:09, 7 May 2006 (UTC)

WAREL back?

See [21]. I don't read Japanese so I can't tell if the change is correct, but it's exactly the type of change we might expect from WAREL if he came back. --Trovatore 15:24, 10 May 2006 (UTC)

OK, I hate machine translation but it has its points. He changed the article to point to a nonexistent article on ja.wiki, called "Commutative field". It's WAREL alright; please block him with all deliberate speed. --Trovatore 15:41, 10 May 2006 (UTC)

KLIP (talk · contribs) blocked. -lethe ^{talk +} 17:20, 10 May 2006 (UTC)

James Stewart

Just created the page on Stewart, James Stewart (mathematician), your contributions would be most appreciated.--Jersey Devil 09:08, 11 May 2006 (UTC)

TeX font size

There is a discussion at the Village pump that might interest a few people here. —Ruud 01:09, 12 May 2006 (UTC)

Koszul-Tate

Is there anybody here interested in tackling the Koszul-Tate derivation topic listed on the "wikipedia:Articles requested for more than two years"? Thank you. — RJH 15:45, 12 May 2006 (UTC)

WAREL

is back again at Field (mathematics). --Trovatore 02:39, 13 May 2006 (UTC)

JLISP (talk · contribs). -lethe ^{talk +}

Zeration

Can someone please review zeration? Thanks. Samw 03:28, 13 May 2006 (UTC)

I'd give it thumbs down, in regard the Δ numbers. That is just wrong, even if referenced in the paper. The rest is more-or-less accurate, although I believe it falis WP:N.

As for hyperexponentials, my first paper (in 1966) references an earlier paper by Donner and Tarski which discusses hyperexponentials on the ordinal numbers. I doubt the primacy of the 1987 paper. — Arthur Rubin | (talk) 04:29, 13 May 2006 (UTC)

Referencing something from 2004 makes it a bit young and possibly fails "established research". Dysprosia 08:44, 13 May 2006 (UTC)

Duly sent to AfD, see Wikipedia:Articles for deletion/Zeration. -- Jitse Niesen (talk) 08:47, 13 May 2006 (UTC)

Spanish category

I wrote the following on Category talk:Mathematics; copying here.

An anon recently changed the Spanish link to es:Categoría:Matemática from es:Categoría:Matemáticas, or perhaps the other way around. It seems that both categories exist and are populated. Would someone whose Spanish is better than mine like to go tell them? I don't know how they handle these things over there; I think things like {{cfm}} are set up language-by-language. --Trovatore 14:54, 13 May 2006 (UTC)

It looks like es:Categoría:Matemática was created just today, by one es:Usuario:Ingenioso Hidalgo, who then took it upon himself to go around recatting over a hundred articles, then apparently got tired. Unless this was discussed somewhere this doesn't strike me as good behavior; someone should let them know. I don't know if they have any equivalent to WikiProject Mathematics. --Trovatore 15:21, 13 May 2006 (UTC)

On second thought, I suppose someone will notice, as the recats will surely show up on some watchlists. --Trovatore 15:35, 13 May 2006 (UTC)

P-adic numbers

There is a discussion on decimal-style notation for p-adic numbers, and what would be appropriate to use, on the talk page Talk:P-adic number which we would like comments on. I added a section which uses a notation which is unusual but not unprecedented, in the section intended to convey the intuitive idea of a p-adic number. It seems to me the notation I used does that more successfully than any alternative for people used to decimal notation. Gene Ward Smith 21:14, 13 May 2006 (UTC)

Real number

User:Oleg Alexandrov seems to me to be engaging in abusive reverts on this page, to a previous verison which is arguably incorrect mathematically and which removes a lot of new material, material for which he has given no argument for removal. He also says, falsely, that my attempt to satisfy his previous criticims amounted to "writing a one-liner" which seems to prove he hasn't even seriously looked at the version he is reverting from. I think we need other people to weigh in at this point. I am very much opposed to simply allowing it to say the real numbers have a number line and calling that a definition. My proposal to say they have a number line, with no "room" to fit additional numbers in, is an attempt to make the one-line introduction correspond to an actual rigorous definition, which will not be the case if we allow Oleg's revert. Gene Ward Smith 22:32, 13 May 2006 (UTC)

Comments at talk:real number are encouraged. My version of things is that Gene is convinced enough that he is right that he is prefers repeatedly reverting to his version to discussing things on the talk page. Oleg Alexandrov (talk) 22:51, 13 May 2006 (UTC)

I think you need to take your own advice; your reckless reversion was done without any discussion. Gene Ward Smith 23:28, 13 May 2006 (UTC)

Regardless of who did what, there is a discussion running at the talk page now. Please engage yourselves there. -- 127.*.*.1 23:35, 13 May 2006 (UTC)

Islamic mathematics

User:CltFn has proposed to move Islamic mathematics to Middle-Eastern mathematics. Please comment at the talk page. —Ruud 02:36, 15 May 2006 (UTC)

A typesetting subtlety

See if you can spot the difference between this:

$a+b+c+d\,$

$+e+f+g+h\,$

and this:

$a+b+c+d\,$

${}+e+f+g+h\,$

without looking at the TeX code, and guess how and—perhaps more subtly—why the difference was achieved.

I think perhaps this should be borne in mind in editing math articles. Michael Hardy 02:37, 15 May 2006 (UTC)

This is presumably because TeX does not apply its operator spacing rules in the first case, while since you've forced an empty group in the second, it does. Preferrably if you're continuing a sum onto two lines, one would add a \quad of space in the second or add a text indent (via a ":"), instead of relying on empty groups. Dysprosia 03:02, 15 May 2006 (UTC)

Sadly, I spotted the difference instantly, and even knew exactly where to look. This has been with TeX for decades, and Knuth explicitly calls attention to it in The TeXbook (ISBN 0201134489, p. 196). You'd never guess he was the type to pay extraordinary attention to detail, now would you? ;-D

"An extra ‘{}’ was typed on the second line here so that TeX would know that the ‘+’ is a binary operation."

The difference is a consequence of the operator handling rules. --KSmrq^T 04:27, 15 May 2006 (UTC)

Personally, I never noticed this until recently. I once asked Donald Knuth why he had issued an infallible pontifical decree about minute details of the design of the lower-case letter delta. He said it's because the design he prescribed was just obviously the right one. Anyway, in non-TeX mathematical notation, I've been something of a stickler about proper spacing with binary operations and binary relations, thinking all the while that there's no need to think about that in TeX, but in cases like this, there is. Michael Hardy 23:55, 15 May 2006 (UTC)

Dysprosia: How does a text indent via an initial colon achieve this result? It only adds space to the LEFT of "+". Michael Hardy 23:57, 15 May 2006 (UTC)

I wasn't exactly precise in what I was meaning above -- what I meant is that if one wants to continue a sum on two lines, one should add space to the left somehow, instead of keeping both lines of the sum aligned, for example

$a+b+c+d\,$

${}+e+f+g+h\,$

as opposed to

$a+b+c+d\,$

${}+e+f+g+h\,$

I probably should have added "and keeping the same indent" to the end of my comment. It's a shame that the TeX system in use here ignores initial spacing via quads and such. Dysprosia 08:46, 16 May 2006 (UTC)

Math error right on this page?

On this page there is a box telling us that hyperreal numbers, superreal numbers, and surreal numbers are "complex extensions"; in fact, they are all real closed fields. Gene Ward Smith 04:34, 15 May 2006 (UTC)

Zero-eigenvalue bifurcation

Could someone take a look at zero-eigenvalue bifurcation? It is proposed for deletion, but it do find some uses of this term on google scholar. —Ruud 00:17, 16 May 2006 (UTC)

The deletion, rather than redirection, seems summary and not necessary. Charles Matthews 11:03, 20 May 2006 (UTC)

I agreed with the deletion because I think that the term "zero-eigenvalue bifurcation" is hardly used by itself (in constract to more complicated phenomena like the "double zero-eigenvalue bifurcation", used as a synonym for "Bogdanov-Takens bifurcation"). But if you want to create a redirect, be my guest. -- Jitse Niesen (talk) 13:07, 20 May 2006 (UTC)

p-adic numbers notation

A debate is in progress at Talk:P-adic number about whether p-adic numbers should be written from right to left or from left to right. The article used to use the right-to-left notation, but was recently rewritten with the left-to-right notation. Contributions to the debate from a wider pool of wiki mathematicians would be helpful, to see if we can reach a concensus. Gandalf61 08:21, 16 May 2006 (UTC)

Okay, after some discussion on its talk page, I have now changed the p-adic number article to consistently use the right-to-left notation, but with a new section that mentions other alternative notations. Any comments on the partial re-write are welcome at Talk:P-adic number. Gandalf61 09:34, 26 May 2006 (UTC)

Moore closure

I propose to delete the bits about Moore closure in the article Kuratowski closure axioms; see Talk:Kuratowski closure axioms#Moore closure. --Lambiam ^Talk 09:05, 16 May 2006 (UTC)

Fine topology (suggestion needed for better name)

I have created a new page on fine topology (as in classical potential theory), but as the title "fine topology" already seems to be taken by a page about general topology (i.e. 'finer topology' rather than "THE fine topology"), I have called my page "classical fine topology" - seems like there ought to be a better solution - any ideas? —The preceding unsigned comment was added by Madmath789 (talk • contribs) .

(Copied from my talk page, I don't have a good answer to this. Oleg Alexandrov (talk) 23:30, 16 May 2006 (UTC))

Call the page Fine topology (potential theory) and use a

{{dablink|[[Fine topology]] redirects here. For the use in potential theory, see [[Fine topology (potential theory)]]}}

at the top of Comparison of topologies? Kusma (討論) 23:43, 16 May 2006 (UTC)

Thanks for that suggestion - I have renamed the page. In a similar vein, I am tempted to write 2-3 articles on the subject of 'thin sets' and 'polar sets' (as used in potential theory, subharmonic functions etc.) and find that these terms also link to pages mainly about set theory. Would it be sensible to call my new pages 'thin sets (potential theory)' etc. What do more experienced wikipedians think? Madmath789 10:10, 17 May 2006 (UTC)

Nothing links to Fine topology, so it might be better to turn this into a disambiguation page rather than redirect to Comparison of topologies, thereby avoiding an awkward disambiguation phrase in Comparison of topologies. Nothing links to Thin set either. --Lambiam ^Talk 11:07, 17 May 2006 (UTC)

Idea: when user clicks on an equation wikipedia explains it

Sorry if this is the wrong place / its already been suggested (I searched :-\), please direct me to the right place if here is incorrect (or tell me its not a worthwhile idea if you think so). This is a suggestion that when a equation is displayed (for example the one on this page) the user can click on the equation and is taken to a special page that explains the contents of the equation and what it means.

OK, let's try it:

$\int_0^\infty 1\,dx.$

Weird! What I see is this:

UNIQ5f19c7bc44ccc704-math2f6e29f1133d184200000001

What I "should" see is this:

$\int_0^\infty 1\,dx.$

When I click on it, it takes me to the right place.

Is this browser-dependent? Michael Hardy 01:50, 20 May 2006 (UTC)

You are seeing artifacts of one of the intermediate interpretation passes that mediawiki does during math markup. When all goes well (e.g. properly formed or properly messed up math syntax) you'll either see the math, or some nice error note. If something unexpected happens (e.g. math in links, math in image captions, etc) then mediawiki will mysteriously dump out that garbage. Basically, you're causing an error that isn't specifically handled by the markup engine, so it gets confused. It's totally browser-independent.

As for the suggestion, I think such a thing would overly burden the database and the authors. It sounds like you're suggesting that a new page be created to explain every equation. That's a lot of new pages to store, and a lot to write. That style of writing probably wouldn't be very popular, since most of us are used to explaining equations in neighboring text. Plus, it would be quite a large programming task to add that functionality into mediawiki. Staecker 02:07, 20 May 2006 (UTC)

Ahh no I meant something automatically generated. By definition a mathmatical equation is exact and parsable by a computer. It will be a bit of work by someone to make it function, but I thought I'd put it out there as an idea.

In the page I referenced above, the reason for the equation is explained, but at the level of someone who understands equations already, not to someone who has no idea what the $\sum$ means. I thought it would make wikipedia more accessible to non maths experts and require the time of one developer (and not the time of every maths editor).

See User:RickiRich\Math_Example for an example of what I think could be programatically created, and a description of How it could be created without too much fuss. After exams I'll have a go at this if no one else has.

--RickiRich 01:01, 22 May 2006 (UTC)

I don't think this is a good idea, I doubt it will get used by anybody if it gets implemented, and I doubt the developers will ever bother implementing that. You should at least get some support for this feature before you decide to do anything about it. But again, I don't think this wil lead anywhere. Oleg Alexandrov (talk) 04:07, 22 May 2006 (UTC)

What Oleg said. Dysprosia 06:31, 22 May 2006 (UTC)

I think it won't work. A significant obstacle is that mathematical symbols can have many different meanings, and a computer just ain't smart enough to distinguish which one you mean. For example, the + symbol could mean addition, or it could mean the span of two vector spaces, or the concatenation of two strings, etc. So much depends on context. (Also you probably wanted a forward slash in the title of that page, not a backslash. See Wikipedia:Subpage.) Dmharvey 21:43, 24 May 2006 (UTC)

Intriguing idea, but I don't think its right for wikipedia. There have been some development along similar ideas both MathML and OpenMath formats have had some aspect of representing the meaning of an equation rather that its purely visible representation. OpenMath in particular has seen a lot of work with people developing Content Directories which are domain specific collections of mathematical definitions. There has been numerous papers on the subject, but I don't think its gained much acceptance apart from as a means of converting from one computer algebra system to another. In the wikiworld meta:Semantic MediaWiki is a wikipedia extension which allows some form of semantic markup.

Why its not right for Wikipedia: basically the wiki concept follows KISS principle (Keep it simple stupid) and this sort of system gets rather complex. Hopefully all the relevant terms should be linked in the text anyway. --Salix alba (talk) 22:17, 24 May 2006 (UTC)

Massive edits foil comparison operation in article history

Sometimes an editor goes thru an article and changes many minor things at once. For example: spelling corrections; deleting unneccessary spaces; replacing & alpha ; with α; etc.. When this is done, the function which shows changes in the history often fails. It may begin matching an old paragraph to the wrong new paragraph and then it never gets back in synch (until one reaches a section header, if that was not changed). Of course, this makes it very difficult to check that the change was done appropriately.

I think that it is probably impractical to correct this bug in the comparison. So I am suggesting that you-all try to avoid this situation in the first place. When you do such massive edits, please first do every other paragraph (to allow the software to get back in synch with an unalterred paragraph). Then do a separate edit to change the remaining paragraphs. Thank you. JRSpriggs 06:06, 20 May 2006 (UTC)

I think you'll need to provide a concrete example of this happening. Dysprosia 09:39, 20 May 2006 (UTC)

The most recent occassion on which this happened to me was in the 18 May 2006 edit of Constructible universe by UkPaolo, called clean up +spelling correction using AWB. See http://en.wikipedia.org/w/index.php?title=Constructible_universe&diff=53858793&oldid=53818751 and scroll down to the section named "L is absolute and minimal". JRSpriggs 09:05, 21 May 2006 (UTC)

For this example it would have helped if the diff algorithm ignored blank lines, that is, tried to match up the two versions after filtering out the blank lines (which should be re-inserted for the final presentation). I suppose there is a backlog of all kinds of wishes for the developers, and I don't know how important this really is, but it is relatively simple to implement. --Lambiam ^Talk 18:48, 21 May 2006 (UTC)

I think that the problem is more difficult than Lambiam thinks it is. In the section to which I referred, the only blank line was the next to last paragraph. Yet the mismatching of paragraphs began at the first paragraph in the section. Apparently the diff-software cannot measure the similarity of the contents of two paragraphs until after it has decided irreversably that they are matching paragraphs. That matching of paragraphs appears to depend only on whether they are identical, followed by interpolation (guessing) between identical pairs of paragraphs. JRSpriggs 07:12, 22 May 2006 (UTC)

Blank lines were removed in the edit following each and every section title. This doesn't show up clearly in the diff, but start an edit on both versions and compare the contents of the edit boxes, and it will be obvious. If then the next paragraph is also modified, the diff algorithm can't line them up. The silly thing in this massive edit is that many of the changes have no substance and consist of replacing two spaces after a full stop by a single space. --Lambiam ^Talk 10:06, 23 May 2006 (UTC)

You may want to mention this on Wikipedia:Village pump (technical) or check the bugZilla where there are currently 93 bugs related to the diff. In this case the edit summary gives some clue, the edits were done using the WP:AWB tool, they are mainly minor edits and it would be hard to break this up into smaller edits, by limitations of the software. --Salix alba (talk) 07:16, 23 May 2006 (UTC)

The problem is apparently caused by a feature of AWB, "Apply general fixes", which removes "excess white space" to which the diff algorithm is sensitive (Wikipedia:AutoWikiBrowser#"Set options"). --Lambiam ^Talk 10:15, 23 May 2006 (UTC)

resolve a revert war at dual space

I find myself in a revert war at the article dual space. It's mostly about style; how much information is too much, whether material looks good or fits. this diff shows the difference between the two users preferred revisions. See also this old version for a much longer revision that I reverted. I am pessimistic with how talks on the talk page are going. We seem not to see eye-to-eye. I would like to get some more opinions. -lethe ^{talk +} 04:42, 23 May 2006 (UTC)

Compound Poisson process question

Probabilists out there, I wonder if you could answer a question posted at Talk:Compound Poisson process. Oleg Alexandrov (talk) 17:25, 24 May 2006 (UTC)

looks right to me. (and the changes i made were mostly cosmetic.) Lunch 19:10, 24 May 2006 (UTC)

I added a final line to the moment generating function calculation, which should clarify matters further. The variance result looks OK, by computing them in terms of the moment generating function. — Arthur Rubin | (talk) 20:27, 24 May 2006 (UTC)

Looks OK to me, too. Michael Hardy 21:17, 24 May 2006 (UTC)

... and generally, the nth cumulant of the compound Poisson distribution, following the notation now in the article, is λt times the n moment of the distribution of the random variable that the article (in its present form) calls D_i. This can be shown via the law of total cumulance. The cases n = 1 and n = 2 are just what now appears in the article. Michael Hardy 21:20, 24 May 2006 (UTC)

Widespread mathematical delusions

I'd like to hear some opinions about the new article Widespread mathematical delusions. At the moment, the article lists only one delusion, and I am not sure what the delusion actually is, but it has something to do with statistical independence. In fact, the article Widespread mathematical delusions criticizes the lead section of statistical independence. Can somebody make sense of the new article?

The user who created the article has also written some articles on eventology, a theory which I haven't heard about. The article on eventology lists ten references, all by the same author, including some papers in good Russian journals so we might want to keep the article even though it violates the Wikipedia:Vanity guidelines. -- Jitse Niesen (talk) 05:12, 25 May 2006 (UTC)

0.999... ≠ 1 must be pretty widespread. And misconceptions about infinity are pretty common. -lethe ^{talk +} 06:58, 25 May 2006 (UTC)

I can't make much sense out of this rant. The "intuitive" meaning offered in the article Statistical independence appears to me to be an informal way of saying P(B|A) = P(B). Using the standard definition of conditional probability, this means P(A ∩ B)/P(A) = P(B), or P(A ∩ B) = P(A) P(B), in other words: events A and B are independent. Where is the delusion? There is no shortage of delusions, including mathematical ones, and the field of statistics and probability theory is particularly rich, but this doesn't seem to be one of them. Its like having a diatribe against saying that 1 < 2 means that 1 is less than 2, while it means nothing except "1 < 2". To AfD? --Lambiam ^Talk 11:16, 25 May 2006 (UTC)

I find it hard to understand exactly what this guy is ranting about, mainly because of the poor translation of his thoughts (presumably from Russian) into English. His maths seems to be correct, but only seems to show that conditional probability can be different in different situations. If this page is to be kept, it surely needs a different title? (and a lot of work on wording) I cannot believe that this really is a *widespread* delusion Madmath789 11:46, 25 May 2006 (UTC)

Whatever else it it is, it is surely OR. Paul August ☎ 11:51, 25 May 2006 (UTC)

The delusion consists in popular attempts to justify or to prove or to deduce the definition of independence of events: P(AB)=P(A)P(B) from other assumptions. Mathematical definitions do not demand proofs, especially in a preamble to encyclopaedic paper on probability theory. The criticism is directed only on style of a preamble. All other sections of paper “Statistical” are quite correct. Thanks for discussion. - Helgus 12:28, 25 May 2006 (UTC)

Helgus: I think you misunderstand what the lead section (what you are calling the "preamble") of Statistical independence, is saying. It is not trying to "prove the definition" rather it is simply trying to provide an intuitive understanding of the concept. In any case any criticism of that article belongs at talk:Statistical independence not in some other article. Paul August ☎ 15:52, 25 May 2006 (UTC)

Probably you are right. Especially it concerns the second section of paper. However the first section without doubts keeps within a well-known encyclopaedic category “Paradoxes in mathematics”. Russian mirror of this paper contains, for example, popular delusions which often meet at discussion on “Fermat's last theorem”, “Parallel lines in Lobachevsky's geometry”, “Events with zero probability”. Can be it is necessary to open a new category “Paradoxes in mathematics” into which this paper could enter? - Helgus 21:58, 25 May 2006 (UTC)

Yes AfD unless its moved to a different name and cleaned up to be less like Orignial Research, give it a bit of time though the page is less than a day old.

Also the eventology page is now proposed for deletion, although the other sub articles and the category are not. Either it should be all or none and I think AfD might be better than prod in this case. --Salix alba (talk) 12:58, 25 May 2006 (UTC)

If the page is to be kept, it should probably be renamed -- "delusions" is not quite neutral, perhaps "misconceptions" would be better. Dysprosia 13:03, 25 May 2006 (UTC)

The eventology pages look suspicious to me. The only reason I created Category:Eventology is too keep them all in one place. I agree that an AfD vote on all of them could be the things to do. Oleg Alexandrov (talk) 15:37, 25 May 2006 (UTC)

It really is OR and a rant. The title reads pretty bad as well, it probably should be deleted.--Jersey Devil 17:37, 25 May 2006 (UTC)

I've removed the prod tag from eventology, If we are to believe the references there, it isn't OR, although it may be non-notable. So I agree with Jitse's, I'm not sure we should delete this. Paul August ☎ 18:09, 25 May 2006 (UTC)

But User:Helgus is Oleg Vorob'ov, the author of 10 out of 11 of the references. Sounds like OR to me. Staecker 02:44, 26 May 2006 (UTC)

No, OR means writing about something which has not yet been published elsewhere. Paul August ☎ 02:48, 26 May 2006 (UTC)

You're right- sorry, I confused it with WP:AUTO. Not surefire grounds for deletion, but it gives me the willies. Staecker 02:57, 26 May 2006 (UTC)

Yes writing about your own work is problematic. And we should take special notice of such. Paul August ☎ 17:10, 26 May 2006 (UTC)

eventology, but not sub-pages now on AfD. --Salix alba (talk) 10:45, 28 May 2006 (UTC)

Lebesgue spine

Being a newcomer here, I would appreciate some brief advice: Lebesgue spine is listed somewhere as a missing link, but when I look at 'what links here', I only find things like Wikipedia:Missing science topics/Maths16. I could write a page about the Lebesgue spine, but would it be any use? Madmath789 20:35, 25 May 2006 (UTC)

Sure it would be useful. Paul August ☎ 02:45, 26 May 2006 (UTC)

Non-negative v. nonnegative

OED lists "non-negative" but Webster's lists "nonnegative". Is this a British/American usage split? I've looked through a few textbooks, but there doesn't seem to be any particular consistency (not all American books use "nonnegative" and not all European ones use "non-negative"). Any opinions? There seems to be a mix among Wikipedia articles (even within a single article) and titles. Thanks. Lunch 22:05, 25 May 2006 (UTC)

I use either when the mood strikes me. If there's no standard, what's the difference? Ryan Reich 22:39, 25 May 2006 (UTC)

I s'pose I was thinking consistency would make things easier to find, and any source I found was always self-consistent whereas the Wikipedia isn't. And now that I look through the textbooks sitting in front of me, four have "nonnegative" (five American authors) and only one has "non-negative" (two Frenchmen). Lunch 23:11, 25 May 2006 (UTC)

In my experience, in American papers and textbooks "nonnegative" is by far the most common. Older works may use "non-negative" to a greater frequency. --C S (Talk) 01:52, 27 May 2006 (UTC)

Stone-Cech compactification name

Most of the references I've seen have a symbol over the "C", which I can't figure out exactly how to generate. (Also, there seems to be a convention that the "-" should be replaced by an n-dash "–".) — Arthur Rubin | (talk) 00:28, 26 May 2006 (UTC)

How about this: Čech? Dmharvey 02:51, 26 May 2006 (UTC)

When I open an edit window, below the Save page button is a box that says "Insert:", followed by numerous special characters. The character in question is one of them, and clicking on it causes it to be inserted into the edit box. JavaScript must enabled in the browser for this to work. --KSmrq^T 03:52, 26 May 2006 (UTC)

What a mess. We have Stone-Cech compactification and Stone-Čech compactification, and Čech points to neither, and probably we need Cech as a redirect as well. Dmharvey 02:56, 26 May 2006 (UTC)

Hm, apparently the redirect at Stone-Čech compactification is my fault; don't really remember doing it. Stone-Cech compactification should be moved to Stone-Čech compactification, but it won't let me move it because the redirect is to a different place. I'll tag the redir for speedy. --Trovatore 03:05, 26 May 2006 (UTC)

OK, fixed now. This time the endash thing came in handy. --Trovatore 03:12, 26 May 2006 (UTC)

How about Štone-Cech compactification? :-) -lethe ^{talk +} 04:01, 26 May 2006 (UTC)

Added. Hey, you never know. --Trovatore 22:34, 26 May 2006 (UTC)

Maths AfDs

A certain User:Mathguru has AfD'd Quasi-Hopf algebra and Quasi-bialgebra. I think it is notable, but as the author, I may be biased.Blnguyen | Have your say!!! 06:39, 26 May 2006 (UTC)

I'm a hair away from closing them both speedy keep. -lethe ^{talk +} 10:48, 26 May 2006 (UTC)

Too late now ... I closed them. -- Jitse Niesen (talk) 12:00, 26 May 2006 (UTC)

well, mathguru, Afd' the Australian Mathematics Competition as well.Blnguyen | Have your say!!! 08:00, 31 May 2006 (UTC)

Also closed as a speedy keep. -- Jitse Niesen (talk) 08:36, 31 May 2006 (UTC)

A query

Does anyone have a reference or proof for Kronecker's lemma? This has been bothering me, mainly in case absolute convergence of Σ x_n ought to be included. Charles Matthews 13:07, 26 May 2006 (UTC)

I think the statement is true as is stands, but I don't have a reference. Using summation by parts,

$\frac1{b_n}\sum_{k=0}^n b_k x_k = S_n - \frac1{b_n}\sum_{k=0}^{n-1}(b_{k+1} - b_k)S_k,$

where

S k

are the partial sums of the x's. Pick any epsilon > 0, choose N so that

S k

is epsilon-close to s for k > N. Then the right hand side is

$S_n - \frac1{b_n}\sum_{k=0}^{N-1}(b_{k+1} - b_k)S_k - \frac1{b_n}\sum_{k=N}^{n-1}(b_{k+1} - b_k)S_k$

$= S_n - \frac1{b_n}\sum_{k=0}^{N-1}(b_{k+1} - b_k)S_k - \frac1{b_n}\sum_{k=N}^{n-1}(b_{k+1} - b_k)s - \frac1{b_n}\sum_{k=N}^{n-1}(b_{k+1} - b_k)(S_k - s)$

$= S_n - \frac1{b_n}\sum_{k=0}^{N-1}(b_{k+1} - b_k)S_k - \frac{b_n-b_N}{b_n}s - \frac1{b_n}\sum_{k=N}^{n-1}(b_{k+1} - b_k)(S_k - s)$

Let n go to infinity. The first term goes to s, which cancels with the third term. The second term goes to zero. Since the b sequence is increasing, the last term is bounded by $\epsilon (b_n - b_N)/b_n \leq \epsilon$ . Dmharvey 13:41, 26 May 2006 (UTC)

Now transcribed to that controversial category Category:Article proofs. linas 01:43, 13 June 2006 (UTC)

Indiscriminate collection of information?

Don't pages like this, Derivative (examples), break with WP:NOT?--Jersey Devil 02:32, 27 May 2006 (UTC)

I have put it up for afd, your input would be appreciated.--Jersey Devil 02:36, 27 May 2006 (UTC)

Mathematics is Article Improvement Drive collaboration

Ladies and Gentlemen! Did you know that the article Mathematics is the current Article Improvement Drive collaboration? --Lambiam ^Talk 22:40, 27 May 2006 (UTC)

Voted for it on the AID page. One user commented that it is in the top ten most viewed pages on Wikipedia and therefore must be a featured article.--Jersey Devil 23:01, 27 May 2006 (UTC)

Eventology AfD

The article Eventology (by the same author as Widespread mathematical delusions) has been nominated for deletion. --Lambiam ^Talk 13:21, 28 May 2006 (UTC)

Delusions in probability theory and statistics on AfD

I've nominated the article Delusions in probability theory and statistics (earlier called Widespread mathematical delusions) for deletion. --Lambiam ^Talk 22:31, 28 May 2006 (UTC)

Disambiguation of sinc function

There are two possible definitions of the sinc function, namely

$\operatorname{sinc} \, x = \frac{\sin x}{x} \quad\mbox{or}\quad \operatorname{sinc} \, x = \frac{\sin \pi x}{\pi x}.$

One possible way to handle this is to split the article sinc function in two, sinc function (normalized) and sinc function (unnormalized), similar to the usual disambiguation process. We are having a discussion on Talk:Sinc function (unnormalized) whether this is the proper way to go about it, and I'm solliciting others to join. -- Jitse Niesen (talk) 05:21, 31 May 2006 (UTC)

Possible confusion over 'subadditive'

There is an article Subadditive which discusses functions satisfying $f(x+y)\leq f(x)+f(y)$ , and there is a link to this article from Sigma additivity in the category measure theory. There seems to be a different definition of 'subadditive' (and also 'countably subadditive') in use in measure theory:

$\mu(E \cup F) \leq \mu(E)+\mu(F)$

(used in developing the theory of 'outer measure'). My question is: do we need a separate page for subadditve set functions, or should we incorporate it into the existing subadditive page? (Or are subadditive set functions not notable and we do not need them?). I might be in a position to write something on the set function version of subadditive (if needed), but would appreciate some views about what might be done - and there are probably others better qualified to write such stuff anyway.Madmath789 11:27, 31 May 2006 (UTC)

I think you're right, subadditive (measure theory) deserves its own article. I don't know any measure theory, but I recall there being interesting theorems about set functions which are additive (on finite collections of sets) and countably subadditive. Dmharvey 11:37, 31 May 2006 (UTC)

Be bold! Write stuff, we move and fix later. Charles Matthews 11:46, 31 May 2006 (UTC)

Barry Simon article

The piece on Barry Simon is from a fan, it seems. Important guy for mathematical physics, and this should be better expressed and sourced, and have more technical stuff about the work. Charles Matthews 11:46, 31 May 2006 (UTC)

A good example of hagiography I guess. --CSTAR 18:54, 1 June 2006 (UTC)

Jun 2006

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

E9 (Lie algebra)

My knowledge of Lie algebras is a single course, but this potentially confusing notation was never mentioned. Has anyone else heard of this? Septentrionalis 18:40, 1 June 2006 (UTC)

I have never heard of this notation. I note that my references list the notation as E₈⁽¹⁾. The subscript here is, as always, the rank. -lethe ^{talk +} 18:51, 1 June 2006 (UTC)

Please review

I have extensively revised and cleaned up Divisibility rule, so please take a look and help to improve it more. As I'm not fully experienced at all the editing tools, I'm sure the formatting and adherence to guidelines and standards could be improved.

I'd like to create a number of other pages related to mental math, so I'd like to get feedback on this one, the first I've heavily edited. (The current mental arithmetic has only the most basic, simple of techniques.

Walt 01:59, 2 June 2006 (UTC)

Category:Billion and cousins up for deletion

See Wikipedia:Categories_for_deletion#Category:Thousand. Oleg Alexandrov (talk) 18:57, 3 June 2006 (UTC)

Poincaré conjecture

Some Chinese news sources have picked up a story about a recent journal article by Cao and Zhu, experts on the Ricci flow, who have written what they (and the journal editors) claim is a "complete" proof of the geometrization conjecture, by giving more details of Perelman's work. Slashdot has also picked up on this. As a consequence, there has been several editors who have insisted on placing mention of Cao and Zhu's paper in the lead section. I have disagreed (see talk page discussion and also some of my edit summaries for extensive reasons). Please continue discussion there. I would also appreciate if people could pop in and check that things don't get out of control. Thanks. --C S (Talk) 02:15, 6 June 2006 (UTC)

American Institute of Mathematics

The article on American Institute of Mathematics has been nominated for deletion by someone. R.e.b. 13:02, 6 June 2006 (UTC)

PlanetMath Exchange project milestone

The PlanetMath Exchange project has today reached a new milestone, with 40% of all PlanetMath articles reviewed.

For those of you who have not been following the project, I thought I would take this opportunity to report on the status of the project, and the progress which has been made to date. The purpose of the project is to review all PlanetMath (PM) articles (which are licensed under GFDL) and to incorporate any appropriate PM content not adequately covered on Wikipedia (WP).

There are over 4800 PM articles listed, of which over 1900 of which have been reviewed so far. Of the reviewed articles, 143 PM articles have been copied to WP, creating entirely new WP articles, and 121 have been merged into already existing WP articles. Additionally, a further 75 PM articles have been identified as needing to be copied, and 349 needing to be merged.

The project maintains 49 lists of PM articles grouped by topic (e.g. 11 Number theory, 26 Real functions, 54 General topology). The entire list of lists is compiled into a "Article lists" table, and statistics are maintained for each topic's list.

19 editors have identified themselves as participants, and 26 have reviewed at least one PM article (see Editor contributions).

Oleg Alexandrov, has provided several excellent tools to facilitate the project. He and Mathbot created the original 49 lists (first created in Feb 2005, and updated with new PM articles in March 2006). They also perform daily updates of statistics in the "Article lists", and "Editor contributions" tables. In addition, Oleg has created a convenient tool to assist in converting a PM article to wiki markup.

I heartily encourage everyone to join the fun.

Paul August ☎ 02:06, 8 June 2006 (UTC)

Direct logic up for deletion

See Wikipedia:Articles_for_deletion/Direct_logic -Dan 15:36, 8 June 2006 (UTC)

Another misguided nomination for deletion

Please vote at Wikipedia:Articles for deletion/American Institute of Mathematics. Michael Hardy 23:33, 9 June 2006 (UTC)

Yeah, R.e.b. told us already. -lethe ^{talk +} 00:48, 10 June 2006 (UTC)

I closed that AfD. -lethe ^{talk +} 00:54, 10 June 2006 (UTC)

Functional analyst needed

Hi, I left a question regarding the correct statement of the Ryll-Nardzewski fixed point theorem at Talk:Ryll-Nardzewski fixed point theorem. Cheers, AxelBoldt 04:10, 11 June 2006 (UTC)

As stated it's wrong. The semigroup is required to satisfy another property, that it be "distal". Also I don't think it can be used to prove existence of Haar measure on general locally compact groups, although I think for compact groups yes. I think this is in Rudin's functional analysis book for instance. Also see Frederic Greanleaf's little book (now horribly outdated) on "Amenable Groups".--CSTAR 12:41, 12 June 2006 (UTC)

Rewrite Poincaré_conjecture?

I invite interested parties to make comments at Talk:Poincaré_conjecture#Peer_review. --C S (Talk) 12:48, 11 June 2006 (UTC)

Jaques Hadamard or Jacques Hadamard?

An anon recently redirected the wikilink in Chaos Theory from the first to the second. Is this legitimite? Are these the same person? — Arthur Rubin | (talk) 15:30, 11 June 2006 (UTC)

Yes, same person. Correct spelling is Jacques [22]. I have changed the Jaques page to a redirect and fixed the link in the single remaining article that used the wrong spelling. Gandalf61 15:53, 11 June 2006 (UTC)

Zipper theorem

I wanted to {{prod}} this article. But to be sure I thought I'd check. Is this article nonsense or not? I couldn't google the name, but that doesn't always mean anything. Garion96 ^(talk) 00:20, 12 June 2006 (UTC)

The theorem and its proof in the article are correct. The theorem was not known to me under this or any other name. --Lambiam ^Talk 00:53, 12 June 2006 (UTC)

Thanks, so I won't {{prod}} it. Anyone here wants to clean that article up? Cause the way it looks now, it's not understandable for the non mathematician reader. Like me. :) Garion96 ^(talk) 12:04, 12 June 2006 (UTC)

Hmm, perhaps I should have looked at at the article again. It already is cleaned up. Thanks. Garion96 ^(talk) 12:05, 12 June 2006 (UTC)

I think it's a neologism. I think it should be deleted without some evidence of that name having widespread currency. Dmharvey 12:15, 12 June 2006 (UTC)

I've heard it referred to in that way ("zipper theorem"); dunno if that's enough evidence for you. I also can't think offhand of a place I've seen it in print, though. I could ask around. Lunch 18:53, 12 June 2006 (UTC)

I'm skeptical that the name is very common. I can't imagine the theorem would even have a name amongst mathematicians. So I think the term would only be used in certain kinds of introductory course work. Google gives no results (off Wikipedia), so nobody that has mentioned it, for example, in a course webpage. The only place I can think the term may exist is in some textbooks somewhere. Even in that eventuality, I don't know if it's worth having an article based on that amount of usage. I guess it does no harm, but I'm also hard-pressed to imagine a situation where we would want to link to it. --C S (Talk) 19:18, 12 June 2006 (UTC)

Merge it into Limit of a sequence#Properties? —Blotwell 17:01, 13 June 2006 (UTC)

I've asked a few people around, and none other than me have heard this result referred to as the zipper theorem. I guess it's not as popular a term as I thought. Maybe zipper lemma instead? ;) Maybe it'd qualify for a list of some sort of elementary properties of limits; if not, maybe stick it in the article on limits. BTW, this theorem is true for any metric space, but is it true for non-Hausdorff spaces? How much can the requirements of the theorem be relaxed? Lunch 21:57, 20 June 2006 (UTC)

The exact same proof, translating epsilons into open sets, proves it in every topological space. This result has about the same significance as, say, the linearity of differentiation, and should probably go in a list of limits like the list of derivatives. Ryan Reich 22:48, 20 June 2006 (UTC)

Sure, a list of limits article would be a good idea. And I guess you can just replace balls with neighborhoods; I think I was confusing myself with the non-uniqueness of limits in non-Hausdorff spaces. Lunch 23:33, 20 June 2006 (UTC)

Sorry if I was curt with that reply. I'll be happy to put together a basic list of limits. Actually, following the model of the list of derivatives, there isn't any need to touch zipper theorem, just link to it from the list. Unless we really don't like it for some reason. Ryan Reich 00:22, 21 June 2006 (UTC)

looks good! Lunch 17:58, 22 June 2006 (UTC)

integrable systems

Over at Talk:Constant of motion, I've been reduced to babling and waving my hands to the effect that a "system of differential equations with constants of motion == integrable system == system with symmetries" and conversely, "non-integrable system == system with no constants of motion". However, it occurs to me that I know of no grand theorems making this claim. Are there any? Is this in fact a collection of small results in narrow fields that have accreted into a grand truth? Guidance? How can one make this clear at a college-math level? It doesn't help that the article integrable system is somewhat foreboding in its current form. linas 01:30, 13 June 2006 (UTC)

Maybe I'm being lame? Maybe its just the Frobenius theorem coupled to the idea that the submanifold has a natural symmetry, ergo by Noether's theorem has constants of motion? I've never had formal skoolin in this matter. linas 03:13, 13 June 2006 (UTC)

I think I'm grasping for Liouville's theorem (Hamiltonian). I swear this stuff goes in one ear and out the other. I'm babbling even now. linas 03:27, 13 June 2006 (UTC)

You make a good point about the current article being somewhat forbidding. I would go a step further. I don't think integrable system should redirect to integrability conditions. An integrable system usually (?) refers to a Hamiltonian system with a full set of Poisson-commuting flows. Naturally, integrability conditions do play a role, but there is more structure a priori in an integrable system. For the point about conserved quantities for an integrable system, since the Hamiltonian flows commute, there should be loads of conserved quantities. (As you ask, is there a general theorem here? Does Noether apply? etc). Hence a system without "enough" conserved quantities will be non-integrable. I'm not so sure about the converse. Silly rabbit 13:15, 13 June 2006 (UTC)

Thanks. What I've been reading gives the name completely integrable system to the case of a full set of commuting Poisson brackets. Your "not being sure about the converse" would imply that there are non-integrable systems with a "full set" of conserved quantities. That certainly sets my mind wandering in wild directions. linas 23:27, 16 June 2006 (UTC)

Nice start on integrable systems. It certainly has helped me organize some of my own wild wanderings. I'm clearly not an expert, but it seems to be tricky to give a good definition of an integrable system. (Ok, so first off, yes I meant what you call completely integrable: which is unarguably a better term ;) In particular, there are issues of local versus global integrability. What does global integrability mean anyway? Do the all the level submanifolds have to be closed? Do the constants have to be found explicitly, or can they just be given in some implicit sense? Can a locally completely integrable system have degenerate Poisson brackets on some small dimensional locus, and still have functionally independent integrals? (Here is the "lack of converse" possibility -- if it exists to begin with.) Silly rabbit 23:37, 17 June 2006 (UTC)

Thanks. I'd say a Lie group is the prototype for something that is "globally integrable". I don't know of any systems that are "provably integrable" (constants of motion implicitly given), but whose solution is unknown (no explicit form). I suspect one can find level manifolds that are not closed, certainly things like the horocycle flow ( aka Anosov flow on tangent space of SL(2,C)) has the flavour of being non-compact but this is an off-the-cuff remark. I believe that the whole area of sub-Riemannian geometry is permeated with integrable systems that have cuts and isolated singularities and the like. Next, chaotic systems have "regimes" of regular and chaotic motion that's interspersed; the KAM torus being the famous example, although the easy-to-understand variants are in difference equations. Then there's all this stuff about homoclinic orbits, and stuff like Axiom A, which I dimly understand. Or things I dont:Smale's spectral decomposition theorem. I'm sort of learning this stuff as I go along.linas 04:57, 18 June 2006 (UTC)

Mathematicians for Wikipedia:Version 0.5 Nominations

On Wikipedia talk:WikiProject Mathematics/Wikipedia 1.0 there is a request for the most notable mathematicians whos biographies could be included in Wikipedia:Version 0.5 Nominations. Suggestions for celebratity mathematicians welcome. Possible also assesments of the quality of their article also welcome. --Salix alba (talk) 07:45, 15 June 2006 (UTC)

Thanks to great work by Lethe we now have a fairly comprehensive list of the the giants for mathematics on Mathematics/Wikipedia 1.0. A new template Template:maths rating has also been created together with a set of categories listing the quality and importance of mathematics articles. Mathbot will included these articles in Wikipedia:Version 1.0 Editorial Team/Mathematics articles by quality on a daily basis. Help is now needed in identifying the important maths articles and assigning then a grade (Feature Article/A/Good Article/B/Start/Stub), which can be done by including the template on the talk page. There are a few biographies which may be suitable for listing as good articles and several other on some key figures which are barely more than stubs and could do with expansion.

I'm also thinking that the list of mathematicians could make a good article in its own right, either as a section in Mathematicians or its own article, possible Influential mathematicians. --Salix alba (talk) 09:25, 16 June 2006 (UTC)

We already have list of mathematicians, but I guess you are thinking of a selective subset. I don't know if it is worth its own article. Oleg Alexandrov (talk) 15:37, 16 June 2006 (UTC)

Yes I was thinking of a more selective list, probably anotated as well, briefly describing their main acheivments. It could be an interesting way to tell the history of mathematics through the people involved and the new areas of study they started. This sort of presentation, is quite popular in science books aimed at the general reader and might appeal to certain wikipedia readers. --Salix alba (talk) 20:20, 16 June 2006 (UTC)

Well If you want a selective list one place to start would be Bell's Men of Mathematics. Paul August ☎ 20:55, 16 June 2006 (UTC)

Might I also suggest the obvious web site, MacTutor? --KSmrq^T 04:53, 17 June 2006 (UTC)

Probability/Measure theory glossary?

Does WP have a glossary that translates the language of probability theory to measure theory? I've got a complaint on my talk page that I'm trying to decipher; I don't understand Score (statistics) and Fisher information, although I suspect I would, if they were restated in terms of measure theory. The root of this interest is the rather astounding edit here, which is so remarkable, I abstract it here:

Fisher information is a powerful new method for deriving laws governing many aspects of nature and human society. B. Roy Frieden sets out in detail how Fisher information can ground a great deal of contemporary physical theory, including Newtonian mechanics, virial theorem, statistical mechanics, thermodynamics, Maxwell's equations, Lorentz transformation, general relativity, EPR experiment, Schrodinger equation, Klein-Gordon equation, Dirac equation, Rarita-Schwinger equation, and the fundamental physical constants. Frieden and coauthors have also used EPI to derive some established principles and new laws of biology, the biophysics of cancer growth, chemistry, and economics.

Surely, the ommission of M-theory and intelligent design is just an oversight? linas 00:38, 17 June 2006 (UTC)

See Talk:B._Roy_Frieden for a little bit of discussion and some links to external reviews of Frieden's work. He has some interesting ideas but, it seems, not quite the revolution he makes out for himself. The IP address of the edits is assigned to [http:/csc.canterbury.ac.nz Christchurch College of Education] in New Zealand. Maybe Frieden's been travelling? Lunch 03:49, 17 June 2006 (UTC)

user mathisreallycool

A new user mathisreallycool (talk · contribs) has made several edits which to my mind betray a fundamental lack of knowledge in certain mathematical topics. I have reverted several additions by this user, and I want to vet some other things by the user. For example, the article Konfisakhar space seems unobjectionable, it's referenced. However I've never heard of this idea, it's not in any of my texts, nor is it in my EDM2, and frankly, I find the idea of a fractal vector space hard to believe. Can someone (maybe with access to the book by Schaeffer) verify this concept? Otherwise, I shall want to AfD is. And maybe also this definition of semidirect products for monoids? -lethe ^{talk +} 07:14, 17 June 2006 (UTC)

A web search for Igor Konfisakhar suggests the work of a creative student, violating WP:NOR. The citation of the Schaeffer book is also not quite correct; the second edition (ISBN 978-0-387-98726-2) has two authors. I have no personal knowledge of the topic or the book, but I share your reservations.

PS: I've begun using 13-digit ISBNs, since the official transition is not far off. On online converter is available. --KSmrq^T 10:40, 17 June 2006 (UTC)

I've listed Konfisakhar space for deletion. "Professor Igor Konfisakhar" appears to be an undergrad, notable only for being a 3rd place winner in a Putnam prize contest, which is better 'n me but not good enough for this. linas 03:54, 18 June 2006 (UTC)

I know Igor Konfisakhar personally (or did), and can confirm that he is (at present) an undergraduate. Tesseran 03:21, 19 July 2006 (UTC)

The reference work listed is searchable online at Amazon (see [23]). I find no reference to "fractal" or "Konfisakhar". Paul August ☎ 04:35, 18 June 2006 (UTC)

Problems at Propositional Calculus

(Copied from my talk page. Oleg Alexandrov (talk) 07:51, 17 June 2006 (UTC))

JA: Hi, could you help sort out the continuing tangles at Propositional calculus? First there was that improper name change last month, and I let it go because the user who did it seemed fairly competent and added some good stuff, but now the word "logic" seems to be inviting anonymous users to take the article out of the mathematical logic designation and add any sort of half-baked exposition that they can cook up. I don't know my way around the procedures well enough to keep dealing with sort of stuff. Much appreciated, Jon Awbrey 05:15, 17 June 2006 (UTC)

There had been some noise in the past about moving propositional calculus to propositional logic or classical propositional logic. The move to propositional logic was affected by Charles Stewart via WP:RM last month, then reverted by a history-destroying copy-paste by Jon Awbrey this week. I reverted the copy-paste (restoring the history), then reverted the proper move (preserving the history), so now we're back where we started. If the move is to happen, a case will have to be made again. -lethe ^{talk +} 07:59, 17 June 2006 (UTC)

Use "iff", not "if", in definitions!

Some editors appear to believe that there is a convention which requires the use of "if" in definitions rather than "iff" (short for "if and only if"). A definition is a proposition which equates a new term to a compound expression composed of old terms. So using "if" is wrong. One should use "iff" or an equivalent, such as: "if and only if", "is", "is the same as", "means", "is equivalent to", "when and only when", etc.. JRSpriggs 08:20, 17 June 2006 (UTC)

Though you are technically correct, I don't think it's such a problem to use just an "if" in a definition. It's tedious to always write "if and only if" (and the abbreviation is esoteric), and the full meaning can always be inferred. Of course to require "if" in definitions is certainly bad. -lethe ^{talk +} 08:29, 17 June 2006 (UTC)

I am complaining because thrice recently someone has changed "iff" to "if" in a definition. JRSpriggs 10:03, 17 June 2006 (UTC)

If I saw that happen, I would probably revert. -lethe ^{talk +} 10:25, 17 June 2006 (UTC)

Well, "if" is brief, commonly understood, and colloquial; "iff" is brief, not commonly understood, and precise. What to do? Personal, I dislike "iff", so I either write out "if and only if" or use a phrase like "exactly when". My feeling is that anyone who understands the meaning of "iff" and feels comfortable with it also has enough of that fabled "mathematical maturity" to not misinterpret a definition using "if". I am not aware of a WikiMath guideline, nor a Wikipedia guideline that speaks to this slightly delicate issue involving both accessibility and formal correctness.

A recurring challenge with a multinational pool of editors is melding one's own training and taste with that of others. I cringe whenever I see the word "ditto" in an article, as to me it screams of informality, not suitable for an encyclopedia. I'd love to see both "iff" and "ditto" banned, but I have no sense of how much agreement I would find for that view. --KSmrq^T 11:01, 17 June 2006 (UTC)

I would agree with abolishing "ditto" but not with abolishing "iff". Anyway, I agree with Ryan below. The precision afforded by the usage "iff" is useful for theorems, but not so much for definitions. -lethe ^{talk +} 11:18, 17 June 2006 (UTC)

This doesn't follow any mathematical practice I've ever seen, so why should we insist on it simply because it's technically right? We don't make policy here, just record it. Besides, to counter your argument, "iff" is logically absurd in this context since the term to be defined has no prior meaning; whether or not it applies is determined by the text of the definition. In other words, "only if" is vacuous if the term is unique, and if not, it is erroneous. Someone reading an "iff" definition for the first time will wonder if they've missed some other discussion of the term, and anyone else will be annoyed because it departs from the usual style. I agree with lethe, though: any change of one to the other should be reverted. This is a personal preference. Ryan Reich 10:57, 17 June 2006 (UTC)

We are certainly allowed to make policy here. What we don't do is invent subject matter for our articles. So we can't invent terminologies, but we can certainly decide on conventions for our terminologies. -lethe ^{talk +} 11:18, 17 June 2006 (UTC)

I'd argue more but apparently you agree with me. My objection to inventing policy in this sort of case is that the choices are not all equally acceptable; it's not like choosing an indentation style for C code, where many different styles all have their widespread adherents. I've simply never seen "iff" in a definition. Ryan Reich 11:30, 17 June 2006 (UTC)

I can't quote chapter and verse, but I remember seeing a mathematical style guide recommending "if" in definitions. Personally I prefer "when", to distinguish it from the notion of logical consequence (as in: You are in a dilemma when you don't know which way to turn), although some may decry the temporal connotation. --Lambiam ^Talk 12:07, 17 June 2006 (UTC)

I much prefer "if", and that's what I observe as common mathematical practice. Dmharvey 12:57, 17 June 2006 (UTC)

~~I think "if" is somewhat unclear~~, but I have no problem with "only if", "if and only if", the equivalency arrow ( $\Leftrightarrow$ ) and other such language. The term "iff" I object strongly to, at least in basic math articles, on the grounds that it is jargon that is unfamiliar to many basic students of mathematics who have not done proofs. But don't take my word for it - I've seen countless edits where amateurs have "corrected" iff to "if". Deco 13:53, 17 June 2006 (UTC)

Something unseemingly asymmetrical about accepting "only if" (⇐) and rejecting "if" (⇒). I must say I do not understand your position. -lethe ^{talk +} 14:04, 17 June 2006 (UTC)

The words "only if" do not imply "given the sufficient condition that", and it is a myth that "if and only if" is the conjunction of "if" and "only if". It is merely a way of clarifying "if" using the additional qualifier "only if" that only serves to strengthen that "no we don't mean this is just a necessary condition" but in fact an equivalency is intended. If I say "a number is prime only if it has exactly two factors", the intepretation is clear; it does not even suggest that there might be a prime which doesn't have two factors. Deco 17:23, 17 June 2006 (UTC)

Indeed, "only if" implies "given the necessary condition that", and "if" means "sufficient". And in mathematics, "if and only if" certainly is their conjunction, at least in a formal context, but since this is a formal phrase that is to be expected. Using it in an informal context evokes its formal meaning and is just confusing when you start to split hairs about what it really means, especially given that syntactically, it definitely looks like the conjunction of "if" and "only if". Stating "only if" in a definition is redundant, since the term is intended to be deciphered, not encoded: if I see a long string of conditions which happen to have a nice definition but I don't know it, I will not go looking for one until it's necessary; on the other hand, if I see an unfamiliar term I will go looking for its definition. Putting "only if" in the definition would just mean "whenever you see this term, you can be sure it means this phrase", which is exactly what the process of defining the term means anyway. Combined with the common-sense reason that people just don't talk like that, I say "only if" should stay out. Ryan Reich 18:03, 17 June 2006 (UTC)

Oops, I switched necessary and sufficient, that's not what I meant. I don't object to leaving out "only if" if you find it unclear. ~~I'd like to avoid "if" due to ambiguity if possible~~, but my main concern is that that we avoid "iff", which people generally assume is a typo if they don't know about it. Deco 21:01, 19 June 2006 (UTC)

I strongly support the use of "if" in definitions over either "iff" or "if and only if". By the way this has (of course) been discussed before. I will now provide for your reading pleasure this oldie but goldi, this blast from our past:

(Start of copied text from talk page archives)

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)

(End of copied text)

Paul August ☎ 18:38, 17 June 2006 (UTC)

In regards to Lambiam's comment on a style reference, a popular one is Nick Higham's "Handbook of Writing for the Mathematical Sciences." On page 20 of the second edition it says:

By convention, if means if and only if in definitions, so do not write "The graph G is connected if and only if there is a path from every node in G to every other node in G." Write "The graph G is connected if there is a path from every node in G to every other node in G" (and note that this definition can be rewritten to omit the symbol G).

In my own experience, I cannot recall ever seeing "if and only if" in a definition in formal mathematical writing. Can someone supporting the use of "if and only if" cite a current journal article with this usage or give reference to a style manual that advocates its use? Lunch 20:44, 19 June 2006 (UTC)

Oh, in definitions. I didn't realise this was regarding definitions and not theorems. My apologies for my dissent - of course it's redundant in a definition to state that it's an equivalency. I would not use any more verbose language in this case. Deco 21:03, 19 June 2006 (UTC)

If the consensus is that "iff" may be confusing because some lay-persons do not know what it means and it might be mistaken for a misspelling of "if", then I will not object when other editors change "iff" to "if and only if" or an equivalent. However, I still object to using "if" by itself between the definiendum and the definiens. JRSpriggs 03:52, 20 June 2006 (UTC)

Using a conditional rather than a biconditional in a definition is wrong

"Often ... the definition is a statement that expresses a logical equivalence between the definiendum and the definiens." When we define a mathematical symbol (constant, function, or relation), the definiendum (symbol defined) is a new word being added to our language; and it has no meaning other than that given to it by the definition. The definition is a postulate which gives meaning to the new word. Since it is not normally our intention to add strength to our set of axioms (as the axioms of ZFC), this must be a conservative extension. And we should be able to translate any sentence involving the new word into one which omits it and has the same meaning. If you put a conditonal ("if") rather than a biconditional ("if and only if") between the definiendum and the definiens, then you are doing one of three things:

Using "if" to mean "if and only if" when in the context of a definition. This is potentially confusing to the readers. First, they may not realize that "if" is being used for "if and only if". Second, they may learn to read "if" as "if and only if" in other circumstances where it is mistake to do so.
You are using "if" to mean "if", i.e. you really intend the postulate which is the definition to be a conditional rather than a biconditional. In this case, one could not prove the negation of the new word was ever appropriate. For example, if we defined "measurable cardinal" via "κ is a measurable cardinal if it is an uncountable cardinal with a <κ-additive, non-principal ultrafilter.", then we could not prove that 17 was not a measurable cardinal.
You are assuming that anything which is not provably true is false. Surely, since Gödel's incompleteness theorems, it is clear that this is not a tenable position.

In conclusion, definitions should not be conditionals. JRSpriggs 03:52, 20 June 2006 (UTC)

If you were working in a formal logic, you would not be phrasing your definitions as English sentences at all, and this would not be an issue. The use of "if" in definitions is just one of many places that context is conventionally used to establish the meaning of a symbol. If you did want to make a definition that was not biconditional (for some reason) you could simply use more explicit language such as "A implies that B", "A is a sufficient condition such that B", or implication arrows. Finally, I think the language "B if A" should be avoided in theorem statements in favor of "if A, then B" or "Given A, we have B" or "Whenever A holds, it follows that B", or something a bit less vague; such use would preclude confusion about the meaning of that sentence structure. Deco 04:18, 20 June 2006 (UTC)

The "if" in a definition is not a conditional. It's an assignment, like the = sign in C. This is a well-established linguistic convention (and it doesn't mean "if and only if"; as I said, it's an assignment, and not any sort of proposition at all).

Moreover I have a strong antipathy to using "iff" in formal writing (in any context, not just definitions). It's acceptable on a blackboard, like "wrt", but it should not appear in articles. --Trovatore 04:27, 20 June 2006 (UTC)

Agree with Trov on both counts. That being that "if" in deffintions is perfectly acceptable, while "iff" in definitions is a bit iffy. :) Oleg Alexandrov (talk) 04:39, 20 June 2006 (UTC)

In a context that makes clear we are offering a definition, "if" works for me.

We say that a foo is a bar if it satisfies mumble.

In a context which is not clearly a definition, we must be more careful.

… A foo is a bar if it satisfies mumble. …

Can a foo be a bar even when it does not satisfy mumble? Here I don't know!

So now we come to the question of what to write in Wikipedia articles. Often definitions are not highlighted as such, but appear inline in a form that is ambiguous about the intent. I myself would never use "iff". I would try to word the statement carefully so that it was clear what I meant. When we write, we know what we mean, so we don't always see the possible confusion our words may cause a reader. But when we see a potential problem, the better solution is to reword to make our intent clear, not to throw in jargon like "iff". Flag a definition as a definition, and our readers will thank us. (Well, no. Actually they'll read happily along, never knowing the confusion we spared them. Bad writing is what gets noticed.) --KSmrq^T 14:33, 20 June 2006 (UTC)

I guess I am agreeing with Oleg and Trovatore here. I am happy to go along with pretty much all the authors I respect (Rudin, Lang, Halmos, Ahlfors, ...) and NOT use 'iff' or 'if and only if' in a definition. Either would looks stilted and also be more confusing than helpful to less experienced readers. Madmath789 14:47, 20 June 2006 (UTC)

As KSmrq said "Often definitions are not highlighted as such, but appear inline in a form that is ambiguous about the intent.". For that reason, if no other, we should use language the same way in definitions that we do elsewhere to avoid confusion. JRSpriggs 05:43, 21 June 2006 (UTC)

When KSmrq said In a context that makes clear we are offering a definition I took it to mean that a phrase such as we say that or a foo is called bar if or we define a foo to be a bar if is used. This doesn't mean that Definition. has to appear in front of the sentence. By wording the sentence carefully, it can be made clear that a definition is occuring. If it isn't clear, putting in if and only if won't make it clear; that will only make it look more like a theorem if it already looked like one. I agree with several others, by the way, that common usage avoids the phrase if and only if in a definition. CMummert 12:36, 21 June 2006 (UTC)

We should also make definitions clear by italicising what we are defining. Dysprosia 12:39, 21 June 2006 (UTC)

I can't believe this is still going on. I've already made all the arguments I think are necessary to oppose "if and only if", but I do have two questions: is there anyone, anywhere, who has become confused due to the use of "if" in definitions? Would you actually want to read an article so reeking of pedantic formalism? Also, to respond to your comment above: a more important consistency principle than internal consistency is external consistency; our articles must follow common English writing practice. As KSmirq said, it is always possible to set apart definitions from the text (and this would constitute better writing), thus obviating the internal consistency problem, but it is never possible to set apart Wikipedia from the experience of a native English reader. Ryan Reich 12:50, 21 June 2006 (UTC)

Redirects in the list of mathematics articles

Currently we have 12102 articles in the list of mathematics articles. Out of them, 1070 are redirects (see the complete list). Redirects get created in several ways

Plugging in some redlink in the list (not anymore, as all redlinks are removed automatically)
Merging an article to a bigger article
Renaming an article.

In my view it is the third which makes for most redirects.

While redirects are very important, I see no good reason for why they should stay listed in the list of mathematics articles (I estimate that there are at least 2000 math redirects which are not there).

I wonder what people think of a big purge, removing all redirects from the list of mathematics articles. Of course, if at some point a redirect becomes back an article, my bot will add it back to the list. Thanks. Oleg Alexandrov (talk) 22:37, 17 June 2006 (UTC)

So if I create a redirect to a math article, but the redirect isn't already a redlink from the list, then it doesn't get added to the list? -lethe ^{talk +} 22:57, 17 June 2006 (UTC)

No. The bot adds to the list of mathematics articles via categories. So, if your redirect is made to be in a math category (which it won't, most of the time), the bot will add it to the list. Otherwise it won't. The primary purpose of list of mathematics articles is to list articles I think, not redirects, although a separate list of redirects to math articles may be found useful by some people. Oleg Alexandrov (talk) 23:55, 17 June 2006 (UTC)

Well whatever uses there may be for a list of math redirects, this list cannot serve, since it doesn't contain them all. Therefore, you have my full endorsement to remove them. There is simply no reason to have only some of the math redirects in a list, right? -lethe ^{talk +} 00:00, 18 June 2006 (UTC)

I'm not sure what purposes the list serves. Take Circular arc, which is currently a redirect to Arc (geometry), but the concepts are distinguishable and Circular arc might eventually grow into a separate article. In an index it would be reasonable to include it. If the purpose is to have a way to visit every maths article to check if its conforms to a new policy, then you'd prefer to skip it. (By the way, it currently is not categorized.) Perhaps math-categorized redirect pages could be listed, but rendered in italics, like with the All pages search. (<-This comment was by User:Lambiam who forgot to sign it. JRSpriggs 11:08, 18 June 2006 (UTC))

OK then, so if a redirect is important enough, it should be categorized, and then my bot will add it in. About making redirects italic, that is harder to do, as I would need to daily download a lot of articles to see which are redirects. Oleg Alexandrov (talk) 16:25, 18 June 2006 (UTC)

Done. The log is at User:Mathbot/Changes mathlist. Oleg Alexandrov (talk) 02:39, 19 June 2006 (UTC)

MathML / improved TeX support

Hi people. For those of you who have been watching developments concerning m:blahtex, MathML support on wikipedia, etc, I'm sure you've noticed nothing much has been happening for a while. Well, for the past few months, Jitse and I have been trying pretty damn hard to push buttons in the background to make things happen, but sadly the core developers simply haven't taken the bait. It seems to be a case of "yeah, it looks interesting, but we've got like 10,000 other things we're trying to do, and we just haven't got around to checking out the code yet...". It seems that wikipedia just doesn't have enough engineer-hours to give us the attention we need to get this going, and there's only so much pushing that Jitse and I can do without becoming annoying pains in the arse.

The status now is that I'm certainly not spending any more time on the code until I have some indication that there's a chance wikipedia is going to use it. And I've had enough of all the promotional "hey everyone isn't blahtex wonderful and y'all should be using it". It's tiring and not really my style. I enjoy writing code, not selling it.

So unless the people who hang out on this page somehow band together and make the developers realise that MathML is something that people want, the project is going to die a serene death. I took the initiative about a year ago, and wrote 13,000 lines of code to prove that it was possible. I'm happy to help out some more, and of course I look forward to the day when there is good mathml support in wikipedia. But someone else needs to take the initiative now, because I'm through.

Anyway, I think I'll go to bed now, make sure I'm bright and fresh to watch Australia defeat Brazil 6-0 tomorrow.

Good luck guys. Dmharvey 03:57, 18 June 2006 (UTC)

Perhaps a petition signed by the user community? Which is then passed up to Jimbo? This is an important chunk of code that is being laid at the feet of the sysadmins; surely its something that should be picked up. A few words of caution: (1) although the code may work well for you, sysadmins concerned with high-availability servers have a very very very different view of what it means "to run reliably". You might not have given them warm fuzzies on this issue. (2) The WP servers seem often overloaded, there may be unvoiced concerns about impacting performance. If you think these issues are under control, then a public appeal may be the right route to get attention. If they're wobbly, you might get blown out of the water. linas 04:18, 18 June 2006 (UTC)

I've explored the BlahtexWiki and I have to say, I'm quite impressed. I just have two main concerns for implementing MathML on Wikipedia, if those were fixed, I would gladly push the developers to implement it.

Browser compatability. Almost nothing works for me in IE 6.0
Fonts. It appears as if you need to download special fonts for MathML to display correctly. I'm not sure how many people would want to do that. Also, the radical symbols do not display correctly in Firefox for me.

I would be glad to push for the implementation of MathML in WP if we can somehow figure something out for those two problems. —M e ts501 (talk) 04:26, 18 June 2006 (UTC)

There is no way around the issue of downloading fonts. As far as I can tell, Firefox often lacks some fonts by default. For IE I think one needs the MathPlayer extension.

It is no surprise the developers are weary at accepting a huge chunk of outside code, especially there is not really a huge demand for MathML from users. Any ideas of how to convince the developers to take this step would indeed be much appreciated. Oleg Alexandrov (talk) 05:14, 18 June 2006 (UTC)

Thank you, thank you, thank you for all of your work. Having written some mathematical typesetting code myself at one time, I have a feeling for what a challenge it is to do a good job. There are so many subtle issues of fonts and stretching and spacing and symantics and positioning and compatibility and on and on, that only someone who has been in the trenches can really appreciate the magnitude of this endeavor. It really takes a champion, like Roger Sidje on the Mozilla project or David Harvey on BlahTeX.

I believe I can speak to systems programmers with some credibility, and I would be happy to do so on behalf of BlahTeX. A noisy outcry from Wikipedia's technical writers might also prove influential. Beyond mathematicians, we have physicists, chemists, biologists, and engineers of all stripes, all of whom could benefit.

The latest word from the STIX Fonts Project is

"After reviewing the tasks required for completion of the project, September was established as a revised target for the beta test. The final production release will likely occur in December, but the TeX package may not be ready until January 2007."

Although the STIX project has not been exemplary in meeting its targets, it does appear that it is real, it is happening, and in a matter of months there will be little excuse to complain about a lack of fonts for MathML.

I cannot imagine that server load is a realistic concern. Currently MediaWiki converts <math> mkup to images, which requires parsing, pseudo-TeXing, image generation, and then serving the images. Unless BlahTeX is very poorly written indeed, it is unlikely to be more of a load. All BlahTeX has to do is transcribe TeX syntax to MathML syntax; and bloated as it is, MathML is still much smaller to serve than the equivalent image. Caching may be used currently to amortize the cost of image creation, but there is no good reason the same could not be done for BlahTeX. And, again, storing cached images requires more space than storing cached MathML.

That leaves the concern of bullet-proofing. For that, we have the empirical argument that the code has been tested against every single equation currently used at Wikipedia, of which there are hundreds of thousands. Yes, a few hundred do not translate; but that's a small matter of manual conversion because they depend on the bastardized TeX currently supported (texvc). In compensation, future editors will have use of a broader range of TeX features, something arrow-pushers will appreciate.

It occurs to me that if the developers are recalcitrant, perhaps Jimbo Wales might be persuaded. Pressure from the top could then be more effective than pressure from the bottom.

Thanks again for all the hard work so far. Given Wikipedia's culture of consensus, it seems only fair that others now help shoulder the burden. --KSmrq^T 10:33, 18 June 2006 (UTC)

But so what is the next step? Campaign to get it installed on test.wikipedia.org? What can we do to help? Send messages to mediawiki-l? I notice searching through the archives, that you have previously announced releases of blahtex to that mailing list, and they have never had any response. Have you ever had any dialogue with anyone from mediawiki development about this code? Whom do we talk to? -lethe ^{talk +} 10:43, 18 June 2006 (UTC)

At the risk of sounding too critical, how difficult would it be to make things work for the current "bastardized TeX"? The idea of breaking old revisions of articles without it being obvious why that is makes me kind of queasy ...

Is this a major issue? How do things fail after the change? Backwards compatibility is something that needs to be addressed, even if it cannot be guaranteed.

Not that I think this is a huge problem, if the scope is that small.

Otherwise, I'm with lethe. Whom do we talk to, and what's their favourite ice cream flavour (for bribes, you know)?

RandomP 11:00, 18 June 2006 (UTC)

We have a list of all the broken bastardized tex instances. There are a couple of hundred, which we've slowly been fixing, one at a time. We would obviously want to finish them off before we went live. -lethe ^{talk +} 11:21, 18 June 2006 (UTC)

I'd just like to qualify my remarks: it seems that even today, "history" won't get you anything like the old version of an article, at least when that article uses images from the commons.

I think it would be really cool if someone wrote, essentially, a simulated wayback machine for wikipedia, that went back to the wikicode, images, and math layout as they were when the revision was created. I thought that's what history was, but apparently, not so.

So that's not an issue either, and can we please have mathml now?

RandomP 14:09, 18 June 2006 (UTC)

Brief replies to above questions

Linas's question about server overload. This is a complete non-issue for several reasons, some already mentioned by KSmrq. I haven't done any benchmarking for a while, but here's what I remember. Both blahtex and texvc spend almost all of their time (at least 90%) on PNG generation. Blahtex is somewhat faster at PNGs, maybe 2 or 3 times faster, since I switched to dvipng instead of using imagemagick+dvips. (And Brion Vibber has endorsed the use of dvipng in the past, ask Google for more information.) MediaWiki already has code for caching the images, so this time only gets spent during the first edit, not on subsequent page views or edits. Second, I haven't directly compared the parsing and mathml generation time of blahtex to the parsing time of texvc, but I do know that my desktop machine can generate mathml for the entire wikipedia corpus in about 30 minutes. There's 200,000+ equations in there, so it's not lightning speed, but you ain't gonna overload their servers. And MediaWiki also has code already for caching the mathml, so again that only happens on the first edit. Third, some tests Jitse and I ran a while back suggested that texvc's parsing is unbearably slow on long input data; blahtex on the other hand processes that kind of input really fast.
Linas's point about reliability. Of course it's got bugs. All software has bugs, especially software that hasn't yet been exposed to the real world. Someone mentioned above that it's been tested against all the input in wikipedia and doesn't pretty darn well, which is a start, but of course that's not the point. The real question is whether it survives a determined adversary with source code access. Well, I don't know, I suppose most likely it's not secure. But all software has to start somewhere. I'm not asking to have the code installed tomorrow and force everyone to use it. Heck, at this stage I'm not even asking for the "minimal interesting configuration", which is that it's only available for registered users who select MathML in their preferences, and that we stick to texvc for all PNG output, and only allow mathml for the equations for which texvc can already generate graphics. All I'm asking for is that some core developer gives us more than ten seconds of their time to render an opinion. If they tell me the code is crap and I'm a chump, that's fine, I can live with that, at least it's an answer. If they tell me I need to rewrite it in COBOL, that's fine, it gives me something to do. If they tell me I need to write a comprehensive test suite, that's great, I can do that. But so far the longest reply I've had from people like Brion Vibber, Tim Starling, etc, is a one-line email from Brion:

It sounds great, but I've not had a chance to look at it yet...

He also replied on the mailing list once, here's what he said:

Neat!

I understand 100% where he's coming from, but it's still incredibly frustrating.

Mets501's question about fonts. As KSmrq points out, the STIX fonts project is going to get there eventually, not tomorrow or the next day, but eventually. I believe it will solve all the font problems, because e.g. Firefox will just be able to bundle the fonts in the default installation and it will all Just Work. So for now, no good answer, but eventually, yes.
Mets501's question about browser compatibility. Short answer: it sucks. Firefox/Mozilla is the best out there in my opinion, and it's not quite good enough yet. (I've heard about your problem with broken radical signs; I believe it's a recent regression.) I think the reason browsers haven't quite made it yet is because there just isn't the content out there yet. Well, we can change that, because if wikipedia switched on mathml support, it would overnight become the largest repository of mathml on the web. (I don't have stats for that, it's just a guess.) And here's something else: when I first mentioned to the firefox people, like roger sidje, that wikipedia was planning mathml support, suddenly a whole raft of mathml-related bugs in firefox got fixed, bugs that had been lying around unattended for 2-3 years. These open-source guys love wikipedia. If we deliver, they will follow. On the other hand, I don't have any illusions about MSIE.
RandomP's question about backward compatibility. It's a minor problem in my opinion. See http://blahtex.org/errors.html for a complete list, as of March. Maybe that list looks long, but remember it's across 13 languages, and represents about 0.1% of the total. We could fix them all in a few days. And anyway, Jitse's glue software falls back on texvc if blahtex fails, so it's easy to make the problem vanish entirely.
Everyone's question about who to talk to. I don't know. I've run out of ideas and energy. That's why I'm turning the initiative over to all of you. If enough of you make enough noise, and if the powers that be are hearing voices other than that of the guy who wrote the program, maybe something will happen. Dmharvey 12:28, 18 June 2006 (UTC)

Caching: As KSmrq suggests, the MathML is cached and hence it needs to be generated only once.

Backward compatibility: To expand on what David says, the code as currently written uses texvc to generate HTML and PNG and blahtex for generating MathML. If texvc fails, then blahtex will also generate PNG. Therefore, the few formulae that are not understood by blahtex (for instance because they use invalid latex syntax) will still be rendered as PNG, but there won't be any MathML. In other words, just like the present situation. -- Jitse Niesen (talk) 13:02, 18 June 2006 (UTC)

my email

I sent this email to mediawiki-l just now:

From: lethe at charter dot net
Subject: Blahtex: what's the next step
Date: June 18, 2006 8:08:37 AM CDT
To: mediawiki-l@Wikimedia.org

David Harvey and others has been working hard on Blahtex, the next generation in MediaWiki math rendering technology. Visit http://www.blahtex.org/ for more information and http://wiki.blahtex.org/go/Main_Page for a running demo hosted by Jitse Niesen.

Harvey suggests that blahtex will afford a significant performance advantage, but the main impetus is the ability to render MathML. Support for MathML is not widespread at the moment, so the need for Blahtex is not urgent, but it is the future, and we have reason to believe that Wikipedia's adoption could goad browser developers to speed their efforts (the answer to the old chicken and egg of who comes first, browser support or use by web pages could be: Wikipedia comes first).

It has to happen someday, and today is as good a day as any. Harvey says the software is ready for the next step, and wants to move forward, but doesn't know whom to talk to in order to make this happen. I'm writing you to voice my full support for Harvey's and Niesen's efforts, to find out what needs to be done to take the next step towards rolling this software out, and to ask if there is anything I can do to help the developers to get this software ready for deployment.

Thanks
lethe

I was hoping that several others of you would chime in on the mailing list. If we had a chorus of complaining voices, we would be harder to ignore. Currently, the developers watching that mailing list have ignored me completely. What should I do? Send another, more plaintive, email? -lethe ^{talk +} 11:51, 20 June 2006 (UTC)

Are you sure this is the right way to go? I'm not sure about the relation between mediawiki, the software that actually serves wikipedia, and that mailing list. Is the authoritative version of mediawiki the one serving en:? Are decisions about changes to that software, beyond bugfixes, made on that mailing list, the meta wiki, wikipedia (en) talk, or where?

RandomP 11:56, 20 June 2006 (UTC)

The short answer is, I don't know. Where is the right venue to discuss changes in the software, and who is the right person to talk to? I don't know. Does anyone know what is the right course of action to take? How to we get software changes evaluated and committed? As for whether en runs the official version, the answer is yes. They rollout new versions on test.wikipedia.org first, I think. But then they roll it out for en.wikipedia.org. Should I email Brion Vibber or Rob Church or something? I don't want to be a nuisance, but I think Dmharvey's request to get a response from them at least to say "sorry, we can't accept this" is not unreasonable. -lethe ^{talk +} 12:20, 20 June 2006 (UTC)

Hmm. This is a problem. I've looked around for a good place, but the best I've found is the MediaWiki bugzilla, which currently has two bugs [24] [25] matching blahtex, and I don't think either is what we want.

Can someone create a new feature request there and link to it (I'd also suggest linking back to a Wikipedia page from the new bug, so we can have discussions without all getting out to get accounts on yet another bugzilla)?

That might be a first step to, at least, documenting we're trying to get it in through the official channels ...

Again, I'm just confused by the whole thing. There's a wiki, a mailing list, a bugzilla, and apparently an IRC channel, and I still don't know where and if development discussions happen. However, at least a bugzilla is permanent and will get someone's attention, one would hope ...

Can we move the discussion to Wikipedia:Blahtex or something? It's of interest to physicists, economists, biologists, etc, too! (Or should be.)

RandomP 12:53, 20 June 2006 (UTC)

m:Blahtex would be a place to have a centralized dicussion, after we sent spam to all the physicist, economist, etc Wikiprojects. But that would only be necessary if we are completely unable to open up a discussion with developers in one of the developer channels. If we can do that, then let's just have the discussion there. -lethe ^{talk +} 13:02, 20 June 2006 (UTC)

I have submitted a bug report and sent another email to mediawiki-l. You can vote for the bug at this location. I have no idea what voting for bugs accomplish; I wouldn't be surprised to find out accomplishes nothing. -lethe ^{talk +} 13:23, 20 June 2006 (UTC)

I'm told that most discussions take place on IRC, but I haven't seen any. There are two relevant mailing lists: mediawiki-l for the software as used on Wikipedia, other Wikimedia sites, and other wikis not related to Wikimedia; and wikitech-l for technical matters (hardware and software) involving Wikimedia (Wikimedia is the foundation running Wikipedia, Wikibooks, Wiktionary, Wikisource etc). Either list would be appropriate, and I think they mostly have the same readership. Then there is bugzilla, as mentioned by Lethe, and we also have Wikipedia:Village pump (technical) here. There are also two central wikis, http://meta.wikimedia.org/ which used to contain everything related to the software, and http://www.mediawiki.org/ where the documentation is being brought over to. So it is rather confusing.

I put the items in the order that seems to be best to get the attention of the powers to be (with IRC on top). However, in the end it boils down to an individual developer taking a decision. The concept of consensus plays rather a small role on that level.

I'd advise against emailing the developers individually. -- Jitse Niesen (talk) 14:02, 20 June 2006 (UTC)

I guess the response you may get from IRC depends on who's in the room. I went there first, before anything else, a few days ago as soon as Dmharvey posted his request, and got no biters there. They suggested I might have better luck on the mailing list. Perhaps I try IRC again at a busier time. -lethe ^{talk +} 14:08, 20 June 2006 (UTC)

Discussion continued

I'm not a developer, nor am I Jimbo, but putting myself in their shoes I'd be much more worried about the font issue than about accepting an apparently well-tested huge chunk of outside code. In fact, not being in their shoes this worries me. Many people access Wikipedia from computers they have no control over, and are in no position to download and install fonts for, even if willing to do so. Others may try to and fail. Most wouldn't even try, and miss out on all Wikipedia has to offer that involves formulas. I think it is important to keep blahtex alive, but aim at introduction after the availability of the required fonts has become common. --Lambiam ^Talk 13:53, 18 June 2006 (UTC)

Thus MathML won't be enabled by default. Only people who know what it is, have capable computers, and want to see it, will see MathML. When the day comes that every windows, mac, and linux computer has by default MathML able browsers and plenty of fonts, then we can have MathML by default. But for today, let's have Blahtex which is smarter in all ways. This is a non-issue. -lethe ^{talk +} 14:22, 18 June 2006 (UTC)

Yes, I agree. I will help push for this to be implemented as much as I can. I do think, however, that the default should not be MathML (yet). Users who sign up for an account should be able to select MathML from the preferences page, but the option should link to a page called Wikipedia:MathML, which would say what MathML is, which browsers support it, and which fonts/whatever is needed for MathML to work. I would definitely not give up on this project and I hope that it will be implemented soon (I love experimenting on the BlahTeX wiki!) —M e ts501 (talk) 16:54, 18 June 2006 (UTC)

We've really got to stomp out some myths. The most important fact is that BlahTeX only adds capability to MediaWiki, it does not force removal or breakage of anything that already works. A complete set of mathematics fonts will be available Real Soon Now to everyone on every platform with every browser. Don't have the necessary fonts on the computer you happen to be using? Not a problem; stick with the old-fashioned images and HTML hacks. Browser not set up to support MathML? Not a problem; don't ask for MathML. In other words, adoption of MathML is strictly voluntary.

So why BlahTeX? Because it offers so much more than texvc, which is old and seriously deficient. BlahTeX handles a broader range of TeX input, including things that are currently a real pain to work around. Even when it generates PNG output, not MathML, BlahTeX is superior to texvc.

And why MathML? Because it is the future of mathematics on the web, for reasons such as the following.

A text-to-speech processor can read MathML aloud for vision-impaired users, or for ordinary folks who merely want to know how a formula is spoken.
All the fonts and layout of a MathML display can be scaled up or down, just like the rest of the text on a web page, to either zoom in on a detail or zoom out for an overview.
MathML can include arbitrary Unicode characters, something texvc is unlikely ever to do.
A MathML formula is smaller and faster to serve than a PNG.
MathML can allow internal line breaks, while images cannot.
Programs like Mathematica allow cutting and pasting MathML formulae, so an equation can be transfered easily for evaluation or graphing.
MathML has already found favor on technical blogs, like The String Coffee Table.
Because MathML is built on XML, it can be processed with XSLT and used across diverse media. In particular, MathML will be much more compatible with print than any fixed-resolution PNG rendering.
One of my favorite benefits is that the contents of a MathML formula are available to search in my browser, whereas a PNG is an opaque monolith.

Note that the MathML 2.0 Recommendation from W3C was released on 2001 February 21, and the 1.0 version dates back to 1998 April 7. That's an eternity ago in web time!

But to reiterate: BlahTeX offers considerable benefits even for those who do not choose to view MathML. It can't hurt. It can only help. Please support its rapid adoption by MediaWiki, in whatever way suits you best. --KSmrq^T 19:22, 18 June 2006 (UTC)

I think you should put that in an email to the mailing list. Perhaps wait until mine shows up and make it a reply so it's all in one thread though. We want to generate some noise so that it seems like there is a whole rabble of us clamoring for this. And of course we have to quelch the false assumptions that people will make to justify not using the software. -lethe ^{talk +} 19:29, 18 June 2006 (UTC)

Thanks, KSmrq, that's a nice piece of writing. Not for the first time, I admire your writing skills.

Apparently, the best way to contact the developers is via IRC (#mediawiki on irc.freenode.net). Another thing we haven't done is to contact our colleagues at the other language Wikipedias. I imagine that especially editors writing in a different script than ours would be interested. -- Jitse Niesen (talk) 04:23, 19 June 2006 (UTC)

Hey, KS, I think maybe this nice list of yours should be copied over to m:Blahtex where it would be the skeleton of a FAQ. A central repository that we can refer to easily to stop out myths. What say ye? -lethe ^{talk +} 14:38, 20 June 2006 (UTC)

If you like it, use it. --KSmrq^T 20:14, 20 June 2006 (UTC)

Do you think that we should write an email to Jimbo about this? Do you know how aware he is of BlahTeX? If we could convince him, it would definitely get implemented. —Mets501 (talk) 20:40, 20 June 2006 (UTC)

Let's try to confine our efforts to those people who will actually have a hand in the software direction, which I don't think Jimbo does. Anyway, the latest correspondence sounds like Vibber is going to set up Jitse with an SVN account. We might be in business, so let's wait to hear from Jitse and Dmharvey what happens with that. -lethe ^{talk +} 20:47, 20 June 2006 (UTC)

[via edit conflict] Hang on for the moment guys. Brion gave a more positive reply to one of Lethe's recent emails, see here. Jitse and I will work out what to do with this development, and we'll keep you all posted. Dmharvey 20:49, 20 June 2006 (UTC)

Yay! Good luck guys! Make sure to let us know about any developments. —Mets501 (talk) 13:11, 21 June 2006 (UTC)

Some progress has been made

See here. I'm not precisely sure about terminology here, but perhaps this makes Jitse a Developer. This is good news, but I don't promise mathml tomorrow. Still some work to do. We'll keep you posted. Thanks guys for your encouragement, and especially lethe for the insistent emails on mediawiki-l :-) Dmharvey 12:00, 22 June 2006 (UTC)

Or perhaps he's saying that he's responding to Jitse, and he will be adding the BlahTex extension (because he put in a comma). Either way, its good. —Mets501 (talk) 12:35, 22 June 2006 (UTC)

It only makes me a minor developer. The standard tariff is to sacrifice one virgin every full moon as otherwise Bad Things Happen. However, I can also be placated with papers on which I can put my name as co-author. ;) -- Jitse Niesen (talk) 13:19, 22 June 2006 (UTC)

Well, I can give away my virgin mathbot as a groom to the brand-new bride-to-be Jitse's bot (who am I am sure is a she, or otherwise can be made so just by flipping a bit). Oleg Alexandrov (talk) 16:10, 22 June 2006 (UTC)

So who is "jitsenielsen" anyway? Dmharvey 14:11, 22 June 2006 (UTC)

I'm pretty sure Brion Vibber made a spelling error :-) —Mets501 (talk) 14:30, 22 June 2006 (UTC)

Request for book recommendations

Maybe this is not the place for this (I am aware that this is not un all-purpose forum), but here it goes. I intend to order some math books from Amazon, but I'm not sure what to get. As it seems to me that there are some very good mathematicians here, I think you could help me a lot with some recommendations. Now for some background, to understand what I specifically need: I'm an undergraduate math student (though also an economics graduate and working economist) and I pursue math mostly for my own curiosity and because I truly enjoy it (more than economics :D). I need something mainly appropriate for self-learning, so I'm targeting good classic texts on major fields or other good books. I prefer books that don't shy away from advanced/abstract concepts, but preferably give motivation for concepts and some intuitive explanaition/interpretation. Also, I learn the most from books which include examples worked-out in detail and/or solved relevant problems. Also, note that unfortunately cost is an issue, so don't recommend too many books that are only somewhat helpfull (though by all means recommend books that you consider good, even if they are not very popular). Hope that you will have some advice for me... AdamSmithee 20:48, 18 June 2006 (UTC)

A great place to ask this question, which is indisputably appropriate (unlike here, which is apparently disputably so :)) is the sci.math newsgroup. You can get there through Google groups if you don't already know. This page is really just for discussing the Wikipedia mathematics project. Ryan Reich 20:57, 18 June 2006 (UTC)

I am sure that we could give a great deal of advice (though some of us will contradict each other!), but we do need a bit more info about your mathematical interests and level: which branches of maths are you most interested in? what sort of level are you at in that level? Perhaps it might be best if you could tell us some maths books that you believe you have mastered, and we could suggest some books that would make a "good next step"? Madmath789 21:02, 18 June 2006 (UTC)

Myself, I'm a graduate student and I like algebraic geometry and sometimes number theory. Or did you mean him? :) Ryan Reich 21:42, 18 June 2006 (UTC)

LOL! I did mean 'him', but our edits crossed, and I got the indentation wrong :-) (but if you want some suggested reading on algebraic geometry, I can probably oblige :-) ) Madmath789 21:46, 18 June 2006 (UTC)

The most affordable route is used books, especially if you live in or near a decent university or college. Some of the much older books are easier to learn from, because not so long ago mathematics texts had a bad habit of being horribly written for learning, though packed full of detail for reference. More recently there may have been a corrective swing, so that one can benefit from both a modern viewpoint and decent pedagogy. But in a field like algebraic geometry, the really old stuff has lots of geometry while the modern stuff has almost none. Depending on your tastes, one may appeal more than the other. Another fact about older books is that often recent books try not to duplicate the work of the early masters, so if you want to get the original insights from the folks who had them you have to step back in time. It reminds me of something that was said about the programming language ALGOL, that it was an improvement on many of its predecessors, and also on many of its successors. Lastly, it is vital to choose books at the right level at the right time, lest an otherwise great book become a doorstop. --KSmrq^T 22:39, 18 June 2006 (UTC)

Well, first of all tx for replying! As I said, I know this is not the place (and I'll probably try sci.math, which I didn't know about), but I tried it because I came to trust many of you guys. As for my background and interests: I'm an undergraduate student in math at this time. So far, my exposure was almost entirely to Romanian textbooks, which are very tightly written and unfortunately are generally very good for reference but not for learning (this is somewhat of a characteristic of Romanian academic books). On the other hand, I've read quite a few American graduate level textbooks in economics and I noticed that, generally, they are much better for learning (also, reading some freely available online math books lead me to believe this is also true for math). To give an example, at this time I'm struggling with linear connections and covariant derivative, but my (Romanian) books insist to much on tightely written modern coordinate-free stuff, giving virtually no motivation and no explanation, and I'm having trouble understanding why the stuff is defined that way, what does it mean and what is it good for.

At this moment my interests are rather wide and I just want to get a reasonable background in the main fields. However, I do have a sweet spot for abstract algebra, and I'm interested in probability and statistics (including links to measure theory, numeric analysis etc.) for the aplications to economics. But I'm also very interested in stuff like differential geometry for instance. As an example of one book that I have heard about, and I might get, I know about Jacobson's 'Basic Algebra' (though I don't know how that is), but I have no idea what else is there.

Regarding level, it is hard to say what undergraduate in Romania means compared to other education systems, but it is possibly more advanced than American undergraduate level (?maybe?). AdamSmithee 23:25, 18 June 2006 (UTC)

Hi, I suggest browsing Dover Publications online catalogue (use Google to find, I am lazy :P). They republish a lot of classical and important texts. By rule of thumb, eastern Europe is more advanced in beggining of undergraduate studies. -- 127.*.*.1 01:14, 19 June 2006 (UTC)

Poussin proof

I have just had a brief look at the page Poussin proof, and apart from being a short stub, at least half of it seems to be mathematical rubbish. I would like to have a go at making this into a sensible article - but about the Dirichlet divsor problem (the first sentence of the Possin page), as I can't find anything about this elsewhere. If I have missed it, and there really is a page about the Dirichlet divisor problem, plase let me know before I waste too much time ... Madmath789 12:11, 19 June 2006 (UTC) (OK, having read it again, it is not total rubbish, but badly worded.)

Change of project scope at Wikisource

(I've copied the following from Talk:Mathematics. — Paul August ☎ 16:56, 19 June 2006 (UTC))

I would like to call the communities attention to and personally protest a decision at Wikisource to exclude and delete a significant portion of the material that was part of its original charter. Prior to April 29 of this year, Wikisource:What is Wikisource? listed the following as included material:

"Some things we include are:

1. Source texts previously published by any author
2. Translations of original texts
3. Historical documents of national or international interest
4. Mathematical data, formulas, and tables
5. Statistical source data (such as election results)
6. Bibliographies of authors whose works are in Wikisource
7. Source code (for computers) that is in the public domain or compatible with the GFDL"

On that date the project page was changed to explicitly exclude:

Mathematical data, formulas, and tables
Source code (for computers) that is in the public domain or compatible with the GFDL
Statistical source data (such as election results)

Obviously, this represents a major change in the scope of the project. It is based on a single poll conducted between April 4 and 27, 2006 Wikisource:Scriptorium/Archives/2006/04. Previous discussions had been held with opposite results Wikisource:Wikisource talk:What Wikisource includes. A primary reason given for the new change is that the editors participating do not feel competent to maintain this material and have little interest in it. However apparently no effort was made to notify participants in the previous discussions, nor to recruit new editors that might have an interest. Note that there are many active projects pages in mathematics and the sciences where such people might be found.

There was also no discussion of methods for reducing the load on editors, such as locking material after review. In general, reference material does not need or benefit from frequent edits.

I certainly respect the efforts of the regular editors on Wikisource and agree that their views should be shown some deference. However the process they chose is not sufficient. At the very least, I think there needs to be broader community input into such a massive change in the scope of a Wikimedia project. Even if this material is best excluded from Wikisource, I believe it deserves to be part of an encyclopedia and that any material already contributed should be moved elsewhere rather than be deleted. The simplest solution would be to move mathematical and scientific reference material to Wikipedia, where there are large communities to evaluate and protect this information. An argument could be made that mathematical data belongs in Wikicommons because it is, or potentially can be, language neutral. Or perhaps there should be a new Wikireference project. Computer source code deserves a separate discussion, since there are so many other open source code repositories available.

At this point hundreds of articles have been marked for deletion. See Wikisource:Category:Deletion requests/Reference data Some material has apparently aready been deleted. There is nothing left in Category:Mathematics. I would propose that all article deletions on Wikisource based on this change be frozen until a fuller, community-wide discussion can be held.

I have also posted these comments at Wikisource:Scriptorium, where I think the primary discussion should be held.--agr 16:01, 19 June 2006 (UTC) --agr 16:01, 19 June 2006 (UTC)

This call to arms would look better at Wikipedia talk:WikiProject Mathematics. It is about mathematics at wikipedia, not about the article Mathematics on wikipedia. -lethe ^{talk +} 16:12, 19 June 2006 (UTC)

(end of copied text)

It was actually my intent to post the here. I just messed up. I am removing the link from the math talk page.--agr 20:16, 19 June 2006 (UTC)

(Cross-posted from Wikisource)I would like to quote my own remarks on opening up this disscusion back on April 3:

I realize this has been discussed several times in the past, to the agreement of accepting such material. However, the current state of reference data on Wikisource is unacceptable. The community members who are active on this site have little interest, and in some cases understanding, of the data we have been hosting. Although there have been editors that were adamant that this material should be included here, they have not remained active in the organization nor matainance of it. Much of this material is beyond the active administrators ability to even distinguish vandalism from corrections. Because of this current state of affairs there have been nominations for deletion for some of this data. However I feel we need discuss the larger questions of the place of reference material on Wikisource before we make any deletions.

It is disingenuous to suggest we ignored previous discussions or made no efforts to find other solutions short of deletion. In fact I opened up the discussion back then to put a stop to this material being brought up piecemeal at Proposed Deletions. In all honesty, at the beginning of the April disscussion I expected that we would arrive at a solution for keeping a portion if not a majority of this material. No one who was interested in this material bothered to even suggest any alternatives much less volunteer to implement any solutions in over 2 months since then. As for calling this to the "community's attention", you imply we are trying to hide it or be secretive. This is false. I personlaly have left notes on WP talk pages of people showing recent interest, as well as mentioned the decision in passing on foundation-l. Not to mention the write up done by Pathoschild in Wikisource news during and after disscussion. The decision was also mentioned on wikisource-l. The idea that this was "based on a single poll" is also misleading. It is based on consensus taking into account ideallistic comments made in prior disscussions as well as the pragmatic reality of maintaining this site. (Added Note: Not a single person spoke up for inclusion) My negative opinions about inviting in the entire Wikimedia community into these sorts of decisions are given in much detail at the foundation-l archives. The thread begins with this post (Note this thread is not about Wikisource, but deals with the subject of alerting other Wikimedia projects to dissucions of policy changes within one sister project). I will quote myself from a later email in that thread:

I think [Ec has] hit the nail on the head with "Good rules support existing practice rather than shape it." The problem with the original suggestion is such advertisement would atract people who have no understanding of existing practice. That is my concern. I feel anyone familar with existing practice will be aware of policy disscussion through the normal in-project channels.

The deletions are proceeding slowly and carefully with any wanted info being moved to other sites. There were no mass deltions on April 29th. If you can find a home for anything we could not I will restore the pages for your access, please give me a list. I think the topic of this post is out of line and [agr's] proposal has little merit. Especially the idea that we should hold this material until and new sister project of "Wikireference" gets off the ground--Birgitte§β ʈ Talk 18:16, 19 June 2006 (UTC)

Added Note. This disscussion as seen by those unfamilar with Wikisource may be misleading in our inclusion policy. I just want clarify that if there is an otherwise acceptable publication with apendices of Mathmatical tables, the enitre work including the tables is accepted at Wikisource. The exclusion only regards standalone data which is not a transcription of an acceptable publication such as s:Trinary numbers.--Birgitte§β ʈ Talk 18:27, 19 June 2006 (UTC)

Yes, I would like a list of the material that has been deleted. I think it is totally reasonable to expect some notice and time for us to decide what should be kept and where. I get the message that this material is not wanted at Wikisource, but that is no excuse for simply deleting it without informing anyone who might be interested. The fact that no supporter of the material spoke up during the April discussion should have been a clue that there was not adequate notice. --agr 20:16, 19 June 2006 (UTC)

I find your topic header both here, and on the Scriptorium, to be inflammatory, inappropriate, and wildly out of place. To quote from our own article on book burning: "Burning books is often associated with the Nazi regime." Jude (talk) 00:14, 20 June 2006 (UTC)

I certainly was not trying to suggest that anyone is behaving like Nazis and I apologize if the title is too harsh. As I said in my original post, I believe the regular editors at Wikisource are due some deference in their decision making. But I find the wholesale deletion of articles belonging to topics no longer in favor, Mathematics in particular, to be very disturbing. It is one thing to change the scope of a project, another to simply discard material submitted and accepted in good faith.--agr 00:38, 20 June 2006 (UTC)

Just to clarify, nothing was deleted because the topic fell out of favor. I would love to see mathmatical texts added. We actually have some being worked on now. Data is being excluded no matter the topic. --Birgitte§β ʈ Talk 00:58, 20 June 2006 (UTC)

The entire category of mathematics was wiped out. Absent a list of what was deleted there is no way to tell what might have been of interest.--agr 11:54, 20 June 2006 (UTC)

Of the 1741 pages that have been deleted since April 29, 2006, on Wikisource, and June 18, 2006, 1381 of them were in the main namespace. Of those 1381 deletions, 152 pages contained "efer" or "ref" in the deletion summary. You can find the complete list of them here. Jude (talk) 13:26, 20 June 2006 (UTC)

(edit conflict)Categories are currently little used at Wikisoucre (i.e. s:Category:Epic poetry lists 5 poems, believe me there plenty more), that one is empty does not mean we have nothing on the topic. I do not know how narrowly you define Mathmatics but some projects currently underway are s:A Treatise on Electricity and Magnetism (the proofreading of OCR is being done on the image pages); s:The New Student's Reference Work#Arithmetic; s:1911 Encyclopædia Britannica/Infinitesimal Calculus These are just a few example of current work. Most anything listed on this website would also be a welcome addition as I believe they are all out of copyright. The topic of Mathmatics has not fallen out of favor!

You are complaining that pages you might have been interested in (if you had a list of them to examine, as you do not seem to know what actually existed) were deleted by people who examined and disscussed them on project's main discusssion page as well as at Proposed Deletions. This complaint's scope is based on an empty category on a project that does not currently use categories in an organized fashion. This complaintent despite speaking for the inclusion of data at Wikisource in November, never made a single edit towards the maintanence or organization of that material in the 5 months between then and the April disscussion. Despite your strong interest in the deleted data, you refuse to do the legwork on compilng a list of titles for me to restore. Titles which you did not put up, did not edit and did not add to your watchlist. I dislike turning this in your direction, but I really dislike the the misrepresentations being made about what happened at Wikisource. I will repeat that this topic heading is quite out of line and would appreciate it if you struck it. I imagine you realize the Plan on phasing out reference data will procede without interuption, please make any requests for temporary restoration on my talk page.--Birgitte§β ʈ Talk 14:15, 20 June 2006 (UTC)

To cool things down a bit, I have changed the topic heading here and at scriptorium. User:Bookofjude has finally provided a list of the material deleted after others told me to search through the logs. That is a big help. I really don't want to make this personal, but I must point out that after the November discussion led to a clear consensus on keeping reference material, I submitted a detailed proposal on what tabular material to include to the discussion page on January 18, 2006. It received no further comment. I think I had every reason to think the matter was settled. --agr 14:52, 20 June 2006 (UTC)

Thank you for the alteration. I sympathize that you believed things were settled, but I have learned that settled doesn't exist on a wiki.--Birgitte§β ʈ Talk 15:13, 20 June 2006 (UTC)

Although I am a bystander in the debate, though in favour of keeping math tables on wikisource, I would like to remark that I read Wikipedia Signpost regularly and I don't remember any remark about voting about massive deletions of existing material on Wikisource. Considering that fact that Wikisource is not so high profile and people here could be interested in the voting, I think it's a bit unfair. Samohyl Jan 16:47, 20 June 2006 (UTC)

I read the Signpost regularly as well. Although they seem to report very well on Wikimedia Foundation issues, I think their coverage of other projects and other languages is quite minimal. I don't know that I would say it is unfair of them, after all the Signpost a product of the English Wikipedia. Anyone interested in Wikisource policies should regularly read the Scriptorium. There is nothing of importance that is not at least mentioned there. I think the archives are quite nicely organized as well for those interested.--Birgitte§β ʈ Talk 17:08, 20 June 2006 (UTC)

Deleted math articles

As best I can determine, here is a list of the math-related articles that have been deleted. Birgitte§β has kindly restored them temporarily:

Wikisource:Prime deserts - a fairly short short list of gaps in the primes
Wikisource:Fibonacci numbers 1-500
Wikisource:Mersenne primes - up to number 30, 2^132049−1
Wikisource:Phi to 30,000 places - There was also an article listing Phi to 20,000 places

Also there were computer source code articles with the following titles:

I'm not sure these have mcuch value. Finally, I believe there were once articles listing pi and e to a million places. These would be easy to reconstruct if anyone wants to make a case for them.

I think a case can be made for moving at least the first two or three articles above to Wikipedia, presumably retitled as "Table of..." Comments?--agr 18:35, 20 June 2006 (UTC)

Babylonian mathematics, Ibn al-Banna

The section Old Babylonian Mathematics (2000-1600 BC) of this article seems to be a copy of this page (starting with "Perhaps the most amazing aspect of ..."). It's especially funny in sentences like "In our article on Pythagoras's theorem in Babylonian mathematics we examine...", where in reality, no such article exists on Wikipedia. What should be done about it?

On a somewhat related issue, User:Chem1 has created the article Ibn al-Banna (1256-1321), to whom he attributes the invention of the iterative process $x_{n+1} = \frac{1}{2}(x_n + \frac{N}{x_n})$ for finding the square root of a number - aka the "Babylonian method". This doesn't seem right. -- Meni Rosenfeld (talk) 14:41, 21 June 2006 (UTC)

I'll take a shot at a re-writing and wikifying the Old Babylonian Mathematics (2000-1600 BC) section. Gandalf61 14:54, 21 June 2006 (UTC)

I've removed that section from Babylonian mathematics as well as and following section as possible copyright violations, leaving a notes on the talk page of that article, and the editor who added it. Paul August ☎ 15:31, 21 June 2006 (UTC)

Okay, I've now trimmed, re-written, wikified and re-ordered the offending section. I think it is now sufficiently different from the source to be no longer copyvio, so I have put the re-written version back into the article. Gandalf61 13:17, 22 June 2006 (UTC)

Iff in formal writing

I would like to propose that all usages of "iff" to mean "if and only if" be replaced by "if and only if", as iff is not a very common abbreviation. Thoughts? (I actually did a bit of this but Oleg Alexandrov advised me to ask here – if there is a consensus for me to remove those edits it will be no problem for me to do it.) —Mets501 (talk) 20:24, 21 June 2006 (UTC)

I disagree that iff isn't very common, but I support removing it in favour of "if and only if", particularly in articles that might be of use to people who aren't expert mathematicians. RandomP 20:28, 21 June 2006 (UTC)

I would say that iff is quite common in textbooks, and I use it all the time, personally, but this is an encyclopedia, and I believe (quite strongly) that iff should be avoided everywhere (especially in definitions, whether formal or informal!) Madmath789 20:45, 21 June 2006 (UTC)

Yeah, iff is a bit of a neologism (which I think fell out of fashion by now :) and should surely be avoided in defintions. Is it a good idea however to just do a mass iff removal from all math articles? Makes me wonder if it is worth the trouble. Oleg Alexandrov (talk) 21:05, 21 June 2006 (UTC)

It's not really trouble. It just takes a bit of time, but I'll put the time in if we get enough consensus here to remove it. —Mets501 (talk) 21:08, 21 June 2006 (UTC)

I prefer "if and only if". Life is short, but if your life isn't that short, I say go ahead and change them. Just be careful with articles like if and only if and IFF. Dmharvey 21:14, 21 June 2006 (UTC)

(Edit conflict) Well it may not be trouble for you to do it, but you have kind of washed out my watchlist. This is slightly annoying, but tolerable for a good cause. Is there any precedent for bot flags for people using AWB? -lethe ^{talk +} 21:15, 21 June 2006 (UTC)

No precedent that I know of. I'm sorry about the watchlist, I know what you mean (my watchlist is full of math articles too). Hopefully I can get it all done today so that only one day's watchlist is screwed up :-) —Mets501 (talk) 21:18, 21 June 2006 (UTC)

If I recall, "iff" is allowed in any Springer book or journal. It is in the Merriam-Webster dictionary (supposedly). I think that disqualifies it from being a neologism. I personally never use it, but I wouldn't impose a moratorium. Don't you think this is a bit heavy-handed? Silly rabbit 21:39, 21 June 2006 (UTC)

It's there. At least it's in their online version, and I predict that iff (heh) it's there, it's either in their print edition, or will be in the next print edition. --Jay (Histrion) (talk • contribs) 17:33, 22 June 2006 (UTC)

I support making this change, with the exception of "iff" used in definitions which should be changed to "if". In fact I think we should expand the Math Manual of Style to discourage the use of "iff".Paul August ☎ 21:56, 21 June 2006 (UTC)

I support editing out all uses of "iff" from Wikipedia, and augmenting the MSM to discourage future use. However, I think a more delicate touch is required. In definitions that are clearly such, change to "if". Elsewhere, it is often better to rewrite the sentence rather than merely changing "iff" to "if and only if". I realize that may be much more labor intensive, and require more insight and judgement on a case-by-case basis, but the alternative could look ugly. Uglier than "iff", I don't know. My practice has been simply to make this kind of change as I encounter instances, and as the mood strikes me. A note in our conventions, a note in the Manual of Style, and widespread awareness among mathematics editors may be enough to stamp out the problem.

I also go after a few other issues as I see them. I've mentioned "ditto" previously. Others are the Latin abbreviations "i.e." (id est, "that is") and "e.g." (exempli gratia, "for example"). Although I know what they mean and am perfectly comfortable with them, I think they pose an unnecessary barrier to many readers; and since the English glosses are perfectly good substitutes, I see no reason to use the abbreviations here. The list goes on, but that's enough for today. --KSmrq^T 23:40, 21 June 2006 (UTC)

So what is the proper rewrite for "a triangle is right if and only if its sides satisfy a² + b² = c²"? -lethe ^{talk +} 23:49, 21 June 2006 (UTC)

Depends whether you're defining the term "right" or whether it's been defined previously. Dmharvey 23:55, 21 June 2006 (UTC)

I'm asking KSmrq how to rephrase a theorem whose converse is also true, so assume "right" has been previously defined as, say, "contains a ninety degree angle". -lethe ^{talk +} 01:27, 22 June 2006 (UTC)

I'd need more context to be sure; good writing doesn't happen one sentence at a time. Since this is a theorem asserting an equivalence, I would not object to "if and only if", and perhaps not feel the need to edit it. However, if I were writing this ab initio myself, I might choose different language. For example, if I wanted to highlight the assertion I might write

Theorem. Let a triangle have side lengths a, b, c, with c the longest side. Then the following two statements are equivalent:
1. The triangle is a right triangle.
2. a² + b² = c².

For an inline statement, but still feeling the double implication is important, I might write

For any right triangle with sides a, b, c, the sides satisfy a²+b² = c², where c is the longest side. The converse is also true: any triangle whose sides satisfy the equality is a right triangle.

But it really depends on the topic, the audience, the assertion, and the context. For example, in a larger context where this is a minor point, and the paragraph in which it appears is building a more important concept, I'd try to keep it as short as possible consistent with clarity. Does that answer your question? --KSmrq^T 12:53, 22 June 2006 (UTC)

It does answer my question. But I don't like it. You want to double the length of the assertion so that you can mention the statement and its converse explicitly? I would really much rather stick in an "if and only if". Listing the equivalent conditions is nice when there are three or four equivalent conditions, but rather burdensome for only two. Therefore I cannot support the idea to revise the MSM to suggest that "if and only if" be avoided (for theorems, that is. I'm on board avoiding this turn of phrase for definitions though). -lethe ^{talk +} 03:54, 23 June 2006 (UTC)

Yes, I described two variations that are longer. But the last thing I said was that in certain contexts I'd prefer to keep it as short as possible, so as not to detract from a larger point.

Here's one way to think about it. I have an assertion in mind. It's a nifty little assertion and I quite like it. But my first question is, does it help the article? Is it important either as an end in itself, or as support for a larger goal? Or perhaps as entertainment or enrichment? If it does not help the article, no matter how much I like it I shouldn't use it. OK, I decide it stays. Is it a brief aside, or is it something the reader really should understand? If the latter, then brevity is less important than clarity. Both of the longer versions I offered are predicated on the assumption that each direction of the implication is important for the reader to absorb. If it's that important to say, then spend a few extra words and do it right. If it's not that important to say, then maybe we don't really need it.

Prose that packs five major ideas in one paragraph is not reader-friendly. We tolerate it in mathematics texts if we must, but we don't enjoy learning from it. (I'm reminded of a graduate algebraic geometry class that spent the better part of a term covering the first chapter of the text: Hartshorne, ISBN 978-0-387-90244-9.) That kind of density intimidates mathematics graduate students; surely it is inappropriate for an encyclopedia.

As for the MSM, my proposal was to ward off "iff", not "if and only if". --KSmrq^T 23:03, 23 June 2006 (UTC)

OK, since it seems like no one is opposed to changing iff to if and only if, I'm going to continue. As far as replacing some with just "if", that can be done afterwards. —Mets501 (talk) 01:24, 22 June 2006 (UTC)

I think that's a misreading. Both Paul August and I explicitly objected to making the change in the context of a definition, a view widely supported by others in prior discussion. Is there some reason you can't be careful about that? --KSmrq^T 13:00, 22 June 2006 (UTC)

Basically, what I've gotten out of this discussion is that nobody objects to changing "iff" to "if and only if" (they do mean the same thing), but that you both support removing some of the "if and only if"s and making them just "if"s, or removing them altogether and rephrasing definitions. It will be no harder for you to do that when it says "if and only if" than when it had said just "iff". If you want to go back and do that, well, all the pages that have "if and only if" are now grouped in my most recent contributions. —Mets501 (talk) 13:18, 22 June 2006 (UTC)

I also would like to add that through my going through all the "iff"s I came by very few definitions. —Mets501 (talk) 13:21, 22 June 2006 (UTC)

I don't think this is a big problem. Paul August ☎ 17:54, 22 June 2006 (UTC)

I would point out, however, that this is one of the reasons we have a link for iff; so if someone doesn't understand it, it can be explained.Septentrionalis 00:15, 2 July 2006 (UTC)

Fraction refraction. :-)

I've never poked my head into the Math WikiProject before, but a few months back I did some work on Fraction (mathematics) before I had to take a break to tend to both Real Life and my proper job. Looking around, I can't help feeling there's a lot to be done, and it's not just a matter of the one article:

If Vulgar fraction and fraction (mathematics) are not to be merged, then duplicate material needs to be excised. If they are to be merged, then let's merge 'em!
Fraction (mathematics), while slowly improving, needs cleanup, and needs it badly, but the lengthy material on the arithmetic of fractions really belongs in an article all its own. Or, for that matter, in a Wikibook, but...
the Wikibooks material is scant, sometimes incorrect, and things are often hard to find, or can be found in more than one place. Looking for fraction arithmetic, for instance, I found it under both Algebra/Arithmetic and Applied Math Basics, but not under Beginning Mathematics. Are Wikibooks out of the scope of this WikiProject?
Amongst the mess, there's probably more duplicated material about Egyptian fractions than there needs to be.

I'd keep going, but another task is calling me from my PC. I know that fractions might not be a hip'n'trendy subject, but I work as a tutor at a community college and there are a few math topics that come up a lot, and manipulating fractions is one of them. :) I'd be willing to take the lead on this, as long as I have the support of the Project. --Jay (Histrion) (talk • contribs) 21:09, 21 June 2006 (UTC)

New template

I just created a new template, {{In sqrt}}. It basically displays the radical (√) and the the number with an overline. For example, if you enter {{In sqrt|x}}, it will produce √x. It works great for all CSS capable browsers, otherwise it just displays a radical sign. I was wondering, should we put this in the mathematics manual of style as a recommendation for all inline square roots? —Mets501 (talk) 01:15, 23 June 2006 (UTC)

"it will produce √x." J ɪ m p 04:26, 31 May 2007 (UTC)

otherwise it just displays a radical sign

So what happens if I enter √x+2 in a non-CSS capable browser? Is it going to appear as √x+2? Dysprosia 01:50, 23 June 2006 (UTC)

"if I enter √x+2" J ɪ m p 04:26, 31 May 2007 (UTC)

Yes, I think it will. However, there are so few non-CSS capable broswers that this is not an issue. Or if people here think it is an issue, then don't use this template for polynomials. —Mets501 (talk) 01:56, 23 June 2006 (UTC)

If it's going to fail and effectively look incorrect for any number of users, then it's not a Good Thing. As KSmrq said, √(x+2) is always correct. Dysprosia 03:57, 23 June 2006 (UTC)

I take it the benefit is the vinculum (overline)? Otherwise, √2 produces √2 just fine.

I'm leary of this for a few reasons. One is that a browser that doesn't support CSS properly doesn't have a graceful fallback to show the grouping, so readers can't distinguish √x+2 from √x+2, whereas with √(x+2), √(x+2), they can. The second problem is that the radical sign doesn't stretch up or down, so that something like √^x⁄_y or √x²+y² won't look right. It seems I can't write the fraction using the {{fraction}} template, because there is no nesting; still, I suppose this doesn't come up often. But template use incurs extra server overhead; is it worth it?

My last concern involves the arrival of BlahTeX. Currently the notation <math>\sqrt{x^2+y^2}</math> produces a PNG, $\sqrt{x^2+y^2}$ . BlahTeX can serve this as MathML that renders beautifully inline. However, this creates a predicament for the template. How should the template adapt? Should it be revised to produce the <math> form, or continue to produce the Unicode/CSS form which is now less attractive for many readers?

Your thoughts? --KSmrq^T 03:45, 23 June 2006 (UTC)

"can't distinguish √x+2 from √x+2, ... something like √^x⁄_y or √x²+y² won't look right" J ɪ m p 04:26, 31 May 2007 (UTC)

On my machine (Firefox on Mac OS) it renders like this:

. Honestly, if I saw something like that in an article, I would change it to <math> straight away. I think it looks awful. I looks like "square root of the conjugate of x+2". It's marginally better in Safari. Dmharvey 11:04, 23 June 2006 (UTC)

I really dislike the idea. Sure, presentation is important for Wikipedia, and we all (or at least some of us) are looking forward to seeing a beautiful print version of wikipedia in the library one day (or just a nicer version on a high-resolution display with large fonts).

However, at least as far as I'm concerned, the real value's in the database being created. I'm already somewhat skeptical of the guideline to avoid using inline math. Templates make it even harder to understand what's going on, are limited in their applications, and I'm not sure they'll ever do exactly what you want with screen readers. Blahtex promises to be a better way out, for now, with MathML salvation on the horizon.

(I don't think Wikipedia should be using TeX-derived syntax forever, though. An advanced language that would allow us to specify not only what our formulas should look like, but also what they mean, and allow wikilinked symbols, might be a good idea when MathML has become accepted).

RandomP 12:08, 23 June 2006 (UTC)

Thanks everyone for your input. I will stop using the {{In sqrt}} template (it appears as if that's what everyone above thinks), and have removed the changes to the square root article (the only one which I changed. Oh god, we need BlahTeX! It's so ugly with inline PNG square roots and even uglier with the √ sign. —Mets501 (talk) 12:51, 23 June 2006 (UTC)

While we're on the topic, something else I should mention is that blahtex knows how to get the vertical alignment of a PNG equation correct (thanks to dvipng). That is, it aligns the baseline of the equation with the surrounding text. This is not enabled on the demo wiki, because it requires some (minor) changes to mediawiki's database schema, and we don't want to be pushing our luck yet. It is however enabled on the interactive demo. Things like inline square roots become a lot less uglier when the baseline is correct, especially if the font size is approximately correct. Dmharvey 13:20, 23 June 2006 (UTC)

Yes, I forgot to mention baseline issues as one of the advantages of BlahTeX. MathML display, of course, automatically gets it right without clever hacks. --KSmrq^T 14:21, 23 June 2006 (UTC)

Yes, I've experimented more with the interactive demo, and it does render much better. How long do you guys think it will be before it's implemented? (or is not quite finished yet?) —Mets501 (talk) 17:53, 23 June 2006 (UTC)

Don't know. We're working on it. (In between the real lives that we sometimes pretend to have.) Dmharvey 18:02, 23 June 2006 (UTC)

What, you're not still faking that whole doctoral thing, are you? Or do you mean serious pursuits like sleep and beer? Oh, now I remember; you were planning to spend time celebrating Australia's 6–0 win over Brazil! Ah, well; at least you didn't have to play Ghana. ;-) --KSmrq^T 20:26, 23 June 2006 (UTC)

In case the function of the template is changed in the future (which would be a good thing seeing as it's otherwise unwanted) I've made copies of the text which transcludes it and added subst: so that the text as it originally looked will still be able to be read. J ɪ m p 04:26, 31 May 2007 (UTC)

Category:Degenerate forms up for deletion

Wikipedia:Categories for deletion/Log/2006 June 23#Category:Degenerate forms Oleg Alexandrov (talk) 01:48, 23 June 2006 (UTC)

Need third opinion at Operation (mathematics)

JA: Could use a third opinion at Operation (mathematics), a page that was created as a gloss on the generic concept but is now being converted into "hwk-helper" with material that either belongs or is pretty much already covered at Binary operation and other places.

JA: Looking down the road, in both directions, I am seeing here a more generic issue for the WP math community. For instance, the article in question was categorized as Mathematical Logic, and is now being recategorized as Elementary Mathematics. I think that there needs to be a standard operating procedure for sorting out and coordinating "tutorial" and "standard" articles. I notice that the physics folks already have a template for doing this. Anyway, something to think about. Thanks, Jon Awbrey 17:56, 23 June 2006 (UTC)

As the other editor in this dispute, let me summarize my position. "Operation" is an elementary term in mathematics. Someone helping their kid with his or her homework would likely end up at Operation (mathematics). The term belongs in Category:Elementary mathematics. In editing the article I preserved the full formal definition. The entire article fits on one screen. There is no need in this case (though there certainly may be in others) for "tutorial" and "standard" articles. (I gather by "standard" JA means aimed at specialists.)

No specialist is harmed by having to skip over a dozen or so lines of introductory material to get to a formal definition. If there were a need for a specialized page for the mathematical logic community (and I fail to see why since they are using the ordinary meaning), a proper name for such an article might be "Operation (mathematical logic)." According to Wikipedia policy WP:NAME: "Generally, article naming should give priority to what the majority of English speakers would most easily recognize..."

I agree with JA that a broader discussion would be helpful. I have no problem with highly technical articles that treat their subject rigorously, but where it is possible to do so introductory sections should be included that speak to a wider audience. I have tried to do this in several places and I consider it some of my best work. See homotopy groups of spheres for example. Wikipedia should try to demystify math, not obfuscate it. --agr 17:28, 23 June 2006 (UTC)

My personal opinion that the article requires a general definition as well as examples. In this version, the examples are nicely covered in introduction (one more example: operations on sets and functions, which I have just added). Operations in math logic is just one of the examples, and I think that elementary mathematics is more appropriate. (Igny 19:10, 23 June 2006 (UTC))

In this specific case I see no reason not to combine an elementary treatment with one for the specialist. And let's be honest, a specialist has no need to look up such basic stuff, so actually general understandability is more important. One thing that is not made clear and may be confusing, is that there is no clear distinction in mathematics between the meanings of function, operation, and operator. For example, the article Operation (mathematics) now mentions square root as an example of a unary operation, while the article Square root itself only mentions "function". It is largely a matter of historical convention when which term is used. --Lambiam ^Talk 19:26, 23 June 2006 (UTC)

JA: This is like deja vu of discussions that we had on Function and Relation, and so I'd rather focus on the generic problem, as I'm fresh out of ergs to be caring about this stuff unless others do. I created this article because of a recurring need in other articles — check the "what links here" page — for a quick gloss to a suitably general concept of k-adic operations. And now anybody chasing those links is likely to skip the whole darn thing before getting past the TOC. What we have now is two articles whose front ends are devoted to Binary operations, and so it seems like the whole thing is better dealt with by way of a 1-liner up top like: {{for|an introductory treatment|Binary operation}}. Jon Awbrey 19:48, 23 June 2006 (UTC)

First of all, the present intro to operation (mathematics) does not just deal with binary operations. It also describes unary operations. The common mathematical use of the word "operation" includes both. The binary operation page is not that elementary and goes off to discuss groups, monoids and the like, as it should. The unary operation page devotes a lot of its space to computer programming operations. So there is a need for the current version of "operation." This is an encyclopedia, not a glossary, and specialists can put up with a little intro material. Regarding "what links here," I came to this article in the first place when I was editing exponentiation and wanted to link the word "operation.' What I found when I looked there was totally inappropriate. I suspect other editors of elementary articles have come to the same conclusion.

As for the relation (mathematics) article, it already has a long introductory section. It would take very little editing to make its intro beginner friendly, eliminating the need for an initial redirection. Basically defer the jargon for sentence or two. And that I think is the broader issue here. Where it is possible to do so, editors should be able to add short introductions to articles that make them more accessible to non specialists, without a big battle each time. Long tutorials deserve their own article, of course. But an average reader landing on a basic mathematical topic should get an initial explanation they can understand before being redirected.--agr 21:44, 23 June 2006 (UTC)

I suggest creating operation (elementary mathematics), function (elementary mathematics) and relation (elementary mathematics) which would have content aimed at the primary-school/secondary-school/high-school level. This might solve the edit-warring over these articles. linas 00:19, 2 July 2006 (UTC)

Span.texhtml

Please see my proposal here. —Mets501 (talk) 22:20, 23 June 2006 (UTC)

Doesn't anyone want to comment? It's very relevent to all math pages on Wikipedia. —Mets501 (talk) 23:49, 24 June 2006 (UTC)

We've seen it before. There's little enthusiasm for a global stylesheet change for two reasons (at least).

For an inline formula using <math> tags that happens to force a PNG, the "x" will appear in a serif font, which is also the way it appears in most displayed equations (since the typical display is a PNG); consistency in this case dictates that the HTML should use a serif font as well.
Anyone who really cares about using a sans-serif font can do so using using their personal stylesheet, just like the users you noted.

No matter which choice is taken, so long as the monobook body text uses sans-serif and TeX PNGs use serif, we have a conflict. Nor is that the end of it; look at the difference in other characters, such as Greek symbols and operators.

This conflict is unlikely to end with the release of the STIX fonts, as suggested by the following statement:

“Most of the glyphs in the STIX Fonts have been designed in Times-compatible style. Times was first designed under Stanley Morison's direction by Victor Lardent at The London Times in 1932. Many variations of this design have been produced since the original.

“In addition to Times-compatible glyphs, some portions of the STIX Fonts include other design styles such as sans serif, monospace, Fraktur, Script, and calligraphic.”

Thrilling; all of the extra styles except sans serif are essential for TeX. So get used to serif mathematics; it looks to be with us for a long time to come. --KSmrq^T 00:27, 25 June 2006 (UTC)

How about "span.texhtml {font-size=14px}"? That will at least get it to be the same line height as the sans serif.

Will it? For which OS, browser, fonts, and settings? This kind of hair-pulling madness is a tiny fraction of the issues Dmharvey and Jitse Niesen have been wrestling with over in BlahTeX-land. --KSmrq^T 22:38, 25 June 2006 (UTC)

he's baaaacccckkkkk..... "made it clear"

[26] Dmharvey 18:35, 24 June 2006 (UTC)

He never seems to tire, does he? Blocked again... -- Fropuff 05:35, 25 June 2006 (UTC)

In defense of our clarificator, there is an apparent contradiction between the Real number article, in which "a [presumably meaning any here] real number can be given by an infinite decimal representation", and the article Decimal representation, which has: "Every real number except zero has a unique infinite decimal representation" (which is true the way things are defined locally). Instead of blocking, it might be better to smooth away the contradiction. --Lambiam ^Talk 10:00, 25 June 2006 (UTC)

I just removed that section in "decimal representation". It was probably also put there by WAREL and missed by others. JRSpriggs 11:00, 25 June 2006 (UTC)

Actually, if you read that paragraph again, you will notice that it is correct. Every positive real number has exactly one decimal expansion which doesn't end with all 0's, and one decimal expansion which doesn't end with all 9's (usually, these two are the same). That paragraph emphasized the first of these - which looks unusual, so I don't object to the removal. -- Meni Rosenfeld (talk) 18:05, 26 June 2006 (UTC)

The first sentence of the removed paragraph said was "Every real number except zero has a unique infinite decimal representation, that is, one in which not all of its digits become zero after a while. ". Although the subordinate clause tries to rescue it, the main clause is false. Some real numbers have more than one infinite decimal representation. It is senseless to discriminate against a terminal string of zeros in favor of a terminal string of nines. If anything, I would do it the other way around. JRSpriggs 10:22, 27 June 2006 (UTC)

The subordinate clause clarifies what was the meaning of "decimal expansion" in the main clause. The main clause would have been false on its own - but it is accompanied by the subordinate clause to form a whole sentence - a correct one. It is the same as saying "every real number a has a unique cube root, that is, a real number b such that b³ = a". The first part could have been seen as false on its own, if we see it in the context of complex numbers - but the second part clarifies that we are only concerned with real numbers. Not much point in arguing about this, though - I do agree that ther article is better off without that section. -- Meni Rosenfeld (talk) 10:35, 27 June 2006 (UTC)

It is more like saying "Every positive real number has a unique square root, i.e. a negative number which when multiplied by itself gives the positive number.". He is treating the abnormal case as the normal. JRSpriggs 11:01, 27 June 2006 (UTC)

That is something I certainly agree with. -- Meni Rosenfeld (talk) 11:28, 27 June 2006 (UTC)

I would agree with all this, but I have to say that I do recall situations in proofs, where it is more convenient to use the version of a real number which ends in a string of 9's (it means that every strictly positive real has a non-terminating decimal representation) - but in this instance, I agree that he is advocating the 'abnormal'. Madmath789 11:48, 27 June 2006 (UTC)

Here is an attempt to say something that is (a) true, and (b) not a manifent consequence of what is already in the article:

Every non-negative real number has an infinite decimal representation. It is unique, except for those positive real numbers that also have a finite decimal representation: these have two infinite representations. For example, the number 5/4 = 1.25 has the two infinite decimal representations 1.24999… and 1.25000….

Is it worth adding this? --Lambiam ^Talk 17:23, 28 June 2006 (UTC)

If you do add it, add it to the existing section "Multiple decimal representations" rather than making a new section. JRSpriggs 04:55, 29 June 2006 (UTC)

Request from non-mathematician

When I do "random article" I occasionally come across mathematical formulae (and sometimes with general science books etc). It would be useful for those of us who are not mathematically informed if there was a "basic explanation" as to use and purpose.

See the examples I put on Wikipedia:Requests for expansion for what I mean. Jackiespeel 16:54, 26 June 2006 (UTC)

In reference to boolean-valued function, boolean domain, and finitary boolean function. Those are pretty short stubs. They need lots of work (or perhaps even to be merged somewhere). In response to your general query: yes, I will try to make every math article I write have explanations, examples, context, and everything else that makes for brilliant writing. Sometimes a stub is better than nothing though. -lethe ^{talk +} 17:37, 26 June 2006 (UTC)

On the request for expansion page, you wrote:

Finitary boolean function, Boolean domain and Boolean-valued function and some of the links thereof - can someone give an explanation in "ordinary English" as to what these functions are. I can see that they are complex mathematical functions - but "what are they"? Perhaps a brief standard text could be added. "This mathematical function is used in xxx, and does yyy." (add more detail as required) Jackiespeel 23:14, 24 June 2006 (UTC)

The article "finitary boolean function" describes a simple generalization of a boolean function. There's not much else to write. Perhaps that article needs to be merged into the "boolean-valued function" article. The article "boolean domain" is just a definition, and is already marked as a stub. The article "boolean-valued function" gives what you ask for: it describes the function and gives several fields where it's used. Could you explain why that doesn't meet what you want? Lunch 18:32, 26 June 2006 (UTC)

Finitary boolean function is not a generalization but a specialization of boolean function. The situation is a bit messy. There is also the article Boolean function, which never defines what a boolean function is. Is there a difference between the concepts of "boolean function" and "boolean-valued function"? What is sorely missing here are examples. There is further an article Logical connective, which treats operators like AND and NOR, the redirect page Boolean operator redirecting to Logical connective, and the redirect pages Boolean operation, Logical operator and Logical operation, which instead redirect to Boolean function. --Lambiam ^Talk 20:03, 26 June 2006 (UTC)

Conventions in graph theory : strongly regular graph

I was busy trying to make a Strongly regular graph separate article, and I was wondering : what will we agree on the conventions.

Graph theory can really be annoying when you really want to do it right. For instance my syllabus agreed on not including disconnected graphs and their complements, which in turn implied $v - 1 > k > μ > 0$ .

The spectrum also changes when you allow disconnectedness: the degree of disconnected graphs becomes an eigenvalue with more than dimension one.

What is your opinion?

Evilbu 18:22, 26 June 2006 (UTC)

My advice would be to have a look at the other graph theory articles to see if their conventions seem reasonable, and try to follow those if so. You can of course use your own conventions too — the most important part right now is to write the article; we can discuss your conventions later. Just be sure to explain what your conventions are in the article. - Gauge 02:39, 28 June 2006 (UTC)

Research first, write afterwards. Halmos, a widely respected mathematics author, says:

"A good, consistent notation can be a tremendous help… Bad notation can make good exposition bad and bad exposition worse; ad hoc decisions about notation, made mid-sentence in the heat of composition, are almost certain to result in bad notation."

Try to conform to standard conventions. But especially, be explicit about what conventions you choose; don't leave the reader guessing. This is essential within Wikipedia, where readers and editors come from different disciplines, different schools, different continents, and different levels of experience.

Graph theory is mathematics applied to many tasks, and the conventions that are helpful for one may be an impediment for another. Since we cannot know why someone is reading an article, we cannot assume that for their purposes all graphs are connected. However, it is fair to introduce a discussion by saying something like, "Here we restrict attention to connected graphs." That's not only good for the reader, it also makes it easier for another editor to come along, see the restriction, and expand the coverage.

You will find this done throughout the mathematics articles. In fact, it can help to start an article that includes both introductory material for a general audience as well as much more abstract material for an advanced audience. First give the accessible and common cases to build intuition, then later remove restrictions.

Specifically with regard to strongly regular graph (and note: don't capitalize the first word just because it's linked!), nothing in the definition of regular graph implies or depends on having a connected graph. If some of the results you want to state only apply with that restriction, say so.

A fine point of TeX usage is that it is incorrect to write

$srg(v,k,\lambda,\mu) . \,\!$

TeX typesets this as if s, r, and g are three single-letter variables being multiplied. I mention this here instead of on the article talk page because it's a common mistake. Instead, try

$\operatorname{srg}(v,k,\lambda,\mu) . \,\!$

The special notation here, "\operatorname{srg}", does several good things; use it. This is not highlighted at Help:Formula, but many other helpful suggestions are; read it. Especially note the trick (which I've used here) to force displayed equations to use a PNG image (which is large and uniform) instead of an approximation in HTML.

I'll also use this opportunity to point out that since there is no reason to capitalize the first letter of a link, there is also no reason to write, say, "[[Adjacency matrix|adjacency matrix]]" instead of merely "[[adjacency matrix]]". The MediaWiki software also performs other background magic, such as simplifying plurals like "[[complete graph]]s", which comes out looking like "complete graphs". Something that often proves handy in mathematics articles is that trailing parentheses in a link, needed for disambiguation, can be automatically removed by using the "pipe" character, "|". Thus we can write "[[graph (mathematics)|]]s" to get the word "graphs" with a disambiguated link, like this: "graphs". --KSmrq^T 04:27, 28 June 2006 (UTC)

Okay, well first of all, I checked my syllabus and found that followig THOSE conditions works out eventually. But I don't want to get into any trouble with my own University for copying very explicitly. The problem is that the University of Ghent is such a big 'player' in the field of incidence geometry, that a lot on the internet (and that is assuming you find something) comes from their sites I bet you also disapprove then of my pg(s,t,\alpha) notation in the partial geometry article? I read that Formula page and even applied one of the guidelines on Paley graph. But I am totally confused with HTML/Tex/PNG, especially since I was instructed very recently to switch my Preferences to 'Always render PNG'. Evilbu 13:09, 28 June 2006 (UTC)

Explicit copying is a bad idea anyway, because this is an encyclopedia, and written for a much wider audience. It's not enough that you understand what you write, or that a university lecturer understands; the goal is that anyone in the world with an interest in the topic (and sufficient background or determination to learn) can understand. We have a mathematics style manual that is helpful. Much more could be said. My personal guidelines remind me to try to include, among other things,

intuition
examples
counterexamples
connections
pictures
humor

Although it is helpful to have an article that is little more than a definition or theorem, it is much more helpful to explain in what area of study the definition is used, why it may be useful or plausible, and to show it in action either directly or with links. And since this is an encyclopædia, we also like to cite at least one academic source (something more reliable and permanent than lecture notes or online course material).

Looking at the partial geometry article, I see again the need to use "\operatorname{pg}" instead of "pg", but I also see two other problems. (And, again, I discuss this here for the benefit of everyone, not just one editor and one article.) The first sentence looks like this:

"An incidence structure S=(P,B,I) is a (finite) partial geometry …"
"An [[incidence structure]] ''S=(P,B,I)'' is a ([[finite]]) partial geometry …"

The italics are misused; only the variables should be italicized, not the equality and not the parentheses. While we're at it, we'd like the equation to have a little breathing room but not a bad line break. Here's a way to do all that.

"An incidence structure, S = (P,B,I), is a (finite) partial geometry …"
"An [[incidence structure]], ''S'' = (''P'',''B'',''I''), is a ([[finite]]) partial geometry …"

The wiki markup is a nuisance, and we eagerly look to the day when BlahTeX will rescue us; but, for now, that's it.

The second issue has to do with your HTML/TeX/PNG confusion. The sad fact is that mathematics markup is confusing. Again we look to BlahTeX, which will simplify this as well. Switching your preferences affects you alone; most of your readers will not be using the "PNG always" preference. For example, I don't. Many of us do not like to see big PNG images jutting out in our inline text. We do our best to confine the PNG to displayed equations, and there we always want to see it.

This leads to a highly annoying dual writing technique: hard-to-edit wiki notation for inline, and TeX notation for display. Either way, we're taking a leisurely stroll through a minefield. We have a diversity of philosophies about what we're comfortable with inline, with some people using TeX whenever they need a special character and others (including me — see here) using Unicode; but we have a broad consensus that "built-up" material such as "{a \over b}" is undesirable inline. So this is a second thing you should fix in the partial geometry article.

I find that TeX (or LaTeX) has many subtleties that the average mathematics writer overlooks; the typesetting of operator names is but one of them. For example, not many people know the correct way in TeX to write the colon in f: R² → R. (Use "\colon" instead of ":" to get the right spacing; try it!) However, our current situation is even worse, because Wikipedia depends, not on genuine TeX, but on a lame partial imitation, texvc. Again we look to BlahTeX for eventual relief!

I appreciate that there is a lot to learn about writing mathematics for Wikipedia, and I hope you will not be discouraged. We're here to help, and eventually we'll have new software to help as well. --KSmrq^T 19:22, 28 June 2006 (UTC)

Bots and automatic Unicode conversion

I noticed User:Bluebot is automatically converting HTML entities to Unicode on various articles. See e.g. [27]. Does anyone have an opinion on whether such conversion is desirable in mathematics articles? Would it hinder possible future efforts to automatically switch to MathML? - Gauge 05:55, 28 June 2006 (UTC)

First of all, MathML only affects math written in <math> tags, and unicodifying only takes place outside <math> tags, so it would have no effect of MathML. As far as being desireable, it makes it easier to read the article in edit mode, especially for newbies who are not used to used to HTML entities. —Mets501 (talk) 12:44, 28 June 2006 (UTC)

I know the automatic conversion of Blahtex would only apply to math tags; I was thinking instead of possible future efforts to convert inline HTML being used for math into MathML (using blahtex with math tags), once it is widely supported by browsers (likely several years off, but worth discussing now). What if different bots use different Unicode symbols for the same HTML entities? - Gauge 18:38, 28 June 2006 (UTC)

It makes a little more difficult to edit the article, especially with HTML entities such as & nbsp; , but it's probably a good thing. — Arthur Rubin | (talk) 17:25, 28 June 2006 (UTC)

Converting Unicode to MathML should be just as easy as converting HTML to MathML I think, so ∫ --> \int and ∫ --> \int should not be that different. I would be opposed however on such bots (or worse, semiautomatic editors) doing mass unicodification very often, they just obscure watchlists with no good purpose. Oleg Alexandrov (talk) 19:02, 28 June 2006 (UTC)

Somewhere we've had this discussion before. My recollection is that many editors objected to replacing an HTML named entity with Unicode because the HTML name and the TeX name were the same, making consistency easy. That objection does not apply to numerical entities, but those are so unpopular that we rarely see them. MathML can cope with any Unicode (UTF-8) character for a symbol; in fact, it knows special things to do with many more than are supported in TeX. I don't recall exactly how BlahTeX copes, but it either can or will do better than texvc, at least for passing things on to MathML. My personal preference at the moment is to stop the bot, on the grounds of previous rejection and of TeX (not BlahTeX) incompatibility. --KSmrq^T 19:38, 28 June 2006 (UTC)

On a different note, will we deprecate HTML math formulas with the arrival of BlahTeX? —Mets501 (talk) 20:19, 28 June 2006 (UTC)

I think not. Not in the immediate future.

To address KSmrq's question: currently blahtex does not allow non-ASCII characters in math mode material, on the grounds that people would abuse it, and it would lead to the database becoming horribly incompatible with standard tools. People should be using the TeX commands instead. It does allow arbitrary non-ASCII in text mode, which gets passed through to the MathML <mtext> element. I suppose this could lead to the same sort of abuse (like <math>\text{∫}_0^1</math> -- yuck!). It might become desirable to limit the characters that could be used in text mode (e.g. extended latin, and other scripts like japanese, chinese, klingon, etc). Dmharvey 20:49, 28 June 2006 (UTC)

Why wouldn't we deprecate HTML math formulas, though? If we put it in <math> tags, then BlahTeX will render it as HTML, anyway. So there seems to be no reason why we should keep using math formulas written in HTML. In fact, I'm not quite sure why we use inline HTML now for things like variables or "flat" equations that would render (in <math> tags) now as HTML now anyway with texvc. —Mets501 (talk) 01:13, 29 June 2006 (UTC)

The main reason to use HTML now instead of texvc for inline stuff is that the texvc conversion of TeX to HTML on "simple formulas" is so pitiful. Blahtex would generate MathML output for math tags for people who want it, but I think it still falls back to the old texvc HTML conversion for people not using MathML. Also, there are certain things that texvc will tend to encode as PNG rather than HTML (any sort of spacing, for example), so one might be forced to use HTML for the desired result anyway. - Gauge 19:59, 29 June 2006 (UTC)

In response to KSmrq's comment about prior discussions involving unicode in mathematics article, on this page, there have been at least three:

Unicode in math articles (Sep 24 2005)
Mathematical characters usage (Oct 18 2005)
IE compatibility (Mar 28 2006)

Paul August ☎ 21:37, 28 June 2006 (UTC)

Thanks Paul. I found this quote by Dysprosia that I thought was worth repeating here:

The difference is that the Unicode alpha is just another character in the text, like "t", or "q". The HTML entity is the string "α". All good computer systems should support ASCII, and the HTML entity consists of only ASCII characters, so no matter if you use a computer that supports Unicode or if you don't, the string will be unchanged. However, some browsers that don't support Unicode simply ignore the Unicode characters, so if someone edits with one of those browsers, it will look like all the Unicode characters in the article have suddenly disappeared. If the browser chooses to render "α" with a Unicode character, that's fine, but it doesn't mean that that Unicode character is somehow equivalent to the HTML entity -- they aren't. Hope that explains things a bit better...

I think this is reason enough to discourage proactively converting HTML entities to Unicode. Let the browser decide which symbol to use instead of forcing a particular Unicode symbol. Also, what is the state of screen reader support for Unicode as of about 5 years ago? It seems reasonable to give handicapped users some time to upgrade their software if Unicode is going to be proactively deployed. I don't mind if people use Unicode in articles, but they shouldn't be converting HTML entities to Unicode wholesale without some discussion. - Gauge 22:53, 29 June 2006 (UTC)

\mathscr anyone?

Are people interested in having the \mathscr command available? (Provided by \usepackage{mathrsfs}.) Here's what it looks like:

The top one is \mathscr, the bottom is \mathcal (which is what we have now). I've noticed that \mathscr (or something similar) is quite popular in certain fields. I've noticed it especially in functional analysis.

There wouldn't be any difference in MathML because MathML only defines a single "mathvariant=script".

Opinions welcome. Dmharvey 19:25, 28 June 2006 (UTC)

It's also popular in algebraic geometry, for denoting sheaves and sheaf-y versions of various things like functors. I've once or twice wished I could use it. It's not essential, but I guess I would say that I'm interested in having it. Ryan Reich 21:11, 28 June 2006 (UTC)

Do we get one or the other, or can we have both? Personally, I find \mathcal very useful at times, and wouldn't want to lose it. If we can have \mathscr for those that want it, without losing \mathcal, then that would be great. Madmath789 21:21, 28 June 2006 (UTC)

You get to have both. Unless you're viewing with MathML, in which case they look the same. This would only become a problem in articles that use the same letter in the two fonts to mean different things. It would be possible to disable MathML for \mathscr if that's what people wanted, in which case it would fall back on PNGs. Dmharvey 21:50, 28 June 2006 (UTC)

MathML is only part of the obstruction. Unicode itself has no font variation facility to handle this (that I know of). There is a code point for "B" (U+0042) and "b" (U+0062), and for "Б" (U+0411) and "б" (U+0431), and for "ב" (U+05d1), and for "𝔅 (U1d505) and "𝔟" (U1d51f), and for "𝔹 (U1d539) and "𝕓" (U1d553), and for "ℬ" (U+212c) and "𝒷" (U1d4b7). The idea seems that be that these variations of "B" are in separate alphabets (Latin, Cyrillic, Hebrew, Fraktur, double-struck, and script), not separate fonts. (The difference between uppercase and lowercase is an anomaly, retained for historical reasons even though it's somewhat inconsistent.) So an argument would have to be made to the Unicode committee that there is an essential semantic difference between the calligraphic alphabet and the script alphabet. I'm guessing it would be a hard sell; we all know mathematicians have a boundless appetite for new alphabets and new characters. (We need this alphabet for the space, and that one for the structure over the space, and the other one for the mapping of the structure over the space, and so on.) I think we already have enough distinctions to tough it out if we must! In fact, any author who wants to make a semantic or type distinction between script and calligraphy is already unkind to readers. For those who are still not persuaded, MathML accepts CSS styling, so it's possible to use a Latin code point and ask for a different font-family. --KSmrq^T 01:18, 29 June 2006 (UTC)

All very true. In fact, there are a few more: for example there's also 𝖡 (U1d5a1) which is "MATHEMATICAL SANS-SERIF CAPITAL B" ([28]). Interestingly, the reference glyphs for script letters given on the mathml site ([29]) appear to be the same as the \mathscr above, even though the fonts that I got from the Mozilla site render more like \mathcal. I wonder what the STIX ones will look like. Dmharvey 01:42, 29 June 2006 (UTC)

Is anyone aware of any sources that use both a mathscr-like font and a mathcal-like font, with different semantics? There's a thread on the www-math mailing list discussing this now. If anyone could build a case, we might well get two different font variants in MathML 3.0 (which is on the drawing board). Dmharvey 18:39, 5 July 2006 (UTC)

he he he

You know how we all put something like "\,\!" at the end of <math> blocks to force the output as PNG? Well I was just doing some database work and happened to be trying things out on the hebrew wikipedia, and discovered that they all put "\ " at the beginning of the equation! (e.g. [30]) Or is it the end of the equation? I don't even know... the </math> comes before the <math>... Dmharvey 22:02, 28 June 2006 (UTC)

The LaTeX equation itself runs from left to right. In this equation the "\ " is at the beginning. If we think of the eqn as an atom in a right-to-left context, then to the reader the blank space appears to appear to the left of and therefore after the atom (instead of being part of the atom). --Lambiam ^Talk 22:50, 28 June 2006 (UTC)

interesting statistics

More database work.... last time I checked around the beginning of March, the 13 largest wikipedias had 208,000 distinct equations altogether. Now (as of about mid-June) there are about 289,000. That works out at about a 10% growth rate per month. Pretty amazing. Dmharvey 02:06, 29 June 2006 (UTC)

You should write a paper about it. When it gets published, I can write a Wikipedia article about the paper. Ryan Reich 02:53, 29 June 2006 (UTC)

And make sure in the Wikipedia article that you use more formulas :-) —Mets501 (talk) 03:15, 29 June 2006 (UTC)

Help wanted

The "proof that 0.999... equals 1" article is once more under attack — from the inside. And for the n-th time, Melchoir is involved. I'm sick of dealing with him and (now) Supadawg. If anyone is interested, please get involved in whatever way you see fit. As for me, it's come down to a revert war or walking away.

Some of you may be aware I completely stopped editing Wikipedia articles awhile back, except for really minor things like typos. I confined my contributions to talk pages, because I had no more stomach for seeing articles obstinately trashed by editors with inadequate subject knowledge, horrible writing skills, and no social skills. That worked for me, though not so well for the articles I abandoned. In the current instance, I can't see wasting more time debating with someone who pretends a proof using Dedekind cuts and the Archimedean property is original research, and who doesn't see a problem in beginning a sentence with a decimal point, but who knows exactly how the article should be rewritten.

However, if you long for abuse or have a desperate yearning to save the world (or both!), here's your opportunity. You'll need to act quickly, for the Mongol hordes are invading as we speak. They have already insisted that an article devoted to a proof should not be so named, nor should state that in the opening sentence. ("It's unencyclopedic!") Next on their agenda is a complete rewrite. It boggles the mind.

OK, so saving this article probably won't save the world. Still, I'll bet it gets more page views than the snake lemma and the hairy ball theorem put together (no disrespect intended). Please stop by the talk page, or help revert. (This version works for me, tolerably.)

Just for fun:

Question at job interview: "What is one third plus two thirds?"

Mathematician: "It's one."
Engineer (using calculator): "It's 0.999… ."
Accountant (winking slyly): "What do you want it to be?"

Thanks, all. --KSmrq^T 06:42, 29 June 2006 (UTC)

I must say that I find the article unconvincing, also in its earlier incarnations. Surely, it is intended for people who, in a Zeno-like way, feel queasy with the identity. Most of what is in there is completely above their heads. If I was not mathematically educated, and I saw something that needed so many different proofs for its validity to be demonstrated, I would start to doubt the claim made! Can't we just have two proofs:

A solid one from first principles, basically saying (sketch): (1) By definition, 0.999... stands for the limit of the sequence 0.9, 0.99, 0.999, ... (2) That limit is, by definition of limit, equal to one when the elements of the sequence |0.9-1|, |0.99-1|, |0.999-1|, ... eventually become less than any positive number ε you care to state. (3) And indeed, it does: if the decimal representation of 1/ε has n digits before the decimal point, then the n+1st and subsequent elements are all less than ε.
The informal argument: 10x = 9.999...; subtract x giving 9x = 9.000... and therefore x = 1.000..., remarking that this, in fact, informally presents an actually valid mathematical argument.

More is not always better. --Lambiam ^Talk 09:23, 29 June 2006 (UTC)

First of all, thanks for your imput Lambiam, but I'm afraid that's a no (from me at least). It doesn't need so many proofs to prove its validity. The many proofs are to present alternate methods of prooving this "theorem". Any one of those proofs would serve to prove that 0.999…=0.

Second, KSmrq, I think that you're actions were not appropriate above. We don't have a consensus yet either way, and you're already assembling a revert army, or so it seems from your statement above. Also you did not provide a link to the infinite geometric series proof, and only to your version of the article, without the proof. If we do achieve consensus to delete the section, I will let it be deleted (although personally I would rather it stay – perhaps you remember when I added the proof on April 1 of this year, and you swiftly removed it), but until we have that consensus, it will stay in the article. —Mets501 (talk) 13:00, 29 June 2006 (UTC)

Please direct all follow-ups to the article talk page. They will properly be associated with the article history, and won't annoy the vast majority of mathematicians who don't long for abuse. Thanks. --KSmrq^T 15:44, 29 June 2006 (UTC)

I'm happy to join the corps of reverters for that article, but I cannot in good conscience revert to the version you link, which is buried behind over a hundred edits already. The best I can do is add the article to my watchlist and revert future changes. -lethe ^{talk +} 15:37, 29 June 2006 (UTC)

Not a problem. I had a hard time picking through all the debris to find a good target, with all the additions and reversions that have been happening lately, so I went back further to be safe. Thanks for anything you feel comfortable doing to help. --KSmrq^T 15:44, 29 June 2006 (UTC)

Redirect question

Is there a way to have a redirect focus the point on a specific section of the article? Specifically, I have in mind the redirect from Koszul connection to covariant derivative, which reads

# REDIRECT [[covariant derivative#Koszul connection]]

If you follow the link explicitly, by clicking the above link, then the point focuses on the relevant section. But if you follow the link Koszul connection, then you are taken to covariant derivative without the change in focus. Any thoughts or advice? Silly rabbit 17:32, 29 June 2006 (UTC)

See Help:Link#Redirects_with_section_links. I recall reading a different document that explicitly said that they had no intention of ever allowing section links within redirects, but I don't know where that went (the "Help" is not always very much help here; they make it very hard to find the detailed manual and I always forget how). Ryan Reich 18:05, 29 June 2006 (UTC)

Hehehe... I just found some related results, and was about to come here and answer my own question: Meta:Help:Redirect#A redirect to an anchor and bugzilla:218. It's kind of annoying that this seems to be impossible. Any stylistic pointers on how to handle a merger of this sort? Silly rabbit 18:13, 29 June 2006 (UTC)

Redirect to the top of the page. If the article is well-written then the appropriate section header will be in the TOC and clearly visible (i.e. the preamble won't take up much space). If not, well-rewrite it. In any case, if you have a page that used to link to Koszul connection, you could just put a pipe in that link and avoid the redirect entirely. Ryan Reich 18:45, 29 June 2006 (UTC)

Split of List of mathematicians

Sorry if I startled you, the WikiProject, but I boldly separated the List of Mathematicians article into eight smaller articles. Prior to this, the article was giant: it ranked in the Top 50 on Special:Longpages. Seeing as this is problematic, since not all of our users have the patience to load a page that is hundreds of kilobytes in size, I took the liberty to divide it into smaller pieces. I'm sorry if it's unacceptable to the WikiProject, but I was doing what I felt was good for the list. —THIS IS MESSED OCKER (TALK) 02:50, 30 June 2006 (UTC)

Relax. :) As I told you on your talk page, the big problem is that you did not realize a bot is used to update that page, and it will just happily overwrite your changes, or worse, will get confused by it and then the page will be messed up.

The list of mathematicians is 164 kilobytes. Time to split? Should it be split modeling the list of mathematics articles, that is, separate lists for each letter, or should there be a grouping into bigger lists, say A-C, D-F, etc.? Oleg Alexandrov (talk) 02:55, 30 June 2006 (UTC)

Yes a split seems a good idea. I would go for one list per letter. I can't really see an an advantage of A-C lists etc. I suspect most people who use the list will be looking for a specific person and so it will be easy enough for them to click on a specific letter. Further, the number of mathematicians per letter is already quite long for about half the letters. --Salix alba (talk) 08:41, 1 July 2006 (UTC)

I thought of the same thing. I will work on it when I find time. Oleg Alexandrov (talk) 16:56, 1 July 2006 (UTC)

Done. Oleg Alexandrov (talk) 03:52, 15 July 2006 (UTC)

Geostatistics

This article is extremely POV, particularly considering the open criticism of Geostatistics within the main page. I was hoping that someone with more experience could build some equations and expand on the evolution of geostatistics. Considering how widely geostatistics is used for the natural sciences, environmental planning, climate studies, oceanic studies, military analysis, urban planning, and Geographic Information Systems, this topic warrants some attention from math experts. SCmurky 03:56, 30 June 2006 (UTC)

JanWMerks is at it again. He's been editing geostatistics, semivariance, spatial dependence, variogram, sampling variogram, kriging, junk science, consensus science, Tolstoy syndrome, and Bre-X; I may have missed some. He's been admonished in the past for his crusading; see his talk page and his list of "contributions". It might be nice if more people added these pages to their watch lists to undo his edits. (BTW, SCmurky, why did you delete my previous comment?) Lunch 17:50, 30 June 2006 (UTC)

Maybe it is time to take more serious action Wikipedia:Resolving disputes posibly a request for mediation. --Salix alba (talk) 20:03, 30 June 2006 (UTC)

Jul 2006

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

Serre conjecture vs Serre's conjecture

Do we need a disambiguation page for these? Dmharvey 21:56, 1 July 2006 (UTC)

It would suffice to put a disambiguation link at the top of Serre conjecture, the Quillen-Suslin theorem being the only likely ambiguity. Having "Serre conjecture" and "Serre's conjecture" mean different things is asking for trouble. --KSmrq^T 22:48, 1 July 2006 (UTC)

Done. Septentrionalis 00:24, 2 July 2006 (UTC)

OK for the present, but Serre has dozens of conjectures, I believe. --Charles Matthews 10:58, 5 July 2006 (UTC)

Rogue wikibots

This unicodification stuff made me realize that as just one editor I have very little control over what people decide to do with their bots on wikipedia. I asked the guy running User:Bluebot politely to stop proactively converting HTML entities to Unicode in math articles (and am waiting for a response), but if he doesn't comply what recourse do I have before all of the articles are converted anyway? Apparently he already refused Dysprosia's request.

It seems to me that bots could do a lot of damage in a very short amount of time (shorter than it would take to get the hosting user banned, for instance), and the damage might also be difficult to fix, probably requiring someone to write up a new bot just to fix the mess that the former bot created. How long will it be until someone truly malicious tries to write a bot that trashes (or worse, subtly introduces sign errors, for instance) in hundreds or thousands of articles? Are there any measures in place to prevent this sort of thing from happening? - Gauge 23:38, 1 July 2006 (UTC)

As a bot owner, whose bot has, on occasions, gone rogue, I can say that it does not take long for somebody to notice something odd and notify the bot owner and/or block the bot. Bots are fifth class citizens (in order: Jimbo/bureaucrats/admins/users/anons/bots), they are shown no mercy. :) Oleg Alexandrov (talk) 00:04, 2 July 2006 (UTC)

If an ordinary user can block a bot, how is this done? When should one do it? JRSpriggs 10:09, 2 July 2006 (UTC)

Blocking a bot, like any user, requires an admin. (There are several in this project: Oleg Alexandrov, Jitse Niesen, Lethe, Charles Matthews, Mindspillage, Fropuff, Michael Hardy, Mikkalai, Toby Bartels, The Anome, Isomorphic, Charles Stewart — did I miss anybody? — and me.) Paul August ☎ 15:58, 2 July 2006 (UTC)

TeX tips

While working through many pages with equations listed as acceptable to texvc but incorrect according to BlahTeX's parsing, the single most common issue seems to be a construction like

<math>x^\sqrt{2}</math>,

which must be changed to

<math>x^{\sqrt{2}}</math>.

This often arises with a subscript like

<math>x_\mbox{kind}</math>,

which must be changed to

<math>x_{\operatorname{kind}}</math>.

The corrected appearance is as follows.

$x^{\sqrt{2}}$

$x_{\operatorname{kind}}$

It would be helpful to keep this in mind when editing: Use the braces. --KSmrq^T 02:16, 5 July 2006 (UTC)

Since TeX rightly rejects x^\sqrt{2}, so texvc should also, hence texvc is being Bad. Dysprosia 02:26, 5 July 2006 (UTC)

I am currently rewriting blahtex in python. Along the way I am reworking the parser. As a result it detects even more TeX incompatibilities than the current blahtex version. Dmharvey 02:38, 5 July 2006 (UTC)

You mean texvc problems? Dysprosia 02:42, 5 July 2006 (UTC)

Yes. I mean that the new version of blahtex will produce error messages for certain inputs that texvc accepts and that the current version of blahtex accepts but for which TeX produces an error. Dmharvey 03:13, 5 July 2006 (UTC)

I'm sure the BlahTeX developers are aware of this, but I want to point it out before people go out and mangle the TeX code in articles. The current BlahTeX sandbox seems to support <math>x_{\mbox{kind}}</math> as well, which has the semantic advantage that the word kind should get set as text. The MathML output seems to put operatorname into <mi> and mbox into <mtext>. I don't know the MathML standard, but I doubt these are guaranteed to be the same font. I think operatorname should be reserved for operators. According to the sandbox, BlahTeX also supports the AMS \text command for putting text into math formulas. CMummert 02:44, 5 July 2006 (UTC)

Here's what I can tell you about blahtex's behaviour. The \mbox command is treated very similarly to \text. Pretty much the only difference is some fiddly stuff to do with text sizes. So in x_{\mbox y}, the "y" is the same size as the "x", but in x_{\text y}, the size of "y" is what you would expect a subscript to be. The arguments of \mbox and \text are both treated as text mode material; so for example whitespace is significant, and you can't use mathematical symbols. (This is also why <mtext> is used.) On the other hand, \operatorname takes a math mode argument; it's supposed to be used for things like \operatorname{sin} when you don't have a shortcut like \sin. Using \operatorname has spacing implications too. Compare the output of \operatorname{lim sup} X, \mbox{lim sup} X and \operatorname{lim\,sup} X. It's still got some bugs, for example \operatorname{sin}\limits_2 doesn't do the right thing, for reasons I don't yet completely understand. Dmharvey 03:13, 5 July 2006 (UTC)

Assuming folks are reading this with the typical PNG output, here's a comparison of subscript options (with a deliberate error message):

input		output
<math>x_{\mbox{Hello world}}</math>		$x_{\mbox{Hello world}}\,\!$
<math>x_{\text{Hello world}}</math>		$x_{\text{Hello world}}\,\!$
<math>x_{\operatorname{Hello world}}</math>		$x_{\operatorname{Hello world}}\,\!$
<math>x_{\operatorname{Hello\ world}}</math>		$x_{\operatorname{Hello\ world}}\,\!$
<math>x_{\mathrm{Hello\ world}}</math>		$x_{\mathrm{Hello\ world}}\,\!$

It should be obvious why I suggest "\operatorname"! (Or perhaps "\mathrm".)

Also keep in mind that the design of MathML mixes "presentation" and "semantics" in peculiar fashion. The distinction between <mi> and <mo> is named "identifier" versus "operator", but it's hard to know what that really means. --KSmrq^T 04:16, 5 July 2006 (UTC)

Possibly <math>x_{\mathrm{Hello\ world}}</math>, which gives $x_{\mathrm{Hello\ world}}$ would be acceptable too.--LutzL 10:08, 5 July 2006 (UTC) || other possibilities: bold face $x_{\mathbf{Hello\ world}}$ , sans serif $x_{\mathsf{Hello\ world}}$ , italics $x_{\mathit{Hello\ world}}$ --LutzL 06:54, 6 July 2006 (UTC)

Worth noting. I've added it to the table. --KSmrq^T 19:24, 5 July 2006 (UTC)

The problem is that neither \operatorname nor \mathrm is the right font for textual identifiers; it is a shame that texvc only accepts operatorname. It looks like there is nothing that can be done until if and when BlahTeX is implemented. Then <math>x_{\text{Hello world}}</math> will work. CMummert 12:10, 5 July 2006 (UTC)

I'm not sure what you're hoping for as the "right font". Within MathML I believe it could be inherited from the surrounding document, giving a sans-serif font like Arial. Within TeX, that's not going to happen. And even if that's fixed, we already have a mix of fonts for variables, serif within TeX and sans serif in wiki markup.

I remind you that, although it does not choke BlahTeX, usage like

<math>x_{Hello world}</math>, producing $x_{Hello world}\,\!$

is still rampant. --KSmrq^T 19:24, 5 July 2006 (UTC)

Boy do I hate that, using words and text in variable-mode. I see

D i f f (M)

a lot for diffeomorphism group,

h o m (a, b)

for hom-sets, etc. -lethe ^{talk +} 18:38, 6 July 2006 (UTC)

Mathematics Templates

I'm not that good at creating/organizing templates, but I'd like to throw out the idea that using templates in mathematics-related articles would be quite helpful/unifying. There could be an overall Template:Mathematics which includes every topic from elementary algebra to knot theory; we could also make individual topic-related templates such as Template:Calculus. So far as I can see, there are currently very few mathematics templates, with apparently only one in Category:Mathematics templates and a handful in Category:Mathematics navigational boxes. 66.229.182.113 09:03, 6 July 2006 (UTC)

For my part, I don't like linkfests or find them helpful; we had some a while ago, and deleted them after consideration as random collections of articles. Septentrionalis 18:39, 6 July 2006 (UTC)

The template Template:mathematics-footer may already provide what you're looking for. -lethe ^{talk +} 18:48, 6 July 2006 (UTC)

I agree with Septentrionalis, one should keep templates small and use them very sparingly. Templates can be distracting linkfarms in many cases. Oleg Alexandrov (talk) 18:55, 6 July 2006 (UTC)

I am not sure but I think it may be useful to have infoboxes for theorems, inequalities, conjectures, lemmas, mathematicians. (Igny 21:12, 6 July 2006 (UTC))

I would strongly disagree with any of that. I don't quite understand what you mean by infoboxes, but from what I can tell they will just amount to more clutter. Oleg Alexandrov (talk) 22:08, 6 July 2006 (UTC)

I just would like to say that many people have infoboxes, see Abraham Lincoln, Isaac Newton, Friedrich Nietzsche (note the nice infobox the philosophers have), Blaise Pascal; but not so many mathematicians are with infoboxes, see Friedrich Bessel, Andrey Kolmogorov, Henri Poincare, Fermat etc. (Igny 02:56, 7 July 2006 (UTC))

I see. I thought infoboxes are some kind of glorified templates allowed to be transcluded on hundreds of pages. I agree now that they could be useful, although the danger of creating unnecessary clutter is still there. Oleg Alexandrov (talk) 03:20, 7 July 2006 (UTC)

Additive Group

Can someone look at Additive group and clean it up. It's marked as a disambiguation page. --Usgnus 18:20, 6 July 2006 (UTC)

And so it ought to be: it is a disambiguation page. It links to three different articles which are in three different branches of mathematics, and all of which could be the topic for additive group. If you mean Abelian group, written additively, go there. Septentrionalis 18:37, 6 July 2006 (UTC)

It's marked for disambiguation cleanup. --Usgnus 18:41, 6 July 2006 (UTC)

Oh, so that means it doesn't conform to Wikipedia's disambiguation page norms. Well I'm not sure what those norms are. Perhaps this request should go to Wikipedia talk:WikiProject Disambiguation instead, seems like more their cup of tea. -lethe ^{talk +} 18:46, 6 July 2006 (UTC)

(Edit conflict) Yeah, I'm not sure what the problem is. I don't see a need for an article about additive groups. On the other hand, I might support redirecting additive group to abelian group, so long as the latter article had a segment about underlying additive groups and other additive group functors. -lethe ^{talk +} 18:43, 6 July 2006 (UTC)

I'm asking for help here because the last time I tried to clean up a mathematics-related "disambiguation" page, I was scolded. --Usgnus 18:55, 6 July 2006 (UTC)

Ha! Asking mathematicians to disambiguate is asking the fox to guard the chickens. We even have a little ritual phrase, "by abuse of notation", to cover some — but by no means all — of our wanton ways. Anyway, since you don't want to offend anyone who is passionate about one of the meanings as being "the right one", asking for participation in such edits is wise. --KSmrq^T 20:38, 6 July 2006 (UTC)

The {{disambig-cleanup}} tags are an unnecessary evil, a policing of format by editors who often don't understand the subject matter. The complaint here seems to be that each line of a dab page should link to an article for that meaning, if one exists, and ideally there should be no other links. I have revised the format; I trust that will do. Septentrionalis 20:22, 6 July 2006 (UTC)

Huh? Did you miss to save your edit? It's still in the unwanted many-links-per-line format. --Pjacobi 21:03, 6 July 2006 (UTC)

No, I intentionally left some links, because those terms may not be clear to the dabber. I see the link to addition has been restored, which is probably unnecessary. Septentrionalis 02:19, 7 July 2006 (UTC)

Thanks for your help, Septentrionalis. --Usgnus 21:11, 6 July 2006 (UTC)

I'm confused about these definitions, and currently none of the links point to anything about the first term additive in the definition. So from the article I can know that an additive group can be a group, ring, field, or functor, but nothing about additive apart from its and addititive group if we choose to call it such.

Consider a deliberately perverse example. Take the multiplicative group of non zero integers. Instead of writing × for the symbol write +. Now by the first line this staisfies the definition for an additive group, even though it has a very different structure.

The mathworld article has a stricter definition for the first line, (identity must be called zero and the inverse written as -a) and is much more extensive. I'd suggest making the page a real article rather than a disambig. Either that or just redirect to group. --Salix alba (talk) 19:16, 7 July 2006 (UTC)

Point of detail: in your example, do you mean the integers, or the rationals? (The details of the answer will be different if the group is {-1,1} or the non-zero rationals). But the gist is the same: yes, I'd call that perverse; but I'd also call it an additive group. Septentrionalis 19:28, 7 July 2006 (UTC)

I would support a redirect (but to abelian group, not to group). In fact, it used to be one. Charles Matthews changed it to a disambig. Maybe he can offer some arguments why we need that disambig. As for making it an article in its own right, I don't support that. There's nothing to say about additive groups that isn't actually a statement about abelian groups, right? -lethe ^{talk +} 19:41, 7 July 2006 (UTC)

Probably my fault for scolding User:Usgnus. There have been cases where editors, who are not very good at math, have been marking various pages as needing merges or splits or disambiguation, etc. These show up on cleanup project pages, whereupon other editors, who know nothing at all about math, attempt to do a good deed, and perform the recommended split/merge. And make a mess, because the article should not have been tagged in the first place. I caught one such in progress and pseudoscalar, and posted some nastygrams recommending that this project be contacted first .. which is what Usgnus did. linas 03:43, 9 July 2006 (UTC)

new article: algebraic equation

I'm not sure the definition given is that widespread. Seems a bit too restrictive. Author gives Mathworld as a source. Please comment at Talk:Algebraic_equation. Dmharvey 20:16, 6 July 2006 (UTC)

Nice double arrows

I just figured out how to do nice looking double arrows in texvc exact sequences. Here is a demo:

${\mathcal F}(U)\rightarrow\prod_i{\mathcal F}(U_i){{{} \atop \longrightarrow}\atop{\longrightarrow \atop {}}}\prod_{i,j}{\mathcal F}(U_i\cap U_j).$

The point is to put some phantoms above the top arrow and below the bottom arrow which apparently forces the arrows to space more closely together. I also did a native TeX diagram for splitting lemma this way, using names for the arrows. I hope someone finds this useful. - Gauge 00:26, 7 July 2006 (UTC)

Of course what you really want is this... Dmharvey 01:24, 7 July 2006 (UTC)

I noticed that the character ⇉ looks too short and stubby in MathML compared to the png output. It doesn't rescale when I change the text size either. Maybe it's because I'm missing the Symbol font? I still haven't found a reasonable explanation of how to get Symbol to work on my Gentoo box. I successfully installed all of the others required for MathML. Running Firefox 1.5.0.4, of course. - Gauge 04:11, 7 July 2006 (UTC)

It sounds like a font thing, but it might also be a problem with Firefox's scaling code. It knows how to stretch some operators but not all. Dmharvey 22:04, 7 July 2006 (UTC)

Regular number up for deletion

Please comment at Wikipedia:Articles for deletion/Regular number. --Trovatore 16:52, 7 July 2006 (UTC)

That article was deleted, but there is a genuine (and different) concept here; so I wrote a new one. Weissstein got it wrong. If anyone insists on AfD'ing the new article, fine; we can discuss it there. Septentrionalis 21:42, 13 July 2006 (UTC)

I think this one should be fine; I made a mistake in my MathSciNet search the first time and missed a few references to sexagesimal numbers, Babylonians, etc. There appear to be six articles (with only one by Sachs), which while not overwhelming, is probably more than enough, going by the usual standard. There are more or less the same number of hits for other definitions of regular numbers though, in number theory, group theory, etc. So it may be best to create a disambig page for "regular number". --C S (Talk) 23:11, 13 July 2006 (UTC)

The Bernouilli-number definition I would put at regular prime; what are the others? But it may be simpler if we write Regular number (disambiguation) and then decide on what goes where. Septentrionalis 02:26, 14 July 2006 (UTC)

A regular number can refer to the order of a regular element of a finite reflection group; Springer is apparently the name here. Actually, looking up "Springer" and "Regular element" brings up a lot more hits; I imagine regular number is mentioned much more often in the actual articles, rather than in the MathSciNet reviews. Springer's 1974 article "Regular elements of finite reflection groups" already defines regular number in that context. There are also k-regular number fields; here, the usage may be different, but is similar enough to require some disambiguation in my opinion. There's also several other usages that appear in a MathSciNet search for "regular number", but it's hard to tell how common they are (as it shows up only if it's in the title or review). So it looks like there is some work to be done here. --C S (Talk) 16:16, 14 July 2006 (UTC)

Scalars

A proposal to merge Scalar has turned into a protracted discussion of whether or not the term 'scalar' means the same thing in different disciplines. See Talk:Scalar. --Smack (talk) 05:13, 10 July 2006 (UTC)

Gosh Numbers

(copied from Portal talk:Mathematics)

Wikimathematicians, if you are interested, please help determine this afd discussion about Gosh Numbers. Thanks! Bwithh 04:40, 10 July 2006 (UTC)

AFD listings

The following articles have been listed at AFD and not picked up by the current activity 'bot:

Basic matrix (mathematics) (AfD discussion)

Please contribute to the discussions. Uncle G 23:18, 10 July 2006 (UTC) The following articles have been listed at AFD and not picked up by the current activity 'bot:

Maths A (AfD discussion) (including Maths B and Maths C)

Please contribute to the discussions. Uncle G 13:17, 18 July 2006 (UTC)

sextic equation

A microstub of dubious utility. AfD? -lethe ^{talk +} 06:19, 12 July 2006 (UTC)

It was already (correctly IMO) changed to a redirect. However, alternatively, we could snatch [31] from PlanetMath if anyone can confirm the veridicity of the information. AdamSmithee 07:53, 12 July 2006 (UTC)

Arthur Rubin for admin

I nominated one of us, Arthur Rubin, for administrator. If you are familiar with Arthur's contributions, and would like to vote, see Wikipedia:Requests for adminship/Arthur Rubin. Oleg Alexandrov (talk) 04:38, 13 July 2006 (UTC)

I definitely will. RfA is the biggest popularity contest these days and it seems that scientists and mathematicians aren't very popular amongst the general public. See Wikipedia:Requests for adminship/Edgar181 to see what I mean - some people who do 2000 small edits and write 1 article get twice as many votes. Blnguyen | rant-line 04:45, 13 July 2006 (UTC)

I disagree about scientists and mathematicians. It seems to me that most of them sail through RfA without hardly a sideways glance. -lethe ^{talk +} 22:44, 18 July 2006 (UTC)

In any event, Arthur Rubin was promoted to administrator a few minutes ago with a 99/2/3 final tally. CMummert 02:40, 20 July 2006 (UTC)

User:Tokker and ...illions of redirects

He's created approximately 200 redirects from names of large numbers to Jonathan Bowers. Any chance a mathematically inclined admit could delete these, or at least automate the RfD script.... — Arthur Rubin | (talk) 05:17, 14 July 2006 (UTC)

It looks to me like the page Jonathan Bowers is a candidate for deletion:

It has a lot of unsourced material which I doubt is verifiable
It is a biography of a non-notable person.

Also Bowers style acronym looks like original research. CMummert 12:49, 14 July 2006 (UTC)

Good idea. I've alraedy summarily deleted the names of the large numbers and the notations for creating large numbers from the article, as naming things and re-creating notations are not notable unless the new notation catches on. I'm investigating whether the Polychoron family should be deleted as well, as being a neologism, not used in professional mathematics. (15 of the first 20 examples of the netscape search for "polychora" are Wikipedia, Bowers' site, or MathWorld. The other 5 may be from one of the other members of the Uniform Polychora Project. I've contacted a professional recreational mathematician named in one of the articles for further information.) — Arthur Rubin | (talk) 14:44, 14 July 2006 (UTC)

The word "polychoron" would not appear in classic Coxeter because it is more recent. We use 4-dimensional polytopes often enough that it is helpful to give them their own name. Both Johnson (of Johnson solids) and Olshevsky were students of Coxeter, which lends a certain amount of credibility to what they say. Here's the story of the name, as reported by Olshevsky on his web site:

POLYCHORON (plural: polychora) is my term for a four-dimensional polytope, analogous to polygon in two dimensions and polyhedron in three. The only other names for such a figure that I had seen in the literature, “polyhedroid” and “hypersolid,” seem uninspired and inappropriate, because they’re too close to terms for three-dimensional polytopes; the ending -oid connotes similarity or resemblance; and the prefix hyper- is badly overused. A four-dimensional polytope resembles a polyhedron no more than a polyhedron resembles a polygon, so it should have a similarly distinctive root following the poly-. The Greek root choros means “room,” “place,” or “space,” describing the three-dimensional polytopes, or cells, that make up the polychoron. In early versions of this website, I called such a figure a polychorema (plural: polychoremata), but Norman W. Johnson persuaded me of the benefits of the shortened form, and I changed this document everywhere accordingly.

Therefore "polychoron" is relatively new, but that doesn't mean it isn't also respectable. Remember that “polytope” itself was a neologism of Alicia Boole Stott before it was popularized by Coxeter. A possible contact to assess academic acceptance of the name might be computational geometry expert David Eppstein, a professor at UC Irvine famous for his Geometry Junkyard pages. Another academic contact might be Brown University professor Tom Banchoff, well known for his interest in things four-dimensional.

My impression is that although neologisms are rampant among enthusiasts, this term has gained traction and has been around long enough that it will probably persist. --KSmrq^T 20:01, 14 July 2006 (UTC)

Our article says that Coxeter uses polytope; unless there is some differentiation for polychoron, there is probably consensus against it. The images and facts should probably be salvaged. Septentrionalis 16:39, 14 July 2006 (UTC)

If polychoron is strictly dimension 4, that is the required difference. Septentrionalis 21:59, 14 July 2006 (UTC)

Even if I were an admin (see the above nomination), I'd need help keeping up with these. Someone is creating separate articles for the sections I deleted from Jonathan Bowers, and creating more pieces. (Is there something I could put in my .js which would, with a single click, add an {{rfd}} to the above redirect, and add it to a list in a user subpage so I could copy the list to WP:RfD. This is would be tiring.) — Arthur Rubin | (talk) 17:02, 14 July 2006 (UTC)

I don't think those redirects are actually that bad. Having them makes it less likely that someone will create stub entries on those numbers. It's kind of like the redirects we have at names of large numbers, which otherwise people would create stub articles on those numbers. Voortle 17:26, 14 July 2006 (UTC)

If those redirects are original research, they should be deleted also. Oleg Alexandrov (talk) 17:31, 14 July 2006 (UTC)

Dear Lord [32]. I suggest a massive speedy delete campain. Any comments on that? Oleg Alexandrov (talk) 17:27, 14 July 2006 (UTC)

Wikipedia:Articles for deletion/Other names of large numbers dealt with this issue, and the decision was to delete back them. Oleg Alexandrov (talk) 17:29, 14 July 2006 (UTC)

Yeah, redirects to other names of large numbers should be deleted, as that page doesn't exist. However, redirects from -illion names are not bad, because they prevent someone from creating stub articles on these numbers. Voortle 17:32, 14 July 2006 (UTC)

Redirects to other names of large numbers should be deleted, as that page shouldn't exist. Redirects to Bowers' names of large numbers are just as bad. — Arthur Rubin | (talk) 17:41, 14 July 2006 (UTC)

I don't think it would be any great loss to delete all of these. Paul August ☎ 17:52, 14 July 2006 (UTC)

Nominate for deletion all Jonathan Bowers related pages?

Is Jonathan Bowers that important a person? To me he appears to be a crank, and not even notable at that. How about nominating for deletion his page and all his other stuff? Oleg Alexandrov (talk) 17:37, 14 July 2006 (UTC)

Anyone got a script? I think we need to delete most of the Polychoron pages, and the other people linked from Uniform Polychora Project. — Arthur Rubin | (talk) 17:41, 14 July 2006 (UTC)

I would agree with deleting the whole lot. I don't believe they enhance wikipedia at all. Madmath789 17:44, 14 July 2006 (UTC)

Note that Oh Crap (talk · contribs · deleted contribs · logs · block user · block log) has created a malformed AfD for Jonathan Bowers and L. Craig Schoonmaker. Is there any way to separate them. (The issues are not related.) — Arthur Rubin | (talk) 18:05, 14 July 2006 (UTC)

See Wikipedia:Articles for deletion/Jonathan Bowers. Oleg Alexandrov (talk) 18:07, 14 July 2006 (UTC)

STOP! First off lets look at the members of the Uniform Polychora Project among them was the late Norman Johnson a student of Coxeter, and perhaphs one of the most important recient figures in the field of polyhedra, having created the Johnson solids, and also the nicest way of classifying the uniform polyhedra List of uniform polyhedra by vertex figure (Johnson, N. W. Uniform Polytopes. Cambridge, England: Cambridge University Press, 2000). So Johnson then went onto study the four dimensional polyhedra and enlists the help of various amature mathematicians, Bowers being one of them. Bowers is responsible for discovering most of the uniform 4D polyhedra and as discoverer probably gets the naming rights. Bowers names are probably becoming the defacto standard for 4D uniform polyhedra, considerably more pratically useful than the long names (First due to Coxeter, modified by Wenninger and later by Johnson). So we have a group resposible for discovering most of the uniform 4D polytopes. So its run by amatures who don't bother to publish in maths journals. Well the whole field of polyhedra is very much dominated by the amature, the most read book on the subject is Wenninger polyhedra models and Wenninger is in an order of Monks, not a professional mathematician.

As for the array notation. I'm not sure but I think is is capable of representing larger numbers than the closest contender Conway chained arrow notation. In my book thats worth a page, published or not. This stuff is important as it has close links to transfinite cardinals, helps us get a feel for the true emensity of natural numbers and is also a good way to bring people into apreciating mathematics, a natural extension of the game of naming bigger and bigger numbers we all played as kids.

I'm less bother about the names of large numbers, although the largest finite number so far conceive by man, seems to be of some interest. Here I'd take a pragmatic approach, we will always be getting people adding these very large names. Theres two options, spend our lives reverting Names of large numbers or keep a seperate out of the way page for these numbers to appear.

To sum up Wikipedia isn't great because it's like the Britannica. The Britannica is great at being authoritative, edited, expensive, and monolithic. Wikipedia is great at being free, brawling, universal, and instantaneous. — Cory Doctorow --Salix alba (talk) 18:11, 14 July 2006 (UTC)

I strongly object to wholesale deletion without closer scrutiny. As I noted above, the name "polychoron" was created jointly by Olshevsky and Johnson, both of whom worked and studied with Coxeter, and both of whom were involved in creating the Uniform Polychora Project. Partly we are confronting a problem of volume and organization: there are too many of these beasts! They can hardly all be well-known, it's a pain to enumerate them, it's a pain to name them, names are still in flux, and so on. Frankly, I doubt many people can name the convex regular polytopes in four-dimensional Euclidean space, or even recall how many there are — and these are surely notable. Or how about the Archimedean solids? Our page lists 13 of them, over half with more than two names! Please, ease off on that trigger finger; don't shoot first and ask questions later. I'd suggest that few polychora deserve a page of their own, and that we surely don't want to duplicate the content of the project; but don't throw out the baby with the bathwater. I'd also suggest it would be absurd to delete the page on Norman Johnson. --KSmrq^T 20:29, 14 July 2006 (UTC)

I'm not in a hurry to delete the polychora; I'm still researching. Mr. Bower and his pet names are not notable. Messers. Olsehvsky and Johnson may be more notable. — Arthur Rubin | (talk) 22:19, 14 July 2006 (UTC)

First, Norman Johnson is not late. He is alive and well.

About Jonathan Bowers and polychora, I am familiar with his work and have met him at a conference. I am also acquainted with Olshevsky, and know Wenninger and Johnson fairly well. Jonathan Bowers would be classified as an amateur mathematician, but has an astounding ability to work with four-dimenionsal figures. He can sketch three-dimensional cross-sections of polychora as easily as I might sketch, say, an equilateral triangle.... He is in close contact with Johnson, and Johnson is trying to incorporate Bowers's work into an upcoming book to be published by Cambridge University Press.

User Tom Ruen is also working on the Wikipedia pages on polychora.

This group is at the forefront of work on polychora. The project is to enumerate all uniform polychora in four dimensions. The problem of enumerating the 75 uniform polyhedra in three dimensions was solved only in the 20th century and has an interesting history. I think it is reasonable to assume that any work done in the area (in 4D) will be known to this group.

I only recently read about Bowers's work on naming large numbers. I think that subject should be discussed independently of his work on polychora.

I would argue that Jonathan's work is legitimate, even though he doesn't have appropriate 'credentials.' You might not wish his work in the Wikipedia for other reasons, but it is certainly not spurious. Vince Matsko 21:10, 9 August 2006 (UTC)

The work is legitimate. The classification theory seems notable enough; however his naming conventions (both for large numbers and for polytopes), any of the individual names that have articles, and the term "polychoron" may need to be removed, unless some legitimate geometer publishes those names. — Arthur Rubin | (talk) 00:55, 10 August 2006 (UTC)

Evolution of an article!

I am still fairly new to wikipedia, and I would really appreciate a view from a more experienced wikipedian about the evolution of the article Homogeneity. I have looked at the history of this article over the last year or so, and it seems to have 'evolved' in an extremely strange way. Please take a look at the Revision as of 07:02, 10 February 2006, and compare with the Revision as of 08:34, 10 July 2005. What on earth is going on here??? I am totally baffled by the latest incarnations of this article, but if more experienced editors tell me it is OK, I will accept their wisdom ... Madmath789 22:47, 14 July 2006 (UTC)

It looks like an editor decided that there is basically only one meaning for "homogeneity", i.e. its use in statistics, and then proceeded accordingly. --C S (Talk) 10:50, 15 July 2006 (UTC)

Yes, indeed, but I can't make much sense of the article as it stands, despite being a reasonably competent mathematician with a fair knowledge of probability and statistics! I am also a little suspicious of the possibility of OR here, as much of the editing of Homogeneity and a linked article Reliability (statistics) seems to have been done by David Cruise or by Cruise, and a couple of external links from Reliability (statistics) point to 'visualstatistics.net (e.g. The problem of negative reliabilities ) which seems to be authored by David J. Krus / Cruise scientific. I might be off-beam, but I am very suspicious of these articles. Madmath789 11:37, 15 July 2006 (UTC)

Yes I agree the article does look very out of ballance. Go ahead and bring it back into line. --Salix alba (talk) 11:53, 15 July 2006 (UTC)

Apart from the present article being whacky, I also think that Homogeneity (instead of Homogeneous) should be a disambiguation page, with Homogeneous a plain redirect to Homogeneity, and the statistical concept being handled at Homogeneity (statistics), which now redirects to Homoscedasticity, a different concept in statistics. --Lambiam ^Talk 12:34, 15 July 2006 (UTC)

Whacky indeed! I have spent some time trying to decide if this article homogeneity is genuine or totally off-the-wall. Can I make a plea: if anyone here knows more than I do about this sort of statistics, could you please advise as to the validity of this weird-looking stuff? Madmath789 16:56, 16 July 2006 (UTC)

Greek letter proposal

Please see my proposal for Greek letters at Wikipedia talk:WikiProject Mathematics/Conventions CMummert 23:27, 15 July 2006 (UTC)

Computability Articles

JA: User:CMummert is making a mass of what appear to be improper page moves, renames, and reorgs to computability related articles. Could somebody please sort all that out and makes sure it's by the book? Thanks, Jon Awbrey 15:58, 16 July 2006 (UTC)

What I've seen looks legit to me. --CSTAR 16:23, 16 July 2006 (UTC)

I would be glad to explain, if anyone asked me; one the other hand, I am an expert in the area. For a while, there have been two articles: Computable function and Recursive function. These titles are synonyms in the current vernacular, and having them as separate articles is confusing. I have moved Recursive function to Mu-recursive function which is the consensus on what that article is actually about. I made Recursive function into a disambiguation page, which is important because there is a CS meaning for the term that was not reflected on the previous page. Then I chased almost all the things that linked to Recursive function. Many of them actually wanted to link to Recursion or Recursion (computer science); the previous page had no relation to the material in articles that were linking to it! So I fixed many of the links to Recursive function to point to a more helpful location. I also made a start towards fixing Mu-recursive function. CMummert 16:35, 16 July 2006 (UTC)

STIX Fonts update

Many of us have been eagerly awaiting the culmination of the STIX font project. A major milestone was recently announced.

On 10 July, the STI Pub group received the final delivery of requested glyphs for the STIX Fonts Project. This final set is being reviewed by the STI Pub Technical Review Committee, and packaging instructions for the beta test of the fonts are being prepared. Tables of STIX glyphs will begin to appear on this website within the next few weeks, and the beta font set will begin to be constructed.

So far every deadline has been overly optimistic; still, progress has been real. It appears the race is on, between universal adoption of the STIX mathematics glyphs and Wikipedia adoption of BlahTeX! Regardless of which tortoise crosses the line first, we all win. Huzzah! --KSmrq^T 09:47, 17 July 2006 (UTC)

Fleiss' kappa

I don't know if this is the right place to ask about this, but I've been working on Fleiss' kappa, and I'd like to get someone who actually knows what they are talking about to look over it. I have the paper here, but I worked out what is what by trial-and-error because I am pretty much maths illiterate. I'd appreciate it if anyone could look over it, and add {{accuracy}} or something if I've made a mistake. Thanks - FrancisTyers · 16:01, 17 July 2006 (UTC)

See my comments on the talk page of Fleiss' kappa. VectorPosse 22:44, 17 July 2006 (UTC)

Discussion at Category talk:Mathematics user templates

Hi all,

Just wanted some of the editors opinion on a discussion I started at Category talk:Mathematics user templates. The discussion is about userboxes, a bit technical, but not serious. I don't want to advertize, but the fact is that in most cases, category pages are usually watched by the creators only, and probably even worse in this case, only be the sysop who moved the category. Thanks, — Ambuj Saxena (talk) 17:17, 18 July 2006 (UTC)

Homogeneity

The 'whacky' article Homogeneity is up for deletion - please take a look and comment at Homogeneity. I think it really needs looking at by a statistician. Madmath789 06:33, 20 July 2006 (UTC)

Following some moves by Michael Hardy, the AfD seems to have vanished, and the material I was worried about now lives at homogeneity (statistics) - does anyone see a good reason for not having an AfD discussion about this stuff? Madmath789 15:11, 20 July 2006 (UTC)

I've now listed a new AfD at Wikipedia:Articles for deletion/Homogeneity (statistics) and voted speedy keep on Homogeneity, previous votes have been copied across. --Salix alba (talk) 16:22, 20 July 2006 (UTC)

User:David Cruise

I would like someone with experience look at edits made by User:David Cruise, User:Cruise, and also IP 65.39.86.104 ([33]) to the mathematical articles, in particular, Supermatrix, matrix addition, matrix subtraction, canonical analysis, homogeneity (statistics) (this article is currently listed at AfD and this actually triggered my interest in the user Cruise) and probably many other articles as well. Note references to Krus' publications and links to Cruise Scientific ([34]), also note many links from Cruise Scientific (see for example, [35]) to the Wikipedia articles in question. I would like someone to sort out contributions with scientific value from original research. (Igny 18:21, 21 July 2006 (UTC))

I have only looked at the article on matrix addition, but it certainly has all the earmarks by being hijacked. Alterations include non-standard definitions and notation, as well as self-promoting links. --KSmrq^T 19:41, 21 July 2006 (UTC)

I think I am responsible for bringing this to peoples attention, but I have "trodden carefully" as a comparative newcomer to WP (but a comparative 'old-comer' to maths!). I have been looking at the things mentioned above for a few days, and have to say that I believe that most of the content of the articles Homogeneity (statistics) and Canonical analysis are mathematical gibberish, and the matrix stuff is probably nonsense (I have seen many examples of such over the last 4 decades, but these examples are quite staggering!). I do not wish to appear to be waging a vendetta against any contributor to WP, but I have to say that I cannot find anything worth keeping in the previously mentioned articles, and feel that trying to rewrite them would best be done by deleting everything and starting from scratch. Madmath789 20:54, 21 July 2006 (UTC)

I don't think the material at canonical analysis is nonsense, but it is not clearly explained in a manner that makes it comprehensible to mathematicians in general. Similarly at homegeneity (statistics). Michael Hardy 22:29, 22 July 2006 (UTC)

Our discussions here may become academic, as User:David Cruise seems to be trying to blank contributions he has made - see for example: Canonical analysis. I know I have been a harsh critic of some of his contributions, but I am unsure if this is the right way to proceed. What do others think? Madmath789 16:56, 23 July 2006 (UTC)

Ones contributions are an irrevokable gift (if they are not an infringment of someone else's copyright). So we are free to resurrect them by reverting his deletions. Also we should take care that he does not also delete the contributions of other people. But perhaps any such corrections should be done only after he has been blocked so that he will not commit more such vandalism. JRSpriggs 03:16, 24 July 2006 (UTC)

Blatant spam is of course not needed. But as for 'nonstandard stuff', I don't take stock in nonstandard stuff, because doing stuff in a non-standard way can lead to new ideas. As for matrix addition and matrix subtraction, I reverted one of the articles back to the way it was with his changes, and later removed some spam-like stuff from references and external links. I ask someone who knows more than the textbook definition of matrix addition/subtraction that I do to look over whatever new matrial he put in, save actual methodology that works and is substationally useful. I'm not so sure such a lengthy section is needed on a particular application of matrix subtraction, for example, involving variance. Kevin_b_er 04:45, 24 July 2006 (UTC)

David Cruise's additions to matrix addition and matrix subtraction are probably correct (though they are badly explained, so I can't be sure of that). However, his definitions are not used in the field of matrix theory. They may well be used in statistics or social sciences, but all we have are some papers written by D. Crus in nonmathematical journals. In contrast, the standard definitions are in every linear algebra textbook. I do not think that "doing stuff in a non-standard way can lead to new ideas" is a good reason for including nonstandard definitions in an encyclopaedia. I think that the nonstandard material to these two articles should be removed, or at least greatly reduced, unless somebody tells us that these definitions have found widespread use in some disciplines. -- Jitse Niesen (talk) 05:13, 24 July 2006 (UTC)

I noticed that David Cruise just vandalized two sections of this very talk page. From the history:

11:52, 25 July 2006 Gandalf61 (Talk | contribs) (rv blanking)

11:48, 25 July 2006 David Cruise (Talk | contribs) (entries containing libellous statements)

Fortunately, Gandalf61 reverted the vandalism. I think that the first administrator who reads this should immediately block David. JRSpriggs 06:02, 26 July 2006 (UTC)

I was considering asking an admin to look at this myself, in view of his blanking of parts of this page, and also his removal of the AfD notice (and other stuff) from Homogeneity (statistics). I am aware, though, that he has also made contributions from another account User:Cruise (not active since 17th April) and might use that one while blocked. I will keep an eye on it. Madmath789 08:13, 26 July 2006 (UTC)

I haven't been around much, so I don't know the details, but a single blanking at this page, while unacceptable, is probably not sufficient to block. I've placed a warning on his talk page. If his behavior continues, a block can certainly be considered. By the way, if we do decide to block, using sockpuppets is grounds for blocking the second account, so that's not a problem. -lethe ^{talk +} 08:18, 26 July 2006 (UTC)

As I understand things, he has already been given a one week block by User:IanManka. Madmath789 08:27, 26 July 2006 (UTC)

Terminology clarification and first use references: "Hypercomplex Number"

Hello,

I'm currently trying to clarify the use of the term "hypercomplex number" over the years and to-date. The goal is to update the hypercomplex number article. Since this may result in a rewrite, it would be great if any ideas or comments could be posted in talk:hypercomplex number, so the reasoning behind a potential rewrite would remain with the article.

Thanks, Jens Koeplinger 21:27, 22 July 2006 (UTC)

PS - It may be that the term "hypercomplex number" is to-date a rather freely used term, like "numbers with 2 or more dimensions and at least one non-real axis". If so, I'll scratch together what I can find in some common places (here, mathworld) and rewrite hypercomplex number in a fashion that puts different systems into different categories (like Cayley-Dickson, split-complex, etc). Thanks, Jens Koeplinger 13:28, 24 July 2006 (UTC)

I've just posted a rewrite of the hypercomplex number article. While I tried to carry over all previously existing information and statements into the new version, it now contains much more detail and categorization. I would appreciate any comment or help. Thanks, Jens Koeplinger 22:29, 31 July 2006 (UTC)

Hello; I haven't received much feedback yet about the hypercomplex number rewrite, so I figure it can't be too bad. There are two obvious weeknesses: "The term hypercomplex number has been used over the years rather freely ..." - if anyone knows about references to be added, please do so. I've seen two more book titles mentioned in the internet, but I'm reluctant to referring to books or titles I didn't read. Without references, my statement has no support within the article.

The second weakness is that I'm writing about "Arguably the most common use of the term hypercomplex number [...]" and only provide links to some other numbers. I'm comfortable with this wording, but to the least I'd like to add a section that groups together these 'arguably not so common uses' of the term "hypercomplex number" (surreal, hyperreal, transfinite, superreal nubers, and - as I recently learned - Mark Burgin's hypernumbers which appear not to have an article in Wikipedia yet).

Maybe we could tailor the "hypercomplex number" article into an overview over all number systems that somehow go beyond or extend the reals. This might help to have the current number article focus on commonly used systems (from natural to complex numbers), and clean-up references to other less frequently applied numbers.

But first I'd like to put the "hypercomplex number" article on better feet, and remove the 'stub' notice once done. Any comment is greatly appreaciated. Thanks, Jens Koeplinger 12:40, 8 August 2006 (UTC)

Good articles

While trying to expand the list of important articles in Wikipedia:WikiProject Mathematics/Wikipedia 1.0, I've come across a few articles I feel are close to Wikipedia:Good articles status and nominated them appropriately. of these Euclidean geometry, Georg Cantor and David Hilbert has reached GA status. Pi, Fractal, Gottfried Leibniz, Ronald Fisher have failed. Fractal needs someone to check recent additions made by reviewer, Leibniz needs some work organising the references and Pi and Fisher needs more extensive work. If anyone would like to have a look at these articles it should not take much to gain GA status. --Salix alba (talk) 09:47, 23 July 2006 (UTC)

84.40.138.111 (talk • contribs • deleted contribs • WHOIS • RDNS • trace • RBLs • http • block user • block log) and -http://www.apronus.com/provenmath/ links

We've got a new IP address adding external links to the above mentioned web site. I'm tempted to revert en mass, but I'd like a second opinion. — Arthur Rubin | (talk) 17:52, 24 July 2006 (UTC)

I had just noticed this too, and I agree the links don't belong here. Dmharvey 18:36, 24 July 2006 (UTC)

Yes, noticed them earlier, and find them hard to read (but they may well be valid) - the notation used on that website is 'tedious' to read - see [36] I agree they don't belong here. Madmath789 21:19, 24 July 2006 (UTC)

If I read this page correctly, they claim to have their own proof of the equivalence of Zorn's Lemma and the Axiom of Choice; I hope I'm being unfair, but... What next, the Pythagorean Theorem? Septentrionalis 23:03, 24 July 2006 (UTC)

Proving induction

Please take a look to the article proof of mathematical induction. As a consequence of a remark of mine [37] an editor made some addition to the hypothesis of the proof to make it work. I would like to understand if this proof is "standard" (it should be other wise would be original research) and what is his original form (in particular which hypothesis should we require). What do you think?--Pokipsy76 15:41, 23 July 2006 (UTC)

The concept of "proving" induction is strange. Typically we use an axiom scheme that explicitly states that induction works. A quick glance at this leaves me feeling that it's a bad article. --KSmrq^T 19:02, 23 July 2006 (UTC)

The concept of proving the principle of mathematical induction is certainly not strange - it is a well-known part of mathematical logic and the development of the number system logically. The article might need a bit of work, but the idea is good. Madmath789 19:15, 23 July 2006 (UTC)

I'm not quite sure what you mean by "proving". For example, here's a quote from Peano axioms:

Informally, the Peano axioms may be stated as follows:

0 is a natural number.
Every natural number a has a successor, denoted by Sa or $a'$ .
No natural number has 0 as its successor.
Distinct natural numbers have distinct successors: a = b if and only if Sa = Sb.
If a property holds for 0, and holds for the successor of every natural number for which it holds, then the property holds for all natural numbers. This axiom of induction legitimizes the proof method known as mathematical induction (induction over the naturals).

I draw your attention to the last item. Essentially it says we "build in" induction; we don't deduce it. Although there are many ways to approach foundations, I don't think we can avoid something along these lines; natural numbers and induction are inseparable. If natural numbers are defined per Peano this whole proof article is silly. If not, the article is confusing; it's not clear where we're beginning, nor exactly what is being accomplished.

If we are going to discuss the article further, we should do so on its talk page. --KSmrq^T 23:19, 23 July 2006 (UTC)

Proving just means deduction from axioms. Clearly, in PA, mathematical induction is an axiom, but in developing maths from ZFC, it is not an axiom, so it needs to be proved from the axioms. Madmath789 06:51, 24 July 2006 (UTC)

I have to agree with both KSmrq and Madmath: The idea of proving the induction principle is not "strange" in itself, and yet the article in question is a bad article (and I have my doubts that any article with that title would be good). Induction is not assumed explicitly in, say, the usual formulations of ZFC, and can be proved once you've defined the naturals. But there's less here than meets the eye; it's a boring technical detail rather than something particularly significant, and having an article about it might give the misimpression that there's something fundamental being done. The existing article is worse than that; it starts with the assumption that the naturals are wellordered. From there the induction principle really is a triviality. --Trovatore 19:56, 23 July 2006 (UTC)

It's not clear to me in which sense can we be supposed to prove induction principle from the well ordering assumption: the well ordering itself is useless unless we have some extra assumption to work with (for example the assumption that x#0→x=y+1)--Pokipsy76 20:04, 23 July 2006 (UTC)

I gave that article a prod. -lethe ^{talk +} 20:37, 23 July 2006 (UTC)

Maybe you could have waited a little bit to let us discuss about it before going to vote.--Pokipsy76 20:55, 23 July 2006 (UTC)

Prodding does not involve a voting process. We have ample time to discuss this. --Lambiam ^Talk 00:39, 24 July 2006 (UTC)

Are you sure? Look here.--Pokipsy76 20:59, 24 July 2006 (UTC)

The PROD, which involves no voting and can be halted in an instant, was forced into AfD, which requires voting and admin participation. The official decision was no consensus. My unofficial summary of the comments: the article needs improving, and probably the proof should be merged into the parent article. It would be nice for one of the "keep" voters (Pokipsy76?, Ryan Reich?) to volunteer. --KSmrq^T 00:18, 1 August 2006 (UTC)

Done. I "morally" merged the article; the actual material in it was sort of long-winded. I also put in the stuff on transfinite induction and included a reference to Kolmogorov and Fomin. The original proof article remains, with a {{merging}} tempate added. Ryan Reich 02:23, 1 August 2006 (UTC)

Thanks, that's much better. --KSmrq^T 09:56, 6 August 2006 (UTC)

Good. I've changed the old article to a redirect now. Ryan Reich 15:25, 6 August 2006 (UTC)

Articles listed at Articles for deletion

The following articles have been listed at Articles for deletion but not caught by the 'bot:

Wilkinson's polynomial (AfD discussion)

Uncle G 11:54, 25 July 2006 (UTC)

it is now. Septentrionalis 21:25, 26 July 2006 (UTC)

The decision on Wilkinson's polynomial was keep, after a number of editors worked on cleaning it up and clarifying its significance. --KSmrq^T 00:15, 31 July 2006 (UTC)

The following articles have been listed at Articles for deletion but not caught by the 'bot:

Imaginary logarithm (AfD discussion)

Uncle G 17:24, 28 July 2006 (UTC)

The bot runs once a day; it may be preferable either to wait a day and see if it is picked up, or add this to the list by hand. Septentrionalis 22:49, 28 July 2006 (UTC)

The decision on imaginary logarithm was redirect to complex logarithm, agreed unanimously. --KSmrq^T 09:54, 6 August 2006 (UTC)

article variational number theory is back

User_talk:Karl-H has recreated the page. He's also made edits to calculus of variations and number theory among others. Somebody familiar with the subjects and the original RfD might want to take a look. Lunch 19:09, 26 July 2006 (UTC)

Integral equations has been edited too. Lunch 19:14, 26 July 2006 (UTC)

Reverted all of those. — Arthur Rubin | (talk) 21:18, 26 July 2006 (UTC)

Removing the redlinks in the list of mathematicians

Currently the list of mathematicians has a certain number of redlinks. I would argue that that was a good thing when Wikipedia was new and plenty of famous people did not have articles and when there was no bot to maintain that list.

I would think that now we would be better off having the list of mathematicians list articles which actually exist, with redlinks (requests for new articles) going to Wikipedia:Requested articles/Mathematics instead. Removing the redlinks from the list of mathematicians would also make it easier to see what mathematician articles got created/deleted by inspecting the Current activity.

In short, how about removing all the redlinks from the list of mathematicians? Oleg Alexandrov (talk) 20:32, 29 July 2006 (UTC)

I think that's a good idea. Can I also encourage people to add to the requested mathematician list? As a grad student, I'm hesitant to create articles for mathematicians that work at my school. I'd feel more comfortable if they were on the requested list. Thanks. Originalbigj 19:45, 30 July 2006 (UTC)

The bot now removes redlinks from the list of mathematicians (log). Oleg Alexandrov (talk) 23:53, 31 July 2006 (UTC)

It appears that you removed the redlink to Thomas Jech from the list of mathematicians, but did not add it to the list of requested articles on mathematicians. If a redlink is removed from one, I think that it should be added to the other (if not already there). And what if someone destroys the article or moves it to another name? JRSpriggs 03:10, 1 August 2006 (UTC)

Update. I just created a stub for Thomas Jech. I did not see the redlink removal in the log. But I remember creating a redlink for him a month or two back. JRSpriggs 03:27, 1 August 2006 (UTC)

I did not add the redlinks to Wikipedia:Requested articles/Mathematics on purpose, it is not clear if those redlinks are indeed "Wanted" articles.

If an article gets deleted (which only administrators can do) my bot will remove it from the list of mathematicians. If an article gets renamed, the bot will reflect the rename in the list. Oleg Alexandrov (talk) 04:55, 1 August 2006 (UTC)

Oyam's Pyramid

The article Oyam's Pyramid is currently proposed for deletion. It seems to me that it would be likely to be covered by some area of mathematics rather than being a complete hoax, but I've been unable to track down any evidence for its existence with this title. Could somebody take a look and see if a) it's a valid but wrongly-titled article, b)it needs merging or redirecting to some other concept, or c) it's complete garbage. Thanks Yomangani 10:46, 31 July 2006 (UTC)

Since there are no Google hits for any of this (except to Wikipedia), it is definitely made up. In my opinion it doesn't make much practical sense if you actually mean to build a pyramid. (Disclaimer: I have no actual experience in pyramid construction.) Mathematically it seems to be a pointless triviality. --Lambiam ^Talk 23:00, 31 July 2006 (UTC)

Piotr Blass

I was wondering what people thought of the article Piotr Blass and the anon User: 69.163.189.9 who has created it and spent some time inserting the name of Piotr Blass into the articles of several distinguished mathematicians, e.g. Hassler Whitney and Heisuke Hironaka. I spy several dubious claims to fame in the Blass article, e.g. inventing the World Wibe Web. There's also a very interesting assertion that he's the student of a number of famous mathematicians (such as the ones I mentioned prior). Blass is apparently enough of a famous mathematician that the statement that Whitney taught "mathematics education" to Blass is an important thing to include into Whitney's article.

Blass' publication list looks fairly average and is bolstered by a number of publications to a journal that he founded and that I've never heard of. To be fair, I noticed that Zariski surface exists and was created by User:r.e.b.; it appears that Blass named Zariski surfaces and has some papers on them in respectable journals. So I wouldn't advocate a deletion of the Blass article. But it seems there's a lot of what might be called "tooting one's own horn" (if the anon is indeed Blass). --C S (Talk) 17:14, 31 July 2006 (UTC)

A quick google reveals Blass was given Grothendieck's prenotes for EGA 5. [38] So he certainly knew some influential people. There also seem to be proof of editorship of journal [39], standing in elections as a write in candidate (lots of links). Slashdot (that most relaible of sorces) mentions hims in conection with some dubious compression algorithm work with ZeoSync [40]. --Salix alba (talk) 19:35, 31 July 2006 (UTC)

And another quick look at Google Schoolar shows 24 publications mentioning his name, including some on Zariski surfaces. Google Print also gives few hits. On the other hand, the article needs copyedit and other claims ('one of the fathers of the Internet) seem more dubious.--_{Piotr Konieczny aka Prokonsul Piotrus | talk} 02:53, 2 August 2006 (UTC)

I removed links to his name from several well known mathematicians. Math Genealogy lists two advisors: James Milne and Melvin Hochster. Others may have taught him some undergrad classes but anyway this is not notable. Using ip trace I found a clear evidence that he is trying to promote himself and is using WP for political purposes. I actually don't mind (and don't care) whatever is on the page on him but find inappropriate the insertion of his name averywhere. Inventor of WWW is simply laughable (he does give half the credit to Sir. Tim Berners-Lee). Mhym 14:36, 2 August 2006 (UTC)

15 of his 33 publications are in the Ulam Quarterly, which he founded. This journal was founded in 1987; before going defunct in 1997, it published a whopping 10 issues, each of which contains at least one (sometimes two) articles co-authored by Piotr Blass. This journal is, according the journal website, also the first electronic mathematics journal and is apparently the basis for Blass' claim of being inventor of the WWW.

It's not just the WWW claim that is dubious. A number of his achievements listed are suspect. Simply knowing and interacting with famous people is not an achievement. In fact, a number of people do this...that goes hand-in-hand with being famous (a lot of people know and talk to you). Organizing seminars at IAS is not an achievement. Being a member (even visiting), would be.

Blass' claim to fame is doing some of the early work on Zariski surface and naming it. I'm not sure if he's even as notable as Norman Johnson. But like I said, his bio should probably stay, but it needs to be heavily edited by people other than Blass. --C S (Talk) 16:51, 2 August 2006 (UTC)

I got the founding date of 1987 for the journal from the anon/Blass edit, but apparently the first issue came out in 1992 according to the journal website (see contents of first issue) and MathSciNet. I don't suppose this really matters or adds anything except to give a more accurate context for Blass' WWW claim. --C S (Talk) 17:29, 2 August 2006 (UTC)

There is some wonderful dirt on Blass [41]

[42] I don't quite understand it all but it seems to involve a company called CyberNet, 5 Star Trust Bank, kids in abusive treatment center, Diebold. Seems like Blass had evidence of defects in Diabold voting machines, being hacked by kind from Bay Point School correction facility (where he taught), but he withheld information due to ties with an atoney with connections to the republican party (the attony helped Blass get his son out of another correction facility).

So to add to inventing the WWW, we might add Blass was responsible for Bush getting into the whitehouse in 2000. --Salix alba (talk) 18:19, 2 August 2006 (UTC)

AfD it is Wikipedia:Articles for deletion/Piotr Blass. --Salix alba (talk) 19:11, 2 August 2006 (UTC)

Aug 2006

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

Prerequisites

I was reading an amusing interchange on the talk page for Lie groups just now. (Sorry, I don't know how to link to the specific section in the talk page. Maybe someone can help me with that.) Anyway, a user who clearly didn't understand the complexity of Lie group theory was trying to suggest that the page was worthless. This user suggested that the complexity of the article meant that the uninitiated could not follow it and the initiated didn't need it since they knew it already.

While I vehemently disagree with these sentiments, the discussion did lead me to think that maybe we need some system by which we can communicate prerequisites to those seeking information on a topic for the first time. No textbook would ever discuss Lie groups without either mentioning in the preface the need for a solid background in smooth manifolds, or else providing a reasonably comprehensive introduction to the subject in the book itself. I fully realize that Wikipedia is an encyclopedia and not a textbook. Nevertheless, a newcomer to Lie groups should know first thing that they ought to be comfortable with smooth manifolds (and probably some group theory too) before attempting to read (let alone criticize) an article on Lie groups. (I am thinking about this for all math topics, not just Lie groups, of course.)

What do y'all think? VectorPosse 05:58, 6 August 2006 (UTC)

The link you want is to Talk:Lie group#is this useful?. I am not familiar with templates, but perhaps we need a template for pointing to another article containing the prerequisites for reading the current article. JRSpriggs 06:44, 6 August 2006 (UTC)

I strongly disagree with putting any list of prerequisites on top of articles.

First, if a user never heard of differential geometry before, and complains that Lie group is hard to read, he/she has only himself/herself to blame. Reminds me of somebody who complained that logarithm is a useless article, because that person could not find a motivation for that article to exist.

Second, a well-written article should have a good introduction, and relevant links to other subjects should be embedded in context. That's encyclopedic.

All in all, while I strongly agree that articles should be accessible, boxes of prerequisites are not the solution. Oleg Alexandrov (talk) 07:07, 6 August 2006 (UTC)

An encyclopedia article is not a textbook, nor even a chapter of a textbook. Also, the web of knowledge admits no simple linear ordering. We get complaints about mathematics articles being opaque on a regular basis. The appropriate response depends on the state of the article, and on the topic.

People can arrive at an article in many ways. Perhaps they were searching the web for a word or phrase. Perhaps they were reading another article that thought this would be a useful link, either for background or enrichment. Maybe someone overheard the topic in a conversation and wanted to get a feel for what it's about. Or maybe someone has a text that is less than clear to them and thought Wikipedia could help. (We wish!)

Sound like a challenge? It is. A good mathematics article on a popular topic is especially hard. If that topic includes a modicum of technical difficulty, look out. If lots of people think they know something about it, the editing can get controversial.

Unfortunately, "Lie group" should be a major service article. It needs an introduction that a high school student can handle, but also needs to touch on material that can occupy months of graduate study.

We never want to say "if you haven't studied group theory and differentiable manifolds, go away". And what about matrices, since many of our examples occur as subgroups of GL(n,R)? No, prerequisites are unacceptable.

What might be more helpful is a "related topics" box. We would want to indicate something about the nature of the relationship, and we would need to avoid the temptation to link everything to everything. But I think it could be a major project to begin augmenting our articles in this way, and I'm not sure who would do it. Meanwhile, we do have a "Categories" area at the bottom of the page, which means it is often overlooked. --KSmrq^T 09:48, 6 August 2006 (UTC)

I initiated the discussion without any preconceived notion of what might be a "good" or "bad" way to approach the idea, but now that I've seen some of the discussion, I would tend to agree with Oleg Alexandrov. A well-written introduction can and should refer to the subjects that are required without causing any great disruption to the thousands of pages that already exist. (Having said that, many such pages probably do need better introductions. The more abstruse pages seem very far removed from their basic categories.)

I do not think that prerequisites suggest "go away". If presented correctly, they should come across as helpful. Those who are curious about an advanced topic will try to read the article anyway (and this is a good thing), but at least they are informed as to why the article is confusing to them and where they can go for more basic information. I think there are unintimidating ways of writing an introduction that communicate the essence of a topic, but at the same time point the reader toward articles which may be more appropriate for their level. I would guess that this is an ideal that we can all get behind. VectorPosse 21:30, 6 August 2006 (UTC)

This might be a good time to mention that we do have a Manual of Style specifically for mathematics, and that the first piece of advice offered is:

"Probably the hardest part of writing a mathematical article (actually, any article) is the difficulty of addressing the level of mathematical knowledge on the part of the reader. For example, when writing about a field, do we assume that the reader already knows group theory? A general approach is to start simple, then move toward more abstract and technical statements as the article proceeds."

In my experience, the advice is accurate, but no substitute for experience! Anyway, perhaps that article will help. --KSmrq^T 23:27, 6 August 2006 (UTC)

Proposed merge: "Bicomplex number" into "Tessarine"

Hello. I recently came across the article bicomplex number, which appear isomorphic to tessarines. The latter appear the first use of this arithmetic, and all properties listed in "bicomplex number" are already contained in "tessarine". Another complication is that when Hamilton's quaternions were still new, some also referred to them as "bicomplex number" (but I have not seen this term used for quaternions in articles in the past 100 years). See also talk:bicomplex number.

As a suggestion, we could have bicomplex number redirect to tessarine, and add the isomorphism (with the one reference) there. The tessarine article itself needs some minor work, e.g. to list its algebraic properties first and then refer to isomorphic numbers (I acknowledge having contributed to this disorder while working on rewriting hypercomplex number; sorry for that, I simply haven't gotten to clean up "tessarine" yet).

Any comment, concern, or help is appreciated. Thanks, Jens Koeplinger 13:17, 8 August 2006 (UTC)

After finding at least four different uses of the term "bicomplex number" within just a few hours, we may be looking at (yet another) term that appears to have been used freely in mathematics, where each use was apparently clear within the context of the particular program where it was used. Similar to the use of "hypercomplex number". Well that's just great. I hope for the future that the internet, and in particular establishments like Wikipedia and full-text search, will give authors better tools to research existing terminology when scoping out naming for something they deem "new". Therefore, maybe we should rather make the "bicomplex number" article in a way that disambiguates all these uses. A simple disambiguation may not be enough, because one may want to write a few sentences for each section. Oh well. Thanks for any comment or additional information (see also talk:bicomplex number. Jens Koeplinger 17:18, 8 August 2006 (UTC)

Looks like the current version of the bicomplex number article stub refers to a special type of the multicomplex number program, and appears to be widely used. Therefore, I've added a new multicomplex number stub, with some barebone description, and updated some references and isomorphisms. So the bicomplex number article is really for keepers, but we must also provide reference to the other uses. One use (synonym to quaternions) is outdated and can be referenced as such, another use is actually from a compound term "variational bicomplex" and we can provide a link to this different area (which doesn't exist yet in Wikipedia). I'll follow-up on the one remaining use (appears to be initiated by Aristophanes Dimakis and Folkert Müller-Hoissen about 6 years ago), as name for an algebra program. - - - Thanks for your patience in reading my monologues here; though I'd always be glad for *any* kind of feedback. Thanks, Jens Koeplinger 01:42, 9 August 2006 (UTC)

I noticed that the article Hypernumber (redirected from Conic quaternion) states the following: "Conic quaternions are isomorphic to tessarines". I have to confess ignorance as to the proper terminology in this area, but this should be taken into account if true, or corrected if wrong. --Lambiam ^Talk 01:53, 9 August 2006 (UTC)

Agreed, just updated, thanks for letting me know. For reference on the term "conic quaternion" see e.g. the preprint http://www.kevincarmody.com/math/sedenions1.pdf . Thanks, Jens Koeplinger

Hypernumbers crackpottery

From the immediately preceding discussion I stumbled upon the article on hypernumbers which is, at best, incomprehensible (to me being a mathematician) and probably plain crackpottery. Nowhere does the article state what hypernumbers actually are (presumably certain finite-dimensional algebras over the real numbers, but what properties are sought of them is left entirely unstated), nor is the linked site http://www.kevincarmody.com/math/hypernumbers.html any clearer. (On the other hand, it does contain such ridiculous statements as "New kinds of number [sic] will likewise give rise to new areas of science." or "This enables great advances in consciousness and matter." (page 15 of http://www.kevincarmody.com/math/hypernumberreference.pdf — which claims to be a reference but still does not explain what hypernumbers are).)

The only reference we are given are the papers of a certain Charles A. Musès, all published in Appl. Math. Comput., so I looked them up in MathSciNet and the reviews are eloquent enough (indeed, most reviewers flatly decline to comment, or seem to have found them hilariously funny); in fact, such sentences from the articles are quoted as: "How can any mathematician doubt where the source of new creativity in mathematics lies? […] We suggest that hypernumbers in our unrestricted sense are the key to a coming and deeper nuclear mathematics; that their explanation and delineation will mark as great a step as did the implications of nuclear structure in modern physics." (this is from "Hypernumbers II. Further concepts and computational applications", Appl. Math. Comput. 4 (1978), 45–66). Obviously C. Musès found the editors or referees of Appl. Math. Comput. sympathetic to his kind of crackpottery.

It would be nice to have the Wikipedia article deleted, but as it is nearly impossible to suppress an article, I guess we should just put up a banner of some kind. Ideally, the article would be reduced to a sentence such as: "Hypernumbers are a 16-dimensional non-associative algebra over the real numbers (or certain subalgebras thereof) which was studied by Charles A. Musès who believed in their application to physics, biology and engineering." Perhaps with a description of the generators and relations of the algebra, if anybody can make sense out of them.

(I don't have time to fight this battle or to argue with crackpots, so I'm just writing to make sure other participants are aware of this.) --Gro-Tsen 11:25, 9 August 2006 (UTC)

Your last sentence is remarkable. I thought I had filtered the properties of certain hypernumber types from all of the rest Musès wrote. The filter I applied was that at least two people had published about it (C. Musès and K. Carmody), and that I could understand and confirm it from defining relations. I find Mr. Carmody's works on hypernumber arithmetic clear, sound, and well written. I find the focus on multiplicative modulus of a number interesting, do believe they qualify as their own number system, and do not believe that deletion of the article is an improvement. How do we deal with a situation where the person who discovered something gives ridiculous and even derogatory statements, throws out statements and "proofs" that don't work? I do not find Musès' articles funny, I am actually frequently offended by them. To my knowledge, though, it was him who found the real powers and logarithm of $\varepsilon$ (the non-real root of +1 that is also part of split-complex algebra), and it was K. Carmody who found sedenions with a multiplicative modulus. As far as I can see, what's currently on the Wikipedia page "works" ... What do we do? Thanks, Jens Koeplinger 15:25, 9 August 2006 (UTC)

I think for a start, we should define hypernumbers. I don't understand after reading the article what they are, and I followed the link to Carmody's page, and I can't tell from what he has there what they are either. Everything that is written seems to assume that the reader is familiar with the definition. Take the subsection Hypernumber#Epsilon numbers, from which no one could deduce what an epsilon number is, what epsilon itself is, and what it means for them to be the third level in the program. Not to mention that the seemingly fundamedntal idea of "power orbit" is referenced everywhere but never described (I suppose it means "all powers of a number", but the terminology is new to me, and confusing). I have to say that everything in the article strikes me as typical of what crackpot ideas I've seen: a confusing and grandiose compilation of claimed results without clear definitions, consistent notation, or verifiable statements. Of course, that's the way the articles on Carmody's page are written too, so it's not necessarily your fault...but if there doesn't exist a coherent account of this stuff I would say it's the work of a crackpot. However, if it's been published it may be "notable", so at the very least it would then be our duty to figure out what "it" is in the first place. Ryan Reich 20:46, 9 August 2006 (UTC)

Sounds great to me. I recognize that the article is not well structured and lacks clarity, and it would be wonderful if it could be improved. What about adding an "algebra stub" notice on the article, to highlight that the article cannot remain in its current form? Thank you very much for pointing out several weaknesses. While we may have trouble finding a definition of hypernumbers in general (Musès did not provide one ...), we can put the numbers that are currently stated on the page on defining relations. We could say "Musès conceived hypernumbers as [...thisandthat...] Select examples are [...]" and so on. As for the definitions that are missing, epsilon is a non-real base number with $\varepsilon{}^2 = 1$ and is identical to j from split-complex algebra. The "power orbit" of a number b is

b α

with

α

real. Maybe it would make sense to have two sections in the article, the first section focusing on the hypernumber types containing reals, imaginaries, and $\varepsilon$ bases, and then a section that gives a briefer overview over the three other types currently listed. Well, let me put the stub notice out there for now, hopefully we'll get more responses (possibly on talk:hypernumber?). Thanks a lot, Jens Koeplinger 01:18, 10 August 2006 (UTC)

Already the article on split-complex numbers seems of dubious interest to me: most unfortunately it does not mention the (obvious) fact that, by the Chinese remainder theorem, "split-complex numbers" / "epsilon numbers" can be identified with pairs of real numbers with termwise addition and multiplication (I mean, not only are they a two-dimensional algebra over the reals, but actually they are the direct product of two copies of the real numbers), which makes them sort of boring (why bother about the product of two copies of the reals, not arbitrary tuples?); the identification takes the pair

(a, b)

to $\frac{a+b}{2} + \frac{a-b}{2}\varepsilon$ (the number $\varepsilon$ is called

j

in the article on split-complex numbers; and it's a trivial exercise to see that this is indeed an isomorphism). (Also, incidentally, the article is wrong in stating that split-complex numbers have nilpotents: they don't, they have divisors of zero but no nilpotents.) I'm stating all this to refute the idea that the number $\varepsilon$ is an interesting object. As to it's "power orbit", i.e., a one-parameter subgroup, once we have identified split-complex numbers with pairs of real numbers as I explained, and the number $\varepsilon$ with the pair

(1, - 1)

, it is clear that one-parameter subgroups all lie in one connected component (both coordinates positive) of the multiplicative group of invertible split-complex numbers, and $\varepsilon$ is not there, so it does not have a "power orbit" (no more than -1 has in the real numbers). Similarly, trying to add both

i

with

i 2 = - 1

and $\varepsilon$ with $\varepsilon^2=1$ just gives you pairs of complex numbers, again not very interesting. This is all basic algebra and applications of the Chinese remainder theorem. --Gro-Tsen 10:15, 10 August 2006 (UTC)

I can only agree that many articles need improvement (but I am glad that you did respond). If you repost your last message in talk:split-complex number I'd be glad to respond (it's getting very specific now). Or, to save you time, I'd also be glad to cite your last post there ... This will be funny, I'm looking forward for the reactions.

As for the hypernumbers page, I do thank anyone for the attention, and I'm glad to "let go" and answer question on the talk page, from what I can answer. I'm a physicist, with interest on physics on numbers that are not typically used, and I noticed gaps, missing information, and missing links (isomorphisms) in Wikipedia. So I've added some as good as I can, though I'm not native to the field (mathematics). Any review or improvement is, as always, welcome. Thanks again, Jens Koeplinger 12:08, 10 August 2006 (UTC)

Feel free to repost my comment elsewhere if you think it wise. Personally I won't follow the "split-complex numbers" page because I don't think it's interesting in any way (but it's not really crackpot stuff either: it's just entirely boring) and I don't have time to improve it. I just find it laughable if it turns out that nobody noticed that these "split-complex numbers" are just isomorphic to pairs of real numbers (something which should be obvious from the start to anyone with a minimal background in algebra, e.g., having read Lang's book). Btw, "tessarines" / "bicomplex numbers" are similarly isomorphic to pairs of complex numbers. Any (commutative and associative) étale algebra over the real numbers is a product of copies of the real numbers and the complex numbers, anyway. --Gro-Tsen 12:38, 10 August 2006 (UTC)

I looked at this Kevin Carmody's website, the main reference of the hypernumbers page, and I'd like to point out that he's an unmitigated crackpot. Even if this topic were at all standard, we probably shouldn't be using his website as a reference. I will say that it can be very difficult to tell crackpot math from real math, especially if the crackpot in question studied mathematics in earnest before losing their grip, and especially they attract followers. I think this is the situation we have going here. It just has that certain feel - think of John Nash in "A Beautiful Mind" with the newspaper and magazine clippings. Originalbigj 16:55, 10 August 2006 (UTC)

Please see talk:hypernumber for the list of sources from which I directly drew from, and the reasoning behind it. Thanks, Jens Koeplinger 18:03, 10 August 2006 (UTC)

I would like to point out that "epsilon number" already has an established meaning. An epsilon number is an ordinal $\epsilon_\alpha \!$ such that $\epsilon_\alpha = \omega^{\epsilon_\alpha} \!$ . JRSpriggs 02:58, 11 August 2006 (UTC)

This is one of several meanings of ε, ranging from conic sections to calculus. If Carmody and Musès have come up with another one, so be it. Nor are they entirely original; the use of ε for a non-trivial unit is fairly common in the study of rings - outshone, I think, only by ω. Septentrionalis 13:57, 11 August 2006 (UTC)

Adminship requested

I have requested adminship, largely to deal with the backlogs of move and discussion pages. Since Oleg endorses, I think I can mention it here. See Wikipedia:Requests_for_adminship/Pmanderson. Septentrionalis 20:50, 12 August 2006 (UTC)

Am I the main math admin lobby or what? :) Good luck! Oleg Alexandrov (talk) 20:55, 12 August 2006 (UTC)

Ovoids in polar spaces

Hello,

as you can see I am on the list of participants of the Math Project. I'm still not experienced in creating my own articles.

Any quick look at Ovoid (polar space) would be appreciated, also because of the fact that English is not my native language (I do my best though).

And one fundamental question : what to do with these ovoids, they are often only treated in the case of finite polar spaces, while in fact there isn't exactly anything wrong with the definition for infinite polar spaces.

Thanks a lot,

Evilbu 22:32, 12 August 2006 (UTC)

What's lacking most are the references. --Lambiam ^Talk 02:24, 13 August 2006 (UTC)

You could probably say the same about polar space though at least there's a wiki-link to Tits there. Lunch 02:45, 13 August 2006 (UTC)

Okay, I get the message. There should be references. I am willing to accept any suggestion. The problem is that incidence geometry is not well represented on the net, most of the sources would be (online) courses from my own university. It would help me a great deal if I could know which users are into geometry as well. Evilbu 12:24, 13 August 2006 (UTC)

Use Google scholar as a starting point, and the library resources of your university to find good references, usually either a textbook, or the original articles introducing the concepts. Another acceptable source is the Encyclopaedia of Mathematics. Make sure the article agrees with the reference. --Lambiam ^Talk 18:25, 13 August 2006 (UTC)

Our university does have a library... But on a side note : the first professor's article on that Google scholar link, is my own professor, who taught me the definition of polar space... Evilbu 19:05, 13 August 2006 (UTC)

Verifying a reference

An anonymous contributor has edited A. Cohn's irreducibility criterion to claim that the criterion has been proved to hold for the case n=2, whereas the relevant PlanetMath page says that this is a conjecture. The contributor provided the following link to a dvi file as a reference. I cannot read the dvi file, but I think it contains an article by number theorist Ram Murty published in Amer. Math. Monthly, Vol. 109 (2002), no. 5, 452-458. Perhaps someone with a dvi reader, or with access to the journal itself, can verify that this paper does indeed provide a proof for the case n=2 ? Gandalf61 10:25, 14 August 2006 (UTC)

It gives a new proof for the n>2 case, then a long discussion and another lemma claimed to give the n=2 case as well. JPD (talk) 11:20, 14 August 2006 (UTC)

JPD - thank you for the prompt response. Gandalf61 15:54, 14 August 2006 (UTC)

Well, it seems the Planet Math page is very outdated, giving as the only reference Polya and Szego vol 2, which is actually a very old book: the 1998 version is just a reprint of the 1976 English edition which was translated and revised by someone other than the original authors. Furthermore the 1976 German edition (according to Math Reviews reviewer) differs very little from the original 1925 edition. In any case, the Murty paper mentioned above gives as the first reference a 1981 paper which proves Cohn's theorem for any base (Brillhart, John; Filaseta, Michael; Odlyzko, Andrew On an irreducibility theorem of A. Cohn. Canad. J. Math. 33 (1981), no. 5, 1055--1059.) The review for it on MathSciNet notes that the original Cohn theorem was mentioned in Polya and Szego. So it seems this conjecture has been known to be closed for quite a while. --C S (Talk) 02:07, 15 August 2006 (UTC)

I updated the article A. Cohn's irreducibility criterion to reflect Brillhart et al's priority for the n=2 case. In a future edit I hope to change the letters used for certain subscripts to agree with the Ram Murty paper, because using 'n' it is easy to confuse the base used with the degree of the polynomial. The other improvement that might be suggested is to change the title to 'Cohn's Irreducibility Criterion', because Wikipedia's search function is too feeble to return this article in the first screen when you type in 'A. Cohn'. EdJohnston 22:04, 18 August 2006 (UTC)

Antiderivative

I wonder if there are any comments on this edit (please write them at talk:derivative). Thanks. Oleg Alexandrov (talk) 16:16, 14 August 2006 (UTC)

Did you mean to say write comments at Talk:Antiderivative? I don't see much need for discussion; the matter was already considered and decided long ago, at the top of the talk page. Are you suggesting it should be reconsidered? (Follow-ups to talk.) --KSmrq^T 03:37, 15 August 2006 (UTC)

Mathematics needed

Please help with adding the various mathematical analyses of the game Fetch (game) to the article. (See the references and further reading given in the article.) Uncle G 10:56, 15 August 2006 (UTC)

The process by which a dog tries to catch a ball may be similar to the way that a fielder in baseball tries to catch a ball which has been hit in his general direction. I know that that has been analyzed mathematically, but I do not remember the details. JRSpriggs 05:10, 16 August 2006 (UTC)

Abel Prize more prestigious than Wolf Prize in Mathematics?

That is what one anon has insisted, but I believe this is unsubstantiated and actually OR. See Talk:Wolf_Prize for my lengthy comment with diffs. Perhaps a personal remark here is in order. When the anon replaced the mention of the Wolf in the intro to Serre's article (saying Wolf is not more prestigious than Abel), I was willing to let it go as I thought at least that the Abel would be more familiar to the lay reader (due to the extensive media coverage); however, a later edit revealed that this person regards the Abel as more prestigious than the Wolf and that would be appear the basis for the first edit. I would appreciate if people could take a look, particularly mathematicians who have been been in the mathematical community for a longer time than me who can gauge this issue with their more extensive experience. I think this is kind of an interesting math cultural issue. --C S (Talk) 11:33, 15 August 2006 (UTC)

I take the Wolf Prize to be, de facto, the top lifetime achievement award. That being said, we can't possibly talk about prestige in the abstract (would have to be via quotes). I suggest just removing all loose talk. Charles Matthews 12:19, 15 August 2006 (UTC)

Ditto. Prestige is in the eye of the beholder. Speaking of which, please report all rumors on the talk page of Grigori Perelman! ---CH 07:17, 16 August 2006 (UTC)

That's also how I would rank them, but looking at the winners they seem to be the best of the best for both, so now I wonder, what would actually make one more prestigious than the other? For the Fields Medal, could it play a role that it is only awarded once every four years? And of course you can't be an old geezer, so it does not honour a lifetime of ~~servitude~~ service to mathematics, but specific memorable achievements.

Problem editor

All mathematics editors should be alert to the ongoing behavior of Bo Jacoby (talk). In article after article Bo has tried to use invented (original research) notation. Then Bo lures others into endless discussions on the talk pages, where a host of editors again and again waste their time saying the same thing: "Don't do it." Examples include

A related wrong-headed persistence has been seen at Talk:Wilkinson's polynomial. I do not know the cause nor the intent of this behavior, but we need to find some effective way to deal with it. Patient responses on article talk pages have not been effective. Please be vigilant to catch more abuses, and please do not let Bo turn article talk pages into his own chat room. --KSmrq^T 14:23, 16 August 2006 (UTC)

I would add to that talk:polynomial and talk:formal power series. I believe we are dealing with a person without formal math education, and it takes a long time (and many editors sometimes) to convince him that he is wrong. Oleg Alexandrov (talk) 16:25, 16 August 2006 (UTC)

Aha, I would also add Talk:Lebesgue integration. That explains a lot.--CSTAR 16:53, 16 August 2006 (UTC)

And Talk:Binomial transform. Bo's behaviour, while annoying and disruptive, is minor in comparison to some of the mono-maniacal and outrageous behaviour I've seen recently seen (e.g. my talk page, ughhh). linas 03:49, 17 August 2006 (UTC)

Wikipedia:Lamest where it applies. Charles Matthews 21:12, 17 August 2006 (UTC)

Could someone check out inferential statistics? This is an article that seems to have been largely written by Bo. Statistics is not my field, but some of the technical terms defined in the article, like "deduction distribution function" and "induction distribution function", don't seem to appear anywhere else on the web (at least, not with the same meaning). A closer look by a statistician might be warranted. Another article largely written by him, in which he cites his own publications, is Durand-Kerner method. Again, I have not checked this and make no claim as to whether it is good or bad, but it might be worth a closer look given Bo's past behavior. —Steven G. Johnson 15:45, 21 August 2006 (UTC)

Durand-Kerner is ok, he earlier claimed to be the inventor of the method, since he did not find related information, but changed or allowed to change to the more usual name. The method is, as it seems, not widely known, but (personal communication by prof. Yakoubsohn at Toulose) common knowledge in the root finding community.--LutzL 17:04, 21 August 2006 (UTC)

There's still the vanity link/redirect at Jacoby's method. Lunch 20:38, 23 August 2006 (UTC)

Also, in the article to which this redirect points, Durand-Kerner method, there are two references to Bo Jacoby added by Bo Jacoby. Being relatively new to all of this, I'm not sure if this counts as WP:NOR or not. VectorPosse 22:44, 23 August 2006 (UTC)

See also Talk:Fourier transform. —Steven G. Johnson 16:29, 21 August 2006 (UTC)

Meaning of QED

Should QED be:

a page about the phrase quod erat demonstrandum, with a dablink to QED (disambiguation),
a page about quantum electrodynamics, with a dablink to QED (disambiguation), or
a disambiguation page, with links to both the above and to lesser uses.

My opinion is clearly (3), but come share yours at talk:QED (disambiguation). --Trovatore 20:40, 17 August 2006 (UTC)

You have shown via your question that the term is ambiguous; therefore, it should be a disambiguation page. QED Ryan Reich 20:50, 17 August 2006 (UTC)

The discussion is taking place at talk:QED (disambiguation), not here; this is just a notice. --Trovatore 20:52, 17 August 2006 (UTC)

At least admit that it was good for a chuckle. Ryan Reich 20:57, 17 August 2006 (UTC)

You could have that on your tombstone. Charles Matthews 21:14, 17 August 2006 (UTC)

I'll take mushroom, black olive, and anchovies. --Trovatore 22:53, 17 August 2006 (UTC)

I've had pizza that chewed like marble myself...Septentrionalis 01:53, 19 August 2006 (UTC)

Oppose anchovies. --C S (Talk) 04:56, 19 August 2006 (UTC)

Per the ethics of terminology, QED as quod erat demonstrandum has priority by several thousand years over all the New QEDs On The Block. Jon Awbrey 05:26, 19 August 2006 (UTC)
- Well, my feeling is that, if we were to take the intrinsic importance of the subject into account, it would have to swing massively the other direction: quantum electrodynamics is one of the most fundamental attempts to describe nature yet devised by the mind of man, whereas quod erat demonstrandum is just a phrase, a piece of historio-linguistic trivia. (Obviously this is quite distinct from any consideration of the importance of the idea of proof, or even of individual proofs at the end of which Q.E.D. has appeared; those are separate discussions altogether, and the Q.E.D. article isn't about them.) Perhaps more to the point, just from a practical point of view, it's an observed fact that lots of people link to QED from physics articles, which has bad consequences if it's a redirect to the Latin phrase.
- Still, if you want to "vote", this isn't the place to do it; I've given a pointer above to the actual debate. --Trovatore 05:46, 19 August 2006 (UTC)
  - Trovatore, Quantum Electrodynamics is a temporary theory. It is a set of rules, and the theory is not entirely well-defined mathematically. On the other hand proofs are very important, not only in mathematics, but also in theoretical physics.Hillgentleman 03:22, 7 September 2006 (UTC)
    - Luckily, there was no need to judge the relative importance of quantum electrodynamics and proof. Proof is an extremely important topic; quod erat demonstrandum is not. --Trovatore 03:32, 7 September 2006 (UTC)

JA: The just notable difference tends to be relative and shifty from year to year. That's why we have rules like prior use. Of course, this is WP, and the rule is to find the "most illiterate use" and go with that, so why am I not already sleeping, he asks himself. Jon Awbrey 05:52, 19 August 2006 (UTC)

ICM Madrid

Starts 22 August, I believe. It would be good if we geared up for the Fields Medal awards. By which I mean: get ready with a story to offer the Main Page here; have articles ready on Terence Tao and Grigori Perelman who are the hot tips; be prepared to do something quick and dirty for anyone else on the list. Compared to 2002, the world's press are likely to turn to enWP for enlightenment, as soon as the news hits the wires. Charles Matthews 21:18, 17 August 2006 (UTC)

Uh, so who else is on the list? --C S (Talk) 05:51, 19 August 2006 (UTC)

So, as part of that, anyone ready with good pictures for Kakeya problem page? Charles Matthews 21:21, 17 August 2006 (UTC)

Update: plenty of excitement as Perelman was a no-show; need work on Andrei Okounkov (I've just mailed Princeton to see if they have a photo), Wendelin Werner. Matter arising from the latter: self-avoiding random walk is surely worth an article. Charles Matthews 12:15, 22 August 2006 (UTC)

A Google Image search turns up photos for everyone, rights status unknown. --KSmrq^T 12:34, 22 August 2006 (UTC)

Perhaps self-avoiding random walk could start as a section of Random walk before being spun off on its own. Michael Kinyon 15:48, 22 August 2006 (UTC)

There is a raw definition somewhere there, true. Quick-and-dirty is to redirect and forget ... given a Fields has been awarded, there might be rather more to it. Also, an article on Charles Loewner would be good (there is a MacTutor article); I just had time to start some of Werner's lecture notes which do hark back to Loewner's work of the 1920s. Charles Matthews 16:10, 22 August 2006 (UTC)

Wikiversity Mathematics School open

I cordially invite the partisipants of this project to the newly founded wikiversity school of Mathematics. We are still working out the policies, but any help is appreciated. --Rayc 23:55, 17 August 2006 (UTC)

Eigenvalue, eigenvector and eigenspace

Eigenvalue, eigenvector and eigenspace is up for a featured article review. Detailed concerns may be found here. Please leave your comments and help us address and maintain this article's featured quality. Sandy 22:04, 18 August 2006 (UTC)

A novice editor has created an article for the Jacobi eigenvalue algorithm; a few fixes there could be a big help as well. --KSmrq^T 12:14, 19 August 2006 (UTC)

It seems like there is a need for some people to do some copyedditing on the article. These been a lot of suggestions on fixes to the article needed to get it to FA status but no one is acting on them. Volunteers welcome! --Salix alba (talk) 07:28, 14 September 2006 (UTC)

Talk:Pi#Move Pi to π, the official discussion!

This move idea has come up again. Please discuss. (I made the point that software limitations mean that the actual move, if this passes, will be to Π.) Septentrionalis 01:59, 19 August 2006 (UTC)

Kerala school?

I copied this message from Portal talk:Mathematics. -- Jitse Niesen (talk) 14:34, 19 August 2006 (UTC)

What do you guys think about the Kerala School article and the possible transmission of mathematics from Kerala to Europe? Should the theory get a mention on our articles about calculus, newton, wallis etc? Frankly, I'm a bit alarmed about the points brought up here. Borisblue 07:51, 19 August 2006 (UTC)

I came here to post a message on Madhava, and saw this... Actually, I remember reading somewhere that several conferences have been convened worldwide to discuss the possible transmission. But none of them, AFAIK, have been able to come to a conclusion. However, the theory has never been discounted, because the people who back it, have a very strong point. IMO, (and this is not because I'm from Kerala), this should be mentioned as a theory that is prevalent. All my attempts at introducing it in some articles failed, (primarily because I happen to be from Kerala). It certainly would be nice if someone would be willing to take initiative in this regard (after a discussion, of course).-- thunderboltz^{a.k.a.Deepu Joseph |TALK}14:44, 23 August 2006 (UTC)

An RFC will be nice. However, I have a lot of difficulty finding academic papers that discuss and critique this issue (can't find any record of conferences either?), I think because this theory is so new. Hence, it will be difficult to satisfy verifiability in a lot of the claims, at least untill a few more historians come up with some peer-reviewed papers. Science and math issues require very reputable sources. Borisblue 04:51, 24 August 2006 (UTC)

Unicode article names

User:CyberSkull moved T1 space to T₁ space, that's on the heels of a move of Mu operator to Μ operator. I believe that these are cheap Unicode tricks and not a solution to the fact that Wikipedia can't represent faithfully some mathematical notation.

T1 space should ideally be "T₁ space". Since that's impossible, I think T1 space is a better name than the T₁ space gimmick. Comments? Oleg Alexandrov (talk) 21:18, 19 August 2006 (UTC)

Unless Unicode tricks can solve all our problems along these lines, I would agree that we would be better sticking with things like T1 space. I think it would be better to be consistent and avoid gimmicks - and hope that some future version of the software will give a more sensible solution. Madmath789 21:32, 19 August 2006 (UTC)

My thanks to Oleg for fixing Mu operator and Mu-recursive function which had been moved inappropriately by User:CyberSkull. I agree that titles of articles and categories should not contain characters other than printable ascii characters. It is hard enough dealing with unusual characters in the text of an article. Having such characters in a title is much worse. One might look in the wrong place in the category listing (as I did for the two I mentioned above). Or one might fail to find them with a search or even be able to enter the correct title into the search box. Or the title might not display correctly depending on one's fonts. JRSpriggs 08:48, 20 August 2006 (UTC)

Fields template

If Grigori Perelman has declined his Fields Medal, how should Template:Fields medalists read? Charles Matthews 15:42, 22 August 2006 (UTC)

How about "Perelman (declined)"? Yes, I realize that if he has declined, then technically he is not a medalist, but there should be some indication that the award was offered to him. Michael Kinyon 15:46, 22 August 2006 (UTC)

According to the New York Times, Sir John M. Ball, president of the International Mathematical Union, said, "He has a say whether he accepts it, but we have awarded it." So maybe Perelman is technically a medalist. Having said that, I believe that Michael's suggestion is adequate. VectorPosse 20:50, 22 August 2006 (UTC)

Now of some urgency, since Template:In the news has the Fields as leading item. Charles Matthews 16:16, 22 August 2006 (UTC)

Since the fact the Perelman declined will be discovered at his article, perhaps it's enough to do nothing special. Or at least postpone a more clever solution. The exact details still seem mysterious, so letting the article explain seems wise. If "(declined)" is included, be sure to use   between it and his name to prevent an awkward break in the future. (Actually, the current breaks are none too appealing.) --KSmrq^T 18:38, 22 August 2006 (UTC)

It seems that he has indeed specifically declined to accept the Fields Medal. I agree with "Perelman (declined)" in the template. ---CH 23:39, 22 August 2006 (UTC)

There's a New Yorker article on Perelman that got slashdotted: rather interesting read, gives insight into why the prize was declined. http://www.newyorker.com/fact/content/articles/060828fa_fact2

BTW: Manifold Destiny (article) --Pjacobi 20:20, 28 August 2006 (UTC)

Grigori Perelman

I've extensively rewritten this twice in the past week to incorporate latest news and clean up "edit creep" (well intentioned edits by inexperience writers--- or thoughtless ones--- which disrupt the flow of ideas, exhibit poor diction, and generally tend to eventually render an article unreadable.) There has been some apparent trolling by editors who want to discuss the Israeli-Palestine conflict, so watch out. Sheesh! ---CH 23:38, 22 August 2006 (UTC)

Madhava of Sangamagrama

Hello! This article is about Madhava, a mathematician who lived during the middle ages. Despite being one of the greatest mathematicians (he is, in fact considered as the founder of mathematical analysis), most of his work has been discredited. The talk page of the article has a large number of unanswered questions. It would be nice if someone well versed in mathematics take a look at them. I am not submitting the article for collaboration, because it fails the nomination criteria. However, it would be wonderful if people would come forward to cleanup all the confusion and chaos on this article. Thanks! -- thunderboltz^{a.k.a.Deepu Joseph |TALK}14:34, 23 August 2006 (UTC)

Articles listed at Articles for deletion

Simplex algorithm method (AfD discussion)

The 'bot hasn't picked this one up, it appears. Uncle G 11:43, 24 August 2006 (UTC)

Request from Non-math Person

I feel certain that this comes up a lot, but as a relatively well-educated and well-read individual who has only a general interest in mathematics, I am consistently stumped by even the simplest of mathematics entries on wikipedia. Granted, some math issues, conjectures, and theories are plain ol' difficult, but it seems like Mathematics entries on wikipedia are by far the least accessible entries (for the average reader who comes to an encyclopedia for general information). The Clay Institute's descriptions of the Millennium Prize problems [43], for example, do a much better job of describing and analogizing the problems for us lay-folk. With so much to work on, this may not be a valid top priority for the Project, but as an outsider I would greatly appreciate if it became a focus. Thanks! aww 18:34, 25 August 2006 (UTC)

Well, it's a known issue. For us here, I suppose, the point of view might be that the mathematics is only about 1% of enWP; but its place in sustaining the reputation and credibility of the project is much greater than that would suggest. We have certainly emphasised getting 'professional' mathematics here. An analogy would be with medicine: no one would want the clinical medicine articles to be accessible only to doctors, but on the other hand if a doctor can say "that's just wrong", that is also not good.

Let's look at the Clay description of one of the problems in detail.

Mathematicians have always been fascinated by the problem of describing all solutions in whole numbers x,y,z to algebraic equations like

x² + y² = z²

Not true. In the eighteenth century this kind of number theory, namely Diophantine equations, was consider a backwater. That attitude prevailed for a long time.

Euclid gave the complete solution for that equation, but for more complicated equations this becomes extremely difficult.

See Pythagorean triples.

Indeed, in 1970 Yu. V. Matiyasevich showed that Hilbert's tenth problem is unsolvable, i.e., there is no general method for determining when such equations have a solution in whole numbers.

True.

But in special cases one can hope to say something. When the solutions are the points of an abelian variety, the Birch and Swinnerton-Dyer conjecture asserts that the size of the group of rational points is related to the behavior of an associated zeta function ζ(s) near the point s=1.

Actually, writing 'abelian variety' rather than elliptic curve is reprehensible here: far too general. If I tried to write down the equations defining an abelian variety, you wouldn't thank me. It would be much better to say cubic curve, in fact. This slurs over the fact that if such a curve has a singular point, we don't call it an 'elliptic curve'; but that case is already done by the Euclid method, anyway.

In particular this amazing conjecture asserts that if ζ(1) is equal to 0, then there are an infinite number of rational points (solutions), and conversely, if ζ(1) is not equal to 0, then there is only a finite number of such points.

We don't use words like 'amazing', naturally. This is OK, and could usefully go in an article here. (Then for experts we have to remark something on the analytic continuation question, supporting the idea that the zeta function is even defined at the actual point.)

Right then, this was an exercise. I would criticise the exposition for not using the proper term (Diophantine equations). Anyone browsing our Category:Diophantine equations should at least be able to pick up what the subject is about.

Charles Matthews 19:09, 25 August 2006 (UTC)

So this Clay write-up was perhaps good in explaining things to the interested layperson, and lousy for professional mathematicians. We have many articles that are lousy in explaining things to the interested layperson, and perhaps good for professionals. We also have some articles that are lousy for both. Why be so defensive about it? Can't we just admit that we'd like to have more articles that do a good job for both? Unfortunately, we don't have that many editors who combine the required background with the necessary writing skills and also have unlimited time to devote to the project. --Lambiam ^Talk 01:34, 26 August 2006 (UTC)

I thought the middle way was found a long time ago. Articles should have a good and easy to read introduction. Moving down an article, things will become more complex, and for good reason.

I don't think Charles was trying to be defensive (he's rather good at writing expositionary articles, without formulas pile-ons :) We have some good articles, and some bad articles. And math articles could be harder to read than say biology articles because we use much more symbolism and abstract concepts, and that for good reason. Oleg Alexandrov (talk) 05:45, 26 August 2006 (UTC)

Well, I was certainly enjoying myself looking at other expositions for change, rather than patching up our own. And I hope I made a point about what the mathematics articles here are good for, at least: we do have a very thorough coverage (23 Hilbert problems you can look up here, not just one). There are plenty of popular mathematical books around that will give you a 'feel' for Fermat's Last Theorem, Riemann Hypothesis, Monster group. What you can find here is one step up from that: the level was defined as undergraduate student, back a couple of years ago. Anyway, let's do it again, for the Hodge conjecture (defined as On a complex algebraic variety, every homology class that could reasonably contain a subvariety does contain a subvariety here). The Clay gves us this:

In the twentieth century mathematicians discovered powerful ways to investigate the shapes of complicated objects. The basic idea is to ask to what extent we can approximate the shape of a given object by gluing together simple geometric building blocks of increasing dimension. This technique turned out to be so useful that it got generalized in many different ways, eventually leading to powerful tools that enabled mathematicians to make great progress in cataloging the variety of objects they encountered in their investigations. Unfortunately, the geometric origins of the procedure became obscured in this generalization. In some sense it was necessary to add pieces that did not have any geometric interpretation. The Hodge conjecture asserts that for particularly nice types of spaces called projective algebraic varieties, the pieces called Hodge cycles are actually (rational linear) combinations of geometric pieces called algebraic cycles.

So they try not even to mention the words manifold and topology. Pieces that did not have any geometric interpretation. Yes and no: de Rham cohomology is fairly geometric. The statement leaves out the technical points that the varieties are over the complex numbers (OK, that's the default), and are non-singular (which one can't really get away with).

Someone writing in the style of the first three sentences here would get them edited to more precision of statement pretty fast. The idea buried in the fourth unfortunately we do not cover well (homology classes represented by actual subspaces - I think there are results by major topologists not here). Saying 'nice' is a lapse into the way mathematicians communicate to each other.

We are really stuck with a world where on Monday we may be having to try to write up what Andrei Okounkov did to deserve a Fields Medal (breaking news) and the next day supposedly trying to find new paraphrases for things like algebraic variety or manifold. I'd like to point out that we also get criticism from the other direction (see for example Talk:Abelian variety for an extreme example).

Charles Matthews 10:02, 26 August 2006 (UTC)

I can certainly see how that would be. It's the problems of wikipedia combined with a less accessible sets of subjects. I have to say, it dawned on my from your examples that the best way to explain a complex problem to a lay person is with analogy and abstraction, which in certain mathematics articles could just as easily translate into "inaccurate" or "wrong." Nonetheless, I would encourage pushing some of the intros even farther, even if they include such vague statements as "while not exactly (thing), it is similar to (thing)." Then again, I'm a lawyer, and this is how we talk about everything, so there you go. Thanks for the good work, and I'll keep reading and trying to learn. aww 13:40, 26 August 2006 (UTC)

To do a good job on a sophisticated mathematics article, an editor must have detailed technical knowledge, the ability to know what's essential versus peripheral, great empathy for the untrained reader (to see through their eyes), a solid command of the English language, exceptional skill in writing, and world-class patience and diplomatic skills.

A one-paragraph introduction may be the shortest part of the article, but is almost always the most difficult to write. The Millennium Prize Problems are singled out because they are connected to a great deal of interesting mathematics, and because they are very difficult to solve. How do you take a problem that the best mathematicians in the world do not yet understand adequately and present it in a few short, accurate, engaging sentences to the general public?

You may be surprised at the extraordinary stuggle behind a basic mathematics article, such as manifold.

Ironically, mathematics today is so broad and so deep that a specialist in one branch may know almost nothing about an advanced topic in another specialty. Therefore we appreciate a good introduction just for ourselves!

Finally, while some in the world are hungry to learn more mathematics and science, others are actively hostile, or indifferent. One consequence is that we continue to struggle to convince the WikiMedia developers to better support our notational needs. Another is that we see lazy outside editors take a quick glance at an article and slap a fixit tag on it, without even doing us the courtesy of leaving a note on the talk page to describe what they see as the problem. Or we see editors reword things they do not understand, which someone must then notice and fix.

And yet, we persist. We mathematicians have a love of beauty and pattern, which draws us in and sometimes leads us to want to share the joy. And to solve difficult problems, we have learned to persist in the face of constant frustration and defeat. Perhaps if it was easier to write a good Wikipedia article, we'd be less interested! ;-) --KSmrq^T 21:26, 26 August 2006 (UTC)

However, we also have introduction to quantum mechanics and introduction to special relativity and why 11 dimensions because there is simply so much to say about these topics at the introductory level, that a single article cannot do justice to both the introductory and the technical aspects of the subject. linas 22:22, 26 August 2006 (UTC)

Department of Injustice

For years I have regarded it as a running joke that named theorems, if they are really important, are almost never named for the "right" person. In funnier, it often turns out that the "wrong" person actually cited the earlier contribution, but nobody listened (or cared)! One can often see that even if famous person F tries to credit obscure person O, the result still usually becomes known for F. Anyway, I invite you to contribute your own examples in List of misnamed theorems, but please be very careful since the syntax is easily munged. If you can't figure out how to do it from the examples in the current version, put your entry in the talk page (with a complete citation if at all possible) and I will move the information to the article. ---CH 05:15, 26 August 2006 (UTC)

Um, isn't this a little bit OR-ish? Granted that lists in general are sometimes given a little rhythm on that point, still this seems especially close to the line, to me. --Trovatore 16:29, 26 August 2006 (UTC)

Surely the many items that cite secondary sources are okay? Melchoir 16:56, 26 August 2006 (UTC)

Its not just theorems. Farey numbers were first noted by Haros in 1802. Care to change the name to Misnamed topics in mathematics?

Its not just theorems and topics: Pell's equation was so named because Lord Brouncker solved it! - How about Misnamed equations? Madmath789 22:35, 26 August 2006 (UTC)

How about misnamed things? Fredrik Johansson 22:39, 26 August 2006 (UTC)

...List of misnomers in mathematics? Melchoir 23:35, 26 August 2006 (UTC)

I'm a little leery of the whole idea. The underlying premise seems to be that something is "misnamed" if named after someone other than the first person to come across it. That is not clear to me. Remember the "Columbus principle": It's not who discovers it first, but who discovers it last; that is, the person who makes the concept permanently available. Not everyone agrees with that idea, which is fine; it's not my purpose to promote it here. I'm just saying that a list that assumes the opposite, for its very existence, strikes me as POV. --Trovatore 17:53, 28 August 2006 (UTC)

Well, maybe there is a way of turning this into more of a history-of-mathematics type article? The few cases that I read about are just that: I read about them because someone else thought it was interesting enough to do some historical research and write about it. Once it is realized that some idea is improperly named, why would people continue to use the improper name? Habit .. laziness . ignorance .. lack of interest. I see no POV problem. FWIW, I recently did a little reading on the principle of least action, the correct attribution of which was littered with denouncemnts and accusations, mediated by councils, and even a kingly decree! At least we don't call it "sos-n-so's principle of least action", but I imagine there are more stories like this. linas 20:15, 28 August 2006 (UTC)

Hm? The POV problem is precisely the claim that such-and-such a name is "improper". --Trovatore 20:19, 28 August 2006 (UTC)

One problem is that many times it is not clear cut who was the "first" to discover something. Usually the modern reformulation is quite different than the original, and then it becomes a long debate whether so-and-so really discovered such-and-such or only a nonimportant special case or whether a later person really added anything essential, etc. Some people go with the "attribute to anyone in the neighborhood" philosophy, e.g. "so-and-so essentially had the idea but didn't know the formalism of the later such-and-such theory" whereas some go with the "attribute to the first person to make that exact statement" philosophy. So there are other reasons besides laziness, ignorance, etc., that somebody may choose to use a particular terminology.

Depending on your particular philosophy, you could argue almost all theorems named after persons are "misnamed". So the list could get quite long and useless. I think, as pointed out by Trovatore, that there are inherent POV issues in this list idea, only some of which have been pointed out. An additional source of concern is that the most reliable sources, say by math historians, will not attempt to assign credit but merely describe what contributions were made. So there's an opportunity here for editors to fall into the OR trap by saying "So-and-so wrote in his book that earlier Bunyakovski did such-and-such. So the theorem is misnamed". --C S (Talk) 22:04, 28 August 2006 (UTC)

Yes I agree with Trov and Chan here. Paul August ☎ 22:10, 28 August 2006 (UTC)

A momentous question

OK, here's a poser for you all, and I'm sure you won't want to eat or sleep until it's settled. If you start a sentence with the phrase von Neumann–Bernays–Gödel set theory, should the "v" be capitalized? I say yes, because you would capitalize it if you start a sentence with "von Neumann", and therefore the article does not need the {{lowercase}} template. Arthur thinks otherwise. Please focus your full intellectual powers on this question, as I know you wouldn't want to make a mistake here. --Trovatore 16:16, 26 August 2006 (UTC)

To up the ante, I don't see anyone crying havoc over Von Neumann architecture, Von Neumann probe, Von Neumann algebra, Von Neumann conjecture, or Von Neumann regular ring. And I've always thought that template was silly anyway. Melchoir 16:55, 26 August 2006 (UTC)

To add to the confusion, the "abbreviation" vNBG (at least, as used in my parents' work on logic and set theory) clearly cannot be uppercased at the beginning of a sentence. I'm now uncertain whether the entire expression, if spelled out, should be lowercased at the beginning of a sentence. I don't have time to research it for another few days, although I made the assertion in the appropriate article. — Arthur Rubin | (talk) 17:32, 26 August 2006 (UTC)

Response to Melchior's comment. It appears that, about 48 hours ago, someone went through and removed the lowercase template from all those pages. That person agrees with Trovatore that von Neumann is capitalized at the beginning of a sentence; I do not know whether this is correct, but it is surely a matter of editorial style, not grammar. In some style guides it depends on the original language (Dutch, German, etc) that the von comes from. The style I am used to would never capitalize von Neumann, even at the beginning of a sentence, and so I think the lowercase template is appropriate. Wikipedia is free to have its own style; my guess is that it is already documented somewhere, although a quick glance at WP:NAME didn't show anything. CMummert 17:34, 26 August 2006 (UTC)

Ah; I looked at the talk pages of those articles, but not their edit histories. I am not familiar with the usual treatment of "von Neumann" at the beginning of a sentence, so I'll back out of that particular issue. Melchoir 20:03, 26 August 2006 (UTC)

(responding to Melchor -- edit conflict) Well, I don't think it's silly on the articles where it really belongs, such as e (mathematical constant). We don't want our students deciding that it's sometimes OK to write it E, say if it's the first letter in an equation. And I'm fine with it, also, at eBay or bell hooks, though I don't think it's as important in those cases. But it should really be expunged from all the articles that start with "de" or "von" or "bin" or "ter"; those article titles are, in my view, correctly uppercased. Anyway, this is getting a little non-mathematical; if you want to get in on the whole earthshaking discussion, please see template talk:lowercase#Inappropriate use of this template (even that discussion should maybe go better at the MoS discussion page). --Trovatore 17:42, 26 August 2006 (UTC)

There's a conflating issue with e, though: in good writing one shouldn't be starting a sentence with it at all. Anyway, while it's a worthwhile goal to avoid misleading readers, usually the first, bolded usage of an article's title is where its correct usage is displayed-- and presumably, where the form will have a greater impact on the reader. In fact, if there's a conflict between the displayed title and the first usage, that alone draws the reader's attention, and that the actual usage is the one to imitate seems implicit. We don't have to beat the reader over the head with it. Maybe I should visit that talk page... Melchoir 20:11, 26 August 2006 (UTC)

(replying to the original question) I would capitalize "von Neumann" if it appears at the start of a sentence. That's at least the rule in German, Dutch and French, and it seems strange that English would deviate from it (though of course spelling is not always logical). -- Jitse Niesen (talk) 02:27, 27 August 2006 (UTC)

John von Neumann was so well known that he was often simply called "John von". So clearly the solution is to go thru all articles whose names begin with "von Neumann" or "Von Neumann" and replace those with "John von". Since this should clearly be capitalized, the ambiguity would be avoided. ;-) JRSpriggs 08:38, 27 August 2006 (UTC)

Navigational templates

I know I'm not a regular to this WP, but I'd like to throw out a suggestion: If the table on Portal:Mathematics/MathematicsTopics could be broken up into templates (as well as one large template of all of them), the templates could be placed on the respective articles to the great improvement of mathematics articles. 24.126.199.129 20:17, 26 August 2006 (UTC)

The majority of folks here despise the use of navigation templates, and delete them summarily. For good reason. linas 22:34, 26 August 2006 (UTC)

For those of us who don't see offhand what's wrong (or what's right) with navigational templates, could someone post a link to an earlier discussion where consensus was reached? The "good reason" linas cites are not evident to me. Michael Kinyon 00:42, 27 August 2006 (UTC)

There are long discussions that took place multiple times in the archives. Mostly, the problems were that the navboxes tended to get very large, chew up a lot of screen real-estate, and contain rather bizarre groupings of topics -- typically, obscure topics lumped in with major fields of study, thus giving undue weight to the obscure topic while effectively hiding the wealth of the major areas. Frequently, the navboxes would be skewed towards a college freshman's view of the world -- 23 ways of solving a differential equation and nothing else matters. If an article is well-written and properly linked, you don't need nav-boxes; you need an attention span that is longer than 15 seconds, which is something most of the editors here posses, but most proponents of nav boxes do not. Basically, you ain't gonna learn no math by surfing, and there's not point in encouraging surfing. linas 04:16, 27 August 2006 (UTC)

Ah. I didn't realize that earlier efforts were bloated and skewed toward the elementary and obscure. Looking at the existing mathematics nav-boxes, I see what you mean. The nav-box for convex, regular 4D polytopes seems fine, but someone stuck E7½ in the exceptional Lie groups nav-box. That was obviously inappropriate. The problem is clear: since the nav-boxes can be edited by anyone, of course they would bloat. Michael Kinyon 13:43, 27 August 2006 (UTC)

I am new to this discussion. I actually came here to propose such an idea! lol... I tend to like how the German wiki does it. For example, look at de:Gruppentheorie, "Group theory" (you may not speak German, but you can probably guess what most of the terms in the nav box mean.) It has three boxes, designating what field of math we are in, what is more general than a group, and what is more specific. It makes browsing around more enjoyable. Even if we dont have a sidebox, a box at the bottom of the articles could be nice. Am I redundant to some earlier conversation? - grubber 02:08, 23 September 2006 (UTC)

I tentively support an idea like de:Gruppentheorie. Personally I find the mathematics articles hard to navigate, and we do get ocasional comments from our readers who get lost engaging in a definition chase. Inline links present the reader with an unstructured web, whease a suitable nav box scheme would provide a more structured tree navigation scheme. Further the inline links can make navigation harder, you need to scan the text to find the appropriate links, these links may not always appear in standard places like the lead and see also sections making navigation even harder. A well thought through nav box system could make it easier for readers to find their way around the vast number of mathematics articles. --Salix alba (talk) 08:15, 23 September 2006 (UTC)

Infoboxes

Also: what is the consensus in WP Mathematics on infoboxes? Michael Kinyon 00:45, 27 August 2006 (UTC)

Dunno. Seem pretty enough in those places where they make sense. linas 04:16, 27 August 2006 (UTC)

Announce: Mathematics subject classification template

I created Template:MSC for use on category pages, for those who are into classifying things. I also did a brutal and summary redirect of Mathematics Subject Classification; specialists are encourages to write a blurb on those topics that don't have a blurb.

Speaking of templates, I'd like to remind everyone again about Template:Springer for links to articles in the Springer-Verlag online encyclopaedia of mathematics. —Preceding unsigned comment added by Linas (talk • contribs)

I undid the redirect as it doesn't make sense. The page on the AMS' Mathematics Subject Classification shouldn't redirect to a page that attempts to list and describe areas of mathematics (using the MSC as a "starting point"). The MSC is an interesting and encyclopedic subject in itself; its article should not only explain the classification scheme, but its differences (from the 2000 and 1991 versions), how it was created, who uses it, etc. --C S (Talk) 23:11, 26 August 2006 (UTC)

OK, well, its just was a nasty and brutal little article that threatens to try to duplicate the conetent of areas of mathematics, and I saw no point in encouraging duplication. linas 04:20, 27 August 2006 (UTC)

A little bit of politics

I'm going to ask here for help from native speakers (German particularly needed) in translation my Candidate statement for the Board Elections starting next week.

Putting together two comments above (User:KSmrq on the need for mathematical software support, and my own on the credibility the mathematics coverage disproportionately brings), having a mathematician on the Board might seem a positive step, to some here anyway.

Charles Matthews 14:23, 27 August 2006 (UTC)

Please place a notice here to assist those (like me) who would like to participate in the voting when it begins. I expect Wikipedia mathematicians will be especially interested in learning about a candidate who is a known mathematics editor. --KSmrq^T 20:33, 27 August 2006 (UTC)

meta:Elections for the Board of Trustees of the Wikimedia Foundation, 2006/En. But I spy a link at the top of this and most other pages. Charles Matthews 21:14, 27 August 2006 (UTC)

Update: I've had some very useful translation assistance, and am working on Italian right now. Spanish, Polish, Russian? Voting opens shortly. Charles Matthews 21:25, 30 August 2006 (UTC)

Soap bubble

Soap bubble is up for a featured article review. Detailed concerns may be found here. Please leave your comments and help us address and maintain this article's featured quality. Sandy 17:21, 27 August 2006 (UTC)

Citation templates

Hi all, please use these wherever possible. In particular, when citing an on-line article, please note that very few Wikipedia readers have an academic appointment and are using their office computer to access a journal's website, whereas anyone can download an arXiv eprint for free, so

in the case of published papers which are on-line, please use a link to the arXiv abstract page (not everyone prefers to download a pdf!; postscript is much faster for those with a postscript printer!) rather than a link to the journal website,
in the case of eprints, please use the arXiv citation template.

Here is the tutorial (created for the defuct WikiProject GTR, hence the gtr-related examples):

Book:

*{{cite book | author=Misner, Charles; Thorne, Kip S.; and Wheeler, John Archibald | title=Gravitation | location=San Francisco | publisher= W. H. Freeman | year=1973 | id=ISBN 0-7167-0344-0}}

Article in a research journal:

*{{cite journal | author=Kerr, R. P. | title=Gravitational field of a spinning mass as an example of algebraically special metrics | journal=Phys. Rev. Lett. | year=1963 | volume=11 | pages=237}}

Article in a research journal which was previously an arXiv eprint (check the arXiv abstract page to see if any publication details are noted):

*{{cite journal | author=Bicak, Jiri | title=Selected exact solutions of Einstein's field equations: their role in general relativity and astrophysics | journal=Lect. Notes Phys. | year=2000 | volume=540 | pages=1-126}} [http://www.arxiv.org/abs/gr-qc/0004016 gr-qc/0004016 eprint version]

arXiv eprint (not yet published):

*{{cite arXiv | author=Roberts, M. D. | title=Spacetime Exterior to a Star: Against Asymptotic Flatness | year = 1998 | version=May 16, 2002 | eprint=qr-qc/9811093}}

Article in a book:

*{{cite conference | author=Ehlers, Jürgen; & Kundt, Wolfgang | title=Exact solutions of the gravitational field equations | booktitle=Gravitation: an Introduction to Current Research | year=1962 | pages=49–101}} See ''section 2-5.''

Biography in the MacTutor archive:

{{MacTutor Biography |id=Friedmann|title=Aleksandr Aleksandrovich Friedmann}}

Article at the Living Reviews website:

*{{cite web | author=Gönner, Hubert F. M. | title=On the History of Unified Field Theories | work=Living Reviews in Relativity | url=http://relativity.livingreviews.org/open?pubNo=lrr-2004-2 | accessdate=2005-08-10 }}

These have the following effects:

Misner, Charles; Thorne, Kip S.; and Wheeler, John Archibald (1973). Gravitation. San Francisco: W. H. Freeman. ISBN 0-7167-0344-0.
Kerr, R. P. (1963). "Gravitational field of a spinning mass as an example of algebraically special metrics". Phys. Rev. Lett. 11: 237.
Bicak, Jiri (2000). "Selected exact solutions of Einstein's field equations: their role in general relativity and astrophysics". Lect. Notes Phys. 540: 1-126. gr-qc/0004016 eprint version
Roberts, M. D. (1998). "16, 2002 Spacetime Exterior to a Star: Against Asymptotic Flatness" arxiv:qr-qc/9811093May 16, 2002.
Ehlers, Jürgen; & Kundt, Wolfgang (1962). "Exact solutions of the gravitational field equations". Gravitation: an Introduction to Current Research: 49–101. See section 2-5.
O'Connor, John J. & Robertson, Edmund F., “Aleksandr Aleksandrovich Friedmann”, MacTutor History of Mathematics archive
Gönner, Hubert F. M.. On the History of Unified Field Theories. Living Reviews in Relativity. Retrieved on 2005-08-10.

Maybe some kind project member can move this tutorial to the appropriate project page? And what about a page called something like "introduction for project newbies" which helps newcomers to editing math-related articles find valuable resources like List of mathematical topics (I like the old name better) and this tutorial? TIA! ---CH 19:17, 28 August 2006 (UTC)

Five points:

These templates are more flexible than shown; more info is available at WP:CITET.
When giving page ranges, please use an en dash (–) rather than a hypen-minus: "49–101", not "49-101".
When giving ISBN data, please be forward-looking and convert to ISBN-13 (with online converter): "ISBN 978-0-7167-0344-0", not "ISBN 0-7167-0344-0". (And, please, do provide a valid ISBN.)
When citing a journal, please provide ISSN data using the {{ISSN}} template: ISSN 0031-9007.
Many online journal publications have a doi link; please use it if available.

A great deal of work has gone into writing these elaborate templates, and for good reason. They can really help the citation process. --KSmrq^T 23:00, 28 August 2006 (UTC)

Thanks for bringing these to my attention. Why should I use them "wherever possible"? What is the "good reason"? Thanks. -- Dominus 10:08, 31 August 2006 (UTC)

Official Wikipedia policy has not yet determined a standard set of templates, nor dictated their use. A journal or print encyclopedia or other formal publication does have standards. For readers, consistency makes references easier to search and easier to understand. For editors, use of templates makes a consistent preferred style easier to achieve.

Fill in the blanks, and the rest happens automatically. Should the author be listed "John Doe" or "Doe, John"? What gets italicized, quoted, bolded? What punctuation goes where? Where does the date go? All these questions and more are avoided, because the template knows what to do. Experienced authors of technical material have long relied on BibTeX databases and automatic formatting. We do not have a Wikipedia-wide database, but we can at least take advantage of templates.

Consider a novice editor who would like to cite Coxeter's classic Introduction to Geometry. Here's the template:

{{cite book | last = Coxeter | first = H. S. M. | authorlink = Harold Scott MacDonald Coxeter | title = Introduction to Geometry | edition = 2/e | publisher = Wiley | date = 1989 | pages = 366–368 | id = ISBN 978-0-471-50458-0 }}

and here's the result:

Coxeter, H. S. M. (1989). Introduction to Geometry, 2/e, Wiley, 366–368. ISBN 978-0-471-50458-0.

A novice might not italicize the title, without the prompting of a template might not include an ISBN, and so on. Journal citations are a still greater challenge. Yet merely populating the slots of a template:

{{cite journal | last = Lawvere | first = F. William | authorlink = William Lawvere | title = Taking categories seriously | journal = Revista Colombiana de Matemáticas | volume = XX | pages = 147–178 | publisher = Sociedad Colombiana de Matemáticas – Universidad Nacional de Colombia (Bogotá) | date = 1986 | url = http://www.tac.mta.ca/tac/reprints/articles/8/tr8.dvi | format = [[DVI (file format)|]] | id = {{ISSN|0034-7426}} }}

produces this lovely citation:

Lawvere, F. William (1986). "Taking categories seriously" (DVI). Revista Colombiana de Matemáticas XX: 147–178. Sociedad Colombiana de Matemáticas – Universidad Nacional de Colombia (Bogotá). ISSN 0034-7426.

Finally, use of such templates across Wikipedia makes a global change in convention, perhaps for another medium (or a non-English wikipedia), a minor change to implement. For example, we could switch to omitting quotation marks, or to using the typographically preferred curly quotation marks. --KSmrq^T 21:08, 31 August 2006 (UTC)

Have the recommendations, examples and points to remember in this section been posted somewhere more permanent and publicly visible? — merge 13:46, 31 August 2006 (UTC)

The math-specific template examples could be put in a subpage, which could be added to the list of math Project Pages at WP:WPM. EdJohnston 02:12, 1 September 2006 (UTC)

But wait! The WikiProject Mathematics page says there is already a math-specific manual of style: Wikipedia:Manual of Style (mathematics) . How about putting the new template advice in there? For extra visibility, also add the manual of style to the list of math Project Subpages? EdJohnston

One question re arXiv version versus versions published in journals. I would suspect that these will not be exactly the same as the journal version is likely to have gone through a review process before publication. Whats the best way to handle this? --Salix alba (talk) 18:47, 31 August 2006 (UTC)

Sep 2006

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

13-digit ISBNs

Above KSmrq, suggests the use of 13-digit ISBNs. However, since many (most?) sites (e.g. Amazon) can not handle 13-digit ISBNs, using them will make many of the "Find this book" links fail when clicking on the ISBN links. For example clicking on: ISBN 0-7167-0344-0, then clicking on "Find this book" link for the Amazon.com entry under the section "Individual online booksellers" finds this page, while doing the same thing for ISBN 978-0-7167-0344-0, gives this result So we might want to hold off for now on using 13-digit ISBNs. In the future I'm sure some enterprising bot will come along and convert all our ISBNs for us anyway ;-) — Paul August ☎ 16:03, 1 September 2006 (UTC)

The future arrives four months from today. Rich Farmbrough has a bot [User talk:Rich Farmbrough/Archive/2006Sep#The bot and ISBN-13 contemplating] an automatic change-over. In the linked discussion I mention a few other issues as well. I'm wondering if it would be too cumbersome to provide both ISBN forms (especially for print). Perhaps the MediaWiki ISBN magic could handle it for online use, like the handling of date formats; but, as always, implementation is not in our hands.

Meanwhile, my feeling is that the ISBN-13 form is future-proof and international, and allows the intended book to be found, even if it doesn't find all the sellers the ISBN-10 form matches. Every ISBN has annoying limitations. A paperback and a hardback have different numbers, as do versions of classics provided by different publishers; and each edition has its own number, which is at times good and at other times an obstacle.

Regardless of which ISBN you prefer, please do take a moment to provide one (and, ideally, check its validity).

Another way to assist readers in finding books is to check against online versions. Some texts can be found at Project Gutenberg, but mathematics is a minority there. Fortunately, we have alternatives.

These sites also include links to others. --KSmrq^T 18:19, 1 September 2006 (UTC)

Good articles

I've been going through the list of mathematics Good articles and I'm not sure that some of them really meet the grade. Riemann hypothesis is what I would consider to be the standard for a good article. My main concern is that the articles are either lacking in any history of the topic failing criteria (3a). Also it would be good to see some illustrations (6).

Fair division - clearly failed, just too brief. Now delisted.
Measure (mathematics) - lacks history. Could easily be expanded. Listing on Wikipedia:Good articles/Review
Homotopy groups of spheres - lack history, could do with some more illustrations. Recently successfully went through review. Comment on talk page.
Fractal - is a failed GA, though considerably better than the above.
Renormalization - listed as a maths article but really physics, should there be an article on the mathematical use of the term?
Ordinal number - I think fails criteia 1.(a) it has compelling prose, and is readily comprehensible to non-specialist readers, this article is heavily linked from the various number pages and other general articles, eg. floor numbering or Roman numerals. For readers clicking on a link from those pages the articles pretty incomprehensiable. Hence I'm listing it on Wikipedia:Good articles/Review. --Salix alba (talk) 11:48, 3 September 2006 (UTC)

Moreover, I think there is some need to discuss what makes a mathematics good article so we can establish a standard. Maths articles seem to be a bit of a special case as they are often highly technical, so they are likely to have problems with GA criteria 1a: it has compelling prose, and is readily comprehensible to non-specialist readers. We also seem to run into problems with 2b the citation of its sources is essential, and the use of inline citations is desirable, although not mandatory. Often inline citations are not really appropriate as the topic as a whole will be covered in cited textbooks.

Generally our number of GA's is very low with only 15 articles. Are there any other articles out there which people think are especially good? --Salix alba (talk) 10:37, 3 September 2006 (UTC)

I think the article on knot theory is a good target to turn into a GA, and eventually maybe even an FA. It doesn't try to do too much, and what is there currently should be fairly easy to brush up. I note that the section on Conway notation and planar graph notation is incomplete, but shouldn't take too much time to complete. There are several obvious ways to add good illustrations (and illustrative examples) to the article. --C S (Talk) 11:10, 3 September 2006 (UTC)

There's also quite a bit of bickering going on at Grigori Perelman, but it seems to me that this article has recently undergone a great deal of attention and editing and if all disputes can be resolved, I expect it could become a GA. Perhaps even Poincaré conjecture...but that will require a lot more work, and I've dropped the ball on that for which I apologize. But eventually I'll have a decent writeup of Perelman's proof ("alpha" version is at User:C S/todo/PC proof) and we can rewrite the article around that or whatever. --C S (Talk) 11:21, 3 September 2006 (UTC)

Yes I agree that knot theory could be a good target. Are people happy to defend the article, if so I think it should be nominated.

Grigori Perelman and Poincaré conjecture are probably too volitile at the moment GA 5 It is stable, i.e. it does not change significantly from day to day and is not the subject of ongoing edit wars. , that said it might be a good time to list if there are active contributors.

I'd quite like to create a B+ rating, for articles which are nearly but not quite at the standard of GA, we do have a good number of articles listed on Mathematics 1.0 which would fit this category, for example Pi which is good but has been delisted from GA. --Salix alba (talk) 12:05, 3 September 2006 (UTC)

Rename "Ordinal number"? God forbid!

User:Salix alba wants to rename (move) Ordinal number which is (in my opinion) one of the most important articles in the general area of Set theory. There are more than FIVE HUNDRED articles which link to it by its current name. Now, admittedly the majority of them would just as well be linked to the article which he proposes to put in its place -- an article on "first, second, third, fourth, fifth, etc.", but there is still a large fraction of them which are important mathematics articles. Please resist this disruptive change by talking at Talk:Ordinal number and elsewhere. Notice that there is already a link at the beginning of "Ordinal number" to the section Names of numbers in English#Ordinal numbers which covers the material in which he is interested. JRSpriggs 02:53, 4 September 2006 (UTC)

I agree, of course: "ordinal number" is correct. You can point him to this book, for example:

Halmos, Paul (1974). Naive Set Theory. Springer. ISBN 0-387-900092-6. (reprint of 1960 classic)

Chapter 19 is entitled "ordinal numbers".---CH 21:17, 6 September 2006 (UTC)

McNugget number is up for AFD

I've listed McNugget number for AFD. This is the second nom (first was by somebody else in October). AFD discussion page People may be interested in looking over the first discussion, which ended as "no consensus". --C S (Talk) 01:03, 5 September 2006 (UTC)

Multidimensional Gaussian integrals

User:EulerGamma recently removed a section about multidimensional generalizations from the Gaussian integral article for being "complicated" and lacking sources. The topic is real, but the lack of sources for the details is a valid complaint. Unfortunately, the original author seems to have been inactive for several months. I'm sure some people here are knowledgeable enough to check the content (I'm not); please have a look if you do. Fredrik Johansson 20:40, 6 September 2006 (UTC)

Leonhard Euler is up for FAC

Please see this page for the discussion. Borisblue 00:39, 7 September 2006 (UTC)

Mathematical Wikiers in Chinese

Dmharvy, here is your link. zh:Wikipedia talk:数学兴趣小组维基人列表----Hillgentleman 03:41, 7 September 2006 (UTC)

User:WATARU

New user WATARU appears to me to be almost certainly User:WAREL. However he hasn't yet done any of the things that got him banned before. Let's keep an eye out, but not provoke. "Don't start none, won't be none", as Huey P Freeman would say. --Trovatore 20:30, 9 September 2006 (UTC)

see [44]. --Trovatore 18:33, 11 September 2006 (UTC)

Now he's changed the Japanese link at division ring to something else. I don't read Japanese, so I don't know if it's appropriate or not, but given his history I'm not inclined to trust him. He may well be planning some shenanigans at ja.wiki and making edits here to prepare for them. (It goes without saying that he has long since used up his assumption of good faith.) Would someone with some competence in Japanese please look at this? --Trovatore 21:02, 12 September 2006 (UTC)

And he is insisting on using the Big Omega function on square number, where it is pointless showing off. (See diffs: [45][46].) Given the number of complaints we get for being technical where we have to be, there is no excuse for this in an article that proves that the squares of odd numbers are odd. Septentrionalis 19:48, 13 September 2006 (UTC)

Articles tagged as too technical

For a list see Wikipedia:WikiProject_Mathematics/Current_activity/Lists#Articles_that_are_too_technical. I've noticed, as I'm sure others have, that sometimes well-meaning editors just go through mathematical articles tagging them as "too technical". For example simple module has been tagged; however, I don't really see why it was tagged other than it looks like "gobbly-gook" to someone who doesn't know what a ring or module is. I can't see how this article can really be improved in a significant way to be accessible to someone without such a background. Perhaps an example built from the ground up would help...but that would seem to be the equivalent of writing a wikibook on abstract algebra. In any case, I believe this article (and some others) have been tagged wrongly.

The unfortunate thing about all this is that it makes it hard to find the actual overly-technical articles that can be made much more accessible. As a first step to making articles more accessible, therefore, I suggest that some people take some time and untag as many articles as they can -- those that are very advanced topics or seem to have been made as accessible as possible. --C S (Talk) 02:30, 11 September 2006 (UTC)

I added a sentence about graphical projection to Projection (linear algebra) and removed the tags. There wasn't anything in the talk page about why the tags were added. User:ST47 who added the "technical" tag was bot assisted. User:Srleffler added the original tag didn't leave any explanation. It seems Srleffler's attention was drawn to the article through graphical projection; they also left the same tag on projection (relational algebra) which Jon Awbrey summarily removed. Guess it's just another example of what you're talking about. (I know it's just one article. Sorry.) Lunch 23:15, 12 September 2006 (UTC)

got a bunch more. btw, it seems the current activity list hasn't been updated in a couple of weeks. did the bot run out of gas? Lunch 04:58, 24 September 2006 (UTC)

page move?

the article on Robert Berger, the mathematician, was linked to by several film-related articles mentioning the writer robert berger. i changed those to refer to Robert Berger (writer). might it be a good idea to move Robert Berger to Robert Berger (mathematician) and put a redirect in its place? how does one go about doing this? tia. Lunch 03:38, 11 September 2006 (UTC)

The easiest is to use the "move" tab at the top of the article to move Robert Berger to Robert Berger (mathematician). This will automagically leave a redirect in its place. --Lambiam ^Talk 05:31, 11 September 2006 (UTC)

But looking at this stubby article, I think there is not enough info to merit having a separate article here, as was noted by others on its talk page. --Lambiam ^Talk 06:16, 11 September 2006 (UTC)

Two points here: (1) Are you sure that these are two different people? Sometimes one person does work in two completely unrelated fields. For example, ~~Dorthy Lamour (hope I remembered the right actress)~~ Hedy Lamarr was both a film actress and the inventor of a method of encryption. (2) There is no point in moving the page unless you replace the redirect with a disambiguation page listing various people named "Robert Berger" and giving links to their pages. JRSpriggs 07:05, 11 September 2006 (UTC)

Try Hedy Lamarr for the inventive star. --Lambiam ^Talk 10:09, 11 September 2006 (UTC)

My thanks to Lambiam for the correction. JRSpriggs 05:26, 12 September 2006 (UTC)

According to his entry at the IMDB, the writer Robert Berger was credited as "Robert H. Berger M.D." for being a consultant for the movie Final Analysis. As that movie is about a psychiatrist, that Robert Berger is very likely too a shrink. Citations of (Berger, Robert. "The undecidability of the domino problem". Memoirs of the American Mathematical Society, 66, (1966), 1–72) all appear not to give a middle initial. --Lambiam ^Talk 10:35, 11 September 2006 (UTC)

This Robert Berger seems not to have an entry in the Library of Congress, but he IS in the Harvard library catalog! He is given as Berger, Robert (born 1938), author of the AMS memoir on domino undecidability. They don't know his middle initial. I also looked up the memoir itself, and it includes no middle name, middle initial, thesis advisor, and no acknowledgments that I could find. There were four references, including one to a paper of Hao Wang. WP's entry for Wang says he was at Harvard from 1961 to 1967, so it's reasonable he could have been Berger's advisor. AMS MathSciNet does not seem to have any papers by this Robert Berger besides the domino memoir. EdJohnston 19:36, 11 September 2006 (UTC)

the harvard library catalog lists several holdings under the title "the undecibility of the domino problem." one of them is the AMS publication. another one of them is a copy of his dissertation. the title page there probably has his advisor's name. i'll be visiting there at the beginning of november; if i get a chance, i'll look it up. (i'm also morbidly curious to see ted kaczynski's dissertation, too, so i might actually take the time. :) UMI has him listed at harvard in 1965, too, but they don't have a copy of his dissertation (not even the abstract).

what originally brought me to the article was just a haphazard meandering. i saw the article on the list of "too technical" articles and was curious why it was there. when i looked at the list of "what links here," i noticed the three (four?) links to the movie writer/producer. although a quick check through IMDB now makes me think there are at least three robert bergers of note: the mathematician; Robert H. Berger, M.D., the writer/consultant for "final analysis"; and robert berger, the producer. this last fellow was making films as far back as 1962 so unless the mathematician robert berger was also a rookie film-maker during his harvard days, they're not the same person. (and incidentally, robert berger has produced almost three dozen movies; maybe there should be an article on him.) that doesn't rule out that the mathematician went out and got an M.D. and got into the film business, but i'd hazard a guess that didn't happen.

anywho, all this attention seems way out of proportion, but i'm glad to see some other amateur sleuths out there too. :) i s'pose my two bits is that i go back an un-wiki-link robert berger, the writer/consultant of final analysis; make a stub on robert berger, the producer; and move robert berger, the mathematician. whaddya all think? too much?

thanks. Lunch 20:21, 11 September 2006 (UTC)

(oops, kaczynski did his PhD at michigan. he was an undergrad at harvard. oh well, maybe some other time.) Lunch 17:27, 22 September 2006 (UTC)

OK with me. The Harvard library catalog shows many, many Robert Bergers. But this man is the most famous of the mathematical Robert Bergers. Google Scholar still shows 216 citations to the domino paper, so he is notable. EdJohnston 22:55, 11 September 2006 (UTC)

The plan sounds fine. Just be careful of the other mathematician named Robert W. Berger who wrote quite a few papers, mostly in German. His genealogy can be found here. I don't know how notable he was/is.

By the way, this book review (a postscript file) asserts that the Robert Berger we have been discussing was indeed Hao Wang's student. Michael Kinyon 23:10, 11 September 2006 (UTC)

thanks. (i think the link is [47] for the postscript or [48] for the pdf, but i think the pdf got chopped off.) to address lambiam's early point, should the robert berger article mention all three since separate articles would be too short? i started a stub for Robert Berger (producer); potentially it could be much longer (he was rather prolific), but isn't long now. i dunno how long the article on robert berger the aperiodic tiler could be, or how long the article on robert w. berger could be. Lunch 00:12, 12 September 2006 (UTC)

WP:BLP violation at Louis de Branges de Bourcia

I've changed to a far better version while trying to incorporate some of the recent factual additions. But the previous version definitely had way too much speculation, ramblings, and just poor sourcing. Given the number of people (although maybe some of the IPs are really the same person), who have edited it into this state, I think it's wise if people keep an eye on this page. --C S (Talk) 06:04, 11 September 2006 (UTC)

Some of the details are from Sabbagh's book, but I have not seen it recently enough to edit. Septentrionalis 20:32, 11 September 2006 (UTC)

What does it mean?

I find that many math articles give definitions in a way that is 100% accurate but only 10% useful. (This is true of math writing beyond Wikipedia.) For example, until recently the definition of symmetric matrix simply stated that $A i j = A j i$ . That's all well and good—it correctly defines the term—but it does not answer the question "what does it mean for a matrix to be symmetric?". As best I can tell, the answer is "it means the eigenvectors are orthogonal", which I added. After all, this is what mathematicians think when they think "symmetric".

I propose a concerted effort to get answers of this form into the definitions of math terms—answers that allow readers to think like a mathematician rather than stare at syntax. Perhaps a template Template:what_does_it_mean? —Ben FrantzDale 23:35, 11 September 2006 (UTC)

As for the statement you added, it wasn't quite correct, so I fixed it in the article. (It turns out to be exactly the symmetric matrices that have orthonormal bases of eigenvectors which makes your addition even more appropriate to this particular article.)

As for your suggestion, I agree with you in principle but not in practice. A mathematical definition is just that--a definition. While it may be equivalent to any number of conditions, some of which are intuitively more appealing than others, the definition is usually the more straightforward one. In this case "symmetric" means literally that the matrix entries exhibit some kind of symmetry, in this case with respect to the matrix transpose. That's why we have a whole article to follow; the article should explain "what does it mean". A good article probably does not need any additional template if it's doing its job correctly.

Having said this, thanks for your contribution and suggestion. We do need to make sure that the math articles fully explain the "why". VectorPosse 00:26, 12 September 2006 (UTC)

what do you mean by "mean"? ;) that there is a complete set of orthonormal eigenvectors of a symmetric matrix (along with real eigenvalues) is usually called a theorem, and the symmetry of matrix entries is usually called the definition. of course, it is equivalent to do the reverse. (and there are several other definitions that result in equivalence.)

but the symmetry of matrix entries is by far the simplest definition, and the eigenvector/value property is listed shortly thereafter in the article (and this is good practice). also, the symmetry of matrix entries does have significance: if two vectors are related by multiplication by a symmetric matrix, then changes in entry i wiggle entry j as much as entry j wiggles entry i. symmetry is also preserved under a congruence transform (as like with change of coordinates applied to a quadratic form - not to be confused with a similarity transform, a change of coords for a linear system). physicists love these sorts of things. (as do mathematicians, engineers, and a whole party of people. :) but i'd stick this in a list of properties...

i guess my point is that people usually go with the simplest possible definition and stick equivalent definitions under "properties" or "lemmas/theorems". Lunch 00:43, 12 September 2006 (UTC) (oops. edit conflict.)

maybe i'd add that "simplest" doesn't always mean "most intuitive" or "most informative about why this is useful/interesting/wheretheheckdidTHIScomefrom". you're right in thinking that an article on such a subject deserves a bit of history/motivation in the leading paragraph(s). or maybe i'm not thinking what you're thinking. Lunch 00:54, 12 September 2006 (UTC)

Lunch, I think we are on the same page when you say “‘simplest’ doesn't always mean ‘most intuative’...". In the case of this example I'd argue that the obvious definition of symmetry, while important, is essentially intuition-free and so not very helpful for newbies. That's why I like the format "X is defined as y but really a mathematician is thinking z." Overall I'd like to see a move towards systematically answering “wheretheheckdidTHIScomefrom”. —Ben FrantzDale 02:40, 12 September 2006 (UTC)

you mean you didn't like my wiggling components analysis? ;) not to beat a dead horse, but as a mathematician who spends a lot of time doing linear algebra, i do think in components often enough. imho, the component-wise definition of a symmetric matrix is a good one and does have intuitive appeal. (i'd also add that linear algebra is almost always first introduced to students from a components point of view -- and with good reason.) Lunch 19:47, 12 September 2006 (UTC)

VectorPosse, as for the template idea, to clarify I was thinking a cleanup-style template not an infobox—something to tag an article with when it feels like it's skirting the "mathematician's intuition" definition. —Ben FrantzDale 02:40, 12 September 2006 (UTC)

Oh, I see what you mean now. Well, I'm not sure that changes my opinion much. I'm rather new here myself so I don't know much about templates; nevertheless, I suspect there's already a common template to indicate that an article needs more explanation or clarification. I'll leave that to more experienced editors to decide. I still agree, of course, that any "mathematical intuition" should be explained in the article (but not in the definition). VectorPosse 04:44, 12 September 2006 (UTC)

I'm not sure this is really necessary. Mathematical objects can have many properties, and one of them is not necessarily more important than others. We have a whole article to explain these properties and what is useful/interesting about them, and the intro should summarise the article. JPD (talk) 08:08, 12 September 2006 (UTC)

I agree that what does it mean? is really context-dependent. We would probably not say that Rⁿ means "cofunctor of an abelian variety". A symmetric matrix may appear in several contexts without reference to spectral properties. pom 15:06, 12 September 2006 (UTC)

A distance matrix is symmetric. This is an easily understood elementary property. Few mathematicians will think: "Oh, I know what that means. It has an orthonormal basis of eigenvectors!' --Lambiam ^Talk 15:11, 12 September 2006 (UTC)

Good point, and good example. I assume the eigenvector symmetry property isn't interesting in that case because the matrix isn't used as a transformation. For a distance matrix, it seams that symmetry is a trivial and not-too-interesting fact. The distance matrix page could do with some "what does it mean" love itself, actually; it says what one is and the fields in which they are used but not how they are used.—Ben FrantzDale 18:09, 12 September 2006 (UTC)

Symmetry isn't trivial or uninteresting in this case: it's one of the three key axioms defining a metric. —David Eppstein 21:28, 12 September 2006 (UTC)

I've been bold and added a Mathematical intuition project sub-page to try to address this issue. —Ben FrantzDale 18:14, 12 September 2006 (UTC)

Please help with extension (mathematics)

I created extension (mathematics) as a new disambiguation page with more than 30 entries. I think it ought to get organized into sections and subsections. Could Wikipedia's many mathematicians please help? Michael Hardy 21:31, 12 September 2006 (UTC)

I put them into some vague sections, people should feel free to subdivide further. Of course, most of these are algebra. -- Deville (Talk) 22:02, 12 September 2006 (UTC)

Does anyone else think it's a little weird that Extension problem is strictly about group extensions, while the stub Group extension mentions fields and other algebraic structures? Michael Kinyon 18:25, 15 September 2006 (UTC)

Yeah, I thought it was weird, so I changed Group extension to mention only groups and added a link at the bottom to Ring extension. This is a stub that could be greatly expanded. The article Extension problem actually has a lot of the material I would put in Group extension if it were up to me. Ah, if I only had the time... VectorPosse 19:03, 15 September 2006 (UTC)

What problems would result from just switching the names around? Michael Kinyon 20:07, 15 September 2006 (UTC)

I like it! If we did that, we would need to restore the few words I removed (probably with some editing), but I think this is a great idea. The page Extension problem ought to be a small-ish, more general page about any kind of extension problem. Then its links direct readers to the particulars of specific kinds of extensions. There is something in the page's discussion about calling it Extension (algebra) (which currently redirects to Group extension) and I think that would be necessary for this solution. Otherwise, one would have to include material on extension problems in all fields and that would be the same list that started this thread to begin with. VectorPosse 23:23, 15 September 2006 (UTC)

It seems fine to me. I am going on a Wikibreak for a bit more than a week starting tonight, and you have thought in more detail about what would be needed than I have. So my "vote" is: go for it! Anyone else have any thoughts about this? Michael Kinyon 03:47, 16 September 2006 (UTC)

Discussion at Euclidean space

There is a discussion occurring at Euclidean space concerning how best to write the introduction to be more accessible (see: Talk:Euclidean space#Obnoxious article and following). Interested parties may wish to join the discussion. Paul August ☎ 23:23, 12 September 2006 (UTC)

Peer review: Boy's surface

Boy's surface (talk) is up for peer review. Please offer any insights (there, not here).—msh210℠ 21:36, 13 September 2006 (UTC)

Martingale paradox

Martingale paradox has been put up for deletion: Wikipedia: Articles for deletion/Martingale paradox. The author has spent a lot of effort on Usenet at promoting this material, e.g. [49] (see User:AntiochCollege for suspiciously similar material). --C S (Talk) 00:21, 15 September 2006 (UTC)

What happened ?

I created a page for Pierre Rosenstiehl yesterday. It just disappeared today (even the traces of the changes I made). I am sure to have saved it after editing and the page is still in my watchlist... If it has been deleted, it would have been fair to post some message on my talk page. Otherwise, what did happen? pom 10:26, 15 September 2006 (UTC)

Here's the entry from the deletion log:

02:10, 2006 September 15 Jeffrey O. Gustafson (Talk | contribs) deleted "Pierre Rosenstiehl" (A7)

Go complain. --KSmrq^T 12:13, 15 September 2006 (UTC)

I put a message on Gustafson's Talk page asking him to consider restoring it and, if he still thinks Rosenstiehl is non-notable, putting the article up for AfD so that the rest of us can have some input. Michael Kinyon 12:42, 15 September 2006 (UTC)

Speedy deletion under A7: unremarkable people or groups/vanity pages. An article about a real person, group of people, band, or club that does not assert the importance or significance of its subject. If the assertion is disputed or controversial, it should be taken to AfD instead. I think that was wrongly applied. Charles Matthews 13:31, 15 September 2006 (UTC)

I think the "proper" method would be to take it to DRV. Or you could just recreate it with a {{hangon}} tag. But asking the deleting admin for reconsideration is always in order.

The page came back and I put a {{hangon}} tag. Actually, I am not sure it should be kept as I am not aware of the threshold considered by Wikipedia for notability. Whatever decision is taken does not care too much. However, deletion / restoration without a slightest explanation from an admin is an attitude which does not encourage editing at all. pom 16:05, 15 September 2006 (UTC)

Notability is well known to be a difficult concept to apply in practice. A better question: who would consult Wikipedia as a reference about a given person (excluding family, friends, colleagues)? For a member of Oulipo, it is easy to see that many people might look here. It is an argument you could all there-are-no-minor-poets: of course almost all poets are 'minor', as almost all mathematicians fail to be 'major'. But if someone likes a poem and has only a name, then, yes, they might use a reference work to discover more. Charles Matthews 21:44, 15 September 2006 (UTC)

Ok, but from a practical point a view, what should I do if I want to start to write pages on living combinatorists? Should I consider there is limit on the number of bigraphies and that I should prioritize the additions. If so, what would be the order of magnitude of this limit? pom 22:34, 15 September 2006 (UTC)

Mr. Gustafson pulled the trigger on the article (and perhaps should have known better), but an anonymous user User:151.200.246.168 was the one who tagged the article for speedy deletion in the first place. In the span of just over two hours, they tagged 18 articles for speedy deletion. It wasn't quite vandalism; many of the articles were marginal at best, but didn't quite seem like candidates for speedy deletion either. Weird. Lunch 17:18, 15 September 2006 (UTC)

Weird, indeed. In good faith, perhaps it is just someone who doesn't understand the speedy deletion criteria. In any case, I think this WikiProject can congratulate itself on how this was handled. (But will our backs hurt from patting them so hard?) Michael Kinyon 18:15, 15 September 2006 (UTC)

Etymology

Some unusual updates have been made to the etymology at pentagon (disambiguation), heptagon and polygon. I'm no expert, but I never heard that these terms had a Sanskrit origin before, so I am rather doubtful about the accuracy of these updates. Any comments ? Gandalf61 10:31, 15 September 2006 (UTC)

Here are some etymologies from the OED:

pentagon In A, ad. L. pentagon-us, a. Gr. pentagwn-oj pentagonal, five-cornered, f. penta- penta- + -gwn-oj from stem of gwnia angle. In B, ad. L. pentagon-um, Gr. pentagwnon, the neuter adj. used as sb. Cf. Fr. pentagone sb. (13th c. in Littré), whence the Eng; form in -gone.

penta- penta, before a vowel pent-, a. Gr. penta-, combining form of pente five, occurring in many words in Greek as a variant of the earlier pente-, and forming the initial element in various modern technical words adopted from Greek, or formed from Greek elements or on Greek analogies.

I'm not convinced that those articles need any etymologies, much less ones that seem to have little support in standard references. It may be possible that the words came to Greek from Sanskrit, but without any documentation I think it is better to just remove the anonymous edits instead of correcting or expanding them. CMummert 10:49, 15 September 2006 (UTC)

The Greek did not "come from" Sanskrit any more than the Sanskrit came from Greek. I've removed these changes. --Lambiam ^Talk 17:19, 15 September 2006 (UTC)

I asked on wikitionary and got

Er – no, it's wrong. All these related ‘shape’ nouns are from Greek. The Greek suffix was -γωνος, literally ‘angled’, and in this case combined with πεντα-, from πέντε ‘five’. The Sanskrit forms are cognate (i.e. both Sanskrit and Greek are descendants of Proto-Indo-European *penkʷe ‘five’), but Sanskrit is not the immediate source of the English word. Very few words in English come from Sanskrit. -- Widsith

So now we know. --Salix alba (talk) 17:44, 15 September 2006 (UTC)

There was a habit of calling Proto-Indo-European "Sanskrit" a century ago, before the decipherment of Hittite and the present understanding of IE vowels. It should be suppressed where found. Septentrionalis 18:48, 15 September 2006 (UTC)

Polar coordinate system

Hi everyone! An article that I've been working on quite a bit, Polar coordinate system, has just become a good article. We've requested a peer review to find out how it can be improved to featured article status, and it's great so far. Any other comments would be appreciated. Thanks. —Mets501 (talk) 14:20, 16 September 2006 (UTC)

Subcategory for geometric graph theory?

I've been working on a few pages lately that have the flavor of geometric graph theory — that is, about graphs that are either embedded in a geometric space themselves, or that arise from configurations in a geometric space. I'm wondering whether it would be appropriate to make a new category for them, as a subcategory of both geometry and graph theory.

Existing pages that could add or change to include this as a category: Fáry's theorem, Unit disk graph, Crossing number, Interval graph, Graph drawing, Visibility graph, Visibility graph analysis, Euclidean minimum spanning tree, Scheinerman's conjecture
Redlinks: Intersection graph, Gabriel graph, Nearest neighbor graph, Unit distance graph
Potential additional topics: Boxicity, Sphericity (of an intersection graph, would need a different name than the unrelated existing Sphericity page), Steinitz's theorem

Evidence that organizing things this way is not just my own hobby horse: Pach's edited collection Towards a Theory of Geometric Graphs (to which I contributed a paper on geometric thickness, a subject that would fit here as well but one that I think someone else should add if it deserves adding).

Anyway, this seems a widespread enough change that I felt I should open up the question for debate here rather than just going ahead and doing it. So, does anyone have an opinion on this possible reorganization? —David Eppstein 21:30, 17 September 2006 (UTC)

Category:Geometric graph theory sounds good to me. --Salix alba (talk) 21:14, 17 September 2006 (UTC)

I don't know if it will be so easy to make the distinction between Geometric Graph Theory and Topological Graph Theory. For instance: the usual crossing number is of topological nature, while the rectilinear crossing number is of geometric nature. Don't you think it could be better to (at least temporarily) merge the two in a Topological and Geometric Graph Theory subcategory? Of course, there are purely topological or geometric results (rotation system / Erdős–Szekeres theorem) but most have several aspects. Graph drawings may rely on spectral analysis or poset related properties (like track drawing). The classification of theoretical results may also be problematic (e.g.: Schnyder's theorem is about planarity, poset dimension, decompositions into particular forests, and induce a straight line drawing on a linear grid). All of this does not mean I am against subcategories, but rather that I am afraid by the number of topics which will cross the boundaries of categories. pom 21:59, 17 September 2006 (UTC)

To me the distinction seems clear enough: topological graph theory concerns graphs embedded on 2-manifolds such as the Euclidean plane, with vertices as points and edges as curves, while geometric graph theory either considers similar type embeddings with edges as straight line segments or other restricted geometric curves (polygonal paths with few bends, or circular arcs, though I doubt there is much already in WP that mentions these), or graphs coming from other geometric constructions (intersection graphs, visibility graphs, arrangements, etc). But of course there is overlap between the two; fortunately WP allows entries to have multiple categories. Perhaps I shouldn't have included Crossing number above since it's about the topological version of the problem; it's a long article so it might make sense to have a separate article on Rectilinear crossing number or Geometric crossing number (two different names for the same thing). Fáry's theorem seems like a good example of an article that overlaps both categories since it states that a topological graph has a stricter geometric representation; Scheinerman's conjecture is also of that type. —David Eppstein 03:20, 18 September 2006 (UTC)

You are fully right. pom 05:41, 18 September 2006 (UTC)

Can we put the Leonhard Euler FAC nomination on the project page?

Leonhard Euler is nominated for Featured Article status. I know that the nominator of the article has already posted this 10 days ago on this talk page but I think it would also be worth putting the info more prominently on the welcome page of the project. There's not that much work left to do on it to push it up to the desired quality and it's clearly a goal that should be among the project's priorities. Pascal.Tesson 23:44, 17 September 2006 (UTC)

In related news I've put Ackermann function on FA review. I think it lacks in laymans explination and is not up to current FA standards. --Salix alba (talk) 00:03, 18 September 2006 (UTC)

Speaking of which the primitive recursive article is also in a very sad state. But I digress. Pascal.Tesson 06:17, 18 September 2006 (UTC)

the apes are in question

I just contributed here calculating something. It would be nice if someone could verify what i wrote, because it seems the article contains a mistake. Nerdi 17:50, 18 September 2006 (UTC)

Exponents of mathematics, please help with this

I was going to move the link to the musical ensemble The Exponents from list of exponential topics to exponent (disambiguation) and add this (using the "dablink" template, since the various "otheruses" and "alternateuses" templates are an odious and execrable abomination abhored by all good people):

For other senses of the word "exponent", see exponent (disambiguation).

But the latter page does not exist. This caused me to notice that the list of exponential topics is quite incomplete as a list of Wikipedia articles already existing that belong there. Here's what needs to be done:

Enter "exponent" in the search bar and click "search", not "go".
Add to the list of exponential topics the mathematics articles that belong there.
Add to a new exponent (disambiguation) page the many "exponent" topics on non-mathematics topics, and also add the list of exponential topics to that page after a few of the most prominent mathematical senses of the word, with a note saying the list is fairly long.

I'll be back later to participate in this, but maybe not till tomorrow. Michael Hardy 21:20, 18 September 2006 (UTC)

Ackermann function

Ackermann function is up for a featured article review. Detailed concerns may be found here. Please leave your comments and help us address and maintain this article's featured quality. Sandy 15:46, 19 September 2006 (UTC)

256^(4.7*10^9) on prod

It's not in any math categories, so it won't show up on current activity; listing here. --Trovatore 21:15, 19 September 2006 (UTC)

and current activity hasn't updated for a week; is something wrong? Septentrionalis 23:25, 19 September 2006 (UTC)

Tagging talk pages and assessing articles

Wikipedia Assessments within AWB. Click on the image to see it in better resolution

Hi. If you still have work to do tagging talk pages and assessing articles, my AWB plugin might be of interest to you.

The plugin has two main modes of operation:

Tagging talk pages, great for high-speed tagging
Assessments mode, for reviewing articles (pictured)

As of the current version, WikiProjects with simple "generic" templates are supported by the plugin without the need for any special programatic support by me. I've had a look at your project's template and you seem to qualify.

For more information see:

Hope that helps. If you have any questions or find any bugs please let me know on the plugin's talk page. --Kingboyk 14:01, 20 September 2006 (UTC)

Manifold Destiny (article)

It has been suggested to me that this page, dealing with a controversial New Yorker dirt-digging story about Perelman, needs semi-protection. I can't quite see that it fits the guidelines at Wikipedia:Semi-protection policy, although there have been some anons making edits there that could get WP into legal trouble. In any case this page is potentially something very troublesome. Charles Matthews 21:28, 21 September 2006 (UTC)

I think you've been mislead by Lubos Motl's comment on your talk page [50]. Look through the history of the article. In particular, look at all the anon edits. I don't see what is trouble some about them; the worst I can see is a new user (not anon) that added an unsourced statement that Tian had never spoken to the New Yorker, but it was later removed by an anon.

One anon even reverted this incredibly biased addition by Motl [51] (there is one anon edit before this revert that added a pov check tag, probably because of Motl's previous edit). This was subsequently reverted by Motl, who does not seems to understand that saying that an article has an "unflattering potrayal" of someone does not imply to anyone that it is true (his edit summary reads: "anonymous edits reverted. The article really can't talk about "unflattering image" of a person because this indicates that the article is true, and Wikipedia would have to become a subject of lawsuit)"). Perhaps realizing that his previous edits were straightforward violations of NPOV, he then made the following "softening" edit: [52], which had the advantage of adding that "many" thought the "biased article" was filled with lies and conspiracies. Anyway, this is clearly this a violation of NPOV, so I reverted it; however, to address the complaint I did add some more info and used the words "paint an unflattering potrayal" to emphasize that this is a potrayal by a specific publication and Wikipedia is not in fact endorsing this is true.

I think given that this article exists, the edits that have been made by new or anonymous users thus far, are in fact of decent quality, certainly better than some by registered users! So I don't see any valid reason someone could want the page semi-protected.

Whether this page should exist is another issue. I didn't used to think so, but given the media coverage, it seems to me that this article is sufficiently notable. Some may not like what is going on, or that dirty underwear is being aired, but this kind of thing is par for the course on many topics. The mathematical community does not have any special protection on Wikipedia against this kind of stuff and shouldn't. Sure, the article could be potentially troublesome, but that is true of many controversial articles. We should deal with it like any other. Keep an eye on it and make sure people don't turn it into a version of their blog. --C S (Talk) 10:56, 22 September 2006 (UTC)

Thanks for filling me in. As I said, after I had been asked my conclusion was not to semi-protect. As you say, watching should be enough for the present. Charles Matthews 11:08, 22 September 2006 (UTC)

Order 3 groups are cyclic proof

Order 3 groups are cyclic proof is up for deletion. Chime in at the appropriate spot. Michael Kinyon 00:28, 23 September 2006 (UTC)

Gleason's theorem

This page was tagged as needing attention. It was a stub which simply stated the theorem in question. I have expanded it quite a bit, and removed the tag; I hope that my edits were sufficient to do so! My expansion has centred mainly on the application of the theorem, in quantum mechanics and the philosophy thereof. On the talk page, someone suggested sketching an outline of the proof of the theorem, which could be a worthwhile addition at some stage, but since most references to the theorem are centred on its uses and implications, this is probably not necessary at the moment (the proof is also hideously long and complicated, and not easy to summarise for an encyclopaedia article). Anyway, I wanted to find out the following. Now that the tag is gone, does your magical bot remove the page from the "needing attention" lists your project maintains? Or should I do that manually? I didn't want to just go ahead and do it, in case it interferes with the bot somehow...do let me know! Byrgenwulf 18:06, 23 September 2006 (UTC)

thanks! the article certainly no longer is a stub (and the "expert needed" tag was probably misplaced). and don't worry, the 'bot will eventually pick up on the tags. Lunch 05:12, 24 September 2006 (UTC)

Maybe this should be raised on the article's talk page, but I don't get the bit about P(y) being 1 for every lattice point y. Is 0 not also a lattice point? Doesn't this require y to be the sum of n (instead of any r) orthogonal atoms? And if true, isn't "the probability is fixed" a weak way of saying: the event is almost sure? --Lambiam ^Talk 07:36, 24 September 2006 (UTC)

That's a typo...the "=1" shouldn't have been there (it's gone now). So: any y can be expressed as the union of some (not necessarily n) number of orthogonal atoms x_i. The probability P(y) is the sum of the probabilities P(x_i) (all r of them). "The probability is fixed" simply means "uniquely determined" in this context. Byrgenwulf 10:19, 24 September 2006 (UTC)

Regarding the bot, there is some problem with the computer on which it runs. I'm on the other side of the planet and can't reach the computer remotely. I should be able to bring it up next week after I return to my office. Sorry about the problems (but it is nice to see that people are noticing). -- Jitse Niesen (talk) 14:45, 27 September 2006 (UTC)

Ear curve

Ear curve is up for deletion. Opine at its AfD page. Michael Kinyon 11:22, 24 September 2006 (UTC)

number needs attention

The section on real numbers is quite weak and maybe even misleading. Michael Hardy 02:15, 25 September 2006 (UTC)

I do agree that it is weak. Did you have something particular in mind when you say it's misleading? VectorPosse 02:39, 25 September 2006 (UTC)

I don't know what Michael Hardy had in mind; but the real numbers section conveys the impression that some of them (e.g., 0.1010010001...) are not constants. That is definitely misleading. JoergenB 13:31, 25 September 2006 (UTC)

While we're at it, the "Infinitary extensions" subsection is very misleading, and the "Transcendental numbers and reals" subsection is worth a look (the first paragraph does not deal with transcendental numbers at all). -- Meni Rosenfeld (talk) 10:49, 25 September 2006 (UTC)

It was less misleading after my edit, just before I posted this comment. It was written so as to make it appear that a real number is by definition a decimal expansion. I suppose in some ways that's no worse than saying a real number is a Dedekind cut, or that it is an equivalence class of Cauchy sequences, or any of various other members of that same isomorphism class, but the prevalence of popular errors about the definition of rational and irrational numbers (thinking that those concepts are defined in terms of decimal expansions) makes me cringe at that way of introducing the idea. Michael Hardy 19:47, 25 September 2006 (UTC)

Two remarks:

the "needs attention" note is still in. It would help if you could copy-and-paste your detailed explanation to the talk page, so people can have a shot at fixing it.
defining real numbers as (equivalence classes) of decimal expansions, and rational numbers by properties of such expansions, is correct, if awkward.
I'm not aware of a definition of real numbers that's better than the one via decimal representations, but still has some connection with non-mathematical culture, and can easily be grasped by non-mathematicians. Dedekind cuts and Cauchy sequences, I'm afraid, are right out for that.

RandomP 20:03, 25 September 2006 (UTC)

Saying real numbers correspond to points on a continuous line certainly can be grasped by non-mathematicians. Michael Hardy 20:06, 26 September 2006 (UTC)

For most people, formally defining any kind of number is a strange ritual. Does a definition of positive integers in terms of sets or successors connect with non-mathematical culture? Mathematics itself was very slow to make numbers formal objects. But in terms of historical development, there is evidence that the Dedekind cut idea is the earliest of the four major approaches. (These are: cuts, decimals, sequences, field axioms.) Cuts are also technically simple, while decimals are a beast. However, the number article should mostly leave the formalities to specialized articles, and concentrate on the big picture, which is that real numbers — however defined — "complete" (fill in the gaps of) the line (rationals). Concretely, what's the diagonal of a unit square? What's the area of a unit circle? --KSmrq^T 14:54, 26 September 2006 (UTC)

This may be OR, but I've found that a good way to explain real numbers is by a sequence of shrinking intervals – possibly of zero width, although that's not essential – [L_i, R_i] with L_i ≤ L_i+1 and R_i ≥ R_i+1, and R_i − L_i → 0. The claim is that this determines a unique real number x that is contained in all intervals: L_i ≤ x ≤ R_i. It is easy (for us) to see that this induces a Cauchy sequence as well as a Dedekind cut. There is no need to require the L_i and R_i to be rationals when explaining the idea. The point is, rather, to formalize the notion that "there are no gaps", a closure property. I've found that for psychological reasons I can't explain the notion of an interval shrinking "in the limit" to zero is easier to grasp than limit in general, even for a monotonic sequence. --Lambiam ^Talk 22:13, 26 September 2006 (UTC)

You and your students might appreciate Archimedes' proof that the area of a circle is the same as that of a right triangle with base equal to the circumference and height equal to the radius, found in "Measurement of a circle". (See Heath's translation, ISBN 978-0-486-42084-4.)

We want to be careful about the distinction between conveying intuition, which "number" should do, and establishing a workable definition, which "real number" should do. Working from the definition alone we need to be able to do arithmetic, comparisons, and proofs. That's one reason why Dedekind cuts are more appealing than decimal expansions for formal work. Compare with the modern definition of "compact space" in topology, where the "finite subcover" idea is less intuitive but more effective than "closed and bounded".

Back to your original point: Mental models are important for teaching; they are also important for functioning in the real world, a theme that artificial intelligence research has explored under the names "naive physics" or "qualitative reasoning". (See Smith and AAAI for sample reading.) --KSmrq^T 15:56, 27 September 2006 (UTC)

In which subject areas is the term basis function used?

There seems to be disagreement over whether the term basis function is used in functional analysis. I don't know enough about the subject to have an opinion. Could someone comment at Talk:Basis function? --Jtir 13:04, 25 September 2006 (UTC)

There is a problem with the weakness of the article. There must be several areas, eg wavelets, where this is a relevant concept. Charles Matthews 13:12, 25 September 2006 (UTC)

Correct. I looked at the what links here list and found wavelets, plus articles in chemistry, physics, engineering, and business that link to Basis function (I've put a culled, classified, and alphabetized list of linked articles at Talk:Basis_function). A wikipedia search finds many other examples of the term being used. It is starting to seem to me that making the article a dab would be preferable to trying explain all possible uses of the term. I don't have enough WP experience, though, to know what the implications are. --Jtir 21:26, 25 September 2006 (UTC)

A dab page makes mainly sense if we have separate articles on different meanings of the words "basis function". In mathematical use, isn't there a common meaning: an element of some basis of a vector space whose elements are functions? The main problem of the article may be that it starts with the words "In functional analysis" instead of "In mathematics". --Lambiam ^Talk 22:38, 25 September 2006 (UTC)

an intro sentence might be, "In mathematics -- particularly analysis -- a basis function is an element of the basis for a function space. The use of the term is analogous to basis vector for a vector space." (NB: some of those words are dab pages so the links are Analysis (mathematics) and Basis (linear algebra).) Lunch 00:56, 26 September 2006 (UTC)

With this formulation, couldn't all the technical content of the article be removed? Basically the article is saying that basis function is a synonym for basis vector in some usages. If so, the article could become a redirect to basis (?) which could parenthetically note the same thing. --Jtir 16:10, 26 September 2006 (UTC)

I don't think a simple redirect to Basis is a good idea. When dealing with bases in function spaces, a Hamel basis (which is what that page focuses on) is usually not the tool of choice. Instead one typically deals with a Schauder basis or, in the more specific Hilbert space setting, an orthonormal basis. Sometimes the word is stretched a bit, such as in the context of Riesz basis (which I think is really just a frame). Michael Kinyon 16:20, 26 September 2006 (UTC)

(I'm gonna CC the conversation here to the basis function talk page. There's some good stuff here that hasn't been mentioned there, and vice versa (along with some repeats). Come on over and join in!) Lunch 19:04, 26 September 2006 (UTC)

Should "Recursively presented group" redirect to "Presentation of a group"

Both finite and recursively presented groups are defined on the page "Presentation of a group". At present "Finitely presented group" redirects to "Presentation of a group" but "Recursively presented group" is just a fairly minimal stub. It would make more sense to me if it too redirected to "Presentation of a group". Bernard Hurley 20:38, 25 September 2006 (UTC)

Yes, it would. I think I created the article, and wasn't aware of that (probably because I thinko'd and created it under the wrong title - sorry, I was just upset we didn't have those articles when rereading Rotman).

RandomP 20:53, 25 September 2006 (UTC)

Well, merge and redirect. Charles Matthews 09:36, 26 September 2006 (UTC)

'Determinants' is a featured article on the French Wikipedia

Are we allowed to steal from the other language Wikipedias? See [53] for a rather nifty treatment of Determinants. It's 111K (vs the 55K of our own English article) and has some nice color illustrations. The language used is not 100% familiar to someone whose linear algebra is several years in the past, but maybe this is the latest thing.

Here are the opening sentences:

"First introduced in algebra to determine the number of solutions of a system of linear equations, the determinant reveals itself as a very powerful tool in numerous domains (study of endomorphisms, search for eigenvalues, differential calculus). It is in this manner that we define the determinant of a system of equations, the determinant of an endomorphism or the determinant of a system of vectors.

"For many operations, the determinant can be defined by a collection of properties (axioms) that we summarize by the term "alternating n-linear form". This definition allows us to make a complete theoretical study and to enlarge further its field of application. But the determinant may also be conceived as a generalization to n-dimensional space of the notion of oriented surfaces and volume. This aspect, often neglected, is a practical and illuminating approach to the properties of the determinant." EdJohnston 23:59, 25 September 2006 (UTC)

I believe that the other language wikipedias use the same license which we have here. So you can use their content freely provide that you give them credit for it and offer it to others under the same condition. In other words, go ahead and copy any of their text and translate it into English. But make sure that you attribute it to them in your edit summary -- specify that it was the French wikipedia and name the article, so that anyone can look in their revision history to see who put the material into it in the first place. JRSpriggs 05:50, 26 September 2006 (UTC)

Yes, you can translate and use here freely. Charles Matthews 09:38, 26 September 2006 (UTC)

Actually, translation is not just permitted (and as far as I can see often not accompanied by credits), but encouraged. Read e.g. Wikipedia:Translations into English. JoergenB 10:13, 26 September 2006 (UTC)

You ought to give credit, though. Anything else is risky under the GFDL. Remember that the original authors still hold copyright, even though they've licensed it to you. If you don't comply with the terms of the license (which requires attribution) you could be infringing. --Trovatore 06:43, 27 September 2006 (UTC)

Well, this sounds reasonable; and 'there are some nice templates', which make it very easy to inform the reader of sources from sister Wikipedia, and which you may place under the heading references. It might be a good idea to use them whenever material is translated, which is seemingly not done now. Not only the determinants article lack such information. JoergenB 13:51, 29 September 2006 (UTC)

Regretfully, I'll have to qualify the statement there are some nice templates. After having been around at the template pages a little, getting more and more confused, but finally finding some adequate explanation, I'l have to rephrase it there are two nice templates (namely Template:German and Template:Polnish). I accidently started by looking at a list of recently translated articles from German to English, and then assumed that I knew the pattern... However, there may be other such templates without proper categorisation (and of course they should not be too hard to create, I suppose, if we want to encourage translators to give more credit).

That discussion perhaps should move to another page, though. JoergenB 16:43, 29 September 2006 (UTC)

Something has gone wrong with LaTeX interpreter

Being realtively new to wikipedia I'm not sure where to post this so it's going here. Something has gone wrog with the LaTeX interpreter on wikipedia so that maths pages are full of lots of raw LaTeX. Bernard Hurley 23:27, 26 September 2006 (UTC)

It seems that the server of formula PNGs (http://upload.wikimedia.org/) is unreachable. As a consequence, PNG formulas only appear in their HTML version. pom 23:52, 26 September 2006 (UTC)

Some images also seem to be broken. I suspect this is a tempory problem which will be fixed in a few hours. Its happened before. --Salix alba (talk) 00:29, 27 September 2006 (UTC)

Have you tried control-shift-R? For several days now, I have occassionally been seeing the formulas unconverted. But they always become correct after control-shift-R. JRSpriggs 06:13, 27 September 2006 (UTC)

That is curious because the LaTeX interpreter is on the server. I can't test this because the problem seems to have gone away, but thanks for the suggestion. Bernard Hurley 08:29, 27 September 2006 (UTC)

If you visted the page while the PNGs are not accesible, the HTML version could be stored in the cache and so appear even after the problem is gone. Purging the cache when everything is working again would fix this problem. JPD (talk) 10:31, 27 September 2006 (UTC)

Spurious dashes

Hmm. Gleason's theorem, at least, still has issues with spurious dashes, though. Does this happen to anyone else? RandomP 02:11, 27 September 2006 (UTC)

Yes, I noticed it an hour or so ago in Character theory. Michael Kinyon 06:37, 27 September 2006 (UTC)

This is a bug in the LaTeX interpreter on wikipedia. The LaTeX interpreter seems to add a dash to the end of formulas containing certain letters and ending in certain other characters. So in the following paragraph "B(m,n)" gets an extra dash:

Let $n,m\in\mathbb{Z}$ where

m

is odd,

n > 10 78

and

m > 1

, and let

B (m, n)

be the free m-generator Burnside group, then every non-cyclic subgroup of

B (m, n)

is SQ-universal in the class of groups of exponent

n

If I change it to "B(x,y)" it is OK:

Let $x,y\in\mathbb{Z}$ where

x

is odd,

y > 10 78

and

x > 1

, and let

B (x, y)

be the free m-generator Burnside group, then every non-cyclic subgroup of

B (x, y)

is SQ-universal in the class of groups of exponent

y

A fix seems to be to add a LaTeX space at the end of the formula but in this case the formula gets displayed with a larger font! So using "B(m,n)\ " we get:

Let $n,m\in\mathbb{Z}$ where

m

is odd,

n > 10 78

and

m > 1

, and let $B(m,n)\$ be the free m-generator Burnside group, then every non-cyclic subgroup of $B(m,n)\$ is SQ-universal in the class of groups of exponent

n

Incidentally you can get the larger font by including a LaTeX space so:

"a" gets interpreted as $a$
"a\ " gets interpreted as $a\$

Bernard Hurley 08:23, 27 September 2006 (UTC)

And a thinner space by using \,: "[<math>a\ </math>]" gives "[ $a\$ ]", while "[<math>a\,</math>]" gives "[ $a\,$ ]". --Lambiam ^Talk 10:27, 27 September 2006 (UTC)

There is a bugzilla bug on this. Vote for it to encourage a quick fix. I'd recommend against short term fixes in articles. --Salix alba (talk) 08:27, 27 September 2006 (UTC)

Guys it's totally about the caching. When wikipedia sees an equation it's seen before it re-uses the old image. Sometimes they change the image renderer so you get a version from an old renderer. e.g.:

B (m, n)

B (x, y)

B (a s i x h u x, s d k c j n j z z)

. So it seems

B (m, n)

is from the old renderer.

B (m m m n n, n n n)

Here's another example: $\oint$ . Oh look it's broken. That one's cached. But with the new renderer: $Babcasisxajnsx\oint$ . I think that last one got fixed when they switched over to dvipng. When you do experiements like this you should always insert random text to trick the caching. 'course I could be wrong about all this, it's just a theory. Dmharvey 12:45, 27 September 2006 (UTC)

That seems to make sense. It would be nice if there were some mechanism to force the re-caching of a formula, but I suppose that could be open to abuse, it would also break any pages that rely on an incorrect old rendition. Bernard Hurley 13:02, 27 September 2006 (UTC)

I did a checkout on phase3 (is this the correct tree?) and was able to reproduce the bug with a fresh mw installation. I found a problem in render.ml, and after fixing it, the problem went away (it was necessary to clear the math table, of course). However, this can't explain why the bug does nolonger occur for new formulas. For details, see bugzilla.--gwaihir 16:25, 27 September 2006 (UTC)

Good stuff. Have you tried running with the preference set to MathML if possible. This has the effect of rendering simple maths as html and for these I'm getting the same problem without a image being used anywhere, so <math>B(m, n)</math> produces the html B(m,n)-. --Salix alba (talk) 17:48, 27 September 2006 (UTC)

Ah the cache issue explaines the difference of apprearance, in some equations

$a_n x^n + a_{n-1}x^{n-1} + \cdots + a_2 x^2 + a_1 x + a_0$ .

$((\ldots(a_n x + a_{n-1})x + ... + a_2)x + a_1)x + a_0\,$ .

to me the first looks good, but the letters in the second seem rather blury. I guess the first is cached using an old renderer, but the second is generated using a new renderer. --Salix alba (talk) 08:43, 29 September 2006 (UTC)

Good articles and inline cites

On Wikipedia talk:Good article candidates they have been reworking the criteria, which now currently require the use of inline cites. This resulted in all 11 of our mathematic GA receiving a message warning that the articles may be up for review. Lots of other articles also received the same messages and the physists especially have visiforously protested against the change. Theres now an atempt to reach a consensus on the issue. This particularly affect maths articles as we tend not to use inline cites for the main mathematical content, in Wikipedia:Featured article review/Eigenvalue, eigenvector and eigenspace use of manitory inline cites was contested.

People might like the add their views at on the issue at Wikipedia talk:Good article candidates. --Salix alba (talk) 18:03, 27 September 2006 (UTC)

There is also discussion on Wikipedia talk:Citing sources. This is very relevant as the proposed GA standards would make it difficult for math articles to receive GA status. And there is also discussion on Wikipedia talk:WikiProject Physics. CMummert 03:23, 28 September 2006 (UTC)

Category:Math wars

I nominated this for deletion. The discussion is at Wikipedia:Categories for deletion#Category:Math wars. Comments are welcome. Oleg Alexandrov (talk) 01:51, 28 September 2006 (UTC)

Intro line to analysis

In Areas of mathematics, I think it is misleading to say that analysis is primarily related to rates of change. Many aspects to the theory do not arise in this way. I think it would be better to say that analysis is the study of inequalities, because this is the theme that runs through every branch, at least it seems to me. To quote Krantz (from a book review of 'A Companion to Analysis: A Second First and First Second Course in Analysis') "Analysis is dirty, rotten, hard work. It is estimates and more estimates. And what are those estimates good for? Additional estimates, of course. We do hard estimates of integrals in order to obtain estimates for operators. We obtain estimates for operators in order to say something about estimates for solutions of partial differential equations. And so it goes." Any comments? I tried to change it initially myself, but instantly got reverted. :) I should have started here I suppose, thanks to Oleg for pointing this out to me. Thenub314 03:29, 28 September 2006 (UTC)

Whatever it is, it should match the Mathematical analysis article. (I personally have no really clear "intrinsic" concept of analysis - I know what would be considered analysis amongst the things I know, but if confronted with some mathematics that was totally unknown to me, I might be in doubt as to whether to consider it analysis.

Right now, the areas of mathematics article claims

"Analysis is primarily concerned with change. Rates of change, accumulated change, multiple things changing relative to (or independently of) one another, etc."

which appears to me to be based on real analysis in one variable. Mathematical analysis has:

"Analysis is a branch of mathematics that depends upon the concepts of limits and convergence."

which is what I would consider more appropriate for describing topology. Of course, one approach would be to define analysis historically, as that branch of mathematics that begins with the study of "nice" real functions, integration, and differentiation.

RandomP 03:58, 28 September 2006 (UTC)

Jordan would have probably have considered the "Analysis is... limits and convergence" definition to be correct, but at that time topology did not exist as a separate area of study. It's a matter of historical perspective. The contents of undergraduate analysis courses seem to have been fixed for about the last 50 years, but apart from that it would seem quite difficult to define.

Bernard Hurley 09:31, 28 September 2006 (UTC)

Part of the problem is that "analysis" is actually at least two fields: functional analysis and something which I might term "higher calculus". The former does often concern itself with limits and convergence, but in function spaces rather than spaces like $\mathbb{R}^n$ . The latter considers individual functions on $\mathbb{R}^n$ using calculus-like ideas such as the derivative (of course, in many variables). Then there is the mysterious realm of PDE's, which bleeds into differential geometry, while perhaps the entire field is haunted by the ghost of operator theory. Perhaps the best one-sentence summary is that "Analysis is the field of mathematics which studies functions or spaces of functions using techniques related to the notion of limits and convergence." If I wanted another sentence, I would write, "Although all of its techniques, such as differentiation, integration, Fourier analysis, and so on, have seen vast generalizations (for example, p-adic analysis, generalized measure theory, and harmonic analysis on an arbitrary locally compact topological abelian group), it is over the connected, locally compact, and complete metric spaces $\mathbb{R}, \mathbb{C}$ that they wield the greatest power and demand the most extensive use." This sentence disposes of the vast confusion that arises when you try to generalize about "analysis", since it is now so big. On the other hand, I'm not an analyist, and it seems that by doing this I might be doing the moral equivalent of saying "Algebraic geometry, although generalized to work over arbitrary commutative rings and to answer questions of number theory and even algebra itself, is essentially the study of complex algebraic varieties." Ryan Reich 13:33, 28 September 2006 (UTC)

Funny that this came up; a few days ago, a professor of mine remarked "It's not an exaggeration to say that analysis is the study of estimates". I think there might be some merit to incorporating that word in the definition. Fredrik Johansson 13:36, 28 September 2006 (UTC)

History of Analysis article

I am not a historian, so I probably should not really comment, but is the history section under Mathematical Analysis article seems a bit too good to be true. I did some reading up on the MacTutor math history site. It doesn't seem to indicate that calculus was known in india in the 12th-14th century. Is this really true? In terms of verifiability all I found in any of the articles was a link to some physics prof's web site. Does anyone know more? Thenub314 00:30, 30 September 2006 (UTC)

Citation issues

Lately, there have been many discussions of how to cite science and math articles at WP:GA and WP:CITE. In particular, there are editors out there in Wikipedia-land which would like to see every line in Wikipedia-articles cited. That would include, for example, line-by-line citations for mathematical proofs which I think would be ridiculous. There is currently a proposal at WP:CITE to include an important modification to the guidelines that would state that elementary facts should not/may not be cited. I tried to qualify this with a statement of what things I think (and maybe others think) should be cited in science and math articles and what things should not (and why). Please read, comment, and modify this work here. --ScienceApologist 05:53, 29 September 2006 (UTC)

There is little point giving citations for 'well-known' facts, anyway. Putting a huge effort into that is not going to solve the issue of references for genuinely recherché facts, which are those for which it is valuable to give pointers. Charles Matthews 07:00, 29 September 2006 (UTC)

I would go further. Peppering an article with extra citations is harmful, not helpful, for readers.

Extremists at Wikipedia insist otherwise.

One distorting force is the use of inline citations to address the reliability of our articles, which I believe is a fundamental mistake. Editorial debates belong on a talk page, not an article page. A reader should be able to have confidence that the Wikipedia quality control process has done its job, so that they can safely focus on absorbing content from the article.

Excess citations make it impossible to assess salience. If we cite both for "1+1=2" and "the Riemann hypothesis is true", a reader has no indication that the former is trival and uncontroversial while the latter would be a major claim. Nor will many editors wish to verify dozens and dozens of such citations, so garbage can easily creep in.

If only common sense were more common … --KSmrq^T 17:49, 29 September 2006 (UTC)

agree with above, c.f. 0.999, where every trivial thing, it seems, is cited. Mct mht 00:45, 30 September 2006 (UTC)

I encourage people with views like those above to follow and contribute to the discussions at WP:CITE and WP:GA. Discussing this here won't help to convince the editors who recently revised the GA guidelines. "Consensus" was reached on the changes because nobody from the sciences was contributing to those discussions. CMummert 17:57, 29 September 2006 (UTC)

GA status for Addition?

To my eyes Addition seems to be a good quality article. It might be an idea to put it forward to Wikipedia:Good article candidates, if anyone willing to defend it. BTW it is well cited with both inline and overal cites. --Salix alba (talk) 16:30, 30 September 2006 (UTC)

Citation guidelines proposal

I know you've been having similar concerns about citations and Good Articles here as we have over at Wikipedia:WikiProject Physics. I have a proposal to deal with this debacle. Let's establish, by consensus within the project, a set of guidelines for referencing physics and mathematics articles in Wikipedia. Then, at least, we will have a set of clear guidelines and an established consensus to refer to if we start having problems with WP:GA and WP:FA. I think if we write a reasonable set of guidelines, which respect WP:V and WP:CITE, we'll get little argument from the vast majority of the people over there.

I have already written a proposal, available here: Wikipedia:WikiProject Physics/Citation guidelines proposal. It definitely has a whiff of the first draft about it (some sentences seem pretty tortured), but I'm confident we can bang it into something that is clear and concise. I've tried to write the guidelines in such a way that they don't apply just to physics, although the examples are (by necessity) taken from articles I'm familiar with. I'm hoping that we can get the editors from both WikiProjects (physics and mathematics) to form some kind of a consensus for referencing our articles, which would give it increased legitimacy: we could incorporate the guidelines into both our projects.

To keep the discussion (semi-)unified, please comment at Wikipedia talk:WikiProject Physics or Wikipedia talk:WikiProject Physics/Citation guidelines proposal. –Joke 16:59, 30 September 2006 (UTC)

I urge the participants here to go over the proposal and help reach concensus. I expect it will carry more weight if it is a joint proposal of two active WikiProjects. --Lambiam ^Talk 23:16, 30 September 2006 (UTC)

History of mathematical notation - peer review

History of mathematical notation is seeking peer review. --Salix alba (talk) 19:02, 30 September 2006 (UTC)

Oct 2006

This is "Wikipedia talk:WikiProject Mathematics/Archive18". It covers October 2006.

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

WAREL is back again

I wonder if anybody knowing the subject of the articles edited by WATARU could take a look at some diffs and see if it makes sense what he wrote. Oleg Alexandrov (talk) 15:09, 28 September 2006 (UTC)

I think all changes but one have been corrected or removed. I don't know about Japanese sociologists. — Arthur Rubin | (talk) 18:15, 28 September 2006 (UTC)

But he doesn't stop, blocking him seems necessary.--gwaihir 23:37, 28 September 2006 (UTC)

Looking at policy under WP:DE (Disruptive Editing) I think WATARU is somewhere between steps 5 and 6 of the process. According to step 4, a 'Request for Comment or other impartial dispute resolution' should be opened. However this was done back in April '06 [54]. We now seem to have 5, 'Editor ignores consensus'. The suggestions under part 6 are topic ban, site ban or probation. EdJohnston 00:45, 29 September 2006 (UTC)

We reached point 6: 'Blocks fail to solve the problem.' --Lambiam ^Talk 01:46, 29 September 2006 (UTC)

Still up to the same tricks. What's the next step? —David Eppstein 23:15, 30 September 2006 (UTC)

Blocked (along with his IP) for 48 hours for personal attack (against me). I have no objection to a community ban, including the IP. — Arthur Rubin | (talk) 06:00, 1 October 2006 (UTC)

Changed reason to general disruption. The WP:NPA in editing my user page doesn't rise to the level required for a block, but the disruption is still valid. — Arthur Rubin | (talk) 06:26, 1 October 2006 (UTC)

Now Special:Contributions/Suslin --gwaihir 15:40, 4 October 2006 (UTC)

and Special:Contributions/MACHIDA (indefblocked; anyone changing the ja: wikilink on Field or Division ring deservices an immediate temporary block, at this point, and the other edits and style makes it clear what's happening.) — Arthur Rubin | (talk) 12:54, 9 October 2006 (UTC)

and Special:Contributions/MORI (indefblocked), but he seems to have killed the ja: articles. — Arthur Rubin | (talk) 03:10, 10 October 2006 (UTC)

Fourier Transform

Some of us are discussing re-organizing the articles about the fourier transfrom, I thought this might be of general interest, so anyone interested should look at the Topology of articles discussion under the Continuous Fourier transform talk page. —Preceding unsigned comment added by Thenub314 (talk • contribs) (Oops on my part Thenub314 00:29, 30 September 2006 (UTC))

That's not a good page name. How about Fourier transforms on the line? Charles Matthews 07:01, 29 September 2006 (UTC)

There is also a multi-dimensional continuous version, which curiously is mentioned at Fourier transform but not Continuous Fourier transform. --Lambiam ^Talk 11:46, 29 September 2006 (UTC)

The multidimensional version is in there under under a sub-sub-section Extensions. I like the idea of "Fourier Transform on the Line", I had suggested "Fourier Transfrom on R", but no one else seemed to like that idea. But I do dislike the term "continuous Fourier Transform". Thenub314 13:41, 1 October 2006 (UTC)

"Importance" and "vital" tags

I think we need to have a discussion about just what are the criteria for the various "importance" levels, and the "vital" tag, for the {{maths rating}} template. Right now they seem to be the opinion of the person adding the template, which I have no terrible argument with (I certainly don't want to add another level of process), but we need to be aware that there can be disagreements.

My attention was brought to this by Salix alba's addition of "Top importance" and "vital" to the decimal article, an article the need for which I think is frankly marginal, at least from the perspective of mathematics. (I agree it's a very important topic from the perspective of history of mathematics.) --Trovatore 20:20, 30 September 2006 (UTC)

Vital relates to Wikipedia:Vital articles which is actually a cross-language grouping of the vital articles that every language should have. There are about 67 such mathematics articles, most of which are rather basic. The mathematician in this list is: Archimedes, Vladimir Arnold, Diophantus, Euclid, Leonhard Euler, Pierre de Fermat, G. H. Hardy, David Hilbert, Gottfried Leibniz, Muhammad ibn Musa al-Khwarizmi, Henri Poincaré, Pythagoras, Srinivasa Ramanujan, which I find rather arbitary, and does not agree with the list we put together on the main maths assessment page. It is the same list as Wikipedia:WikiProject Biography/Core biographies. The tag is there to have some cross coordination with other efforts.

Yes I wasn't quite sure on the importance of decimal, high importance for school age students, engineers, less important for pure mathematicians.

You do raise a good point about about it being only one persons view. Others may wish to change the ratings, which is fine, indeed encouraged. There have been a few changes in rating happen already. Edit summaries and article talk pages are probably the best places to discuss disputes in the ratings.

The overall definition of importance levels is probably best on the maths assessment page. So far we've only covered about 150 articles, a tiny fraction of the whole mathematics coverage. Quite where the lines should be drawn is still a good question. --Salix alba (talk) 21:13, 30 September 2006 (UTC)

I see; I hadn't understood the exact meaning of the "vital" tag. Maybe the template should be clarified to indicate that. I considered putting "vital=Y" back, but decided to remove decimal from wikipedia:vital articles instead. We'll see how it shakes out. --Trovatore 21:44, 30 September 2006 (UTC)

Have you notices how they have Proof listed under Number theory, I can't quite figure out the best place to put it though! --Salix alba (talk) 21:55, 30 September 2006 (UTC)

As I recall there's a "logic" category there; any reason not to move it there? --Trovatore 22:00, 30 September 2006 (UTC)

I understand that Wikipedia:Vital articles is supposed to be a mirror of Meta:List of articles every Wikipedia should have. However, I spotted quite a few discrepancies.

The following are listed here as "vital" mathematicians, but are not mentioned at Meta: Vladimir Arnold, Diophantus, Pierre de Fermat, G. H. Hardy, Henri Poincare, Srinivasa Ramanujan. Curiously enough, Pythagoras is listed, but in the category "Social scientists"!

The following mathematicians are listed at Meta but not here: Fibonacci, Carl Friedrich Gauss, Christiaan Huygens, Hypatia of Alexandria, Johannes Kepler, Pierre-Simon Laplace, Blaise Pascal, Bernhard Riemann. One could argue that Kepler should be in the category "Scientists", but he is not mentioned at all on our "Vital" list. Same for Pascal as also being a philosopher. Isaac Newton is listed in the category "Inventors and scientists".

Should we do something about these discrepancies, and if so, what is the appropriate approach? --Lambiam ^Talk 22:48, 30 September 2006 (UTC)

I think Wikipedia:WikiProject Biography/Core biographies, it the place most worthy of our attention, as it has the highest profile, being a key part of the WP:1.0 project. The job of selecting just ten mathematicans seems quite arbitary.

Also worrying is the coverage of mathematics in WP:CORE just 5 out of 150 article

Algebra Geometry, Mathematics, Number and Statistics. (Calculus, Mathematical analysis and Non-euclidean geometries got booted off).

WP:CORESUP the suplement with 150 more articles, and only 5 more maths articles

Arithmetic, Equation, Mathematical proof, Theorem, Trigonometry

WP:V0.5 the first itteration of the 1.0 list, has

Georg Cantor, Carl Friedrich Gauss, David Hilbert, Gottfried Leibniz, Blaise Pascal, Alan Turing, John von Neumann, Algebra, Calculus, Game theory, Linear algebra, Margin of error, Mathematics, Measurement, Trigonometric function, Pi, Fractal, Manifold, Matrix (mathematics).

Thats now closed, selection was based partially of GA/FA's and core topics, plus a few we put forward. There will probably be another iteration before the final 1.0 release.

Possibly the best thing for us to do is assemble of list of perhaps 50 mathematics articles, which are of high importance and good quality. We can then pass these lists onto the various other projects as sugestions for inclusion. The 0.5 people were quite responsive, although we didn't have much to offer them at the time. --Salix alba (talk) 00:10, 1 October 2006 (UTC)

For the record... there are currently 76 top-class articles, of which 3 are FAs, 8 are A-class, 4 are GAs, 12 are B+ class, 27 are B-class, 19 are start-class, and none are stubs. These figures include mathematicians. Tompw 22:43, 6 October 2006 (UTC)

Going back to the original point, which is basically asking how we decide what level of importance to give an article. I think several people (myself included) would naturally tend to equate importance with "importance in mathematics" - so something like the Pythagorean theorem would come out fairly low. However, the criteria given in the WP 1.0 subpage relate to an articles importance for a print encyclopedia. To me, this means we have consider importance to the readership as well as importance in mathematics. Consequently, the Pythagorean theorem comes out as top importance. In a nut shell, I give the artitcle an importance of Max{public importance, mathematical importance}. Because the grading of quality and importance is done by oen person, there will always be potential for disagreement. In that case, it's probably best to discuss it in the talk of the assessment page. Tompw 22:30, 6 October 2006 (UTC)

There's a tendency to equate "mathematics" with "contemporary pure mathematics research", visible both here and in the new version of the Geometry article, that I think should be discouraged. As a formula for calculating distances from Cartesian coordinates, in the kind of mathematics that non-mathematicians are likely to use, the Pythagorean theorem is extremely important. —David Eppstein 22:42, 6 October 2006 (UTC)

I agree with you completly... the point I was trying to make (maybe needing a better example) was that we are trying to rate the importance of the article in an encyclopedia, not the importance of subject matter in mathematics itself. Tompw 22:50, 6 October 2006 (UTC)

I concur with Tompw. The "importance" criteria should be something along the lines of, if you were in a math class that assumed you knew "x" and needed to look "x" up, might you try an encyclopedia, or would you try to find a more specific reference? For example, yesterday, I rated complex number as a Top importance article because it's a concept that is very common (yet often misunderstood) in mathematics and probably should be found in a general reference book. On the other hand, something like holomorphic function (trying to stick with the complex theme here) is very important to mathematics, but it is advanced to the degree that no one would try to look it up in a print encyclopedia. --JaimeLesMaths 04:26, 7 October 2006 (UTC)

The Core biographies importance ratings are helpful:

Top - Must have had a large impact outside of their main discipline, across several generations, and in the majority of the world. (snip)
High - Must have had a large impact in their main discipline, across a couple of generations. Had some impact outside their country of origin.
Mid - Important in their discipline.
Low - A contributor to their discipline and is included in Wikipedia to expand depth of knowledge of other articles.

These are a little more objective, but need a little tweeking to better fit the needs of mathematics articles. So by these Pythagorean theorem is clearly top, whith a very large impact. holomorphic function has a smaller impact outside of mathematics.

Possibly another way of sorting articles would be when they would typically be taught, say primary (up to 11), secondary (11-16), advanced (16-18 and non mathmatics numerate degrees), maths degrees, post-grad. These could be called something other than the emotive importance, say academic level. Possibly also useful as the actual academic level could be compared with the writing style of the article indicating articles with too technical writing for the content. --Salix alba (talk) 09:25, 7 October 2006 (UTC)

New section in Pythagorean theorem should be expanded

I've hastily added a new subsection to Pythagorean theorem on the proof found in Euclid's Elements. Doubtless it could bear further elaboration (since it's not really the full proof, but rather an illustration with an accompanying explanation). Also, could someone who knows how to do such things help with the alignment of the illustration, so the reader can more easily tell which illustration goes with which section? Michael Hardy 01:20, 1 October 2006 (UTC)

I've worked over the illustration layout, introducing right-left alternation, standard thumbnail size, forced clears, and captions.

For those who have little experience with images, there is helpful information at Wikipedia talk:WikiProject Mathematics/Graphics, and at Help:Images and other uploaded files.

Once an image has been uploaded, the standard right-floated thumbnail is produced by a line like the following.

[[Image:Circle ellipse tangents.png|thumb|right|''Figure 1.'' Shared tangents]]

It should immediately preceed the paragraph it accompanies. To force a break, use the following HTML.

 

There's no rocket science here. The hard part is, as always, creating the images. --KSmrq^T 23:05, 1 October 2006 (UTC)

Suggestion to improve most math articles

What I've noticed, in my quick, probably statistically invalid sample of a few articles, is that they could be benfitted greatly from graphs. For example, Venn diagram is clearly illustrated, as is a bit easier to understand than, let's say, Comparison test. Comparison test could benefit from the image on Convergent series, for example... and similar. That, IMO, could help many math articles be a bit closer to FA status. Tito xd^(?!?) 03:03, 1 October 2006 (UTC)

Then you'll be delighted to contribute to Wikipedia:WikiProject Mathematics/Graphics.

Good illustrations don't just happen. Some mathematicians think in pictures, but many do not. So first, someone must have an idea for a figure. Then someone must design it. Then someone must create it. Then it must be uploaded (to Commons) and introduced into the article. You might be surprised how much time and effort can go into a single illustration.

We'd also like more articles, and better introductions for the general public, and more examples, and more references, and more ISBNs for listed books, and more web links, and so on. And, of course, more better writing. (And fewer vandals, and fewer clueless editors, and fewer drive-by "fixit" tags.)

In other words, we may agree with your sentiments, but Wikipedia places the power to make it happen in your hands. Do feel free to ask here, or at Wikipedia talk:WikiProject Mathematics/Graphics, or at the Village Pump if you need assistance. --KSmrq^T 06:06, 1 October 2006 (UTC)

See also Wikipedia:Reference desk/Mathematics#I'm taking image requests. --Lambiam ^Talk 00:51, 2 October 2006 (UTC)

John Dee

John Dee is up for a featured article review. Detailed concerns may be found here. Please leave your comments and help us address and maintain this article's featured quality. Sandy 21:02, 1 October 2006 (UTC)

Major reworking of Geometry

Geometry is just undergoing a major reworking. The previous article was just a history of the topic and has been moved to History of geometry. This now leaves Geometry as a stub, sugestions of how to structure the article welcome on the talk page. --Salix alba (talk) 09:24, 2 October 2006 (UTC)

And this major move had how much discussion? 'Just' a history of geometry - would anyone care to weigh in with a non-historicist discussion of what geometry means? Charles Matthews 09:31, 2 October 2006 (UTC)

Er, no discussion. I guess User:The Transhumanist was being WP:BOLD. Still I think its generally a good idea, as the history only approach was not the best way to structure the article. --Salix alba (talk) 10:14, 2 October 2006 (UTC)

I agree that the earlier incarnation of the article was bloated and didn't give enough of a flavor of 20th century developments, but jettisoning the whole thing was a mistake. I am definitely leaning in the direction of revert. Michael Kinyon 10:31, 2 October 2006 (UTC)

Well, plenty of edits since then. Let it not be said that we (OK, I) ducked the challenge. Charles Matthews 15:02, 2 October 2006 (UTC)

I just assumed you meant the "royal we", Charles. :-) In any case, yes, I'm slowly being convinced this can work. Michael Kinyon 15:36, 2 October 2006 (UTC)

You can call me Prince. Charles Matthews 17:02, 2 October 2006 (UTC)

Though Shing-shen Chern is deceased (so I guess he's not contemporary), it is very odd that he is not mentioned in this article. What is the definition of contemporary again. A fortiori, Cartan I guess would not be contemporary either. --CSTAR 17:10, 2 October 2006 (UTC)

It needs a section just for differential geometry too, of course. Charles Matthews 18:25, 2 October 2006 (UTC)

There appears to be a very long list of topics (in its own article) of articles on Geometry, so I do not think that the main article needs to mention them. It already has a pointer to that list. I would suggest that the main article focus on the most modern concept of Geometry, i.e. David Hilbert's. As the History of Geometry article says "In geometry, there was a clear need for a new set of axioms, which would be complete, and which in no way relied on pictures we draw or on our intuition of space. Such axioms were given by David Hilbert in 1894 in his dissertation Grundlagen der Geometrie (Foundations of Geometry).". JRSpriggs 09:18, 3 October 2006 (UTC)

Axiomatic geometry is interesting, but is only a small part of the subject known as geometry. The article works best as a survey, and seems to be evolving quite well right now. Michael Kinyon 09:43, 3 October 2006 (UTC)

Hilbert's axioms are only 'state of the art' in a very restricted sense. The suggestion that we need a survey based on the contemporary scene is sound; though it shouldn't exclude other things on that page. As for axiomatics, Atiyah says some interesting things about those. I was trying to find where Weil discussed geometry, yesterday, so far without success. The way things are going, we should be finding more quotes to add to various articles. Charles Matthews 09:59, 3 October 2006 (UTC)

Hilbert's axioms provide a great understanding of how mathematics develops and how mathematicians think; You can see that reading any good "mathematical education" textbook (quotes here are used to indicate my disdain for most specialists in education), e.g. Great Theorems of Mathematics: A Journey Through Genius (I forgot the author), that puts side to side Euclid's axioms and Hilbert's. They are a valuable addition to any article on geometry. --Lucas Gallindo 15:10, 3 October 2006 (UTC)

The author is William Dunham. ISBN 0471500305. Gandalf61 15:22, 3 October 2006 (UTC)

I think it is fair to ask how many contemporary papers in geometry are actually based on Hilbert's axioms. Charles Matthews 15:26, 3 October 2006 (UTC)

As far as I know, papers of real relevance, using Hilbert axioms... there are none! But I still think they are enlightening for the newcomer.--Lucas Gallindo 15:40, 3 October 2006 (UTC)

It is also fair to ask how many contemporary papers are based on Euclid's axioms. I don't believe the study of facts about Euclidean geometry on the plane is a major topic in contemporary research. The things mentioned in Geometry about contemporary research in Euclidean geometry, such as geometric group theory, seem like a stretch. CMummert 01:32, 4 October 2006 (UTC)

I take the point abouy geometric group theory, which has a more complicated set of inputs than the other areas mentioned in that section. Euclidean geometry now is the geometry of Euclidean space, or the Euclidean group, post-Klein. Charles Matthews 07:05, 4 October 2006 (UTC)

Synthetic geometry should be more fully described; I know just enugh about it to be cautious of "Euclid-style" without being able to edit myself. Septentrionalis 04:41, 6 October 2006 (UTC)

Numeric spiral

Just a word of warning: The page Numeric spiral was created today by User:Noluz. The same user listed it on List of curves and in the External links of Archimedean spiral, but I just reverted both since Numeric spiral has nothing to do with curves at best, and at worst is numerology. Michael Kinyon 23:29, 3 October 2006 (UTC)

Is this the same or similar to the Ulam spiral? --Salix alba (talk) 00:29, 4 October 2006 (UTC)

~~Yes, I think so. It is similar, in fact, to at least one of the external links [55] on that page.~~ Michael Kinyon 01:55, 4 October 2006 (UTC)

The thing described is not a Ulam spiral. It is a badly designed visual representation of partitioning the natural numbers into equivalence classes modulo 9 while marking the prime numbers. Putting them in the form of a spiral serves no particular purpose and does not help to bring to light any properties. I've listed this article for deletion. --Lambiam ^Talk 05:04, 4 October 2006 (UTC)

It is simply applying Casting out nines to calculate the equivalence class (as Lambiam said) and then treating the fact that primes (except three itself) are not divisible by three as some kind of magic. Really idiotic. JRSpriggs 05:36, 4 October 2006 (UTC)

Yes, I see it now that I finally thought to click on the figure to enlarge it. And only now can I decipher the nonmagical parts of the article. "Cabilist" indeed! :-) Michael Kinyon 07:01, 4 October 2006 (UTC)

Gang Tian

Hi, it seems that a single-issue user (130.158.83.81) is keen to revert the controversy section of Gang Tian from my edits originally made here. His reversions are here and here.

My edits were intended to improve the quality of the writing of that section, to improve the wikilinks (for example, 130.158.83.81 insists on linking to Yau-Tian affair, which doesn't exist, rather than Tian-Yau affair), to improve the accuracy (according to my limited knowledge) and to add citation requests for unsupported assertions.

A later editor removed the controversy section altogether, after the 130.158.83.81s latest reversion. I have since restored the section for the time being, but perhaps removal is the best option. If we want to keep the section, then the version promoted by 130.158.83.81 seems objectively worse than my alternative. There is much room for improvement, but I just sought to make the section better than awful.

Anyway, I don't think that editor is breaking any rules, and I don't want to enter a daily edit war, but I thought I'd bring it to your attention. All the best--Jpod2 08:59, 4 October 2006 (UTC)

I've made a redirect from Yau-Tian affair, removing one minor bone of contention. The content should be very careful, and adhere to WP:LIVING, staying well away from any hint of defamation. We should also remember and respect the fact that these are important professional mathematicians. Charles Matthews 09:11, 4 October 2006 (UTC)

Agreed. I tried to tone down some of the extreme and unusual language in my edit, or otherwise requested citations. I doubt that this version will stay there, though.--Jpod2 09:14, 4 October 2006 (UTC)

I think your edits helped to improve the section, and helped to remove POV from the article. Thanks. It may be that user Reb's solution of removing the unsourced paragraph may be best for now. Good luck, Lunch 15:08, 4 October 2006 (UTC)

I think that might be the best solution for the moment. All the best--Jpod2 16:31, 4 October 2006 (UTC)

Just a couple quick thoughts as my time editing is limited recently. 1) Per WP:BLP do not merely add "citation needed" tags to dubious, potentially libelous information; remove it immediately - do not move it to the talk page. 2) The intro is rather bad as it overemphasizes his recent monograph with Morgan; that is not his most notable achievement or why he is a titled professor at MIT. It should be moved and noted in some kind of contributions section, with a brief description of his specializations in the intro. Also, for some reason he is listed as being a full professor at Princeton in a section. --C S (Talk) 19:27, 4 October 2006 (UTC)

Actually I had the impression he was at Princeton, so I did a little searching and it seems he is there now, although a few years ago he was at MIT and transitioning to Princeton. So this ought to be cleared up in the article. --C S (Talk) 19:42, 4 October 2006 (UTC)

Sylvia Nasar

Besides the fairly well-patrolled Poincare conjecture, Grigori Perelman, Tian-Yau affair, Manifold Destiny, and newer Gang Tian, those with the inclination should keep an eye on S.T. Yau (which doesn't appear watched as much) and Sylvia Nasar (not watched very much either). Recently there has been a couple rather defamatory edits to the Nasar article (based on what appears to be sheer speculation and poor sourcing). --C S (Talk) 22:30, 4 October 2006 (UTC)

Lie theory

The page use to redirect to Lie group [56] but was changed into a small article which is pretty much barren.--Jersey Devil 10:58, 5 October 2006 (UTC)

Looks like it should be merged into Lie (disambiguation); so I did. Septentrionalis 23:01, 5 October 2006 (UTC)

Citation guidelines proposal support

Wikipedia:WikiProject Physics/Citation guidelines proposal currently states: "... editors in Wikipedia:WikiProject Physics want to clarify how these guidelines should be implemented for physics articles ...". Question: Can we change that to: "... editors in the WikiProjects Physics and Mathematics want to clarify how these guidelines should be implemented for physics and mathematics articles ..."? --Lambiam ^Talk 17:20, 5 October 2006 (UTC)

I would support that change. Madmath789 17:25, 5 October 2006 (UTC)

Me too. I like the proposed guidelines a lot. Especially the new part about how simple examples and rederivations aren't WP:OR. —David Eppstein 17:39, 5 October 2006 (UTC)

Yeah, I'm in. I like them, too. Michael Kinyon 18:19, 5 October 2006 (UTC)

Yes. Editors of the mathematics article are setting citation guidelines for that article. It would be far better to follow more broadly accepted guidelines. --Jtir 18:33, 5 October 2006 (UTC)

<comment deleted -- I had said something about the 0.999... article, well I will not delete my comments again> :) --Vesal 20:21, 5 October 2006 (UTC)

The proposed guideline gives no examples of book-cites at the page level, which are used extensively in [0.999...]]. Another problem is that the example article-cites appear in a random order in the notes instead of alphabetically. --Jtir 20:16, 5 October 2006 (UTC)

I wrote some confusing stuff up there and deleted it, sorry about it... I will explain, at first I thought it was a citation style, but this is something much deeper, it's the verifiability guideline, and well as such I don't think it specifies any style at all. So let's discuss the guideline... I have a number of questions, maybe I will ask them on the guidelines talk page. --Vesal 20:25, 5 October 2006 (UTC)

That would be the appropriate place for any and all comments on the draft. Putting them here makes them invisible to editors in other projects. Comments are welcome from everyone. CMummert 20:36, 5 October 2006 (UTC)

Just question to people in this project... has there ever been discussion or edit wars over the proofs or reasoning presented in mathematics articles? I have not seen any such discussion over mathematical details, so I would support the proposal... However, I would not mind, if all mathematics articles were as cited as 0.999.... I don't really see how such citations make reading or editing more difficult. I wonder what the people who worked on that article think about the excessive citing that was required to get it into FA quality. --Vesal 20:36, 5 October 2006 (UTC)

Has there ever! You only have to check out the talk page of that article and its archives. The general consensus I perceive in hindsight is that mild OR is better than nothing, but I've encountered little resistance to the idea that cited material is better than OR. What do I think about the citing? I think it's hard but worthwhile. Not only does it keep you honest and stem accuracy disputes, the search for citations can lead you to the only really interesting material in an article. Melchoir 21:14, 5 October 2006 (UTC)

I have gone ahead and added mathematics in. Seeing as it is a proposal, anyways, it can't hurt. A number of people on WP:CITE and WP:GA seem pretty happy with the proposal too, so I'm optimistic about the chances for this proposal to make an impact for the better. –Joke 21:43, 5 October 2006 (UTC)

I'd just like to say I am really glad the difficulties physics and maths articles faced over WP:CITE and WP:GA are being addressed. Tompw 22:28, 5 October 2006 (UTC)

I'm glad to see the issue recognized. The unthinking insistence at Wikipedia:What_is_a_good_article? that all articles, whatever their structure or sources, must have in-line citations continues, however. The exception in the proposal is entirely reasonable. Septentrionalis 22:59, 5 October 2006 (UTC)

I don't think anything has been resolved at WP:CITE; this is at best a stopgap measure. And WP:GA applications are going to be a dead end for a while unless we get a large number of scientifically knowledgable good article reviewers. CMummert 00:23, 6 October 2006 (UTC)

That's true, but I take the attitude that the articles that are best off without in-line citations are probably not articles that we really want to become "Good Articles" (or, heavens, Featured Articles). It's crucial to recognize that there is a difference between Good Articles and good articles: this is particularly so, and will likely remain so indefinitely, with physics and math articles. Articles such as the Littlewood-Richardson rule and Bianchi classification (these don't exist yet – hint, hint) could probably be quite easily be made into good articles. But it is not at all clear it would be worth the effort to make them into Good Articles. –Joke 00:16, 6 October 2006 (UTC)

We should write good articles, not Good Articles. The more I see of that process, the less I like it. Septentrionalis 03:47, 6 October 2006 (UTC)

More good GA fun. Derivative was awarded GA today and then imediatly reviewed, inline cites being one of the issues. Folks might like to comment. --Salix alba (talk) 16:29, 10 October 2006 (UTC)

Help with grading articles please?

Just a notice... it would be wonderful if more people could help grade maths articles in Wikipedia:WikiProject_Mathematics/Wikipedia_1.0. Anyone can edit in additional important articles that should be included. It's *not* a job where an excessive number of cooks leads to inferior broth. Tompw 19:40, 5 October 2006 (UTC)

I believe that Wikipedia 1.0 is a broken and misguided project, and should be abandoned or reformulated. No thank you. Septentrionalis 22:01, 5 October 2006 (UTC)

That's very nice, but totally irrelvant :-). Tompw 22:19, 5 October 2006 (UTC)

Its not just about Wikipedia 1.0, its about having a good allround coverage of the mathematics articles. Grading helps us identify the strengths and weeknesses in our maths coverage: important articles which are week and need work to bring them up to speed, and also the better articles which could be put forward to GA or FA status. --Salix alba (talk) 22:42, 5 October 2006 (UTC)

How do the comments in the tables in Wikipedia:WikiProject Mathematics/Wikipedia 1.0 relate to the comments in the {{maths rating}} box? -- Jitse Niesen (talk) 05:31, 6 October 2006 (UTC)

Er, week equality. The tables predate the math rating tag, serving as a sort of scratch pad, where we tried to build up a list of the most important topics. Much of the task at the moment is to go through the list there and adding tags to the talk pages. Eventially the automatically generated Wikipedia:Version 1.0 Editorial Team/Mathematics articles by quality will become the definative list. Mathbot uses the comments stored in say Talk:Blaise Pascal/Comments to fill in the comment in the list and also in the talk page, which will be a mechanism for ensuring consistancy of comments. I need to work out how to switch on including these comments in the list.

Slightly related is the field parameter to the tag. It currently does nothing but could be used as a mechanism to group the ratings by the particular topic area. --Salix alba (talk) 08:21, 6 October 2006 (UTC)

Prime numbers

While looking into an OTRS ticket, I came across this edit. Does anyone know if this stuff is accurate? --bainer (talk) 08:31, 6 October 2006 (UTC)

Pretty good nonsense. It has been reverted. Charles Matthews 10:16, 6 October 2006 (UTC)

Graph invariant: a new category?

Graph invariant is a regular page. I propose to make it a subcategory of Graph Theory. Several pages would then belong to it:

Do you agree/disagree? pom 09:22, 6 October 2006 (UTC)

On the point of grammar, Category:Graph invariants would be the usual style. Charles Matthews 10:07, 6 October 2006 (UTC)

Agree (preferrably with the plural form) JoergenB 12:49, 6 October 2006 (UTC)

On a similar note, I just made a subcat Category:Graph families yesterday. Probably several of the entries there could also be cross-listed under invariants, e.g. Dense graph defines density as an invariant. —David Eppstein 15:04, 6 October 2006 (UTC)

I created the category. I am not really happy with the content of the old Graph invariant page, so I did not copy it. How should graph invariants defined within a more general article be categorized and/or listed in this category? pom 16:22, 6 October 2006 (UTC)

Notable invariants should be worked into the main article as prose, as in Knot invariant. Later on, it may even be useful to complete the coverage with a list article, but not yet. Melchoir 16:32, 6 October 2006 (UTC)

The future

There are several fairly active discussions going on about quality, citations and so on. The Project needs one more thing, really, which is an assessment of coverage and where it is going. At a moment when the coverage as a whole looks satisfactory, saying people should concentrate more on quality makes every sense.

We are not there yet, really. It is somewhat muddling to look at lists of articles, or of red links, and to try just from that to say how broad the coverage is. My gut feeling, though, is that 18 months ago we were mid-1950s, and now more like mid-1960s. That is, there is a historical way of thinking about this, and it is a helpful barometer. (In physics, the 1960s would be quarks and quasars, kind of thing, and it is not so odd there to ask about coverage in terms of what is adequately discussed in encyclopedia terms.)

Extrapolating, we might have a reasonably full coverage in about four years time. Don't groan: it would be an amazing achievement to say we had a survey that good. There are always going to be topics left out, but the criterion is that writing an article to fill a gap would not involve a long trail of red links to further concepts on which it depended. The basic vocabulary would be there.

Charles Matthews 10:28, 6 October 2006 (UTC)

Problem edits on RH

I noticed a number of problematic edits by User:Karl-H on topics relating to the Riemann hypothesis. I tried fixing some, but am out of energy at the moment. I believe that the gist of what he's trying to say is mostly correct, but he is not a native English speaker, and he's not a mathematician, and he's writing up original interpretations of research papers he did not quite understand. The edits wreck to flow of the articles, the language is fractured, ungrammatical, mis-capitalized, and worst: the formulas are fractured, incomplete or wrong; see for example Chebyshev function, Hilbert-Polya conjecture, etc. I just can't get to this stuff in the next few weeks. linas 19:28, 7 October 2006 (UTC)

See an awkward ongoing discussion about claims to have proved RH, on Talk: Hilbert-Pólya conjecture. I'm not rushing into anything, but there are unsupported statements about RH on the pages, not sourced, which may need to be removed as original research. There may also be an issue here about what is a 'reliable source' for rumours, how we treat 'non-withdrawn claims' over time, and so on. My view is that in most cases we can have an article with NPOV that ignores fringe claims; so that cutting out rumours is usually OK. Charles Matthews 09:26, 9 October 2006 (UTC)

Order theory

Whereas I 100% agree with We should write good articles, not Good Articles, I want to bring to everybody's attention that the GA candidateship of Order theory is on hold [57] for failing the criteria 2a, 2b,2c of It is factually accurate and verifiable. --Pjacobi 22:31, 8 October 2006 (UTC)

This is a sad example of the prevailing lunacy. Despite the twisted mindset of some editors that "inline citations" = "accurate and verifiable", this article is well documented. Reputable sources given at the end suffice to allow the claims given in the article to be verified as accurate. Wikipedia must learn that mobs and footnotes are no substitute for editorial competence and diligence. --KSmrq^T 23:31, 9 October 2006 (UTC)

Navigational templates

Trovatore drew my attention to the fact that there is a consensus against navigational templates in maths articles of any kind. I was completely unaware of this... could someone kindly explain why this is the case?

I always thought navigation boxes were one of things that made Wikipedia so much better than any print encyclopedia. Also, Calculus topics all have a box at the top right; and {{mathematics-footer}} exsists and is used, so the rule is clearly not applied in all cases.

This cropped up because I had begun implementing the contents of User:Tompw/maths templates. Tompw 15:10, 9 October 2006 (UTC)

<rant>No, hypertext makes Wikipedia so much better than any print encyclopedia. But not everybody got the concept of hypertext, so the "See also" section was invented. Then the attack of the web designers happened, and everything had to be be boxed, colored and templated. Or something like that.</rant> --Pjacobi 15:14, 9 October 2006 (UTC)

I said "one of things"... I agree hyperlinks are definitely the single biggest thing that make Wikipedia wonderful. However, when I browse wikipedia, I want to know about related topics. If I'm looking at the History of Nunavut, I may want to read about the Geography of Nunavut. This wouldn't be linked within the text of the former, but is linked via the nav box. Also, such boxes draw your attention to topics you might have been unaware of. Tompw 15:19, 9 October 2006 (UTC)

Calculus I think is allowed to be an exception: as a service to students, a box provides quick navigation between standard topics. Otherwise templates are much hated. For one thing, if you put both an algebra and a topology box on algebraic topology, you are starting a nasty build-up. This illustrates one point: boxes were used before categories existed, and categories are superior. For another thing, the choice of topics in a box is arbitrary in a potentially annoying way. Who would be able to make a definitive box for group theory? It again looks like subcategories is a better solution. Charles Matthews 15:23, 9 October 2006 (UTC)

(edit conflict). I woudl disagree with the statement "templates are much hated"... more to the point, the advantage of nav boxes is that they are selective, whereas a category has to contain anything and everything taht is vaguely relevant. I agree such selectivity has the potential to cause disputes, but that does not means such disputes cannot be resolved. Tompw 15:38, 9 October 2006 (UTC)

It doesn't mean they are worth having, either. That is a genuine reason for the dislike. Say there is a good selection to be made, for a student at a certain level. Who chooses the level, though? First course in topology, second graduate year in algebraic topology ... ? No end in sight. Charles Matthews 16:34, 9 October 2006 (UTC)

I am very displeased by the {{Geometry-footer}} and {{Analysis-footer}} templates. They are huge, and this kind of things tend to only grow over time. I believe in general that navigational templates are bad, except perhaps by {{Calculus}} as mentioned by Charles and maybe {{mathematics-footer}}. Categories are much preferred. I would suggest these templates be deleted. Oleg Alexandrov (talk) 15:31, 9 October 2006 (UTC)

(Btw, I never intended to create these as finished products. I always knew that they would get changed, probably quite substantially from my intial creation. If people think they are too long/short/weird, then edit the thing. This is a wiki, after all :-) Tompw 15:38, 9 October 2006 (UTC))

Those footers are awful ({{Geometry-footer}} & {{Analysis-footer}}). They are a bunch words strung together with no organization, not even alphabetical. And how is "Category:Geometry" a topic in geometry? IMO, a lack of hierarchical organization is a deficiency in many subject areas that makes it hard to take in the "big picture". The Encyclopædia Britannica has a Propædia that organizes all knowledge in a hierarchy. Since WP is electronic there can be several hierarchies. --Jtir 17:18, 9 October 2006 (UTC)

Fair comment. ({{Geometry-footer}} is now much changed. Will do {{Analysis-footer}} in morning, assuming someone else hasn't got there first :-). Tompw 23:44, 9 October 2006 (UTC)

While hyperlinks are good we need to distinguish between inline hyperlinks and hyperlinks in lists/templates. For purpose of navigation inline links are not ideal, they require the user scan the whole text searching for a given link, they may occur in a narative order rather than a logical/hyerarchal order. I'd quite like to see important related topics in a see also section even though they already appear in the main text. It makes it easier for people to navigate.

Tompw raises a good point about categories in how they tend to get too full to allow the important items to be easily found. One solution is to actually expand the text in the category so a more organised list is displayed. This is what we've done at Category:Polyhedra.

The other approach to a nav box style is to follow the German scheme, where there is a standard configurable box, which may had fields like parent topics, sibling topics and child topics. Each page could then set these fields as needed, avoiding problems with the giant nav boxes. --Salix alba (talk) 17:27, 9 October 2006 (UTC)

Sounds interesting, can you provide an example? I couldn't find one on de.wikipedia.org. --Jtir 17:38, 9 October 2006 (UTC)

There is a familiar precedent for displaying hierarchies: Windows Explorer. When collapsed, an entire hierarchy fills exactly one line. Indeed all modern computer file system browsers allow collapsing and expanding of any part of the hierarchy. The Nautilus file manager that is part of many Linux distributions is good example. --Jtir 17:55, 9 October 2006 (UTC)

Example of German navboxes: DE:Halbgruppe. But they're not used consistently throughout math there. —David Eppstein 18:29, 9 October 2006 (UTC)

Thanks. That looks promising. Now if only those bullets were clickable so the subcategories could be displayed or hidden at will.

~~Could someone translate these headers? BabelFish doesn't do too well on them.~~

Here are the German headers with English translations:

berührt die Spezialgebiete ("touches branches/areas [of math]")
ist Spezialfall von ("is a special case of")
umfasst als Spezialfälle ("contains as special cases")

--Jtir 19:28, 9 October 2006 (UTC)

I don't see it as promising. I see it as promoting a view of math as a very rigid hierarchy, which conflicts with my view of math as a highly interlinked non-hierarchical graph of connections. E.g., to name two topics I've been working on very recently: Happy Ending problem is categorized as Category:Discrete mathematics while until very recently Erdős–Szekeres theorem was categorized only as Category:Ramsey theory — viewing things hierarchically, Discrete Geom => Geom => Math and Ramsey theory => Combinatorics => Math are very far apart. But they come from the same original paper and originally one was used to prove the other. I think a hierarchical view of the world as promoted through navboxes would downplay that connectivity as well as needlessly cluttering the pages and making it harder to find the actual text of the article. —David Eppstein 20:07, 9 October 2006 (UTC)

Literal translation: "touches branches/areas [of math]", "is a special case of", "contains as special cases".--gwaihir 20:17, 9 October 2006 (UTC)

I think each branch would need to be handled a bit different. Some things partition well, others don't. Some pages would have very short boxes, some could have longer. - grubber 21:01, 9 October 2006 (UTC)

I have tossed around the idea with a couple other WPers about the idea of starting a project to develop some math templates like the ones used in the German wikipedia (see de:Gruppetheorie for an example). I think it would be nice to get together some people interested in this, and hash out some ideas and guidelines about what we could use in the English WP. If we were to let a template system grow organically, I think it will quickly get out of control and become inconsistent... being more of an annoyance than a help. But, if we can plan out from the start, I think we could set up a very nice, usable navigation aid that will not detract from the articles. How would you all feel about such a project (it could be a separate wikiproject or a subproject of this one)? - grubber 19:01, 9 October 2006 (UTC)

The link de:Gruppetheorie leads to "Gruppetheorie ... Diese Seite existiert nicht", which I would roughly translate as "No such article". --Jtir 19:19, 9 October 2006 (UTC)

de:Gruppentheorie --gwaihir 19:21, 9 October 2006 (UTC)

The boxes on German wp are incomplete, partly misleading, partly wrong. They originated in the (not uncommon) misconception that algebraic structures should be understood by comparison to "similar" structures. Of course, a given object like the integers has all the aspects of ring, abelian group, monoid. But group theory is not just abelian group theory without commutativity, and ring theory is again completely different from studying the additive and multiplicative structure separately. I do not update these boxes any more, nor create new ones. But I'll ask for other opinions on dewiki.--gwaihir 19:27, 9 October 2006 (UTC)

I wouldn't want a copy of the German version either. But, I believe there is something between "no boxes at all" and "German-version boxes" (plus something new) that would work really nice. It will take a bit of time and debate and organization to hash it all out, but I think it's very doable. - grubber 20:20, 9 October 2006 (UTC)

Group
Field
Algebra
Related topics
Ring
Field
Sub topics
Abelian group
simple group

I quickly hacked together a demo User:Salix alba/Maths navbox shown on the right. It only supports two siblings and two children, but could be extended for more (I'd recomend no more than six for usability reasons). Its adapted from the taoxobox.

Code: {{User:Salix alba/Maths navbox|color=lightgreen|title=Group|parent=[[Algebra]]|sibling1=[[Ring]]|sibling2=[[Field]]|child1=[[Abelian group]]|child2=[[simple group]]}}

Yay! Lots of people are engaging in a mature and adult discussion about this idea. :-) More to the point, I'm not sure a parent/sibling/child box is the answer. The trouble is that one area of maths doesn't always relate to other areas in a hierachichal (sp) fashion. It's not like bilogy, where a genus is considered as a member of a fmaily, in comparison with that family's other genuses, and as collection of its species. So, the concept of sibling areas doesn't really hold. That said, the parent/children bit works far better. With groups, the parent is Algebraic Structures (and Alegbra in general), and the children are things like Abelian Groups, simple grouprs, quotients, products, sub-groups, major theorums etc. The trouble this leads to is a large number of children - see #3 below. People's complaints about my navigation boxes seemed to fallinto three categories:

Categories are better than navigation boxes: My reply is that both can co-exsist quite happily. If you want to to naviagte by category, then the exsistence of nav boxes doesn't prevent you
The layout/organisation/content is bad: This is a wiki. Change it. I created those boxes in the same was I create a stub article - for someone else to come along later and improve it.
What to include will lead to disputes and its cousin These boxes will get too large as people add more articles: The answer to this is a bit more involved. I was planning on creating navigation boxes to cover the next level of detail. For example, Group theory is just represented by two links in the Algebra box. I intended to create a nav box for gropu theory, containing such topics as Abelian Groups, simple grouprs, quotients, products, sub-groups, major theorums. (This deals with the problem mentioned above of excessivrt children). So, if a box gets too many items, simply split off a section into a new box. (Like splitting off History of XXX from the article on XXX). Now, if you think "This means some articles will ave loads of boxes", then you'd be wrong. At worst, an article (such as group theory) would have two navigation boxes - one covering sub-topics, and one cover super-topics (as it were). Tompw 22:19, 9 October 2006 (UTC)

Further, some areas of math are more hierarchal. Abstract algebra breaks down into a tree pretty decent, but number theory may not. Further, if we designated a central area to organize the nav-box content, then all opinions can be collated and we can maintain some consistency. - grubber 23:44, 9 October 2006 (UTC)

Of course, categories and navigation boxes can co-exist. However, combined they take up even more space, distracting from the meat of the article. Let's take the navbox on groups demonstrated by Salix Alba above. When reading group, how important will it be to the reader that groups are studied in algebra, or that the concepts of ring and field are related? How many will follow these links? I'd say that these things are only of minor importance when compared to the other topics of the article. Therefore, I think the article is better off without such an attention grabbing box at the top. -- Jitse Niesen (talk) 05:44, 10 October 2006 (UTC)

I wasn't ever intedning to put the boxes at the top - I was intending to put them at the bottom. In fact, I don't like nav boxes at the top for precisely the reasons you give. Tompw 14:19, 10 October 2006 (UTC)

I am still left with the idea that those navigational templates are a bad idea. For example, {{Analysis-footer}} contains a random bunch of things, starting with calculus, going to harmonic analysis, then List of integrals and Table of derivatives, to finish with the entire Category:Calculus. Linkcruft basically.

I strongly disagree with any hierarchical navigational boxes as suggested above. That would basically duplicate the category system.

If anybody is full of energy, what this project trully needs is to work on categories containing a huge amount of articles, splitting them into smaller one by topic which would also make navigation easier. Oleg Alexandrov (talk) 02:05, 10 October 2006 (UTC)

OK, this is begining to get repetitive....If you don't like it, change it. Please. The argument is here is not about whether one particular nav box is good or bad, but over whether to use the things at all. Tompw 13:10, 10 October 2006 (UTC)

I strongly agree with Jitse and Oleg. The categories need work, so why use potentially different hierarchies in garish boxes at the ~~top~~ bottom of the article that just get in the way? VectorPosse 06:55, 10 October 2006 (UTC)

"why use potentially different hierarchies..." actually, I would regard having an alternative hierachy as a good thing, to allow users the choice.

"...in garish boxes..." garishness is something that can be changed to accomadate tastes (You really these are garish? I'm surprised)

"that just get in the way". Why would they get in the way? It's not as though the exsistence of the box make it any harder to scroll to the bottom of the article where the category links are. Tompw 20:59, 10 October 2006 (UTC)

Okay, so when I said "garish" I was refering more to the other sorts of boxes given as examples in the preceding discussion. (Lots of colors and somewhat more "in the way".) The boxes you showed are not exactly that, so point taken. Let me also clarify my comment about hierarchies. It is clear that there are two different types of hierarchies we are discussing. This has been discussed here at length and seems to be a matter of "top-down" versus "bottom-up" organization. I am merely asserting (as several others have done here) that both types are already present in articles in the context in which they are more natural. (And I agree that "natural" is a subjective word. I am basing my idea of natural on the standards that are currently in place in Wikipedia and seem to function well already.) Categories provide the bottom up approach of reading an article and using its category to go up to the higher level and understand the context in which the specific article functions. As for top-down organization, this is already present in the hyperlinks in the article that will refer to related concepts, and "See Also" sections that do exactly what you propose to do in an extra box. I agree with you when you say that users might want a choice to go "up" or "down" a hierarchy. I'm simply pointing out that such a choice already exists and that more boxes might be redundant. And yes, they would still be a bit "in the way" since they will be basically repeating a lot of the "See Also" section when it exists and appearing right next to a box of categories that might also be saying a lot of the same thing as well. VectorPosse 23:16, 10 October 2006 (UTC)

I agree that the boxes could be partly redundent in some cases. (Although the exsistence of search and hyperlinks arguably makes categories redudent, but I digress). However, WP doesn't have space restrictions, so there is no reason not ave a belt and braces aproach. (The anology is apt - some people like belts, some people like braces. Me using one doesn't stop you using the other).

Where links in the "See also" section are duplicated, then they could be removed from the "See also" section. One of my pet peeves is a huge long list (e.g. Fluid_dynamics#See_also, especially before I put it columns). Also, a category link maens openign up the acetgory page, possibly going to a sub-category (or super-caetgory), browseing through a list organised alphabetically rather than by topic, and then (and only then) seclting a related article... and if you wish to browse through a series of related articles, then you have to repeat the process. A nav box means you can go to a related page in just one click. For those with slow connections or computers, this is defiante plus. Tompw 12:42, 11 October 2006 (UTC)

See, now you're talking about, not only making the text harder to find by surrounding it with more boxes, and not only making the article harder to maintain by keeping redundant connectivity information in the text and in the boxes, but actually degrading the information in the text to support these useless boxes. Also note that a see also section could and maybe should (even though they often don't) have brief notes explaining why one might want to see also, while in the navbox all that textual context is lost and only the link information remains. And your belts-suspenders analogy implies to me that you are pushing for greater inconsistency of formatting in WP — articles maintained by people who like boxes being very different to navigate than articles maintained by people who don't I am strongly opposed to the suggestion of removing see also links from the main article to boxes, and I think due to that more strong in my opposition to boxes. —David Eppstein 14:57, 11 October 2006 (UTC)

Yep, while Wikipedia is not on paper, there is no point in making articles much less usable by cluttering them with boxes. The primary means of navigating between pages is links in the text; the right link at the right time. Oleg Alexandrov (talk) 15:08, 11 October 2006 (UTC)

<--- First up, I am not talking about "cluttering" aryicles with boxes. It's not like there will be hundreds of the things lurking round every paragraph, ready to pounce on and confuse some unfortunate reader. Also, this is *not* a choice between boxes and alternative methods of navigation. We can have both, so that people can choose whichever they prefer. Yes, I agree that inline links as the primary method of navigation, but that doesn't mean they are the only one. (Categories, the search engine, and the address bar being others that spring to mind).

David Eppstein mentioned adding prose to "see also" lists to add context, and preumsably then the list will probably (hopefuly) end up becoming a proper section on "related areas". That be would be wonderful, and I'd like to see that wherever apropriate. So, I have no problem with "see also" lists remaining. (That said, if they did get removed by somone, an editor could still draw on the nav box as a source for related areas). (Yes, I've changed my mind as a result of your argument). Tompw 16:34, 11 October 2006 (UTC)

I think boxes at the top and bottom would be appropriate on some pagss. Some information is "vertical" (like math->algebra->group->ring->field) and others are more of a "level set" (homomorphism, group action, types of groups, etc). - grubber 15:39, 10 October 2006 (UTC)

That would go against the principles of Wikipedia where you connect to relevant related articles via links in text, and categories a the bottom. Such a "bottom-up" approach works much better than the suggested "top-down" approach of going through a lot of articles and making them have a box of related links. Oleg Alexandrov (talk) 15:55, 10 October 2006 (UTC)

Not really. Sideboxes are used quite often for that purpose: to show it relation to other similar things (German language, Dog), to show what its basic properties are (Cesium, Austin, Texas), or to show its position in a series (History of the United States (1918–1945)). Sometimes it is nice to have these types of relationships excised from the text and stated succinctly. - grubber 19:08, 10 October 2006 (UTC)

I don't want to put too much pressure on the people who have so far proposed some templates but...I don't really like what I've seen thus far. I understand that these are works in progress, but unless I see a concrete example that I like, right now these navigation templates seem like more trouble than they're worth. They seem like the infoboxes on bios, which are often, in my experience, just cluttered or useless. I suppose people have been harping about similar things so I'll stop with that.

Let me just reiterate a "philsophical" argument, due to David Eppstein, which I believe has been missed as it is not listed, for instance, in the list of arguments above. I believe the desire to create this kind of hierarchical system is really unnatural for a lot of mathematics. For some areas, it may "work". But here "work" doesn't mean that it really reflects an inherent hierarchy of concepts, but someone's training. So, for example, with group theory, many in the U.S. learn group theory in this rather pedestrian (albeit elegant) way where one starts with the group axioms, proceeds Bourbaki-style, learning eventually about group actions, etc. But for people with a different background or philosophy, this is really quite strange. For example, I believe there are major Russian schools of mathematics that would not teach group theory this way. Ok, enough philosophizing.... --C S (Talk) 08:34, 10 October 2006 (UTC)

Hmmm... interesting. I think in Russia they start with groups as symmetries of some object or set, and define everything that way. (I remember reading an article by Vladimir Arnold complaining bitterly that the axomatic way of teaching group theory left students with no understanding about what was actually Going On.) But I digress. The point Chan-Ho Suh is making is that different groups of people will order things in different ways as a result of their own educational experience, and this applies especially in mathematics. However, I think this would be resolvable, in that there would be general consensus on what topics would be included under group theory (sticking with groups). Yes, people learn about the topics in different orders, but that doesn't stop them from grouped togther in a similar way.

Also, this is the English-language wikipedia, and as such, articles should be written and organised with the English-speaking world as a target audience. Tompw 13:39, 10 October 2006 (UTC)

Funny to take Bourbaki as a representative anglophone. And Chan-Ho has some very good points about the Russians. We would benefit greatly by having more from their angle here. Charles Matthews 15:07, 10 October 2006 (UTC)

I'll weigh in with the majority opinion, that nav-boxes are inherently evil. My complaint is that I find that they provide a distorted view of the world, echoing some structure that was fashionable three decades ago. They typically give prominence to some inane topic while completely snubbing something more important. A well-written article will already contain all of the needed links to all of the topics that need to be linked. The nav-box offers nothing more than a quick escape for those with a short attention span. linas 05:57, 12 October 2006 (UTC)

If you think a given nav box is as you describe, then why don't you change it? Tompw 10:54, 12 October 2006 (UTC)

Changing the navboxes only makes sense if one already agrees that navboxes are a good idea. Some of us do not so agree. —David Eppstein 14:39, 12 October 2006 (UTC)

Circular argment... "Nav boxes shoudln't exsist because they are bad. But if they are bad they should be improved. But they shoudln't be improved because they shouldn't exist, because they are bad." Tompw 17:42, 12 October 2006 (UTC)

It is not a circular argument. We have three choices: (1) use the navboxes we have, (2) make the navboxes better, (3) don't use navboxes at all. All I'm saying is that some of us prefer (3) over the other two choices. —David Eppstein 17:55, 12 October 2006 (UTC)

I removed {{analysis-footer}} and {{geometry-footer}} from articles. The discussion here shows that people would prefer not to have these nav-boxes. Oleg Alexandrov (talk) 15:35, 12 October 2006 (UTC)

Fixing the Categories in Mathematics

As stated in the section above on Navigation Boxes, the Category system is better. However, many categories are over-full, for example, Category:Set theory. In such cases, we should create more subcategories (and subsubcategories, etc.). And we should also remove excessive categories from the articles. A good example is Category:Large cardinals which is a subcategory of Category:Cardinal numbers with little or no overlap. Unfortunately, overlap is common in other cases. JRSpriggs 07:54, 10 October 2006 (UTC)

Yes, Category:Set theory has nearly 250 articles. As a rule of thumb, I would say 100 articles in a category is quite enough.

The trouble can be that you may need an expert to make subcategories that really convince. I wouldn't necessarily trust myself to go into the set theory category and do the right thing for it. Charles Matthews 08:41, 10 October 2006 (UTC)

(I think the discussion in the above section says that some people think the category systems better, while others think nav boxes are better.) If an article can be said to belong to a category and a sub-category, then it should just go in the sub-category. That's why Category:Mathematics doesn't contain every single maths article on wikipedia. Tompw 13:25, 10 October 2006 (UTC)

It's a bad idea to make that a cast-iron rule, though. There are going to be a few exceptions, and it is excessively tidy-minded to enforce it. Charles Matthews 15:05, 10 October 2006 (UTC)

I haven't poked around much through the Wikipedia math categories so this is a bit naive, but I have a question: how well do the categories comport with the Mathematics Subject Classification (MSC) of the AMS? Dave Rusin has a general overview here and uses it in his articles [58]. The AMS has some descriptions of it here and here. I guess I'm thinking it's worthwhile to not re-invent the wheel. Lunch 22:18, 10 October 2006 (UTC)

Thanks for pointing this out. The AMS article has this to say: "... it is not always clear how to classify a mathematical paper or theorem, as these fields and subjects are far from disjoint." --Jtir 22:30, 10 October 2006 (UTC)

In a nutshell: they don't. The AMS classifications are different from the way the categories have evolved. (See Areas of mathematics for somethign more akin to the AMS classification). I did consider at one poitn drawing up a map from Wikipedia categories to AMS classes, but I don't think it would've been of much use for Wikipedia. The important thing to remember is that the AMS system classifies mathematical papers; the WP categories clasify encyclolpedia articles. Tompw 12:25, 11 October 2006 (UTC)

Any fixed system of categories is going to suffer from sclerosis. It is basically very un-wiki to say 'here, use this already-fabricated classification'. Works for biology, perhaps, but in mathematics you are for example going to have areas of combinatorics that take on their own identity as things move ahead. Charles Matthews 15:24, 11 October 2006 (UTC)

Yes, I know the MSC is used for categorizing contemporary research papers. Yes, I know a fixed set of categories isn't going to cut it.

But the MSC has evolved. And it is the result of a bunch of professionals (experts?) who got together and said, "hey, this is a useful way of categorizing stuff in mathematics."

What I'm suggesting is that it is a useful reference point. That papers/articles often fall in multiple (sub)categories. And for anyone looking to improve the verbal descriptions of categories on their pages, or looking for ways to split large categories into subcategories, the MSC might help point a way.

I hadn't seen areas of mathematics before, thanks. Lunch 19:20, 12 October 2006 (UTC)

By the way, there is a new Category:Systems of set theory. Check it out. Add or remove articles as appropriate. Once it settles down, I may remove the members of it from Category:Set theory of which it is a subcategory. Unfortunately, it is on the second page of subcategories (on my screen, at least). JRSpriggs 07:23, 12 October 2006 (UTC)

Of course it is harder to check out right now, because the weird way subcategories are listed means it is on the second page of Category:Set theory... Categories really should not be allowed to go over 200 entries. You really need to refine categories on a page into one or more subcategories, not just add them, or this problem gets no better. Charles Matthews 09:12, 12 October 2006 (UTC)

In the last day, Charles Matthews has made a Herculean effort to improve the organization of Category:Set theory and its subcategories. I hope you will all join me in expressing our profound thanks to him. JRSpriggs 07:14, 13 October 2006 (UTC)

I'll comment that the biggest change was the creation of Category:Basic concepts in set theory, for the counting-on-your-fingers level of things like the union of two sets, and in fact all the standard concepts of naive set theory. Charles Matthews 16:38, 13 October 2006 (UTC)

Proof by symmetry

The Proof by symmetry looks kind of encyclopedic to me. Any comments on that? Oleg Alexandrov (talk) 03:09, 12 October 2006 (UTC)

Surely you mean UN-encyclopedic. Inarticulate and probably OR as well is what I say. Nor is it about "proof" by symmetry at all, but about some more nebulous concept of symmetry in mathematical expressions. It seems to have about the same encyclopedic status as Michael Hardy's "three kinds of induction" that generated such huge debate and was eventually partially merged into mathematical induction. This is the sort of attractive heuristic that someone really skilled in metamathematics could spin into a paper on "equations of balanced symbolism" or some such, but that the author just decided to stick on Wikipedia since it's less work and more public. Ryan Reich 03:26, 12 October 2006 (UTC)

Proof by symmetry was written by User:Aklinger. It refers to Patterns in numbers, written by a certain Allen Klinger, professor emeritus of the computer science department at UCLA. The manuscript is listed as a draft here. I'm thus PRODding it as OR (I assume that Oleg meant unencyclopedic). -- Jitse Niesen (talk) 04:07, 12 October 2006 (UTC)

Sorry, I did mean UN-encyclopedic. Oleg Alexandrov (talk) 15:31, 12 October 2006 (UTC)

The wiki article is rather vague; the linked Klinger preprint slightly less so. However, there is no reason to accuse either of 'original research' in mathematics as such. Both the article and the preprint stresses points that have to do with problem solving methods and with mathematical didactics, not the (IMO rather mediocre) mathematics.

Both present a somewhat exaggerated view of the difference between Klingon's approach and more normal ones. (However, the greatest error was the addition of Category:algebra to the article, to which User:Aklinger seems innocent.) The merits or lack of merits ought to be discussed in a more pedagogical context. Does en:wiki have such pages? Does there exist comments on Pólya's problem solving approach; or even information on the regular international mathematical olympic games and their outcomes? Actually, Klinger does not offer a simpler solution of the problem; but it may be argued that his 'pivot' approach yields yet another approach to the problem, and therefore could be of use e.g. in training high school math athlets. It is also worth to note that he does quote a few printed articles, but in Science and similarly, none in a clearly professional mathematical context.

Of course, pattern searching is important; for interested kids, for the adult layperson, for graduate students, and for established math pro's. Actually, there are patterns for the pythagorean triples, too, which Klinger doesn't mention. Instead, he writes

While students often learn about the Pythagorean theorem and some specific instances, neither the name nor the values in any such triple possess power to stimulate.

One should recall that data equivalent to the Pythagorean triples have been found on mesopotamian cuneiforms, and clearly indicate that the ancient author knew the pattern - and followed it for its own sake, far beyond any practical usage. However, it is correct that we seldom teach the pythagorean triples patterns - or encourage students to find them on their own. My conclusion is: We should have categories on mathematical puzzle solving, more serious problem solving, mathematical competitrions, and approaches in mathematical teaching. In such contexts, an improved version of the article (also based on the published pattern recognition papers) might have some merits; but not in the field of describing mathematics itself. JoergenB

A brief account for the mathematical lack of content: I stopped reading the preprint at page 2, sat down a couple of minutes, and solved the problem by an equation for 'the lowest number', instead of one for 'the pivot (central) number' as Klinger proposes. Then I read on, and found that Klinger's solution hardly differs in complexity. If we got the question at the reference desk, I think some might deny to answer, referring to the 'no home assignments' rule. Klinger does also discuss a few variants of the problem, and how the pivot method illuminates their similarities.

The first problem may be stated thus: Given a positive integer n, find a positive x, such that

$x^2 + (x+1)^2 + \ldots +(x+n)^2 = (x+n+1)^2 + \ldots +(x+2n)^2\!$ . My solution was: Move all but the first l.h.s. terms to the r.h.s., pair $-(x+i)^2\,$ with $(x+i+n)^2\,$ , and sum. This quickly yields $x^2 = 2n^2x + 2n^3+n^2\,$ and $(x-n^2)^2 = (n(n+1))^2\,$ .

Klingers solution: Instead, solve for x in

$(x-n)^2 + (x-n+1)^2 + \ldots + x^2 = (x+1)^2 + \ldots + (x+n)^2\,$ , by moving all but the last l.h.s. term to the r.h.s., and pairing $-(x-i)^2\,$ with $(x+i)^2\,$ ; proceed as before. This is not OR in pure mathematics. JoergenB 18:07, 12 October 2006 (UTC)

A more pertinent question is whether "proof by symmetry" is a neologism, which wikipedia avoids (WP:NEO), or an established term. In the latter case, since several editors say they have never heard of it, a collection of in-print references would be helpful. CMummert 20:02, 12 October 2006 (UTC)

I don't think anyone suggested that it was the mathematics itself that was original. The OR referred to is indeed more along the lines of neologisms, etc. JPD (talk) 08:48, 13 October 2006 (UTC)

So it may be. However, I think that is an abuse of the term 'original research' (possible a common use, still an abuse). An article that does not contain new mathematics could be righteously brandished in many ways, but not by the OR label.

I found some mathematical competition articles, but not (yet) articles on pedagogical aspects of mathematics, or on problem solving. Since IMO these are the only contexts in which any of the proof by symmetry content (duly migrated) might be of any encyclopædic value, I'd appreciate hints where to find them. JoergenB 16:04, 13 October 2006 (UTC)

You could try Category:Heuristics in general, How to Solve It in particular. Charles Matthews 16:10, 13 October 2006 (UTC)

Euclidean group

The article Euclidean group is a large amount of little factoids, which added together make, in my view, a pain to read. The article is primarily the work of User:Patrick. I like much more the original version by Charles Matthews (see current version and good old version). I would vote for a rewrite of the article using the older version or a revert. Comments? Oleg Alexandrov (talk) 04:23, 13 October 2006 (UTC)

Wikipedia:Embedded list is relevant, I think. (I'm guilty of perpetrating lists sometimes as well, but that doesn't mean I think it's generally good style.) —David Eppstein 04:49, 13 October 2006 (UTC)

I always support good writing over grab bags; please do revert and rewrite. --KSmrq^T 05:18, 13 October 2006 (UTC)

I think I added a lot of useful content, in a very orderly way, not as an unorganized collection of factoids. Therefore I am against deleting that. We should be careful in changing lists into prose, it may become less readable (or if we do, keep both, and split off parts if the article gets too long). Constructive input from others would be nice, there has been little activity by others the last year.--Patrick 07:58, 13 October 2006 (UTC)

The new version does have a lot more information, but when I read through it I found it to be very staccato. Some of the lists are clear, but for example the overview of isometries section is very difficult to follow. I don't think a revert is justified, just some editing to make the article flow better. Adding introductory paragraphs to some of the sectins would make the lists more clear, while other lists could be replaced with a series of subsections. CMummert 13:46, 13 October 2006 (UTC)

I've done some work on the ordering of sections, and other tweaks. It shouldn't be too hard to put this into approved 'concentric' style. Charles Matthews 15:35, 13 October 2006 (UTC) OK, that should be somewhat better now. The only point of real concern I have is this: does the article really need the non-closed subgroups enumerated? I would have thought the closed subgroups were enough. Charles Matthews 15:52, 13 October 2006 (UTC)

If the overview is restricted to closed subgroups this has to be mentioned, you cannot say the subgroups are all of type A, B, or C, when there is also a type D. However, to clarify the restriction you have to explain it, so you end up briefly explaining the additional kind anyway.--Patrick 22:08, 13 October 2006 (UTC)

I don't agree: if it is thought of as a topological group, why not just explain the closed subgroups? I don't see the need for any more than that. Charles Matthews 12:23, 14 October 2006 (UTC)

Doesn't this all belong on the talk page Talk:Euclidean group? Let's take it there. CMummert 22:22, 13 October 2006 (UTC)

Good point. I started the discussion here to attract attention, now that people got involved, the discussion can continue on the appropriate talk page. Oleg Alexandrov (talk) 02:29, 14 October 2006 (UTC)

Erdős number categories on CfD

The categories Category:Erdős number 1 etc. (not to be confused with Category:Wikipedians with Erdős number 1) are nominated for deletion. If you have an opinion on this, comment on Wikipedia:Categories for deletion/Log/2006 October 8#Erdős number categories. You probably have to be fast, as the nomination was six days ago. -- Jitse Niesen (talk) 05:40, 14 October 2006 (UTC)

Emmy Noether

I observe that this article has (recently, I believe) become congested with umlauts. Unless, as we are not likely to, we change the spelling of Noetherian ring, this should be straightened out, with a reasonable allowance of "Noether"s for a mathematician who is usually so called in English, and who died on the faculty of Bryn Mawr College. Septentrionalis 15:36, 16 October 2006 (UTC)

And, if I may add, the German Wikipedia also spells the name de:Emmy Noether. So do German libraries, like the catalogue of the Deutsche Nationalbibliothek. And so did she herself. I'm copying this over to the talk page of the article. --Lambiam ^Talk 16:45, 16 October 2006 (UTC)

Lebesgue measure argument

I came across this article recently, and actually made some edits on it. The Lebesgue measure argument (as defined in the WP article) proves the uncountability of the reals via measure theory. As best I can tell the purpose of the argument is that it avoids the use of Cantor's diagonal argument and can be considered constructive,although I haven't actually checked whether the argument is in fact constructive. Googling on Lebesgue measure argument (verbatim) I get only two hits, from wikipedia both. Though the argument is valid and interesting (if actually constructive), does this article not violate WP:OR?

Articles may not contain any unpublished arguments, ideas, data, or theories; or any unpublished analysis or synthesis of published arguments, ideas, data, or theories that serves to advance a position.--CSTAR 17:46, 16 October 2006 (UTC)

This general idea seems to be present in the introduction to Oxtoby, John C. (1980). Measure and Category, 2nd ed., Graduate Texts in Mathematics, no. 2, Springer-Verlag.; you could cite that as a source. —David Eppstein 18:00, 16 October 2006 (UTC)

I don't think it violates NOR, but I also don't think it's a particularly useful article as it stands. The hard part of the argument is that the measure of R as a whole is not zero, and that's not even touched in the article. When you fill everything in, I don't think it's any more "constructive" than the diagonal argument (which is pretty constructive, looked at the right way; for example, it's an intuitionistically valid proof that there's no surjection from ω onto 2^ω). The article also has a very unenlightening title. --Trovatore 18:36, 16 October 2006 (UTC)

It's not original research. It's well-known. I saw it in the first course on measure theory I ever took. I assigned it as an exercise for undergraduates when I taught a probability course at MIT. Of course, Trovatore is right about the "hard" part. Both Cantor's diagonal argument, and also his original argument for uncountability (which is three years older) are of course constructive. Michael Hardy 20:53, 16 October 2006 (UTC)

Oh---now I see that the argument given here is actually more complicated than the one I assigned. The exercise I assigned also avoided the "hard" parts, since the course assumed only first-semester calculus as a prerequisite (at MIT, first-semester calculus is about what first-year calculus is in most other places). See my comments on the talk page accompanying the article. Michael Hardy 20:57, 16 October 2006 (UTC)

Actually my question about whether this was OR concerned not so much whether the proof is OR, but whether the association of the name "Lebesgue measure argument" to the argument is actually supported in the literature. When I first came to WP over two years ago, I wouldn't have given this matter any thought -- any reasonable name would have suitable. However, with what seems the increasing trend toward WP:Wikilawyering at every junction I think this issue has to be addressed.--CSTAR 00:26, 17 October 2006 (UTC)

The name, as I mentioned, is obviously terrible. I'm not convinced the article should exist at all (a small mention in Cantor diagonal argument is probably sufficient) but if kept it should be moved to something more specific. I doubt there's a standard name in the literature, so that's not going to be much of a constraint, or much help. --Trovatore 00:30, 17 October 2006 (UTC)

I think "Lebesgue measure uncountability argument" would be sufficiently descriptive to avoid any claim that we are coining a new name, but as it stands the article is misleading as pointed out above and perhaps should get a disputed tag until the proof is completed.--agr 00:44, 17 October 2006 (UTC)

Based on the above comments, I put a Proposed AfD banner on the article.--CSTAR 02:56, 17 October 2006 (UTC)

This was deprodded by the author, so I smerged it into cardinality of the continuum, but first I prepared by moving the article to Lebesgue measure argument for uncountability of the reals, to avoid the bad redirect. There are way too many Lebesgue measure arguments to have that name reserved for this one in particular (and there's no real chance of a dab page; most of the time an argument doesn't get its own article, unless it has particular historical significance). And I put the redirect on WP:RFD.

If this is reverted we go to AfD. --Trovatore 05:56, 18 October 2006 (UTC)

Oh, just to clarify -- the redirect I put on RfD was Lebesgue measure argument, not Lebesgue measure argument for uncountability of the reals. The latter redirects where the content was merged; it should stay (though it's in my own words, so there'd be no GFDL issue in deleting it). It's the redirect Lebesgue measure argument, created by the move, that I think should be deleted. --Trovatore 06:12, 18 October 2006 (UTC)

"History of numerical approximations of π" really weird edit war---mathematicians please help

Look at the recent edit history of history of numerical approximations of π. User:DavidWBrooks has inserted this bit of wisdom into the article:

“

It has been known for millennia that π, the ratio between the circumference and radius of any circle,

”

("radius"! Sic.)

“

is a mathematical constant, but no method of calculation was available until fairly recently.

”

Of course someone came to clean up this nonsense, but here's what he (user:Henning Makholm) wrote:

“

Unfortunately no practical system for calculating with numbers is able to express π exactly. Though this fact was only proved rigorously in recent time, it has been suspected since the earliest times

”

Is there something remotely approximating some correct statement in that? If so, what is it? (Makholm left the ratio as circumference-to-radius rather than circumference-to-diameter.) Michael Hardy 21:05, 16 October 2006 (UTC)

I think it's all rubbish. Archimedes, like any capable mathematician of his days, knew how to compute the circumference of a regular 3·2ⁿ-gon. While this method is very not practical due to slow convergence, he must have realized, when using a 96-gon to shew that π < 22/7, that he could in theory compute the value to any desired precision. Given all the fuss at some earlier time over the diagonal of a 1 by 1 square not having a rational length, the claim that "this fact [...] has been suspected since the earliest times" has to be bogus. Or was that what the forbidden fruit of the tree of knowledge of good and evil propositions was about? Lacking a definition of what it means that a system is "practical", it is hard to refute the claim about what was proved "recently" (meaning, presumably, 1882). --Lambiam ^Talk 01:24, 17 October 2006 (UTC)

Why presume 1882? That was the year when π was proved transcendental. But that's got nothing at all to do (as far as I can see at this moment) with whether any "practical system for calculating with numbers is able to express π exactly". Anyone who thinks transcendence is about "practical systems for computing exactly" should get committed forthwith to the State Hospital for the Criminally Innumerate. Michael Hardy 02:09, 17 October 2006 (UTC)

Whoa, Michael Hardy shouldn't you be now concerned that a plague of Wikilawyers will descend on that previous claim, invoking countless breaches of this, that or the other rule, policy, guideline, essay, practice or what not and cart you off to wikiprison or maybe even have you wikiexecuted?. You're a brave man, Michael Hardy! --CSTAR 02:19, 17 October 2006 (UTC)

Arbitrarily-precise approximation is different from exact computation: one wants to be able to test, e.g., inequalities of expressions involving pi, and be guaranteed of an answer in a finite time, while you can keep computing as many digits of precision as you like and not be able to tell whether something is or is not equal to zero. And there is a sense in which transcendentalness is a barrier to expressing numbers exactly in a practical computational system, but irrationality isn't: see e.g. this page describing exact representations for algebraic numbers in the LEDA system. It says "LEDA cannot deal with transcendental numbers, at least not without loss of precision - there is no number type class in LEDA that could represent π or e exactly." Of course, the inability to express these numbers in a single system is not the same as a rigorous proof that no such system can exist, and I know of no rigorous proof that it's impossible perform exact computations in the extension of the algebraics by π. So I don't think the statement in the article is quite right... —David Eppstein 06:28, 17 October 2006 (UTC)

Point taken. What I was trying to express was just that one needs to work with approximations in order to do actual computations that involve pi -- but at the same time I was trying to defuse the possible counterargument that one could manipulate symbolic expressions, or juggle around with an entire convergent series of approximations, which is as "exact" as anybody could ask for. Henning Makholm 20:39, 17 October 2006 (UTC)

This should be discussed on the article talk page, but has general interest. Let's not get sloppy about terms. We can represent π exactly in a variety of ways. For example, we can define a series or continued fraction in a finite expression or algorithm. We can also compute π to any desired number of decimal places (or other measure of error). Archimedes demonstrated one approach using polygons to find upper and lower bounds, and we have much faster ways today. Being irrational, no finite computation can give an exact decimal expansion, oddities like the Bailey-Borwein-Plouffe formula notwithstanding. Yet computations with exact rational numbers are already troublesome in, say, computational geometry with lines and planes and so on, because the denominators can grow in a nasty fashion.

As for the article, both the original insertion and its amendment are hopelessly confused, and should be removed. --KSmrq^T 12:06, 17 October 2006 (UTC)

KSmrq is of course right. However, I'm afraid I can make a qualified guess of what the article editors essentially meant. There are too many students who believe that it isn't possible to express 1/3 exact (since they won't get an exact value by pushing 1:3 on their pocket calculator:-). Exact is often identified with exactly expressed in decimal notation with a finite number of decimals. I now and then meet statements such as '1/3 isn't an exact number, but 1/4 is'. Somewhat better informed students may understand that it is possible to 'express 1/3 exactly', if you use numerals with another basis than 10. In other words, I guess that 'no practical system for calculating with numbers is able to express π exactly' essentially is meant to mean 'π is irrational'.

I don't know if it is possible to clarify things enough for eliminating this confusion among some wiki readers; but we may try to lessen it. JoergenB 20:30, 17 October 2006 (UTC)

Oh, and by the way: That some users make this sort of mistake is not sufficient reason enough to accuse them of vandalism, or to call them 'dishonest idiots', however frustrating this kind of misunderstandings may be. JoergenB 20:42, 17 October 2006 (UTC)

My point above was simply that it is possible to express algebraic irrationals exactly, by writing down an integer representation of the polynomial for which they are root together with some disambiguating information to specify which root you mean. It is also possible to express π exactly, by the notation π. But the algebraics as exactly-specified numbers have been made part of a "practical system for calculating with numbers" (namely LEDA reals) while for π we can write "π" and call it a number and compute as many digits as we like but all that isn't sufficient to perform exact computations with it. I don't think the original editor meant an explanation like that, and I agree that the best course of action is to remove the offending statement, but there is a level of explanation at which his statement makes some sense. —David Eppstein 20:43, 17 October 2006 (UTC)

As a matter of fact, something like that was what I was trying to express with "practical system for calculating with numbers". Henning Makholm 20:51, 17 October 2006 (UTC)

David Epstein wrote:

it is possible to express algebraic irrationals exactly, by writing down an integer representation of the polynomial for which they are root together with some disambiguating information to specify which root you mean

By that standard one can also say that "log₂3" expresses a number exactly. Is there some reason to limit it to algebraic numbers? If not, then the year 1882, suggested above, does not seen relevant. If it is possible to define precisely something that Henning Makholm could have meant that is actually correct, then it seems very irresponsible to write in sich a horribly vague way about such a thing, and then claim that something expressed so vaguely was proved. It can't be proved if it can't be precisely expressed. So far we're still left guessing what was meant, even after Henning Makholm's comments here. Michael Hardy 22:58, 17 October 2006 (UTC)

I see your point, David. However, I think you may be mislead by viewing some CASes (computer algebra systems), where you might do exact simplification of expressions involving algebraic roots, but not as easily with π. In the first place, there are CASes and even pocket calculators where e.g. ~~sin π~~ cos π is replaced automatically by exactly -1, if you wish; some CASes may do much more advanced substitutions involving π; and more to the point, already Archimedes performed exact calculations with π (see talk:history of numerical approximations of π#Intro graf). IMO, 'computable' isn't synonymous with 'computable within a present-day CAS'. JoergenB 23:18, 17 October 2006 (UTC)

I made a stupid mistake above, thinking of cos and writing sin. However, I do not think making such ridiculus mistakes make me (or anybody else) qualified for asylums. I actually do know what the elementary values of the trigonometric functions are; believe me. JoergenB 23:30, 17 October 2006 (UTC)

There is, in fact, a specific technical reason to limit things to algebraic numbers: there exist algorithms that allow a computational system to reliably determine whether two given algebraic-number representations represent equal or unequal numbers. Therefore it is possible to guarantee that the result of a test such as x ≥ y, performed as part of some larger computation, will return in a finite time: one applies the equality algorithm first, and only after it returns unequal do you need to evaluate x and y to sufficient precision to tell them apart. There are no similar equality testing algorithms known, and therefore no similar finite-time guarantees, for systems of numbers generalizing the algebraics but also allowing logs, e, or π.

Also, I wouldn't call these systems CAS. They are libraries for performing calculations with numbers as part of computer programs, similar in spirit to a standard floating point library but allowing the representation of exact algebraic numbers in place of approximate floats. But they don't do some of the other operations that a typical CAS would, such as symbolic integration.—David Eppstein 23:41, 17 October 2006 (UTC)

CAS or not CAS is a matter of opinion. In mine, the algorithms by means of which you decide whether or not two expressions for algebraic numbers stand for the same number or not, are rather typical examples for CASes; much more so than is symbolic integration. This is not very important, though. If you restrict yourself to extending the field of algebraic number with one transcendental, e.g. π, you don't really get any harder decision problems than before. If you try to incorporate e.g. all kinds of exponentiation and logarithms, you run into trouble (at least today; I don't know much about the true bounds for undecidability). This is also not very important. The most important point is this: When you use the method of exhaustion by Eudoxos in order to prove that the same constant relates diameter to circumferense and square of radius to circle area, then you are performing exact calculations with the number π, in the best of the modern meanings. This Archimedes did. (This is a rather non-trivial result; as far as I remember, the claims about the constructions in the infamous Indiana Pi Bill implied different values for these two proportions.) JoergenB 00:49, 18 October 2006 (UTC)

There are no similar equality testing algorithms known, and therefore no similar finite-time guarantees, for systems of numbers generalizing the algebraics but also allowing logs, e, or π.

Do you mean ONLY that none is known, or rather that it is known (can be proved) that none can exist? If the former, it certainly doesn't justify saying that it has been PROVED that something specific about π cannot be done. Michael Hardy 23:59, 17 October 2006 (UTC)

I don't think it has been proven uncomputable, I think it's only that none is known. So that part of the statement is I think wrong. —David Eppstein 00:29, 18 October 2006 (UTC)

There are results along those lines. Consider the expressions built up from rational numbers, π, a single variable x, sine, absolute value, addition, multiplication, and composition. The problem "is such an expression equal to zero?" is undecidable. This theorem is due to a certain Richardson and follows from Matiyasevich's theorem. The only reference I have at the moment are some lecture notes, but I probably can find more details if necessary.

Of course, it's a bit of a stretch to refer to this result as "no practical system for calculating with numbers is able to express π exactly". -- Jitse Niesen (talk) 02:17, 18 October 2006 (UTC)

This is a fun and worthwhile discussion for me; I hope I'm not alone in that view.

So far there has been some dancing around the meaning of “practical system for calculating with numbers”, which is intolerably vague.

I would consider Macsyma, Mathematica, and Maple very practical systems for computing with numbers, as well as more general symbolic expressions.
I would also consider the implementation of IEEE floating point arithmetic on an AMD Opteron microprocessor chip a practical system for computing with numbers.
Both LEDA and CGAL are elaborate libraries for computational geometry which also fit the definition.
The GNU Multi-Precision Library is another example.

David Eppstein presumably is invoking the decidability of quantifier elimination for a real closed field, which relates to Tarski's axiomatization of the reals but for a first-order theory. More concretely, this is about George Collins’ seminal work in cylindrical algebraic decomposition for semi-algebraic sets. (I would love to have Wikipedia links for the preceding sentence, but we have none of the relevant articles!) In order to have polynomial-time algorithms for arithmetic, we may restrict our attention to real roots of univariate polynomials with rational (or integer) coefficients, Q[x]; these are the real algebraic numbers. Otherwise, the time required can be far from practical. However, this theory does not allow us to introduce an arbitrary assortment of fancy functions beyond basic arithmetic.

Yet within a computer algebra system we can surely know that 4 tan⁻¹ 1 is exactly π, or that e^iπ is exactly −1. Furthermore, we can do a wide variety of calculations and comparisons with π, more than enough for most practical purposes.

In contrast, using IEEE floating-point as our standard, we cannot express 0.1 accurately! The problem is that the radix-2 expansion repeats periodically. Compare this to √2, which happens to have a periodic regular continued fraction. Or compare to e, whose continued fraction merely requires an arithmetic progression.

The moral is, if we are too sloppy to define our terms, we're sunk. But I repeat myself. --KSmrq^T 15:19, 18 October 2006 (UTC)

Hamiltonian, anyone?

If your expertise allows you to contribute in a meaningful way to articles involving Hamiltonians and their applications, please take a look at Wikipedia talk:WikiProject Physics#Hamiltonian articles. --Lambiam ^Talk 01:35, 17 October 2006 (UTC)

Constructibility

In Talk:Borel algebra the following question is proposed by User:Leocat:

Can someone tell me how to construct an isomorphism between such Polish spaces as the unit ball in L^2[0,1] and the real line with the natural topology?

Now by Kuratowski's theorem, both objects are uncountable polish spaces and hence Borel isomorphic, so "there exists" an isomorphism. My guess is that this isomorphism is constructible, but I don't know enough about constructive mathematics to know for sure.

If anybody knows the answer to this question, you can post it there.--CSTAR 02:30, 19 October 2006 (UTC)

Well, it depends on what you mean by "constructive". There's no single agreed definition of that term. (By the way, be careful of substituting "constructible" for "constructive"; "constructible" has another constellation of meanings.)

Here's one partial answer: The arguments I know for the existence of such an isomorphism certainly use excluded middle. Basically you show that there's a Borel injection from Cantor space into any Polish space, and you show there's a Borel injection from any Polish space into Baire space, and you show there's a Borel injection from Baire space into Cantor space, and then you chase around the triangle using the Schroeder-Bernstein construction. It's the last part that uses excluded middle; you have to distinguish whether a point is or is not in the range of an injection, and without using excluded middle, it's going to be tough to prove that it either is or isn't. --Trovatore 03:47, 19 October 2006 (UTC)

Another empty category

There are currently no articles or subcategories in Category:Infinity paradoxes which is a subcategory of Category:Infinity. Possibly related articles are in Category:Paradoxes of naive set theory which is in Category:Basic concepts in infinite set theory which is in Category:Infinity. Does anyone want to put something in the empty category or shall we delete it? JRSpriggs 08:17, 16 October 2006 (UTC)

I say nominate for deletion. Category:Mathematics paradoxes is a reasonable upper bound, and the Category:Paradoxes of naive set theory was deliberately created to sort out those relevant to infinite cardinality. Charles Matthews 13:09, 16 October 2006 (UTC)

If I understand the rules correctly, I can add {{db-catempty}} to the category on 20 October 2006. Will that result in it being deleted? Or must I also list it somewhere? JRSpriggs 05:55, 17 October 2006 (UTC)

No, just speedy it. It's not like deleting an empty category is a big deal; if someone wants to recreate it, it takes all of five seconds. Melchoir 06:29, 17 October 2006 (UTC)

Although I have suggested (on this page) deleting a category once before, I have never gone thru the process myself. As I understand it, I would have to persuade an administrator to delete it. Do I just ask one, like User talk:Oleg Alexandrov or User talk:Arthur Rubin? JRSpriggs 07:59, 17 October 2006 (UTC)

{{db-catempty}} is actually a a speedy tag. Basically just put it on the page and wait. If no one objects it will go. WP:CSD explains more. --Salix alba (talk) 08:24, 17 October 2006 (UTC)

Apparently, someone beat me to the punch and deleted it already. I was going to add the template tonight. JRSpriggs 02:08, 20 October 2006 (UTC)

Eigendecomposition

I've added "eigendecomposition" as a synonym for "spectral decomposition" in the spectral theorem article: I'm almost completely sure that's right, but my maths is a bit rusty these days -- could someone more up-to-date double-check this, please? -- The Anome 11:59, 20 October 2006 (UTC)

Aaagh: Google says 84K of hits for eigendecomposition. That's already far too many ... Charles Matthews 15:43, 20 October 2006 (UTC)

Do people think it would be a good idea if I had MetsBot tag all pages in Category:Mathematics with {{Maths rating|class=|importance=}}? —Mets501 (talk) 01:15, 15 October 2006 (UTC)

Could you give some background? What would be the advantage of doing that? -- Jitse Niesen (talk) 03:13, 15 October 2006 (UTC)

Eh? How can a bot give meaningful ratings? And, for all of mathematics, how can you? If the ratings are not meaningful, they shouldn't be added. This kind of useless busywork would light up every page on our watch lists, which strikes me as a spectacularly bad idea.

But I'll tell you what a bot could do that would be an interesting exercise, if you want to crawl over all the mathematics pages. Use one of the mechanical tests of readability, such as SMOG, both on the article as a whole and on the intro alone. Report back what you find. We could improve the overall quality of our writing by having short lists of easy-to-read and hard-to-read articles. Of course, better still would be to go beyond that, to teach good writing. But that a bot cannot do. --KSmrq^T 07:35, 15 October 2006 (UTC)

I'm not sure tagging all pages will be a good idea, its something like 10,000 pages most of which will probably stay unrated. For me the real use in the maths rating is identifying and grading the most important articles, I guess about 500 articles. There is some good work a bot could do. Currently only about half the articles listed in subpages of Wikipedia:WikiProject Mathematics/Wikipedia 1.0 have a rating tag, so taging these pages would help. Further as we move away from these hand compiled lists to automated lists like Wikipedia:Version 1.0 Editorial Team/Mathematics articles by quality the shear number of articles will be problematic. Hence a bot could use the field tag of the template to assemble lists for each field of mathematics.

Reply to Jitse. The mathematics article rating is part of a wider project grading much of wikipedia, WP:1.0. There are 135 participating project. The aim of WP:1.0 is to make a CD with the best of wikipedia for which they need wikiprojects to identify their best and most important articles. Grading will also help identify the better mathematics articles, and promote them to GA/FA status, find week spots in our coverage. Overall grading ties with Jimbo's talk at wikimania that we have to start changing the focus from quantity to quality. --Salix alba (talk) 08:45, 15 October 2006 (UTC)

According to Portal:maths, there are over 14,000 maths articles. I'm not sure if this is based on articles in Category:Mathematics, or List of mathematics articles, but either way, the number includes a lot of articles that are only tangentally connected wih maths. A lot would probably come under the scoep of other wikiprojects, and for that reaosn alone, it is not worth tagging every single article. IOne of the main reasons for the tagging is to try and help prioritise efforts, by highlighting important articles that need improving.

Related note: Do people think it is worth having a list (either on the wikiproject main page or a subpage) of high-importance stubs and top-importance start-class articles? (There are now no top-class stubs :-) ). Tompw 10:07, 15 October 2006 (UTC)

Tompw 10:07, 15 October 2006 (UTC)

The number 14,000 is based on all the math articles listed in the list of mathematics articles. It is true that some of them are only somewhat mathematical, as this is a general purpose encyclopedia and the distinction between what is true math and what is math-related can be blurry.

I agree with Tompw's arguments above about not tagging all math articles by a bot. Oleg Alexandrov (talk) 16:11, 15 October 2006 (UTC)

OK, no problem. I was doing it for other wikiprojects who requested it, so I figured I'd ask here. —Mets501 (talk) 19:18, 21 October 2006 (UTC)

Powers

Any consensus on the policy on fractional powers? We write the squareroot sign for powers of one half, but what about cube roots? Do we put the squareroot with the 3 above, or do we put ^1/3? And the others? yandman 09:57, 19 October 2006 (UTC)

Any reason not to use <math>\sqrt[3]{n}</math>? —David Eppstein 15:05, 19 October 2006 (UTC)

Where do we draw the line? $\sqrt[20]{n}$ looks a bit silly to me. yandman 15:31, 19 October 2006 (UTC)

Single digits or single letters only seems like a reasonable rule of thumb to me. —David Eppstein 15:44, 19 October 2006 (UTC)

(Edit conflict). Well, I think it's better than $n^\frac{1}{20}$ , personally. However, $n^\frac{3}{20}$ looks better than $\sqrt[\frac{20}{3}]{n}$ . So, I would be inclined to say use the "root" notation when the root is an interger, and use the "exponent" notation otherwise. Whatever the ourcome of this discussion, I think it (the outcome) should be added to Wikipedia:Manual of Style (mathematics). Tompw 15:56, 19 October 2006 (UTC)

The integer root rule works badly for formulas like O(n^1/32,582,658). As usual, it's an area where common sense and rules of thumb may be more appropriate than strict guidelines... —David Eppstein 16:04, 19 October 2006 (UTC)

I have to say, I don't think I have ever seen the notation $\sqrt[3]{n}$ in a book above introductory college textbooks. In journals it is very common to use the superscript even for square roots when it would simplify notation. (e.g. a lot of people prefer

$\frac{4\pi^6A^{1/2}g_s^2}{\Gamma(1/4)n}$

$\frac{4\pi^6\sqrt{A}g_s^2}{\Gamma(1/4)n}$ ,

and for long formulae you would definitely use parentheses and an exponent instead of a very large square root sign.) Using an exponent has the added benefit that simple formulae with exponents will not render to .png for people (such as myself) who have their math tags set to render to text for simple formulae. –Joke 00:05, 21 October 2006 (UTC)

One I recently edited here was

$c = \sqrt[3]{\frac{2\pi^2}{3}} \approx 1.874.$

in no-three-in-line problem. You could inline it as π^2/3(2/3)^1/3 (or some variation of the same with frac instead of slashes) but I think all the /3's make it confusing, and using the cube root sign makes it very clear visually that everything in the expression has a fractional exponent. On the other hand, I prefer your first formula to your second because the fractional exponent is formatted more similarly to all the other exponents. —David Eppstein 00:14, 21 October 2006 (UTC)

One more advanced instance of radicals that I've seen is in field theory. It is, of course, common to write $\mathbb{Q}(\sqrt{2})$ to denote the field obtained by adjoining a number whose square is 2. Also common, though, is to write $\mathbb{Q}(\sqrt[3]{2})$ to denote the field obtained by adjoining a number whose cube is 2. It would be improper to write $\mathbb{Q}(2^{\frac{1}{3}})$ , both because of convention, and because the exponential notation (for whatever reason, possibly convention) suggests a sort of deterministic choice, especially when its argument (i.e. 2) is real. $\mathbb{Q}(\sqrt[3]{2})$ is an abstract field, and could just as easily be $\mathbb{Q}(2^{\frac{1}{3}} e^{\frac{2\pi i}{3}})$ , where now I've deliberately used the exponential notation to single out particular complex numbers. Worse, of course, and not only in the context of field theory, is the fact that the power functions are of course not one-to-one, so that their inverses are multi-valued, and so using fractional powers only makes sense in the presence of a convention as to the specification of a particular value (like when we take square roots of positive real numbers).

However, since this doesn't seem to be a discussion of whether to use one symbol or the other but rather when, I would say that it's as much a matter of audience as of aesthetics. Certainly the radicals should be avoided for roots which consist of more than a single character or for all but diminutive radicands (i.e. $\sqrt[2]{2}, \sqrt[5]{n}, \sqrt[n]{m}$ , but not $\sqrt[20]{2,535,099,102,664}$ ) but on the other hand, in articles which are expected to see traffic by novices, radicals may be preferred. Fractional powers constitute a mild form of mathematical jargon and certainly represent a reasonably sophisticated idea that, say, students below college might not be comfortable with. Conversely, of course, in professional-level articles, we should probably avoid radicals unless (as in field theory) their use is conventional.

Ryan Reich 21:32, 21 October 2006 (UTC)

I definitely agree. Out of habit I might have used the formula

$c = \left[\frac{2\pi^2}{3}\right]^{1/3} \approx 1.874,$

but I think either looks great, especially compared to the inline formula you produced. –Joke 00:35, 21 October 2006 (UTC)

Note: it is generally a good idea to use linear notation in sub- and superscripts ( $x a / b$ , not $x^{\frac{a}{b}}$ ). Particularly when the formulas are rendered in low resolution as they are here. Fredrik Johansson 22:45, 21 October 2006 (UTC)

Use of the radical forces texvc to produce a PNG, which looks bad inline. Using wiki markup, we can write x^{^a⁄_b}. --KSmrq^T 23:59, 21 October 2006 (UTC)

English composition

Put it before them briefly so they will read it, clearly so they will appreciate it, picturesquely so they will remember it and, above all, accurately so they will be guided by its light.
— attributed to Joseph Pulitzer

Wikipedia mathematics editors are brilliant and well-educated, naturally. Yet many have never studied the art of readable writing, especially for the general public. I’d like to offer a few suggestions. With your approval, they may later find their way into our Manual of Style.

I begin by quoting two well-known mathematicians.

The first rule of style is to have something to say. The second rule of style is to control yourself when, by chance, you have two things to say; say first one, then the other, not both at the same time.
— George Pólya

[T]he problem is to communicate an idea. To do so, and to do it clearly, you must have something to say, and you must have someone to say it to, you must organize what you want to say, and you must arrange it in the order you want it said in, you must write it, rewrite it, and re-rewrite it several times, and you must be willing to think hard about and work hard on mechanical details such as diction, notation, and punctuation. That’s all there is to it.
— Paul Halmos

When I give a lecture or write a paper, I consider myself lucky if I can convey one idea clearly, so that my audience pays attention, understands, remembers, and is inspired. This is more difficult than it sounds! Both mathematicians quoted above agree. Thus the heart of good technical writing is our first guideline:

Know precisely what you want to say.

Halmos next says to know your audience, and again I agree; yet for Wikipedia the audience can include university faculty, the general public, and youngsters. Readability studies suggest several ways to help. Two basic guidelines, with broad empirical support, are:

Avoid long sentences with complicated structure.
Avoid unfamiliar words with many syllables.

And more technically,

Minimize adjectives, adverbs, and passive verbs.

These studies also emphasize the value of structure, as do both our mathematicians. Structure occurs on three levels: sentence, paragraph, and article. All three should be clear, logical, and memorable. And I have just illustrated the next suggestion:

Use twos and threes for organization.

Examples of twos include if–then and either–or. More generally, balanced structure and parallel structure help the reader. This is less useful at the paragraph level; but we can suggest the following.

Give each paragraph a clear topic, preferably in its first or last sentence.

At the article level, the order and content of sections should never leave the reader disoriented. Work for a natural flow, a sense of inevitability. We want readers to know where they’ve been and where they’re going.

Pay particular attention to the introduction, especially the first paragraph. The first sentence should both engage readers, and orient them to what is to come. It need not summarize the article.

All of the suggestions so far apply to any kind of writing. I have a few personal touchstones for mathematics. It is natural to include theorems and proofs, but I also try to incorporate:

Motivation
Intuition
———
Examples
Counterexamples
———
Pictures
Connections

Finally, I do my best to sneak in a little humor. Some may damn this as “unencyclopedic”, but the best teachers have always done so. We all know, when we’re honest with ourselves, that when we laugh, we learn. With that in mind, I end with another quotation.

I hope that posterity will judge me kindly, not only as to the things which I have explained, but also to those which I have intentionally omitted so as to leave to others the pleasure of discovery.
— René Descartes

Perhaps another time I can add links to writing resources. Meanwhile, take what you can of value from these suggestions, and help make Wikipedia better. --KSmrq^T 16:04, 19 October 2006 (UTC)

Sour comment: you know when Samuel Johnson said that if you were particularly proud of a piece of writing, you should cross it out? Here on WP you needn't bother. Someone else will surely edit it out for you. Charles Matthews 16:20, 19 October 2006 (UTC)

That's partly what motivated me to write this. I'm hoping to elevate the awareness of editors, both in their own writing and in critiquing others. I have no illusions that all those who read this handful of suggestions will become great technical writers overnight, or perhaps ever. Still, it may begin to help. Halmos himself said, “The ability to communicate effectively, the power to be intelligible, is congenital, I believe, or, in any event, it is so early acquired that by the time someone reads my wisdom on the subject he is likely to be invariant under it.” Yet he tried. Perhaps those drawn to improve Wikipedia will also wish to improve themselves, and maybe they can. We can hope. --KSmrq^T 19:11, 19 October 2006 (UTC)

"Minimize adjectives, adverbs, and passive verbs.". Umm... no. Without adjectives and adverbs, a sentence contains only nouns and verbs, which would make it less readable. Maybe what you meant was "avoid excessive adjectives and adverbs", which is something I completely agree with. (This is not the same as minimisation. Any sentence can have *all* its adverbs and adjectives removed - the ultimate in minimisation - and remain grammatically correct.)

Also, what is wrong with the passive voice? I use the passive voice occasionally, whenever I feel that the object of a sentence is the important part, rather than the subject. I hope I don't come across as overly-critical here, as I agree with the broad thrust of your comments.

"Always have a quotation handy; it saves original thought". Tompw 22:13, 20 October 2006 (UTC)

This is Wikipedia; original thought is prohibited. ;-)

Readability studies disagree with your objections. Here is one survey you may find enlightening. I also refer you to Strunk & White's acclaimed guide, The Elements of Style. Among their guidelines are these, supporting the one in question.

Use the active voice.
Write with nouns and verbs.
Avoid the use of qualifiers.
Avoid fancy words.

Those who have been force-fed an excess of Strunk & White may appreciate Lanham's amusing Style: An Anti-Textbook (ISBN 978-0-300-01720-5).

Your objection shows you think about how you write. English is a second language for many of our editors; yet even our native-speakers will not become good writers unless they, too, begin to think about their writing. --KSmrq^T 11:58, 21 October 2006 (UTC)

Simenon apparently used to draft his books by locking himself in a room for 72 hours, to get a draft. When he had recovered from that, he went through crossing out all the adjectives and adverbs he could find ... Charles Matthews 15:13, 22 October 2006 (UTC)

Sounds painful. I think that providing people think about what they write, don't write in the same way they speak, and read through what they have written, then few stylistic problems will crop up. (Also, British English and American English do have different styles, and I'm British. I know US manuals on style seem to regard the passive voice as an abomination. The UK and US are two nations divided by a common language...) Tompw 16:06, 22 October 2006 (UTC)

This is not a question of taste, but of readability. If you want to write as readably as possible, you must train yourself to use active voice. That is what readability studies tell us, whether we like it or not. Lest we think only Yanks and Brits have something to say, I quote a German author and a French author, both of some stature:

A writer is somebody for whom writing is more difficult than it is for other people.— Thomas Mann

Those who write clearly have readers; those who write obscurely have commentators.— Albert Camus

While I would not ask James Joyce to write like Ernest Hemingway, I’ll wager The Old Man and the Sea gets read cover-to-cover more often than Ulysses. --KSmrq^T 05:07, 23 October 2006 (UTC)

General Comment about Math articles from a non-mathematician

I think your readership might be better served by providing more background explanation and examples of advanced math concepts designed for a lay audience than your current pages do. Since Wolfram Mathworld already does an excellent job of rigorous textbook style explanations with all of the relevant equations why not just link to them for this content and give Wikipedia readers a simplified plain English version with some real-world applications (along with the graphs suggested above, and perhaps historical development and relevance and maybe some nice pictures of engineering applications etc.) to get them started? --—The preceding unsigned comment was added by 67.174.240.33 (talk) 22 October, 2006

It is probably true that a lot of math articles could be made a lot more accessible than they are to lay audiences. But being accessible to the extent the material allows is not the same as lobotomizing all technical or rigorous content. And I think it's often possible to do a lot better than mathworld in terms of depth and rigor and correctness, and to have content in a single place that's useful for readers at all levels. —David Eppstein 01:25, 23 October 2006 (UTC)

I hope wikipedia is strong enough to be self-contained and not to rely on third party's stuff. --Beaumont (@) 09:10, 23 October 2006 (UTC)

Several points. I'm all for history. MathWorld was invented, basically, to promote the kind of mathematics where formulae are central. It has then branched out. We on the other hand have always taken the whole range of mathematics as our remit. Some doesn't have obvious engineering aspects. In other cases, for example cryptography, we have _both_ the mathematical articles on finite fields, say, _and_ articles dedicated to cryptographic applications. Charles Matthews 09:18, 23 October 2006 (UTC)

Yeah, there is room on Wikipedia for all kinds of articles at all kinds of levels. But indeed, making articles more acessible is a great goal. Adding a more elementary intro, putting a picture here and there, making more connections between math and physics or other applications are very good things, and we are aware of that. Oleg Alexandrov (talk) 14:47, 23 October 2006 (UTC)

I'm aware of a number of articles where the introductory material has been made harder, in some supposed trade-off with accuracy or a more 'professional' feel. It would be interesing to compile a list where the intro is unnecessarily off-putting, and where the article also ought to be of general interest. Charles Matthews 16:03, 23 October 2006 (UTC)

I would really request that any such edits which complicates introductions be reported here. I think there is a consensus over here that introductions must be kept as simple as possible, and we definintely don't want people obfuscating introductions. Oleg Alexandrov (talk) 03:26, 24 October 2006 (UTC)

You mean, like the "articles that are too technical" list here? —David Eppstein 16:37, 23 October 2006 (UTC)

That page is a long list of whinges. I took one at random: D-separation. The list says 'needs more context'. It's obvious when you look at it that it's a technical thing about Bayesian networks, and sometimes technical stuff is irreducible. No, not what I meant. I meant examples of the ratchet at work, where the user-friendly sentences get shredded because some expert decides they are holding up the parade. Charles Matthews 16:47, 23 October 2006 (UTC)

In our defence, writing an intro that is accessible but still correct in all important respects is not as easy as you might think. Look at what an anon editor has created recently in Trigonometry (the Overview section) to see an example of how not to do it. Gandalf61 16:16, 23 October 2006 (UTC)

So long as Wikipedia let's anyone edit, we will have the burden of reverting and explaining why. How many editors have read WP:MSM, which advises writing broadly accessible intros? I also think we could benefit from providing a simple readability measurement tool, as many of today's word processors do. It could help take discussions out of the realm of opinion and stylistic preferences, making them more quantitative. We are fighting a tradition of professional writing that is often unreadable, and we can hardly blame people for imitating what they have seen, attempting to "sound professional". Ironic that, since empirical evidence suggests that more readable papers are more influential.

I don't trust the automatic tools enough to make them a straight-jacket requirement. I would not say, "The intro must be written at a 9th grade reading level." For one thing, there are aspects of readability that cannot be captured by counting words and syllables. Still, if an edit changes a passage from 10th grade to 16th, we can use such a measure to help train the writer.

Train we must, perpetually, if Wikipedia wishes to be a professional quality encyclopedia. As the readability improves across all our articles, it will set an example that may help. However, even that can never substitute for awareness and deliberate attention to the features that make for readability. --KSmrq^T 17:58, 23 October 2006 (UTC)

The article titled uses of trigonometry, which I originated and which is still mostly my material, is an example of the sort of thing requested here. On the other hand, some of the statistics articles tell you what a concept is used for without ever saying what it is. Those would be greatly improved by more technical material. Michael Hardy 20:33, 23 October 2006 (UTC)

One problem I see in intros is that scientists/mathematicians like to start right off with "the most general case", which often involves a complicated formula. Sometime later they reduce that down to the common formula which everybody uses. For ease of reading, the simple case, with a real world example, should appear first, and the general case/derivation should be at the end. For example, I worked on the weighted mean article, and added an example, but it still has the technical "gobbledygook" (like the discussion of variance) up front, which makes this seemingly simple topic seem complicated. (I just moved some of the complex portion to the end, but I'm worried that this edit will be reverted.) StuRat 03:49, 24 October 2006 (UTC)

Yes, each new editor must be "re-educated". It may help to repeatedly cite WP:MSM. Here is a relevant excerpt:

Citation guidelines proposal

Since the discussions seem to have abated for some time now, I am asking the Mathematics and Physics WikiProjects if they support the new citation guidelines that I (and others) have devised. The point of the guidelines is to establish an appropriate, sensible standard for referencing articles in our fields so that we are less likely to run into objections (such as those that have come up recently) when we try to write technical articles that others then tell us are impropoerly sourced. I think these guidelines are now well thought out enough that they can be added to the main pages of the two WikiProjects and perhaps linked from WP:CITE. I should also note that they seem to have attracted some encouragement from outside the WikiProjects, on their talk page, mine, and on WP:CITE.

One outstanding issue is where to move the page. I don't have any great ideas. Wikipedia:WikiProjects Mathematics and Physics/Citation guidelines is too cumbersome. We could just leave it under physics as Wikipedia:WikiProject Physics/Citation guidelines or be BOLD and put it at Wikipedia:Scientific citation guidelines (presumably this would mean we would have to engage with the rest of the community to ensure there is consensus). I submit we should go with Wikipedia:WikiProject Physics/Citation guidelines and once we have consensus here go to Wikipedia:WikiProject Biology and Wikipedia:WikiProject Chemistry (and wherever else seems appropriate) to solicit their opinions, and then move it out of the physics WikiProject. We could even eventually go ask the wider Wikipedia community what they think at WP:CITE but I think that should be left as a longer term project. –Joke 22:14, 16 October 2006 (UTC)

Since there doesn't seem to be any objection to this proposal, I have gone ahead and moved it to Wikipedia:Scientific citation guidelines and added links on the pages of the relevant WikiProjects and on WP:CITE. –Joke 03:52, 26 October 2006 (UTC)

Support

I already offered my support on the talk page of WikiProject Physics, but also with my mathematician's hat on I support this. --Lambiam ^Talk 01:28, 17 October 2006 (UTC)
I like this proposal and support any step that moves it forward to wider acceptance. —David Eppstein 01:58, 17 October 2006 (UTC)
CMummert 02:55, 18 October 2006 (UTC)
I've also left a more detailed comment on the guidelines talkpage. --Salix alba (talk) 07:30, 18 October 2006 (UTC)
Support - excellent draft guideline - clearly written, pragmatic, comprehensive without becoming verbose. Gandalf61 08:10, 18 October 2006 (UTC)
This seems the best way to proceed. I would suggest also posting at Wikipedia:WikiProject Science. Tompw 15:13, 18 October 2006 (UTC)

Object

Neutral/Comment

I generally support it, but I find the statement "articles that link to [eponymous articles] may choose not to cite the original papers, depending on the context" too vague. I would prefer if such cases were handled just like links from a summmary to a sub-article. This would reduce the "dense referencing" and facilitate maintenance, since the sub-article is the best place to discuss and maintain attribution. — Sebastian (talk) 05:35, 19 October 2006 (UTC)
I agree with the text. I questioned some details on the talk page. The only problem I have is that I'm not convinced that it's a good idea to have separate citation guidelines. My impression is that most Wikipedia editors would agree with it, but that the so-called inline citation squad, having strong opinions on this topic, are very vocal at WP:CITE and (for some reason I don't quite fathom) at WP:GA. ~~However, they are not in the maths or physics WikiProjects (or if they are, they haven't come out of the closet yet).~~ -- Jitse Niesen (talk) 14:55, 21 October 2006 (UTC)

Project directory

Hello. The WikiProject Council has recently updated the Wikipedia:WikiProject Council/Directory. This new directory includes a variety of categories and subcategories which will, with luck, potentially draw new members to the projects who are interested in those specific subjects. Please review the directory and make any changes to the entries for your project that you see fit. There is also a directory of portals, at User:B2T2/Portal, listing all the existing portals. Feel free to add any of them to the portals or comments section of your entries in the directory. The three columns regarding assessment, peer review, and collaboration are included in the directory for both the use of the projects themselves and for that of others. Having such departments will allow a project to more quickly and easily identify its most important articles and its articles in greatest need of improvement. If you have not already done so, please consider whether your project would benefit from having departments which deal in these matters. It is my hope that all the changes to the directory can be finished by the first of next month. Please feel free to make any changes you see fit to the entries for your project before then. If you should have any questions regarding this matter, please do not hesitate to contact me. Thank you. B2T2 00:20, 26 October 2006 (UTC)

mathematician-stub

The various mathematician-stub templates are currently being discussed at Wikipedia:Stub types for deletion/Log/2006/October/19 Affected templates {{mathbiostub}}, {{mathbio-stub}}, {{math-bio-stub}}, {{mathematician-stub}}. --Salix alba (talk) 11:32, 26 October 2006 (UTC)

Name of theorem?

I was fiddling with some formulas, and seem to have stumbled over the following theorem: given any topological space X and any homomorphism $g:X\to X$ , there exists a measure $μ$ such that it is preserved by the pushforward $g * μ = μ$ (aka the direct image functor on the category of measurable spaces(?)); equivalently, there is always a measure such that g is a measure-preserving map, and furthermore, this measure is unique. This theorem is little more than a fancy-pants version of the Frobenius-Perron theorem, and the measure is more or less the Haar measure. I was wondering if this theorem has a name? Is it in textbooks? Or is it supposed to be a nameless corollary of the theorem that defines the Haar measure? Thanks. linas 03:35, 21 October 2006 (UTC)

I find uniqueness hard to believe. JRSpriggs 06:40, 21 October 2006 (UTC)

I question existence, since Haar measure depends on having a group structure. --KSmrq^T 12:29, 21 October 2006 (UTC)

Existence is true if X is a compact space, in which case the measure μ can be taken to be a probability measure. This is just the compactness of the space of Borel probability measures in the weak* topology and the fact the group of integers Z is amenable (actually this is equivalent to a fixed point theorem for continuous affine mappings on compact convex sets. See Dunford Schwartz, although I don't have it in front of me so I don't know the exact formulation.) However, in general uniqueness is false even for compact X and imposing the additional requirement that the measure μ is a probability measure. Uniqueness is a special property called unique ergodicity. For non-compact X, existence is also false without some additional assumption on X.--CSTAR 16:08, 21 October 2006 (UTC)

Thank you CSTAR, this pointer is just what I needed. (My X was indeed compact, and my g ergodic. I'm not sure what other additional ~~errors~~ assumptions I might have accidentally made along the way.) KSmrq, I'm looking at dynamical systems, so the hand-waving physics argument for existence is that physical systems always have a ground state, and, for systems in thermodynamic equilibrium (i.e. ergodic), so that all symmetries are broken, the ground state is unique. I'm grappling with general formulations, but this is new territory to me. I assume "Dunford Schwartz" is the book "Linear Operators" from 1958. I presume newer books on operator theory will have similar content. linas 22:17, 21 October 2006 (UTC)

Dunford and Schwartz vols 1 and 2 (vol 3 is much less interesting), though dated, are unsurpassed as general references in functional analysis.--CSTAR 22:30, 21 October 2006 (UTC)

Someone creted an artcle just today, for at least half of what I was looking for: the Krylov-Bogolyubov theorem. linas 23:48, 26 October 2006 (UTC)

Article count?

Is there any way to obtain a count of how many articles are in the Mathematics category or any of the categories beneath it, that is, articles that are in the scope of this project? What about other science projects such as Physics, Chemistry, etc.? CMummert 16:43, 26 October 2006 (UTC)

User:Jitse's bot says its 14953 which is updated daily. Its dificult to give an exact answer as it all depends by what you mean by a mathematics article. --Salix alba (talk) 17:36, 26 October 2006 (UTC)

Thanks. The goal I has was to get a relative sense of the sizes of the various projects. Obviously article counts don't tell the whole story, but they do give interesting numbers to compare the different projects. Is it true the Jitse's bot runs with regular user permissions (no SQL queries or anything like that)? If so, I might someday try writing a script to count the articles. CMummert 17:48, 26 October 2006 (UTC)

What you can do is download a database dump, parse that to find the links table and play around with that to your hearts content without bothering the servers (avoid importing into MySQL as it take forever). I guess there are about 1000 maths categories so querying that does impose some load. Theres lots of other ways to do queries meta:toolserver and http://en.wikipedia.org/w/query.php are both options. --Salix alba (talk) 19:49, 26 October 2006 (UTC)

It's kind of easier to figure that mathematics is 1% of enWP and then you count using the Main Page. (The proportion has been dropping, but slowly ...) Charles Matthews 21:27, 26 October 2006 (UTC)

Unfortunately, the category system here is sometimes surprising. For instance, Lute is in Category:Musical instruments is in Category:Music is in Category:Sound is in Category:Waves is in Category:Differential equations is in Category:Differential calculus is in Category:Calculus is in Category:Mathematical analysis is in Category:Mathematics. For this reason, User:Oleg Alexandrov maintains list of mathematics categories, which lists the categories that are considered mathematics.

There is also a bot called User:Pearle which does something similar to Wikipedia:WikiProject Mathematics/Current activity, but I don't quite know what it does or how it works. -- Jitse Niesen (talk) 02:54, 27 October 2006 (UTC)

And the line between math and nonmath can be blurry indeed. A few days ago my bot added the article Robert Byrd about the US senator to the list of mathematics articles because the guy has been put in the Category:Mathematics education reform. Gosh. Oleg Alexandrov (talk) 03:19, 27 October 2006 (UTC)

There is a shorter path for Lute. Category:Differential equations is in Category:Equations is in Category:Mathematics. JRSpriggs 09:15, 27 October 2006 (UTC)

Erdős number tags

Apart from the fact that I think it's annoying to be told Atiyah has Erdős number 4, as if this was on the same level as a Fields Medal: I think we should point out clearly that any information here should be verifiable. Apart from a complete list of collaborators of Erdős, it is going to be hard to verify numbers at all; certainly the only assertion you'd responsibly get is ≤ 3 and so on. Charles Matthews 19:01, 20 October 2006 (UTC)

Mea culpa; I supported keeping the categories. But I see no reason to mention the number in the text. I believe we can verify 1 and 2 easily, and larger numbers with more difficulty. Not that I'm volunteering to do it! Note date and location of birth can also be hard to track down, and we often manage that anyway. Shall we say every Erdős number tag should be accompanied by a certificate of authenticity on the talk page? That puts the burden on those who wish to add these categories. --KSmrq^T 19:32, 20 October 2006 (UTC)

Cats should only be added if the reason is obvious when looking at the article (and I suppose the talk page). Note the hard part, unless we link to an Erdős number site, is verifying that Atiyah is not EN 3...Septentrionalis 19:38, 20 October 2006 (UTC)

It would be very difficult to present a complete certificate of authenticity for an Erdős number >2; the best you could do would be to present a certificate of the authenticity of an upper bound. How do you prove that someone's Erdős number is really 4, and not 3? -- Dominus 12:28, 29 October 2006 (UTC)

Well, exactly. We have the choice of taking down the EN3 tag wherever it appears, and asking on the Talk page for such a certificate. I'd favour that. There is the perfectly good point that tracking all collaborations of EN1 mathematicians is hard, of EN2 mathematicians is ridiculous, and from then on it becomes plain daft. I vote we get a bit more lawyerish about this. Charles Matthews 12:35, 29 October 2006 (UTC)

For numbers one and two, one can look at the Erdős number project data, and for greater numbers (with the appropriate subscription?) you can use MathSciNet, assuming all the relevant pubs are in their database (a reasonable assumption for mathematicians, not so much for other kinds of scientist). So I don't see the difficulty of finding verifiable data as being much of an obstacle. —David Eppstein 20:21, 20 October 2006 (UTC)

PS Atiyah should be 3 not 4, according to MathSciNet:

Michael Francis Atiyah      coauthored with         Laurel A. Smith         MR0343269 (49 #8013)
Laurel A. Smith         coauthored with         Persi W. Diaconis       MR0954495 (89m:60163)
Persi W. Diaconis       coauthored with         Paul Erdös1     MR2126886 (2005m:60011)

—David Eppstein 20:22, 20 October 2006 (UTC)

Questions is mathscinet a reliable source? It can provide an upper bound on the Erdős number, but not necessarily the exact EN. Also it becomes on the bounds of original research to use the database, as its not a traditional publication. I know some of the people adding these cats are using mathscinet for their info (see my talk page). Still despite these reservations if we ate going to have the numbers its better to get the most accurate number possible. I like KSmrq's solution, maybe we should workup a policy on how to handle these. These cats are going to become an annoying waste of time.--Salix alba (talk) 21:20, 20 October 2006 (UTC)

It's original research to enter two names on a web query form and report the result of that form? It does take some checking afterwards to make sure the papers it returns are real joint publications, but the chain it gives you is readily verifiable, often without further need of their database. —David Eppstein 22:03, 20 October 2006 (UTC)

I guess that Archimedes must have been a lousy mathematician, because he did not have an Erdős number (sarcasm). JRSpriggs 06:38, 21 October 2006 (UTC)

The problem with MathSciNet is that it is not just a web query form. I mean accesibility. Well, one may pay for a subscription; as far as I can understand $2226 will do. I found nothing about such commercial databases in WP:VER policy. Do we really consider it verifiable? I guess we do not. So, inserting info about Erdos number would require a chain of publications as indicated above. As for reliability, MathSciNet should be considered on the top; it is likely to give you the best (often exact) easily verifiable result. Erdos number caracteristic seems to be interesting and notable enough to be mentioned in the bios, at least for EN<=5 mathematicians (and it is not considered as a coeficient related to notability of this mathematician!). Essentially, I agree with David. --Beaumont (@) 09:50, 21 October 2006 (UTC)

The strongest evidence that Archimedes, Euler, and Gauss were not great mathematicians is that none of them won a Fields Medal. (Tongue firmly in cheek.) :D

Relax, no one is obliged to research and incorporate an Erdős number category for any mathematician. It has not yet joined “use massive numbers of inline citations” as a criterion for Good or Featured articles.

For those who want to add these categories, the most verifiable “certificate of authenticity” would be the chain of publications. It is irrelevant whether MathSciNet or some other method is used to assist in finding the chain. I would recommend affixing any such certificate near the top of the talk page, to make it easy to find. --KSmrq^T 12:24, 21 October 2006 (UTC)

Re paying for the service: instead, you could walk into the library of most public universities and use the computers there. —David Eppstein 15:29, 21 October 2006 (UTC)

Errr ... you assuming we are all in the USA, or something? I think those who add such a category do owe us a list of intermediate people, and the best way is to add it to the page itself, by the category, and commented out. Charles Matthews 19:02, 21 October 2006 (UTC)

Err, there are no university libraries in other countries? Or (like some private ones in the US) they don't let you in without some kind of affiliation? In any case I agree that it's appropriate to provide a chain of intermediates; when the EN is mentioned in the text, it would be appropriate to do so there, but your suggestion of commented out next to the cat makes sense too. The few times I've changed these recently I've put the chain in the edit summary, but I guess that's not as easy to find. —David Eppstein 19:09, 21 October 2006 (UTC)

0.999...

Briefly browsing the archives suggests that this has not been discussed here before (and correct me if I am wrong). It seems like a good idea to bring it up now, seeing that said article has recently been the main page featured article and all.

Long ago, KSmrq has rewritten the article (which was then named Proof that 0.999... = 1) to look something like this (I'll refer to that as the "old" version). It stayed in that form for quite a while, until this edit, where Melchoir has begun a massive rewrite, ultimately resulting in something like this (I'll refer to that as the "new" version). In the meantime, the article has been, with overwhelming support, moved to the new title 0.999... to more faithfully represent its new (and old) content (as can be seen in this archive).

KSmrq has strongly opposed the move and the rewrite, and very frequently criticizes the new version and the editors who have worked on it. Needless to say, I have the greatest admiration for KSmrq's opinion, but happen to personally disagree with him on this matter (I accept some parts of the criticism, though, and believe these should be worked on on a case-by-case basis). I also got the impression that there are not many other editors who agree with him. In my opinion, while the fact that this article has become featured in its current incarnation obviously proves nothing, it supports this impression.

I therefore invite everyone here to share your opinions on the matter, with hope to finally settle this matter once and for all. I'll emphasize that it is not necessarily my wish to see consensus supporting the new version (which, again, is more to my taste), but rather to see consensus supporting some version, and having the article become as good as it can be as a result.

Those with some extra time on their hands could also skim through the extremely numerous reactions to the article (in Talk:0.999... and Talk:0.999.../Arguments) from the last two days, and see if they give them any ideas for possible changes to improve the article.

Since Talk:0.999... is a mess right now, I suggest that replies are made on this page. -- Meni Rosenfeld (talk) 16:42, 26 October 2006 (UTC)

Well, the feeling I get most strongly from the reactions is this: We have to figure out a way to get readers who doubt the validity of digit manipulations to skip the 0.999...#Digit manipulation section, or at the very least not get stuck on it. In general, the sections should better describe their relationships to each other. At the same time, it would be useful to create new articles, or improve existing ones, to describe the foundations of decimal arithmetic for all those skeptics.

In general, I'm thrilled to discuss problems on a case-by-case basis. There's a very indirect lesson from the FAC; some of the supporters praised it for having great writing. While that's certainly a welcome sentiment, it isn't ultimately any more helpful than KSmrq blasting the article for having terrible writing. We should focus on specific, actionable issues if we want to understand each other, let alone generate progress and consensus. Melchoir 19:16, 26 October 2006 (UTC)

We should just redirect this page to 1 (number), you know. Merge or not? Charles Matthews 09:29, 27 October 2006 (UTC)

Seems the mailing list discussion was right: you do need tags like <irony>.Charles Matthews

Heh, I often use <sarcasm> tags just to be sure - it is often too easy to get confused about the intention of others. Sorry for misunderstanding. Any other thoughts, though? -- Meni Rosenfeld (talk) 17:01, 27 October 2006 (UTC)

0.9999... should redirect to 0.999.... Oh, it does. Well, scope for ... Charles Matthews 18:49, 27 October 2006 (UTC)

Are you really saying that there is nothing in this article which a general reader might want to know, or benefit from knowing? Obviously, I disagree, and I trust many others will, too. -- Meni Rosenfeld (talk) 10:12, 27 October 2006 (UTC)

My opinion is that its best to do nothing and move on. We have a slightly kooky feature article, which explains a frequently asked question about the reals. Redirecting to 1 (number) is just silly, as the article is actually about any decimal ending in 999... A merge is even sillier as it would give far to much attention to just one aspect of 1.

There plently else we could be doing, Addition is I feel close to FA status, Derivative and Integral could take some work to secure their GA status and Gottfried Leibniz needs some seriuos work to sort out an unusual citation system. --Salix alba (talk) 11:31, 27 October 2006 (UTC)

If this article should be merged at all, the target should be Recurring decimal. - Fredrik Johansson 11:49, 27 October 2006 (UTC)

Please forgive me if I say a few words, but not few enough.

When BradBeattie created the article (appropriately named Proof that 0.999... equals 1) on 2005-05-06, it was a sad little stub that evolved over the next weeks into a minor service article focused on the proof. Starting on 2005-10-27, I (KSmrq) began to work it over to more effectively confront the issues raised in the thousands of posts on the topic scattered around the web. A few other users helped with tweaks and vandalism reversion, of course. (We even got a visit by WAREL, lucky us.) Inevitably, on 2006-03-26, someone felt compelled to insert a pathetic infinite sum proof, which I had deliberated avoided for reasons I detailed at various times on the talk pages. That was the beginning of an accelerating downward slide. Concern for the readers who needed the article was shoved aside as more and more and more pet proofs and passions were stuffed in. I used the talk pages at great length to explain why that was counterproductive. Then, stunningly, on 2006-06-29, Melchoir began slapping on OR tags, adamantly rebuffing everyone who visited the talk page to nudge him out of such extremism. As the end of summer approached and sensible editors took vacations, Melchoir launched an all-out assault, beginning on 2006-08-23 and continuing with twenty or more edits a day. After making a few protests that drew retaliatory threats, I wrote it off as a bad investment of my time and took the article off my watch list.

Today the article has

a few meaningless pictures
section after rambling section arranged in no particular order
explanations of no benefit to those who really need them
topics better left to their own articles (such as Construction of real numbers)
a blizzard of 63 (!) odd, redundant in-line citations, including this series:

27. Griffiths & Hilton §24.2 "Sequences" p.386

28. Griffiths & Hilton pp.388, 393

29. Griffiths & Hilton pp.395

30. Griffiths & Hilton pp.viii, 395
a total of 49 (!) references of dubious utility

This article in its present state does not represent the best of our mathematics community, nor the best of Wikipedia. To the contrary, I find it an embarrassment to both.

I believe it was helpful to have a small service article on the proof, and when Melchoir goaded a naive editor into nominating the article for deletion (before taking it over), large numbers of other mathematics editors agreed with that view. I think it would be helpful to recreate a small article under the original “Proof…” title, with Melchoir prohibited from editing it. Then this abomination can drift into well-deserved oblivion.

Honestly, this is a minor backwater of mathematics. I am happy to have played a pivotal role in moving the proofs away from endless ineffective parroting of "geometric series" and the like, at least temporarily. I am happy to have raised awareness of the role of standard real numbers. I am not happy with what has happened since. I am unwilling to engage in more fruitless debates with Melchoir (or his surrogates). I will not participate in a revert war. And, frankly, I'm inclined never to see this topic ever again, a view I suspect is widely shared!

I am more concerned with the bigger questions implicit in this debacle. However, I have already exhausted my patience, and likely yours as well, so I'll stop here. --KSmrq^T 19:23, 27 October 2006 (UTC)

MediaWiki talk:Common.css#span.texhtml

I've mentioned this before, but I want to get it implemented now. See MediaWiki talk:Common.css#span.texhtml. —Mets501 (talk) 21:48, 28 October 2006 (UTC)

Yes, you've suggested it before. And then, as now, the answer is that you can make it happen in your own personal style sheet, called monobook.css. (See Help:User style or Wikipedia:Help desk.) There is no point in wasting our time again, and certainly not developers' time, with this. The new STIX fonts will be serif fonts, and we'd like to switch over to blahtex as soon as possible. --KSmrq^T 22:58, 28 October 2006 (UTC)

Nov 2006

This is "Wikipedia talk:WikiProject Mathematics/Archive19". It covers November 2006.

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

Archiving automatically (well almost)

As some of you already know, Wikipedia talk:WikiProject Physics recently started using User:Werdnabot to automatically archive its talk sections when ten days have passed since the last new comment. Perhaps we should start to think about whether we want to follow their example. JRSpriggs 11:51, 22 October 2006 (UTC)

Seems a good idea to me. --Salix alba (talk) 19:11, 22 October 2006 (UTC)

Rather than base it on elapsed time alone, I suggest that archiving of old material should only be done when a certain page size is reached. There's no point in archiving a question which hasn't been answered after 10 days, if it's the only thing there. StuRat 04:16, 24 October 2006 (UTC)

Please read the instructions at User:Werdnabot/Archiver/Howto. You will see that the options are very limited. We can change the time interval between the last signed message in a section and the time of archiving, but we cannot control the size of what is taken or what is left. Our choice is reduced, but we avoid having to do all the archiving manually. JRSpriggs 09:05, 24 October 2006 (UTC)

OK. I tried to turn Werdnabot on for this page. It should run every six hours and archive sections 12 days old or older (last edit). I have never done this before, so I am not sure whether or how well it will work. JRSpriggs 09:28, 27 October 2006 (UTC)

By the way, there is one way in which it is not automatic. When we get to November 12, someone will have to create the new archive file for November 2006 and edit the code for Werdnabot invokation to reflect the new file name. The same every month thereafter. JRSpriggs 09:32, 27 October 2006 (UTC)

Werdnabot seems to be broken again. It has not done any archiving (for anyone) since 24 October 2006. (Just as I was trying to get it to work for us, too.) And Werdna himself seems to have dropped out of wikipedia (at least temporarily). JRSpriggs 07:04, 28 October 2006 (UTC)

It ran on the 28th, so at this point I cannot keep up with whether it is on or off. However, Werdna has apparently been working on some security issues -- vandals had figured out how to use Werdnabot to trash pages by directing its output inappropriately. JRSpriggs 11:54, 29 October 2006 (UTC)

To User talk:AzaToth: Since you pushed the list of archive files down into subpage "/archivelist" (which fact is far from obvious), I (after searching to find it) put a link to it at the top of this talk file right after the template. We need a way to get to that list so that we can add new links as we create new archive files (currently once per month). JRSpriggs 08:04, 30 October 2006 (UTC)

Neither you nor I will be around here forever. Future archivers must be able to figure out how to use the system without excessive effort. JRSpriggs 08:08, 30 October 2006 (UTC)

The {{archives}} template have an edit link at top right. _→AzaToth 11:21, 30 October 2006 (UTC)

Sorry, I do not know how I overlooked that edit link. I just tested it by adding a file for November prematurely. JRSpriggs 08:13, 31 October 2006 (UTC)

No problem, perhaps I should had marked it better? _→AzaToth 11:23, 31 October 2006 (UTC)

More User:WAREL clones, and blocking

Current (possibly incomplete) list:

Should we block more of these? So far, I've only been blocking them if the edits are incorrect, but a number of them are still live. Was there any ArbCom action taken against him? I've lost track. — Arthur Rubin | (talk) 21:34, 25 October 2006 (UTC)

There has never been an ArbCom action, and none is necessary in my opinion. I think the clones can be blocked on sight. -- Jitse Niesen (talk) 01:24, 26 October 2006 (UTC)

Yes I think Jitse is correct. The only question I would have is how do we know they are clones? Paul August ☎ 03:22, 26 October 2006 (UTC)

I blocked User:TELL ME that indefinitely after another edit to perfect number. -- Jitse Niesen (talk) 06:13, 26 October 2006 (UTC)

Add User:Lucky Eight; Big Omega in perfect number. Septentrionalis 15:28, 31 October 2006 (UTC)

Texvc changes

Some new stuff in texvc...

Environment array

\begin{array}{c\|lcr} 1 & a & = & a + b \\ 2 & b & = & c^2 + d \\ 3 & c + a & = & d \end{array}	$\begin{array}{c\|lcr} 1 & a & = & a + b \\ 2 & b & = & c^2 + d \\ 3 & c + a & = & d \end{array}$

Under/Overbrace: now they work as intended:

\underbrace{999...9}_n	$\underbrace{999...9}_n$
\overbrace{999...9}^n	$\overbrace{999...9}^n$
\underbrace{\overbrace{0}^{signbit} \!\!\! .101010101}_{mantissa} \times \underbrace{010101}_{exponente} previous version still cached, so added an e to the exponent to render the new image.	$\underbrace{\overbrace{0}^{signbit} \!\!\! .101010101}_{mantissa} \times \underbrace{010101}_{exponente}$

Some new symbols

\jmath
\surd
\ast
\uplus
\diamond
\bigtriangleup
\bigtriangledown
\ominus
\oslash
\odot
\bigcirc
\amalg
\prec
\succ
\preceq
\succeq
\dashv
\asymp
\doteq
\parallel
\longleftrightarrow

(awaiting scape at the moment)

_→AzaToth 19:31, 29 October 2006 (UTC)

Making under/overbrace work properly is great. Many thanks if you are responsible for this. Do you know whether there are any plans to regenerate the PNGs of formulas containing these braces? -- Jitse Niesen (talk) 01:26, 31 October 2006 (UTC)

They will probably regenerate over time, but there will be no mass-purrge, as there is over one million images. _→AzaToth 01:28, 31 October 2006 (UTC)

Why do you think they'll regenerate? I realize you must know a bit about texvc, because you managed to write a patch, but I still have my doubts. Do you know of any way to make them regenerate, except for deleting all PNGs (which is not an option, as you say)?

They won't regenerate, they are static, talked with Tim about the problem, perhaps a solution will emerge. _→AzaToth 12:44, 31 October 2006 (UTC)

Incidentally, what does "scape" mean? -- Jitse Niesen (talk) 12:29, 31 October 2006 (UTC)

see wikt:scap _→AzaToth 12:44, 31 October 2006 (UTC)

Scape done

Ok, the symbols have been scaped now, here they are:

`\jmath`	$\jmath$	`\surd`	$\surd$	`\ast`	$\ast$	`\uplus`	$\uplus$
`\diamond`	$\diamond$	`\bigtriangleup`	$\bigtriangleup$	`\bigtriangledown`	$\bigtriangledown$	`\ominus`	$\ominus$
`\oslash`	$\oslash$	`\odot`	$\odot$	`\bigcirc`	$\bigcirc$	`\amalg`	$\amalg$
`\prec`	$\prec$	`\succ`	$\succ$	`\preceq`	$\preceq$	`\succeq`	$\succeq$
`\dashv`	$\dashv$	`\asymp`	$\asymp$	`\doteq`	$\doteq$	`\parallel`	$\parallel$
`\longleftrightarrow`	$\longleftrightarrow$

also, one symbol was mission from the help page, that is \rightleftharpoons: $\rightleftharpoons$ _→AzaToth 12:05, 31 October 2006 (UTC)

So, is all this stuff incorporated into Help:Displaying a formula now? JRSpriggs 12:13, 31 October 2006 (UTC)

I'm at the moment updating the page at meta, I'll transviki when I'm done. _→AzaToth 12:44, 31 October 2006 (UTC)

Poor man’s eqnarray

Support for the array environment may be good news for equation series, so we no longer must mix TeX and tables. Compare the following use of array to the current version of this derivation.

$\begin{array}{rcl} 0 & < & \int_0^1\frac{x^4(1-x)^4}{1+x^2}\,dx \\ & = & \int_0^1\frac{x^4-4x^5+6x^6-4x^7+x^8}{1+x^2}\,dx \\ & = & \int_0^1 \left(x^6-4x^5+5x^4-4x^2+4-\frac{4}{1+x^2}\right) \,dx \\ & = & \left.\frac{x^7}{7}-\frac{2x^6}{3}+ x^5- \frac{4x^3}{3}+4x-4\arctan{x}\,\right|_0^1 \\ & = & \frac{1}{7}-\frac{2}{3}+1-\frac{4}{3}+4-\pi\ \\ & = & \frac{22}{7}-\pi . \end{array}$

Unfortunately, this example reveals two problems. (1) TeX is not using display style for the equations. (2) TeX cannot handle the elaborate labels with their wiki links. --KSmrq^T 15:53, 31 October 2006 (UTC)

1: dont fully understand, 2: problem is that it's saved as an image, and at parse time we don't fully know the image size, if we did, we could parse wikilinks somewhat and create an imagemap.. _→AzaToth 17:38, 31 October 2006 (UTC)

To see the need for display style, compare the appearance of the right-hand side of the first line when inside an array,

$\begin{array}{c}\int_0^1\frac{x^4(1-x)^4}{1+x^2}\,dx\end{array}$

with its appearance otherwise:

$\int_0^1\frac{x^4(1-x)^4}{1+x^2}\,dx .$

Fortunately, texvc now seems to support the \displaystyle command, so we can work a little harder and produce this.

$\begin{array}{rcl} 0 & < & \displaystyle \int_0^1\frac{x^4(1-x)^4}{1+x^2}\,dx \\ & = & \displaystyle \int_0^1\frac{x^4-4x^5+6x^6-4x^7+x^8}{1+x^2}\,dx \\ & = & \displaystyle \int_0^1 \left(x^6-4x^5+5x^4-4x^2+4-\frac{4}{1+x^2}\right) \,dx \\ & = & \displaystyle \left.\frac{x^7}{7}-\frac{2x^6}{3}+ x^5- \frac{4x^3}{3}+4x-4\arctan{x}\,\right|_0^1 \\ & = & \displaystyle \frac{1}{7}-\frac{2}{3}+1-\frac{4}{3}+4-\pi\ \\ & = & \displaystyle \frac{22}{7}-\pi . \end{array}$

Unfortunately, although the individual lines are acceptable, the spacing between lines is cramped. Compare the example above to the version at the link. The eqnarray environment would automatically handle both displaystyle and line spacing — if we had it. --KSmrq^T 21:40, 31 October 2006 (UTC)

A little experimentation suggests a tolerable solution to line spacing. Here is an example.

$\begin{array}{rcl} 0 & < & \displaystyle \int_0^1\frac{x^4(1-x)^4}{1+x^2}\,dx \\[1em] & = & \displaystyle \int_0^1\frac{x^4-4x^5+6x^6-4x^7+x^8}{1+x^2}\,dx \\[1em] & = & \displaystyle \frac{1}{7}-\frac{2}{3}+1-\frac{4}{3}+4-\pi\ \\[1em] & = & \displaystyle \frac{22}{7}-\pi . \end{array}$

For easy reference, the environment is \begin{array}{rcl}, and the second line has the markup

& = & \displaystyle \int_0^1\frac{x^4-4x^5+6x^6-4x^7+x^8}{1+x^2}\,dx \\[1em]

We're still missing a little of what we need for commutative diagrams, but this is progress. Enjoy! --KSmrq^T 20:12, 1 November 2006 (UTC)

This is how

<math>\begin{align}
0 & < \int_0^1\frac{x^4(1-x)^4}{1+x^2}\,dx                                                     &&                                                                                                   \\
  & = \int_0^1\frac{x^4-4x^5+6x^6-4x^7+x^8}{1+x^2}\,dx                                         && \text{(expanded terms in numerator)}                                                              \\
  & = \int_0^1 \left(x^6-4x^5+5x^4-4x^2+4-\frac{4}{1+x^2}\right) \,dx                          && \text{(performed polynomial long division, an important aspect of formulating algebraic geometry)}\\
  & = \left.\frac{x^7}{7}-\frac{2x^6}{3}+ x^5- \frac{4x^3}{3}+4x-4\arctan{x}\,\right|_0^1      && \text{(definite integration)}                                                                     \\
  & = \frac{1}{7}-\frac{2}{3}+1-\frac{4}{3}+4-\pi\                                             && \text{(substitute one for x, then zero for x, and subtract them—arctan(1) = π/4)}                 \\
  & = \frac{22}{7}-\pi                                                                         && \text{(addition)}
\end{align}</math>

will look after bug 7774 is applied: [59] _→AzaToth 21:18, 1 November 2006 (UTC)

Things in the queue

bug bugzilla:7774 is in the queue now, adding some more goofy stuff. _→AzaToth 21:54, 31 October 2006 (UTC)

Zeroes or zeros?

Just a quick question: do we have any guidelines over which we prefer - 'zeros' or 'zeroes'? This has probably been discussed before, but I can't see where ... Madmath789 18:33, 30 October 2006 (UTC)

My personal preference is for "zeroes". "Zeros" really should be pronounced "zee-ross". But I think there is no great need for project-wide consistency in spelling. --Trovatore 18:40, 30 October 2006 (UTC)

Zeros wins by about four to one on Google. —David Eppstein 18:42, 30 October 2006 (UTC)

Dictionary.com and Merriam-Webster both give either as acceptable alternatives. I prefer "zeroes", on the infamous model of "potatoes" and "tomatoes", "credos" notwithstanding. Still, since both are correct, we shouldn't change either. Ryan Reich 19:00, 30 October 2006 (UTC)

Isn't this just another U.S. spelling vs. U.K. spelling thing? There are already guidelines on that.--C S (Talk) 21:11, 30 October 2006 (UTC)

So which one do you think is US and which one do you think is UK? —David Eppstein 21:19, 30 October 2006 (UTC)

I had thought "zeros" was US and "zeroes" was UK, but I'm not so sure anymore. OED only gives "zeroes" as plural with no mention of "zeros". --C S (Talk) 08:12, 1 November 2006 (UTC)

According to The American Heritage® Book of English Usage. A Practical and Authoritative Guide to Contemporary English. 1996.:

“

Most nouns ending in o preceded by a consonant also usually add -s to form the plural: alto, altos; casino, casinos; ego, egos; Latino, Latinos; memo, memos; neutrino, neutrinos; poncho, ponchos; silo, silos. However, some nouns ending in o preceded by a consonant add -es: echo, echoes; hero, heroes; jingo, jingoes; no, noes; potato, potatoes; tomato, tomatoes. Some nouns ending in o preceded by a consonant have two plural forms (the preferred form is given first): buffaloes or buffalos; cargoes or cargos; desperadoes or desperados; halos or haloes; mosquitoes or mosquitos; zeros or zeroes.

”

Although both are correct, it seems that zeroes is mainly used in UK. A good place to ask could be [60] --pom 23:21, 30 October 2006 (UTC)

Restricting the Google search to .uk addresses didn't seem to make much difference to the much greater number of zeros than zeroes in my Google searches. —David Eppstein 23:28, 30 October 2006 (UTC)

My 1979 copy of the (UK) Oxford school dictionary has zeros as the only plural. So us birt don't have a strong claim to zeroes.--Salix alba (talk) 23:39, 30 October 2006 (UTC)

It seems to be quite mysterious. I found two american books with zeroes as the only plural (Essentials of English Grammar- a practical guide to the mastery of English by L. Sue Baugh, McGraw-Hill Professional 1993 and Prentice-Hall Handbook for Writer by William Charvat, Glenn H. Leggett, 1982). To the opposite I found two "old" books with zeros as the only plural (Practical Lessons in English- made brief by the omission of non-essentials. 1880 and An English Grammar for Higher Grades in Grammar Schools. 1894). pom 23:58, 30 October 2006 (UTC)

ZEROES. Dmharvey 00:11, 31 October 2006 (UTC)

I'm Brit, and I think I've always used "zeros"... that said, given either is acceptable, then it doesn't matter which gets used. Tompw 12:15, 31 October 2006 (UTC)

I looked it up in the OED and found that they had listed 'the' plural as "zeroes". However, I saw that the form "zeroes" was not present in any of the quotations, which all had "zeros", so I sent an e-mail about it and recieved a response the conclusion of which was that "This is a complex matter, and the current recommended form for ZERO, both here and in our dictionaries of current English, is ZEROS". —Centrx→talk • 15:29, 2 November 2006 (UTC)

Tensors

Tensor needs a lot of work. Discusssions a long time ago left the treatment fragmented over pages. Talk:Intermediate treatment of tensors has a recent long comment. I think a merge of Intermediate treatment of tensors into tensor might start some much-needed consolidation and imnprovement. Charles Matthews 10:51, 2 November 2006 (UTC)

On a related note: I've long thought that tensor product needs a complete rewrite. I started a draft at User:Fropuff/Draft 8 some time ago but I haven't had time to finish it. If someone wants to take the material and run with it they are more than welcome. -- Fropuff 05:16, 3 November 2006 (UTC)

Research Wikipedias

I am a member of the small community people who actively research tetration. For the last few years I have operated tetration.org, one of the main resources for tetration on the Internet. I became invoked with Wikipedia when I noted that Wikipedia’s entry on tetration was rapidly climbing to the top of search engine queries on tetration. Being very impressed with the goals and achievements of Wikipedia, I contacted other people researching tetration and suggested that we collectively become involved in editing Wikipedia’s tetration entry.

I guess the other folks weren’t as infatuated with Wikipedia as I was, so I ended up making what I thought were some reasonable edits to the tetration and Ackermann function. Tetration is an area of mathematics that attracts much attention from the public and amateur mathematicians while only now is it just becoming a legitimate are of mathematics research. The problem is that people keep adding their non-peer reviewed research to the tetration page on extending tetration beyond the natural numbers Tetration - Extension to real numbers. I didn’t want to try and play cop on the tetration page, but neither did I feel comfortable remaining affiliated with an entry that I felt continually misrepresented what was known about tetration. The solution to the problem is to publish articles in peer reviewed journals that clarify what is and isn’t known about tetration.

My personal problem is that I have a large backlog of research on tetration and related subjects that I need to organize and publish. Just because Wikipedia is not appropriate for documenting research doesn’t mean that the underlying MediaWiki software isn’t magnificence in documenting research; hey, just ask the CIA. I have a new website at tetration.net using MediaWiki; having Asperger’s and over a dozen years as a software developer MediaWiki helps me to do a brain dump of my work. I like the idea of pulling my research together using MediaWiki, publishing it in a peer-reviewed journals and then releasing the entries constituting the peer-reviewed material under GFDL.

The reason I posted this here is I need help in understanding the etiquette and GFDL issues in using stuff like snippets of TeX from the Wikipedia. Can I just cite a Wikipedia entry for a snippet of TeX or must I release the entry under GFDL. Almost all of the TeX snippets I have used are at least slightly edited, how does that impact things. Daniel Geisler 21:23, 2 November 2006 (UTC)

I think that an isolated brief formula from Wikipedia would fall under the "fair use" exception to the copyright law. So you would not need to do more than acknowledge the source. JRSpriggs 08:37, 3 November 2006 (UTC)

Leon Henkin

Can anyone confirm that Leon Henkin has died? Charles Matthews 13:10, 3 November 2006 (UTC)

Yes, he died on Wednesday, 2006-11-01. Contact Barb at the department via their website if more information is needed. --KSmrq^T 20:04, 3 November 2006 (UTC)

Texvc updated again

This was a rather large update, that's wwhy it took such a long time. First of all, bug bugzilla:1182 is fixed, so non greek greek symbols ( $\Alpha \Beta\,\!$ ) are not displayed as italics. Whats new is as following (\binom is more of a bugfix):

\begin{align} L & = \lim_{\|x\| \to \infty}\ {{\cos {1 \over x} \cdot {-1 \over x^2}}\over {-1 \over x^2}} \\ & = \lim_{\|x\| \to \infty} {\cos{1 \over x}} \cdot {-1 \over x^2} \cdot {x^2 \over -1} \\ & = \cos{1 \over \infty} = \cos{\ 0} = 1 \end{align}	$\begin{align} L & = \lim_{\|x\| \to \infty}\ {{\cos {1 \over x} \cdot {-1 \over x^2}}\over {-1 \over x^2}} \\ & = \lim_{\|x\| \to \infty} {\cos{1 \over x}} \cdot {-1 \over x^2} \cdot {x^2 \over -1} \\ & = \cos{1 \over \infty} = \cos{\ 0} = 1 \end{align}$
\begin{alignat}{2} L & = \lim_{\|x\| \to \infty}\ {{\cos {1 \over x} \cdot {-1 \over x^2}}\over {-1 \over x^2}} &\quad& \text{by me} \\ & = \lim_{\|x\| \to \infty} {\cos{1 \over x}} \cdot {-1 \over x^2} \cdot {x^2 \over -1} && \text{by him} \\ & = \cos{1 \over \infty} = \cos{\ 0} = 1 && \text{Axiom 3} \end{alignat}	$\begin{alignat}{2} L & = \lim_{\|x\| \to \infty}\ {{\cos {1 \over x} \cdot {-1 \over x^2}}\over {-1 \over x^2}} &\quad& \text{by me} \\ & = \lim_{\|x\| \to \infty} {\cos{1 \over x}} \cdot {-1 \over x^2} \cdot {x^2 \over -1} && \text{by him} \\ & = \cos{1 \over \infty} = \cos{\ 0} = 1 && \text{Axiom 3} \end{alignat}$
Foo \bigl( \begin{smallmatrix} a&b\\ c&d \end{smallmatrix} \bigr)$ Bar	Foo $\bigl( \begin{smallmatrix} a&b\\ c&d \end{smallmatrix} \bigr)$ Bar
A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C	$A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C$
\binom{k}{2}\dbinom{k}{2}\tbinom{k}{2}\frac{k}{2}\dfrac{k}{2}\tfrac{k}{2}	$\binom{k}{2}\dbinom{k}{2}\tbinom{k}{2}\frac{k}{2}\dfrac{k}{2}\tfrac{k}{2}$
\sideset{_^}{_n^'}\prod_a^b	$\sideset{_^}{_n^'}\prod_a^b$

Some new symbols that where forgotten

_→AzaToth 14:36, 4 November 2006 (UTC)

Awesome! Thank god for the align stuff, I've needed that many times before. —Mets501 (talk) 14:49, 4 November 2006 (UTC)

Factorization

I have a question about Factorization#Table method. Should it stay? Or is it too textbook-like? Thanks for your opinions. —Mets501 (talk) 15:01, 4 November 2006 (UTC)

L'Hôpital's rule

L'Hôpital's rule has had a couple of new proofs added to it, these were mentioned on Village pump(proposals) [61]. Could someone have a look over the changes[62]. --Salix alba (talk) 18:58, 30 October 2006 (UTC)

I've no time right now, but at first glance both the old and the new proofs look wrong and in any case unconvincing and not well presented. If we need to include a proof at all, let's not do the 0.999... thing but give one solid proof well presented. --Lambiam ^Talk 05:59, 31 October 2006 (UTC)

I'll second that opinion. CMummert 11:39, 31 October 2006 (UTC)

Well, I already removed the "proof by definition", which was egregiously wrong. The other two are "right" in the sense that they can be made to work, but I have not really looked at them. Ryan Reich 14:31, 31 October 2006 (UTC)

The "proof by local linearity" assumes that we can substitute the tangents to f and g instead of both numerator and denominator without changing the limit. This may be a way of explaining the theorem, but it's not a proof. So I removed it. Septentrionalis 15:33, 31 October 2006 (UTC)

You could make that argument work if you went to the trouble of doing epsilons, though. This is not a math book, however, so I agree with your choice. The "canonical" Cauchy proof is good enough. Ryan Reich 15:52, 31 October 2006 (UTC)

This is kind of off-topic, but anyone have any idea on why the titles of the articles on the person and rule uses L'Hôpital instead of L'Hospital? Is the reason that this is more common (if it is)? Certainly for the article on the person, shouldn't we stick with the spelling used by the person (L'Hospital) in question? I believe that is the usual guideline people have followed in other cases (as with umlauts), even when people often mangle the name in error. --C S (Talk) 00:12, 5 November 2006 (UTC)

The French Wikipedia, in its article Guillaume François Antoine, marquis de L'Hôpital, has this to say about it (in my quick and sloppy translation):

His name is also written L'Hospital. Contrary to what one might think, the circumflex accent is not an anachronism: while his book does not include an author's name, his friend Varignon, in the supplements to the book he published (1725), always writes his name with a circumflex accent, and in the encyclopedia of d'Alembert-Diderot one finds “L'Hopital”, without accent nor s.

--Lambiam ^Talk 07:40, 5 November 2006 (UTC)

Problem

Can anyone figure out why this is producing an error?

$\begin{alignat}{2} (a+b)^{m+1} & = a(a+b)^m + b(a+b)^m &\quad& \text{by the inductive hypothesis} \\ & = a \sum_{k=0}^m { m \choose k } a^{m-k} b^k + b \sum_{j=0}^m { m \choose j } a^{m-j} b^j && \text{by the inductive hypothesis} \\ & = \sum_{k=0}^m { m \choose k } a^{m-k+1} b^k + \sum_{j=0}^m { m \choose j } a^{m-j} b^{j+1} && \text{by multiplying through by } a \text{ and } b \\ & = a^{m+1} + \sum_{k=1}^m { m \choose k } a^{m-k+1} b^k + \sum_{j=0}^m { m \choose j } a^{m-j} b^{j+1} && \text{by pulling out the } k=0 \text{ term} \\ & = a^{m+1} + \sum_{k=1}^m { m \choose k } a^{m-k+1} b^k + \sum_{k=1}^{m+1} { m \choose k-1 }a^{m-k+1}b^{k} && \text{by letting } j = k-1 \\ & = a^{m+1} + \sum_{k=1}^m { m \choose k } a^{m-k+1}b^k + \sum_{k=1}^{m} { m \choose k-1 }a^{m+1-k}b^{k} + b^{m+1} && \text{by pulling out the } k=m+1 \text{ term from the right hand side} \\ & = a^{m+1} + b^{m+1} + \sum_{k=1}^m \left[ { m \choose k } + { m \choose k-1 } \right] a^{m+1-k}b^k && \text{by combining the sums} \\ & = a^{m+1} + b^{m+1} + \sum_{k=1}^m { m+1 \choose k } a^{m+1-k} b^k && \text{from Pascals rule} \\ & = \sum_{k=0}^{m+1} { m+1 \choose k } a^{m+1-k}b^k && \text{by adding in the } m+1 \text{ terms.} \end{alignat}$

It didn't like the ' in Pascal's, I can see if I can fix that_→AzaToth 15:43, 4 November 2006 (UTC)

The \text{by adding in the} m+1 \text{terms.} would be in normal LaTeX as \text{by adding in the $m+1$ terms.}, but that's not allowed at the moment. Perhaps fill a bug request about that. _→AzaToth 15:48, 4 November 2006 (UTC)

Thanks! I don't know if that will work in the article though, it's quite a bit too wide. —Mets501 (talk) 16:05, 4 November 2006 (UTC)

I added in some spaces to this example so the text doesn't get jammed up against the formulae. —David Eppstein 17:43, 4 November 2006 (UTC)

Probability-based strategy

I'm planning on nominating Probability-based strategy for deletion (rationale on article talk page), and I suppose the Catalin Barboianu BLP as well. I thought I'd check see if the readership of this page thinks I'm mistaken before I do so. Pete.Hurd 22:10, 6 November 2006 (UTC)

No objection from me, although it's not exactly my field. — Arthur Rubin | (talk) 00:30, 7 November 2006 (UTC)

There is (or was) some material on randomized strategies in some Wp article I worked on over two years ago. This article seems like a confused form of that. --CSTAR 02:01, 7 November 2006 (UTC)

Problem editting a section of this talk page

When Werdnabot ran yesterday, it added the section "General Comment about Math articles from a non-mathematician" from this talk page to the archive, but it did not remove it from this page. I tried to remove it from this page manually, but I could not. There is a part of that section which does not appear in my edit window, and thus I cannot delete that part. Can someone else fix it, please? JRSpriggs 09:10, 7 November 2006 (UTC)

The part which cannot be editted begins with "Suggested structure of a mathematics article" bracketted by "< h 2 >" and "< / h 2 >" (with out the blanks, which I added to prevent the problem from happening again here). JRSpriggs 09:15, 7 November 2006 (UTC)

Manually removed. --Lambiam ^Talk 11:10, 7 November 2006 (UTC)

To Lambiam: Thank you very much for your help. After I logged out yesterday, it occurred to me that perhaps I should have tried to edit using the "edit this page" tab at the top of the article instead of the "edit" button associated with the section. Is that how you did it? Were you using Mozilla's Firefox as I am or did you use Internet Explorer or what? JRSpriggs 06:10, 8 November 2006 (UTC)

That's how I did it using Firefox. Alternatively, I could have edited the various subsections out separately one by one, but that seemed like more work. Did the bot get confused by the html-style header? I did not carefully examine things, but had the impression that some other, not archived sections were decidedly older than this one. --Lambiam ^Talk 10:38, 8 November 2006 (UTC)

I do not know why Werdnabot failed to remove that section. I can only guess that it might have to do with the embedded "< h 2 >"(minus blanks). I suspect that that code generates the same kind of section separation indication which stopped my editting from reaching the remainder of the section (as a normal section header beginning with ==<Section title>== would do). As far as the timing of the archiving goes, Werdnabot seems to base its decision on time-stamps with the format produced by ~~~~. If a different format is used, as with {{unsigned|<name>}}, then it does not count. If you examine the section in question in the archive, you will see that the last entry is on November 1, but it uses the "unsigned" format. JRSpriggs 07:54, 9 November 2006 (UTC)

Portal suggestions needed

The lists of suggestions for selected article / selected picture / "Did you know?" for the mathematics portal is begining to get rather small. Could people try and add some items to the lists? This is especially true of the images, as good/interesting maths images can be hard to track down. Tompw 20:17, 8 November 2006 (UTC)

I guess all the articles in Category:A-Class mathematics articles, Category:GA-Class mathematics articles and possibly Category:Bplus-Class mathematics articles would be candidates for selected articles. I'm slowly building Category:Mathematics images which might be a good source for pictures. --Salix alba (talk) 11:33, 9 November 2006 (UTC)

Pseudo data up for deletion.

Pseudo data is up for deletion. Current version is non-mathematical although the term seems to be used quite widely in statistics.[63] --Salix alba (talk) 12:47, 9 November 2006 (UTC)

Navboxes for awards?

Please comment: Mikio Sato. My comment: silliness. --Pjacobi 09:57, 10 November 2006 (UTC)

Navboxes for awards are a bad idea. I dislike them intensely as they add clutter. Click on the category if you want to see the winners. 165.189.91.148 19:16, 10 November 2006 (UTC)

Probably WAREL

Anyone have any opinions on this edit? I'm almost certain that this "Imadada" is the newest WAREL clone, but that doesn't necessarily mean he's wrong. I can't get Babelfish to translate the Japanese page for me; it coughs up some kind of error and asks me to send an e-mail. --Trovatore 20:42, 12 November 2006 (UTC)

This translation worked for me. darkliight^[πalk] 21:38, 12 November 2006 (UTC)

That link just brings up the ja.wiki article, untranslated. --Trovatore 21:42, 12 November 2006 (UTC)

It is clearly about fields:

The body (you want in algebra, field, körper and corps), it is of gathering which has the algebra structure which can make arithmetical operation free. [...] As for K being monoid in regard to the multiplication, the origin other than 0 forms the group: [...]

The Japanese article links to our en:Field (mathematics), which in turn also links to ja:体 (数学). --Lambiam ^Talk 21:54, 12 November 2006 (UTC)

Postscriptum. I forgot to include: "Whatever kind of origin a of K, concerning b, ab = ba is filled up." The Japanese text (according to the Babelfish translation) the goes into a discussion of the non-commutative case and possible terminological confusion, and does mention, in small print, the term "division ring". Altogether, the link appears reasonable. --Lambiam ^Talk 22:11, 12 November 2006 (UTC)

Postscriptum 2. The inserted link is actually to ja:斜体, which is a redirect to ja:体 (数学), which is the Babelfish-translated article. The term "斜体" occurs in the article and is translated by Babelfish as "non-commutative field", and in the article itself as "skew field". --Lambiam ^Talk 22:23, 12 November 2006 (UTC)

I agree with Lambiam, the link is fine. I'm not convinced Imadada is WAREL, because WAREL maintained that division rings are called 体 in the Japanese Wikipedia. -- Jitse Niesen (talk) 01:27, 13 November 2006 (UTC)

Wiki project mathematics userbox

f(x)

This user is a member of WikiProject Mathematics.

User:NerdyNSK kindly created a userbox for the project, which briefy existed on /Participants. How do people feel about this?

Personally I thinks its on the whole a good idea, as it would help publicise the project. Of couse whether to display the box is entirly up to the user in question. --Salix alba (talk) 18:52, 6 November 2006 (UTC)

What's wrong with {{User WP Math}}?

This user is a member of WikiProject Mathematics.

—David Eppstein 19:01, 6 November 2006 (UTC)

Bad typesetting. Fredrik Johansson 19:07, 6 November 2006 (UTC)

More to the point should we include then on Wikipedia:WikiProject Mathematics/Participants? --Salix alba (talk) 19:09, 6 November 2006 (UTC)

The 'new' box NerdyNSK made is quite OK. However, the 'old' box Template:User WP Math is about a year old, and employed by (say) three scores of users; the new box User:NerdyNSK/Userboxes/WikiProject Mathematics was made less than two weeks ago and is employed by two users, NerdyNSK and Salix alba. I don't see an essential typesetting difference; and while I have to admit that the icon on the old box is a bit negative :-), I don't think most of those math project people who already have acquired the old box would feel sufficient interest or reason to change box. (Besides, I think it looks rather neat.) Thus, for uniformity, I rather recommend including the old box (and recommend NerdyNSK and Salix alba to switch). --JoergenB 18:32, 10 November 2006 (UTC)

Moreover, the old box is consistent with {{user mathematician}} tag. pom 19:02, 10 November 2006 (UTC)

The old one should be modified to put the whole name of this project on the second line as in the new one. Both boxes should be shorter horizontally to reduce the empty space on the right. Then I would prefer the old one. If you want to avoid negativity, try using $e^{2 \pi i}\!$ instead of $e^{i \pi}\!$ . JRSpriggs 08:24, 11 November 2006 (UTC)

I had a play with changing text size in my browser, and found that the text in both boxes is a single line which wraps differently. With a bigger font size they both have wiki project mathematics on the second line, with a smaller size they both wrap this text. It could be possible to add a tag here, however that might be a bad plan as it it might render badly on some browsers, or where the users font size is different. --Salix alba (talk) 22:01, 12 November 2006 (UTC)

The existing box with the existing sizes of the icon and text areas lines up nicely with other WikiProject membership boxes (such as the CS one, which I also use in my user page). A replacement box with different dimensions wouldn't line up so well. So I urge keeping the dimensions and the text font the same as they are now. I don't so much care what happens within the icon, though I think a nicely typeset Euler formula is better than a faux-typewritten generic function. —David Eppstein 00:05, 14 November 2006 (UTC)

Good point, David. I withdraw my suggestion that the boxes be made narrower. JRSpriggs 04:50, 14 November 2006 (UTC)

Game theory and importance rankings

Hello folks - I noticed an inconsistency with your importance rankings, and I thought maybe somebody might want to take a look. Nash equilibrium is rated "high" importance while Game theory is ranked "mid". It seems to me that a concept in a field ought not be more important than the field itself. I don't really care which way it goes, or even if it gets fixed, but I thought I'd let you all know. --best, kevin [kzollman][talk] 20:15, 10 November 2006 (UTC)

Agreed, I've changed the ranking of Game theory since no-one else has commented so far. I think the ranking scheme is pretty informal, so unless anyone else says otherwise, feel free to change the rankings of articles in cases where you feel the change is warranted. Cedars 00:52, 14 November 2006 (UTC)

List of all ten types of Steiner surface?

From Steiner surface: "There are ten different types, including the Roman surface and cross-cap." - List of all ten? -- 201.51.252.63 23:55, 12 November 2006 (UTC)

The article consists of three sentences and a reference. Yes, a reference! In fact, a relevant reference, and online so it's easy to access. Furthermore, that page has many, many further references. Or are you asking us to expand the article with the contents cited? --KSmrq^T 23:53, 13 November 2006 (UTC)

FYI - Definable number tagged as Original Research

Just an FYI, since it falls under this WikiProject, I tagged the article Definable number with the Original Research tag. It's an interesting article, but it does not appear to be based on external published information. Rather, it is an exploration by the article's authors into the concept of definability. In fact, in the introductory paragraph, the article even concedes that the phrase "definable number" isn't a standard mathematical term, which begs the question if "Definable number" is even the proper title for the article!

Anyway, I'd recommend that interested people here check out the article. If you are familiar with references regarding "definable numbers", feel free to add them to verify that the article isn't just original research. Or, if the article does appear to be entirely original research, then it should be deleted from Wikipedia and/or moved to a site that allows for original mathematical research articles. I didn't immediately tag the article for deletion, though, since I thought it would be more prudent to let you guys and the article's authors try and address the concern first. It is, after all, a good read, so I'd rather see it be fixed than deleted. Dugwiki 18:53, 13 November 2006 (UTC)

The concept of a "definable number", under that name and as distinct from computable numbers, certainly appears in the literature, notably in Turing's "On computable numbers with an application to the Entscheidungsproblem" [64]. I think the problem with the article is not OR so much as that it doesn't cite sources and should. —David Eppstein 19:04, 13 November 2006 (UTC)

It appears to me that Turing does not attempt to define "definable number" in that paper, or develop any theory of what a "definable number" in general is. He talks about the existence of a definable number that's not computable, but it's more like "here, you can see that this number is definable", not "this is what a definable number is in general". So I would take that to be more of a nonce term, not something we can write an article about. I would be strongly against writing an article based mainly on Turing's notion of definable taken from that paper, because of the fact that (based really just on a text search; I haven't read the paper yet in detail), he never does really define it. --Trovatore 19:20, 13 November 2006 (UTC)

Moved to definable real number. There is a fair amount that comes up when you Google that term. Charles Matthews 19:23, 13 November 2006 (UTC)

This discussion should move (has moved) to the talk page. CMummert 19:37, 13 November 2006 (UTC)

Commutative diagram

hi, folks. hope someone could help me. how does one make one of those and put it in an article? thanks. Mct mht 05:17, 14 November 2006 (UTC)

We do not have full TeX support, and producing diagrams directly in SVG is awkward, so the usual practice is to use an offline method to create a PNG image. A good example is Image:Snake lemma nat.png, which looks like this (in miniature):

Commutative diagram

The image page documents the means of its production. --KSmrq^T 07:57, 14 November 2006 (UTC)

Math articles lacking external references

(Originally posted on the wrong talk page. Moved here.) Just wanted to give you guys a heads up that in the course of perusing various mathematics articles recently I noticed a surprising number of them had no cited references. The information was accurate in these articles, far as I could tell, but they had little or no external citation. It might be a good idea for someone in this project with access to appropriate texts to try and add references that direct readers to verification.

In particular, it would be very nice if articles that state a theorem provide a reader with a citation that leads to an actual proof of that theorem. I've had a few times now where I read something, said "Hmm, that sounds true", but then wasn't quite sure how to go about proving it. Providing a reference or link to actual proofs would be a nice educational aid. Just a thought. Dugwiki 17:13, 6 November 2006 (UTC)

There are guidelines for citation in math articles that encourage the sort of citation you are looking for. When you read articles, you can use the unreferenced and fact tags to point out where you would like to see citations. If an article has no sources at all, put {{unreferenced}} at the top. Or put {{fact}} directly after a particular fact that you would like to see cited (but if there are many such facts, just use {{unreferenced}}). Pages marked with these tags are listed here for others to see.

Note that some math articles list good reference books at the bottom but don't give explicit inline citations. If you see that there are references at the bottom, it may be more polite to ask for a cite on the talk page first, before putting templates on the article itself. CMummert 17:49, 6 November 2006 (UTC)

I think we should bear in mind that mathematics articles are essentially composed of 'facts', and that for each such fact there will be someone who will find it unfamiliar. We could end up with yards of citations of 'trivia'; they are not trivia, but what has been called 'sorites', the sort of thing a really complete treatment puts in a reference section. This could certainly be detrimental. If someone wants a citation of the fact that the composition of group homomorphisms is a group homomorphism, it is (a) not the sort of thing encyclopedias trouble about, (b) is a timewasting thing to look up, and removing it as unsupported by citation would essentially be vandalism, and (c) it is the sort of thing that anyone is that bothered can and should verify in their own time. Charles Matthews 19:20, 6 November 2006 (UTC)

I think everyone here agrees that those are the sorts of facts that are best sourced by having general references at the end of the article. The new guidelines recommend putting a few inline citations to the best general references at the beginning, and otherwise not putting inline citations for easily verifiable facts; this is a sort of compromise between having no inline citations and having one for every trivial fact. CMummert 19:41, 6 November 2006 (UTC)

Thanks for your interest in improving our mathematics articles. Some comments:

Most advanced mathematics readers and editors depend on expert knowledge for verification, not blind trust in numerous citations or ignorant consensus. One reference to a reputable source at the end of an article is often sufficient. Mathematics is based on proofs, not observations or opinions, so is not as vulnerable to quality control problems as other topics.
If one mathematician 200 years ago proved a theorem, the fact stands for all time. However, the original proof may never have been translated into English, may use methods unfamiliar to modern readers, or may be long and difficult. Even when the proof is modern, it may be unhelpful to most readers who would use the theorem. Notable examples include the four color theorem and Fermat's Last Theorem, where both theorems are easy to state and use, but where both proofs are horrendous. It is quite common for a rigorous textbook full of proofs to omit certain proofs that are especially technical and that provide little insight.
That said, I personally enjoy knowing the history and personalities, seeing original sources, and exploring the rich connections modern mathematics has found among diverse topics. Such peripheral content is welcome, so long as it does not detract from the central content. Unfortunately, this “Further reading” material can be time-consuming to provide, and may be of less interest to the casual reader. Frankly, we count ourselves lucky to have so much as a stub article on many of our more advanced topics, providing information found nowhere else on the web.
If you are curious about a proof, please take advantage of our Wikipedia:Reference desk/Mathematics. And, of course, if an article (not already marked {{stub}}) has no references, a note on its talk page or an {{unreferenced}} tag would help bring it to our attention. --KSmrq^T 19:27, 6 November 2006 (UTC)

Just to reply to some of the above comments, since it appears some of you might think I am an inexperienced user looking for advice on how to tag articles, let me clarify. I'm already tagging articles as unreferenced as I see them when they have no references at all. My post here, however, was to point out to your project that I have come across a disappointing (to me) number of such unreferenced math articles. So this post is to make the project aware of a possible trend that is causing too many math articles to go unreferenced.

Second, for those thinking I'm looking for explicitly detailed citations for every statement, I was not suggesting a line by line citation is necessary. In many cases, a general citation to a text that discusses the topic at hand is probably sufficient, and a single citation to a text discussing or proving an important theorem in an article is likewise probably sufficient reference. The problem is that the articles that spurred my post did not even meet that minimal level of citation.

So what I am recommending is a broad, general citation review and clean-up of the math articles. It is a task that I would gladly do myself, had I the math resources available to provide accurate references. Unfortunately, I don't, so I'm bringing it up here for project editors who do have access to appropriate resources so they can hopefully go through the math articles in a systematic manner checking for and adding references as needed. Hope that clears up what I was getting at. Good luck! Dugwiki 17:57, 9 November 2006 (UTC)

I don't think there is such a trend. I would say the trend that exists is in the opposite direction. Newer articles are usually better referenced, and the ones completely without references (unless just some random stub) are from more than two years ago. This kind of thing has been discussed a bunch recently...that's the reason for some of the responses you've been getting. Rest assured, people have long pondered this matter, discussed it frequently, and well, if things aren't getting done, it's because people are busy. If you want this kind of big effort, it's better to get involved yourself. I expect most people don't see a pressing need to dig up references for the most elementary stuff that a lot of people know; they're too busy with verifying the tricky stuff that sounds plausible but could be utter crap. --C S (Talk) 13:00, 10 November 2006 (UTC)

There are a lot of ongoing disagreements about citation, but I think that every opinion expressed by members of this project has been in favor of an appropriately thorough level of citation. There is a large number of "legacy" articles with no references at all, and this is unfortunate, but these are slowly being fixed (or tagged) as they are discovered.

I wonder if Jitse's bot could make a list of math articles that have no ==References== section. I could do it from a database dump, but when I tried to download a dump a week ago I noticed they haven't been successful for a long time. The goal is: make a list of articles with no references section that are vaguely associated to mathematics. Until this is done, we have to rely on individual pages being tagged. CMummert 01:29, 10 November 2006 (UTC)

Unfortunately, my bot does not download the actual articles, so it can't do that. But the last database dump seems to be okay. Otherwise, go bother User:Mathbot who does download the complete articles, I think. -- Jitse Niesen (talk) 09:13, 10 November 2006 (UTC)

OK, I'll do it. Does you bot have the ability to generate a list of the articles that it considers to be "math" articles? Even as a plain text file, this would be very helpful for me. CMummert 13:26, 10 November 2006 (UTC)

The list of all math articles is available at list of mathematics articles. My bot (mathbot) has a copy of all math articles on Wikipedia but is rather old (several months). I can have it download them again (which would take a couple of days, 14,000 articles is a lot to download one by one :) and I could run a search through them. But if you want to do it with the database dump, that will work too. Oleg Alexandrov (talk) 16:18, 10 November 2006 (UTC)

One place to start if you want to try using a bot might be to search for math articles that do not contain a specific header for either References or External Links. I've also noticed a template for PlanetMath used in some articles; assuming that's an acceptable reference you could also probably filter those out as well. Also, for my part, I've started trying to systematically go through all the math articles and mark ones with no references using the unreferenced tag. My rough guess is maybe 1/5 or so are ending up so tagged, with most of the unreferenced articles being shorter articles talking about specific definitions or theorems as opposed to broader topics (eg Supremum is unreferenced, but Interval (mathematics) has references). So I'm thinking that a main culprit is sub-topics and side articles of larger articles that are split off from the main discussion for space reasons, that sort of thing. Dugwiki 16:39, 10 November 2006 (UTC)

I agree that short articles are the major contributors. I'm waiting while I download a database dump; the script is written and I'll post the results this evening. CMummert 16:53, 10 November 2006 (UTC)

In the process of going through these articles, I took a closer look at PlanetMath and I wasn't sure if it can be used as a sole reference. It appears that PlanetMath is a Wiki style site for math articles, which is great, but like Wiki is doesn't seem to have a formalized fact checking scheme. I couldn't find any formal policy on PlanetMath for verification, fact checking, and so on. Therefore I'm not sure it can technically be used as the only reference for an article. It makes for a good external link, and a good source for creating new Wiki stub articles, but ultimately the Wiki articles would need a source such as a textbook from a major publisher or a math journal with a formal peer review system to use as a formal reference. Unless, that is, I'm missing something about how PlanetMath works. Dugwiki 17:24, 10 November 2006 (UTC)

My feeling is that, at least for elementary mathematics, a lot of material can be self-verifying: the correctness of an article may often be seen from the article itself, while the sources are more important for justifying notability, guarding against WP:OR, and documenting assertions about the history of the mathematics in question. But if the only source you can find is a PlanetMath article, I'd think the notability of that subject would be questionable... —David Eppstein 17:31, 10 November 2006 (UTC)

To expand on that thought, I agree about simple material being self-verifying. However, what wouldn't be self-verifying are, for example, the names of terms and specific definitions. I'll use the Supremum article as an example. The material in the article is correct, and the reader can verify for themselves using material in the article that certain properties of a supremum must hold. But what isn't verified is that the term "supremum" is a preferred formal term, or from where the word "supremum" originates. To verify that the word "supremum" is used in mathematics circles, you'd need to provide a reference that uses the word (otherwise how would you know that you're using the term properly, or that mathematicians prefer to use an alternate term such as "least upper bound").

Another example of information that's not self-verifiable is when a math article mentions a quotation or biographical information about a famous mathematician. For example, the article Complex multiplication mentions in the introduction that "David Hilbert is said to have remarked the theory constitutes the 'most beautiful part of mathematics'." Obviously that statement can't be self-verified; you'd have to provide a source showing that David Hilbert said that.

So while individual, logically self-evident lines of an article wouldn't usually require a seperate reference, you do need general references to verify that the article is using the proper terminology, that otherwise unprovided proofs are available for stated theorems, and that background historical and biographical information is accurate. Dugwiki 17:47, 10 November 2006 (UTC)

My general rule of thumb is that short, uncontroversial articles are fine if they have at least one printed reference listed at the bottom of the page. No page numbers are necessary; the purpose is only to give the reader a place to enter the published literature. There has been a lot of discussion about this, which is closely related to Wikipedia:Scientific citation guidelines. CMummert 18:10, 10 November 2006 (UTC)

The term "self-verifying" is maybe not such a wise choice; try "self-consistent".

I agree that "David Hibert remarked…" begs for a source. I wouldn't remove such a statement from an article for lack of a source unless it seemed a dubious claim; but I probably wouldn't block its removal if someone else objected.

The comments about the supremum article need exploration. If we do a good job for our readers, they can expect:

The contents of the article are correct, unbiased, and adequate.
The article contains at least one reference to a reliable source that discusses the topic.
The article references one or more sources for additional reading.

I claim that it is harmful, unrealistic, and a broken policy to expect references to carry the full weight of verification. Anyone who has done much peer reviewing for journals would be delighted if reviewing could be replaced by reference counting. It can't; and transplanted to Wikipedia, the idea is equally useless.

This is relevant to "supremum" as follows. Terminology conventions vary over time, over subfield, over school, and over author. If I have never heard a term myself, that may simply mean I have not been exposed to those who use it. On the flip side, a single instance of use does not tell us whether the term is rare or idiosyncratic. We are unlikely to find a scholarly survey of usage. Also, the concept is old and minor, so not likely to be found as the topic of a journal article. Even in a text it may receive only passing discussion. Therefore, verification must rely on a discussion among editors with expert knowledge. This is especially true when we move past mere correctness to questions of bias and omission.

References are a Good Thing, but they cannot substitute for the equivalent of peer review. --KSmrq^T 10:08, 11 November 2006 (UTC)

There is a problem, though, KSmrq. Namely that Wikipedia has no formal peer review system to verify facts. Because it has no peer review system, it therefore requires that articles list verifiable references instead to publications that do have a fact checking system in place. Hence the need to include basic references in all articles, including for example Supremum. References are the only formal way an article can be considered verified for inclusion in Wikipedia. Dugwiki 18:58, 13 November 2006 (UTC)

To equate references with verification is like the Indiana legislature trying to equate π with 3.2. The fix to the broken policy is not "stay the course", more of the same, infuse each article with citations until servers groan and eyes bleed. And the down-and-dirty truth is, references are not really how we verify articles; people are. Wikipedia is just afraid to admit it and face the implications. --KSmrq^T 07:05, 14 November 2006 (UTC)

To risk stating the obvious, I found google books to be a good way to dig for references. Yes, there searches bring up only a few pages, but it is often enough to tell whether a given book describes well the concept in question or not. Oleg Alexandrov (talk) 18:12, 10 November 2006 (UTC)

Results of a script looking for references

Using the most recent database dump and Mathbot's List of mathematics categories, I made a list of 7287 articles related to mathematics. I tried to eliminate as many stubs as I could, but some slipped through. Of the 7287 articles,

4328 did not have at least one of Reference(s), Notes, or Further reading as a section header. These are listed at User:CMummert/Unreferenced
2919 of those didn't have any of those sections or an External links section either. These are listed at User:CMummert/Unreferenced_without_external_links.

Thoughts? CMummert 00:11, 11 November 2006 (UTC)

Cool. That means theres 10,000 articles which do have references. We're doing well! --Salix alba (talk) 00:24, 11 November 2006 (UTC)

Salix alba should check his subtraction. 7287 minus 4328 is 2959 which is a lot less than 10,000. JRSpriggs 08:36, 11 November 2006 (UTC)

You should probably not count all the List of ... (there are more than one hundered). pom 10:16, 11 November 2006 (UTC)

Yes, I know the data isn't perfect; this was just a one-hour hack of a script. One reason that I only have 7287 articles instead of 11000 (Jitse's bot) or 14000 (Mathbot) is that I didn't include most of the biography categories. But even with that margin of error, it appears that over half the articles included in my list of 7287 give no printed references, and over one third have not printed references or external links. My next plan is make a list of these articles by category. CMummert 12:14, 11 November 2006 (UTC)

One more piece of information. I sorted the unreferenced articles by category and put the results at User:CMummert/Unreferenced articles by category. There are some stubs included, but the general trend seems to be that short articles stating theorems and definitions are the primary contributors. The top seven categories for unreferenced articles are: #1 Mathematical theorems (222). #2 Linear algebra (99). #3 Group theory (97). #4 Abstract algebra (91). #5 Topology (85). #6 Polytopes (82). #7 Mathematical logic (81). #8 Geometry (76). #9 Probability theory (74). #10 Curves (63). CMummert 18:32, 11 November 2006 (UTC)

Bibliography

For some general references that might be appropriate to add to some of the above unreferenced mathematics articles please see: User:Paul August/Bibliography (this list some books in my personal library, and/or books which are searchable online at Amazon.com) For example I have just created a "References" section for the article topological space using that list. Perhaps we might want to create something like Wikipedia:WikiProject Mathematics/Bibliography? Paul August ☎ 19:48, 11 November 2006 (UTC)

I think this would be a useful resource for editing pages. The point as I see it is to have well-formatted entries already prepared so that I don't have to look up the ISBN over and over for the same book. CMummert 13:10, 12 November 2006 (UTC)

I think a communal bibliography page would be a great idea. I have my own at User:Fropuff/References, but it's fairly small and incomplete. I would suggest we stick to using proper citation templates for any such page. -- Fropuff 15:35, 12 November 2006 (UTC)

The problem if of course that there are thousands of books out there. Ideally, you would type in the ISBN of some book somewhere and get back the nicely formatted citation. I tried to do that using google books, but it does not work as google books does not allow scripts to fetch any data (surprisingly, it can tell if you are asking for data from a real browser, or from a script faking a browser).

The next best thing I came up with is to visit google books, find the book you want, look at the link "about this book", and paste the book information into this script. Then it outputs the Wikipedia citation format. Better than nothing. :) Oleg Alexandrov (talk) 17:47, 12 November 2006 (UTC)

Should some of this be collected in a page Wikipedia:Scientific citation guidelines/Resources? --Lambiam ^Talk 20:40, 12 November 2006 (UTC)

I modified my script to indeed work as a web form, you type in the ISBN (only) without visiting google books, and it outputs the citation in the Wikipedia format. The link to the tool is the same: here. I could easily generate a list of citations for all ISBNs encountered in math articles, but I don't know if that would be worth it, as one could just get a citation with that script each time it is needed. Oleg Alexandrov (talk) 05:31, 13 November 2006 (UTC)

Nice try, but not quite ready for public consumption. First, I gave it an ISBN-13 for a textbook, 978-0-8018-5414-9, and it just hung. Next, I tried the old-fashioned style 10-digit ISBN and got this:

*{{cite book
 | author     = Loan, Charles F. Van, Gene Howard Golub
 | title      = Matrix Computations
 | year       = Oct 11, 1996
 | publisher  = Johns Hopkins University Press
 | year       = Oct 11, 1996
 | id         = ISBN 0801854148
}}

Visible weaknesses (consult {{cite book}}):

Golub should be listed as the first author.
The correct author name is "Golub, Gene H." (though the initial does stand for "Howard").
The second author should be listed as "Van Loan, Charles F." if presented as surname-first.
Split names as "author" and "coauthors", and preferably split "author" as "first" and "last".
Both authors have their own articles, which should be linked.
There is no mention that this is the third edition.
The "year" should be "1996" only, with the month in the "month" field (unabbreviated); or use a "date" of "1996-10-11".
Don't give "year" twice.
I gave a properly hyphenated ISBN, but got back no hyphenation.

I didn't go looking for trouble; this was my first attempt! --KSmrq^T 22:00, 14 November 2006 (UTC)

Paragraph in Fermat's Last Theorem

The page on Fermat's Last Theorem includes the following statement:

The main problem that Wiles had to overcome was to establish a correspondence between semistable elliptic curves over the rational field, and the modular semistable elliptic curves over the rationals, which he did by explicitly showing that there were equal numbers of each. Before Wiles' work on the problem, there had been many attempts to count elliptic curves, but no one had found a way to do it.

I think this is misleading, if not plainly incorrect. It is trivial to count elliptic curves over the rationals: there are denumerably many of them, since they are determined by polynomials in two variables which are quadratic in y and cubic in x, and there are plainly an infinity of them. As I understand it, the issue was not simply to show that there were equal numbers of each; again, this is trivial: there are denumerably many modular semistable elliptic curves. The issue, as I understand it, was starting from a semistable elliptic curve, to find a modular form which defined/determined the given elliptic curve. Perhaps someone who is more familiar with this could take a look and fix that paragraph? Magidin 16:31, 14 November 2006 (UTC)

Cut those. The talk about flavours of set theory also seems completely out of place. And could be original research Charles Matthews 22:32, 14 November 2006 (UTC)

I took care of the set theory part. CMummert 16:06, 15 November 2006 (UTC)

Hypercube nomenclature

There seems to be a discussion going on in Hypercube, Measure polytope, Tesseract, and N-cube about which name should be primary for which page. Tesseract is the 4d polytope, Measure polytope is currently the primary name for the general n-dimensional concept, N-cube has some odd marginally-related number-theoretic content, and Hypercube is currently a small disambiguation page. Contributors including myself disagree on whether Hypercube should redirect to one or the other polytope page, or what the proper name of each page should be. If you're interested, see the talk pages for these articles. —David Eppstein 18:30, 15 November 2006 (UTC)

Monty Hell problem - needs some references

Found another article that needs some references, and thought someone here might be able to track it down. Monty Hell problem (not to be confused with the Monty Hall problem is currently apparently based largely on an internet forum discussion. Unfortunately, forum groups are not acceptable references since anybody can post anything they want on a forum. In particular, what needs to be verified is that the "Monty Hell problem" appeared in a publication of some sort somewhere at some point in time, and was called by that exact name. The specific description of the problem also needs to be verified.

I do believe I've seen this problem before, though, so my guess is it was taken from a publication somewhere and posted to the internet. The trick is finding a book of puzzles or logic or probability problems with this paradox. Dugwiki 23:17, 14 November 2006 (UTC)

I doubt there's going to be more sourcing of this. It appears to be just one of the results of yet another online discussion. AFD is my suggestion. --C S (Talk) 20:30, 18 November 2006 (UTC)

General intelligent design

Is anyone willing to vouch for General intelligent design? It looks crankish to me. CMummert 20:11, 15 November 2006 (UTC)

Crank. JoshuaZ 20:19, 15 November 2006 (UTC)

Might as well review all other edits of R. Herrmann, also see [65]. (Igny 20:53, 15 November 2006 (UTC))

There are two other articles. Consequence operator is standard mathematics, although the article could be improved. Logic-system may be original research (WP:OR), but it seems better than General intelligent design. Each article should be considered on its own merits. CMummert 21:00, 15 November 2006 (UTC)

Proposal:

Delete General intelligent design (as {{db-nonsense}})
Merge Logic-system into Proof theory
Merge Consequence operator into closure operator.

~~As these are related, the discussion should be centralized here.~~ — Arthur Rubin | (talk) 19:47, 16 November 2006 (UTC)

Never mind. Discussion on individual (target) talk pages, User:Raherrmann will be informed, in the interest of fairness. — Arthur Rubin | (talk) 20:06, 16 November 2006 (UTC)

Some material from the two remaining pages has appeared (or will soon, according to Herrmann) in respectable journals, like Journal of Symbolic Logic or Theoretical Computer Science and does not qualify as original research. Unfortunately Herrmann does not post preprints of accepted papers on his website. The main problem I see with the articles is that they are written in an uninformative way that is sometimes too vague about what is going on. CMummert 20:22, 16 November 2006 (UTC)

Even so, does anyone other than Mr. Herrmann use the name "logic system" or "consequence operator" for these concepts? The name can be a neologism even if in a published article, as the reviewers would check (at most) whether the name is commonly used in that field for something else. — Arthur Rubin | (talk) 20:45, 16 November 2006 (UTC)

I'd say "logic system" is a neologism. The same concept, or very similar ones, is part of the bread-and-butter of theoretical computer science; I was taught them as an undergraduate. I've seen them called "inference systems" or formal systems; the latter already has an article, which is a bit stubbish and could use improvement. However the text in logic system is not that improvement; I doubt it would be enlightening to someone who does not already know the subject. I suggest redirecting to formal system. Henning Makholm 21:33, 16 November 2006 (UTC)

messy, messy, messy

Proofs of trigonometric identities is a really messy article in two ways (at least):

Formatting, typesetting, etc. See my most recent edit.
Logical structure. One may prove the identity A = E by writing A = B = C = D = E. That's what I did in my most recent edit. One may also prove A = E by saying A = E if blah, and blah is true if blahblah, and blahblahblah is true if etc.etc., and etc.etc. is a known truth (but one must be sure not to write "If A = E then ...."; the "if...then..." has to go in the right direction.

It also reads like a copyvio from some elementary trig text. Septentrionalis 04:28, 17 November 2006 (UTC)

My inclination is to have this deleted, but I'm unsure about the best rationale. "Messy" will not carry the day. Perhaps OR? Or WP is NOT? --Lambiam ^Talk 06:50, 17 November 2006 (UTC)

I feel this could be a very useful page with a little TLC. I wish I had the time to undertake such a project, but alas I do not. I urge that we do not delete, despite its current (deplorable) state. Is there anyone out there who could spend a little time with this one and bring it into shape? VectorPosse 07:01, 17 November 2006 (UTC)

It could perhaps be deleted under the rationale WP:NOT an indiscriminate collection of information, section 4 titled "instruction manuals". Which states that... While Wikipedia has descriptions of people, places, and things, Wikipedia articles should not include instructions or advice (legal, medical, or otherwise), suggestions, or contain "how-to"s. This includes tutorials, walk-throughs, instruction manuals, video game guides, and recipes. Don't really know my position on that article, but I am just pointing out that that could be used as a rationale.--Jersey Devil 07:02, 17 November 2006 (UTC)

Just delete it. Stuff like this is usually deleted because of what Jersey Devil said. We don't need to encourage more tutorial style articles. --C S (Talk) 20:29, 18 November 2006 (UTC)

Sorry, but I don't see it. I feel like Jersey Devil's explanation was a stretch (which he or she seems to be acknowledging). This is not a tutorial, at least not of the type that WP:NOT seems to be condemning. I also might point out that this is not the only page that has proofs of various mathematical facts. It would take a hardcore exclusionist to suggest that we should delete them all. I mean no offense to Chan-Ho Suh, but I feel that sometimes we have a tendency to get caught up in policies (even ones that don't really apply) and forget that Wikipedia is supposed to be useful. I have dozens of students in my pre-calculus class right now who would benefit from this page, properly done. If consensus dictates otherwise, I will back off, but until that point, I'm going to need a lot more convincing rationale for deletion than WP:NOT. VectorPosse 21:48, 18 November 2006 (UTC)

Nobody here is proposing such unilaterial deletion. So bringing that up is just a strawman. Just because something's useful to somebody isn't a good reason to include it on Wikipedia. That's why we have clarifying pages like WP:NOT and other Wiki projects. Your pre-calc students may find these proofs of trig identities useful, but it's better for them to look in a textbook.

The page is definitely a kind of tutorial. It explains basic things like tangent is sine divided by cosine in excruciating detail. It's not really on par with the pages that have been linked in "see also". For example, the proof of e is irrational really eschews the most trivial details and concentrates on explaining the main conceptual steps. That fact is also of historical importance, with a number of famous mathematicians expending effort at giving varied proofs, although this is not currently described in the article. Same reasoning goes for sum of the reciprocals of primes diverging, etc.

What really is the point of this page? We have articles on trigonometric function and list of trigonometric identities. Is it to help out pre-calculus classes work through some manipulation of trig functions? Sounds like a tutorial to me. --C S (Talk) 22:52, 18 November 2006 (UTC)

Recurring decimal

I made the following edit on the Recurring decimal article, creating a section where I show that recurring decimals can be expressed in the terms of an infinite series. [66] I just wanted to post it up here for others to check up on my edits (obviously people here are more experienced and I would hate to post up factually incorrect information).--Jersey Devil 07:08, 17 November 2006 (UTC)

Systems of Equations

Merging suggestion

In the past few days, I've been editing a thing or two in Elementary algebra, and coincidentally another person was too. We started adding things here and there, but it seems that the information is piling up. I'd say it might be too much information for an article that's supposed to be elementary. The section that I've been contributing in is 'System of linear equations'. There is a reference to the supposed main article, which is System of linear equations. However, I can't help but notice that in the main article, there is a clear theoretical definition of the subject, but it has no examples. However, in Elementary algebra, the subject is hardly defined, while examples are abundant. Moreover, System of linear equations does reference to yet another article about systems of equations, Simultaneous equations- not linear equations, but a system of equations in the end. I'm trying to think neutrally here... But why do we have three articles about basically the same thing? And apparently, they could all use some improvement -and I'm more than glad to help there. I thought maybe a basic reference to the subject could be made (with basic examples maybe) in Elementary algebra, while moving the more in-depth examples and info we are creating to the main article, System of linear equations, at the same time merging it with Simultaneous equations. That way, we would be cleaning up three articles and expanding a whole topic. The three articles are about basically the same (Except Elementary algebra, which has other information as well) but the information seems to be spread. The way I see it, that is unnecesary and confusing.
Again, I'd be glad to help with my (limited at best) knowledge in this particular topic, but I wanted this out of the way first. I really want to contribute to this subject, but I think it would be better if there was just one main topic about it, having of course, reference to it on Elementary algebra (or other articles for that matter). I am asking for opinions because I think it might be too bold to edit, merge and move all those pages based on my opinion alone. What do you think? Is this a good or bad idea? Why should we do this or why not? (Quadrivium 23:17, 17 November 2006 (UTC))

For various reasons I have my doubts about merging System of linear equations (Sole) and Simultaneous equations (Se). (1) If done properly, both articles would be much lengthier. (2) Keeping them separate makes it easier to write a clear article. In particle Sole has a well-defined focus and should have a treatment at various degrees of mathematical sophistication (elementary algebra; other domains than fields). In contrast, after appropriate definitions and generalities, Se is necessarily an incomplete collection of various tricks and heuristics for different cases that may arise. See also my criticism of Se. --Lambiam ^Talk 02:09, 18 November 2006 (UTC)

Thanks for asking first. It is common to “refactor” articles, merging or splitting the material as it evolves; but we do prefer to discuss these changes in advance.

The articles in question should remain separate. However, either a copy or move of some examples may be a good idea.

Linear equations are common, important, and solvable with specialized methods. Simultaneous equations have three major nested divisions: linear equations, polynomial equations, general equations. And elementary algebra is a broader topic than solving equations.

We prefer to limit the size of articles, and to keep a clear focus for each. One way to handle a subtopic is to have a brief paragraph discussing it in the broader context, accompanied by a link to the specialized article. For example, the simultaneous equations article should refer readers to the system of linear equations article for the bulk of the details special to linear equations.

The real problem in this instance is that all these articles are in rough shape, especially considering their importance. Paradoxically, it is usually easier to handle an advanced topic well than to write a clear, complete, and compelling article on a basic topic. Wikipedia may not be the best place to learn such material, but readers usually have good alternatives. --KSmrq^T 08:46, 18 November 2006 (UTC)

Thanks for the feedback- I see what you mean. However, I am still wondering a couple of things.

I think I pretty much understood the purpose of Simultaneous equations. But exactly how much should be included or kept in Elementary algebra about this particular subject? And when you say move or copy examples, what do you mean? Because I'm not too sure if there should be less or more info about systems in Elementary algebra-- and I don't really know what part of that info should be moved or copied somewhere else (and where). I think I see why Simultaneous equations and System of linear equations are separate articles, but what is the purpose of System of linear equations? I think the information is great and it should definitely be kept, but what is the article aiming at? What approach is it taking? Should that article have examples as well? Oh, and should Simultaneous equations have definitions as well, or is it just an examples/ways of solving systems article?

Anyway, I think I'll be trying to solve some of the points adressed in Criticism of Se in the following days, although I am no expert.

Oh, and excuse me if I'm being too annoying with all these questions :) --Quadrivium 17:09, 18 November 2006 (UTC)

Monadic logic

The article (one liner microstub) is on AfD. Could someone take a look what it is worth? TIA Pavel Vozenilek 01:30, 19 November 2006 (UTC)

Calculus: GA collaboration of the week

Yesterday, Calculus was chosen as the collaboration of the week for people that want to push good articles to featured article status. I encourage people from the mathematics project to get involved as this is clearly one of the most important articles on mathematics and likely to be among the most visited. At first glance I would say that there is still a considerable amount of work to be done. Pascal.Tesson 18:32, 20 November 2006 (UTC)

Convention for definitions: Use := or \equiv?

Problem and options

In WP:MSM I didn't see anything about which infix to use for definitions. Some use $\equiv$ , but I find this very misleading, since it already has two other meanings: equivalence (hence its Latex code) and identity. I would therefore advocate := or the equal sign with "def" underneath. (Sorry, I don't know the Latex code for that.) — Sebastian (talk) 04:58, 19 October 2006 (UTC)

We also have a (carefully hidden) page of conventions, but this convention is not among them. I agree that the “triple equal” is not a good choice. The “colon equal” is my preference; I also like to use it for algorithms (where I save bare “equal” for equality tests). I have not found a decent way to stack something over or under an equality or arrow within the tragically limited abilities of texvc, Wikipedia’s TeX engine. Unicode provides a single character for “Assign” (“≔”, U+2254, ≔), a single character for “triangleq” (“≜”, U+225C, ≜), and one for “equal to by definition” (“≝”, U+225D, ≝). I cannot recommend any of these characters at present, because they will not display well (if at all) for many of our readers. Displayed in a larger font size for clarity, here are the choices mentioned:

≔

≜

≝

≡

Although in LaTeX itself we could use \overset{\mathrm{def}}{=}, and blahtex supports this, texvc does not. Thus the two character sequence “colon equal” (“:=”) is left as the only viable choice. However, as always, no matter what convention you adopt, please do not leave readers guessing; tell them explicitly if there is any reasonable chance of misunderstanding. --KSmrq^T 06:58, 19 October 2006 (UTC)

How about $=_{\operatorname{def}}$ ? JRSpriggs 08:55, 19 October 2006 (UTC)

Do it like this: $x \stackrel{\mathrm{def}}{=} x$ _→AzaToth 19:45, 29 October 2006 (UTC)

That's a good idea! Let's do that. — Sebastian (talk) 06:50, 23 November 2006 (UTC)

Actually, it usually is necessary to include a bit more space, so I'm using "\ \stackrel{\mathrm{def}}{=}\ ". — Sebastian (talk) 07:09, 23 November 2006 (UTC)

i am trying to understand why you guys are changing $\equiv \$ to $= \$ for definitions in the first place. why is /equiv wrong for that use? to use it in the definition tells the reader who is glossing over the words that it is a definition and not a derived result of any sort. i don't get it. r b-j 16:51, 31 October 2006 (UTC)

A better question would be: Why do you think that "the reader" would immediately understand \equiv as mening "by definition"? It is not a notation I remember ever seeing before this discussion, even though I've managed to earn a B.S. in mathematics and a Ph.D. in a mathematically heavy area of computer science. In short, it is not as universal as you appear to assume. The only thing meaning any of the symbols can reliably convey is the identity between the defined symbol and its expansion (for which the understandability of = is unrivalled), whereas the fact that something is being defined needs to be spelled out in words if not otherwise clear -- any nonverbal symbolism for that is bound not to be understood by many readers. Henning Makholm 20:49, 1 November 2006 (UTC)

I think that it may be a newer notation, because my AP Physics textbook, published a year or two ago, uses \equiv to indicate definitions. Karl Dickman ^talk 02:48, 6 December 2006 (UTC)

Discussion: "=" vs ":=" vs words

I feel strongly that we should not need the := type symbol here. If something is a definition we should say so in words. The proper use for := is for assignment in computer science. As far as I'm concerned, := is up there with iff as technical language we should always avoid. since it makes articles impenetrable. Charles Matthews 09:00, 19 October 2006 (UTC)

I agree that words are preferable, for the reasons given by Charles Matthews. JPD (talk) 10:23, 19 October 2006 (UTC)

I would agree. Despite having seen := used in some decent books in recent years, I feel quite strongly that in maths, as opposed to computing, the use of := is a bit of a neologism, and the words should be perfectly clear. Similarly, I assume we agree that we should not use inverted A and E for "for all" and "there exists"? Madmath789 11:10, 19 October 2006 (UTC)

Ditto, but := is not so heinous a notation as is being insinuated here ;) Dysprosia 11:18, 19 October 2006 (UTC)

To clarify my position, in most cases I also would use something like “Let x be the reciprocal of y” rather than “x := ¹⁄_y.” I believe, so far, I’ve not needed the latter for Wikipedia. However, situations can arise where it is helpful to adopt a distinct notation. Rather than take a fixed position banning it, perhaps we might strongly discourage it, but offer a notation should the need arise. Frankly, given the fact that current technical limitations preclude any really satisfactory symbol, I think most editors will choose to write around the problem, as we prefer. Our style guide already says the following:

Careful thought should be given to each formula included, and words should be used instead if possible.

Beyond that, if Wikipedia intends to let anyone edit, then we might also want to begin to teach writing skills. A typical mathematical education teaches neither English composition nor technical writing for a broad audience. --KSmrq^T 13:00, 19 October 2006 (UTC)

So it seems we have a consensus that we don't want $\equiv$ for definitions. This Google search shows that we have less than 60 occurrences, so it is practically feasible to weed out the wrong ones.

Many of these cases may indeed be better expressed with words. But I would not completely rule out ":=". Trying to express every definition in words can get clumsy. E.g. I can't think of a way to rephrase "... where $c \;$ is the speed of light and $\gamma \ := 1/\sqrt{...}$ is called the Lorentz factor" withouth distracting at least some readers. Moreover, readers who are unfamiliar with ":=" can enter it in the search field (although unfortunately they can't enter a single colon). — Sebastian (talk) 18:02, 19 October 2006 (UTC)

Users can enter it in the search box, but this will lead them to = (which redirects to Equals sign), since an initial colon is discarded; see Wikipedia:Naming conventions (technical restrictions)#Colon. --Lambiam ^Talk 10:05, 20 October 2006 (UTC)

If its just a list of constants then a simple $\gamma \ = 1/\sqrt{...}$ seems fine. For more complicated definitions then words are more approprate. --Salix alba (talk) 18:52, 19 October 2006 (UTC)

Re the issue with gamma and the Lorentz factor - you can say "... where $c \;$ is the speed of light and

γ

is the Lorentz factor (defined as $1/\sqrt{...}$ )." This avoids any equivalency symbology. It actually puts the information in its proper place, as it makes the full Lorentz factor a parenthetical item for those who do not know the Lorentz factor, whereas those who do can just glaze over it. --Carl ^{(talk|contribs)} 02:29, 28 October 2006 (UTC)

Good idea - if you like you can add it to the table below, or I'll do so later. — Sebastian (talk) 02:46, 28 October 2006 (UTC)

In writing about mathematics and physics, I've never found a problem using an equals sign and then stating, in words, whether what you're writing is a definition. I think anything else is just a gimmick. –Joke 18:54, 19 October 2006 (UTC)

I don't think your Google search finds pages in which ≡ is typed as a unicode character. In fact I haven't been able to figure out how to get Google to search for that character. And the WP search box only gives me ≡ which is uninformative. So finding all instances of ≡ in WP pages may be problematic. —David Eppstein 21:33, 19 October 2006 (UTC)

David, thanks for thinking of this. I still hope that there are not too many Unicode ≡ instances since it doesn't seem possible to use this in a formula. <math>a ≡ b</math> at least yields: Failed to parse (lexing error): a ≡ b .

Salix and Joke: I think you're missing my point. Of course it is possible to write just an equal sign, but you're losing information: The colon tells the reader unobtrusively: "Don't worry about what this $γ$ is all about and whether you've seen it before - it is just a definition." And I agree, it is not a problem for anybody who writes English reasonably well to state in words whether it's a definition. But how do you actually do this in a case like the above without overemphasizing a side issue and breaking the flow of thought? — Sebastian (talk) 22:52, 19 October 2006 (UTC)

It only tells the reader something if it is an established convention, the conversation here indicates its not. Picking a random maths book its full of statements like If A=..., let A=...., We define A=.... and where A=.... The preceding words are enough to unambiguiously tell the readers whats happening. Any other notation will break the flow of the text, making the reason pause to think, 'whats this new notation i've not seen before'. Personally I think we should follow KISS principle and minimise inroducing unnecessary notation.--Salix alba (talk) 23:26, 19 October 2006 (UTC)

Scroll up. Math tags are for LaTeX code, not Unicode characters. $a \equiv b$ uses \equiv, not ≡. Dysprosia 06:48, 20 October 2006 (UTC)

I'd like to make the point that it is particularly important for WP to highlight definitions on pages. Not to sneak them into notation. There is indeed a kind of format issue with the typical 'where' construction after a formula. That, I think, is a separate and useful discussion. Mathematicians can take it to be the syntax "let x be an A, y a B, ...", preceding a statement. In science it certainly is frequently done with a trailing "where c is the speed of light ...". These context-establishing things matter quite a lot. But I really don't see that the := assignment is a good thing in there. For one thing it comes from the wrong programming paradigm (functional programming rules ...). Charles Matthews 08:59, 20 October 2006 (UTC)

I would expect to see mutable variables with assignment in an imperative programming language, whereas a functional programming language would limit its bindings to “let” constructs and function calls. Did you misspeak, or did I misunderstand? --KSmrq^T 11:54, 20 October 2006 (UTC)

An unambiguous indication that something is a definition has its merits, but I agree that we should avoid conventions that are insufficiently established and may be unnecessarily puzzling to our readers. I've seen maths books using ":=" for definitions, but then somewhere in the introductory parts there will be a section on notation explaining the use. I don't think I ever saw this use in a physics textbook. We should go with a simple "=" sign, making sure the context establishes the definitional nature. Would that some unclarity there was the worst problem in the understandability of our maths articles... --Lambiam ^Talk 10:19, 20 October 2006 (UTC)

For a whole week, none of the seven people who found it particularly important to highlight definitions made any contribution to actually achieve this. Since

my main concern is eliminating the ambiguous use of "\equiv";
we have over 300 articles with several occurrences each and
editing the text to highlight definitions takes a lot of time for each occurrence (at least for me)

it seems that simply replacing "\equiv" with ":=" wherever applicable would be the most sensitive thing to do for now. (Replacing it with just "=" is not good since it would delete information, and other alternatives were even less favored.) I am volunteering to do that. After that, I will be done, and the proponents of prose can edit these occurrences at their leisure. Let me know what you think. — Sebastian (talk) 21:00, 27 October 2006 (UTC)

Well, as I wrote earlier (see below): "We can also simply fix such things as we encounter them. In terms of best use of time to increase the quality of maths articles, it is (in my opinion) more effective to work on some stub articles or other pages that have been flagged as needing attention." And I do not only work on maths articles. I'd say this edit qualifies, though. Further, as I explained before, I'm opposed to using := for definitions. The large majority of readers will not be familiar with this meaning. --Lambiam ^Talk 23:50, 27 October 2006 (UTC)

I'm sorry! I didn't mean to include you. I am really grateful for your active contribution to the table, too.

You may be right that many readers of Wikipedia may not be familiar with ":=" - but this is irrelevant in this context. What is relevant is the difference

D i f f e r e n c e = C e q u i v + K e q u i v - K c o l o n

where

C e q u i v

is the number of people who are confused by the ambiguous use of "≡"

K e q u i v

is the number of people who don't know "≡" but notice it to the extend that it hurts their understanding of a formula;

K c o l o n

is the number of people who don't know ":=" and notice it to the extend that it hurts their understanding of a formula;

I may be wrong, but I believe this difference is positive. I believe that $K_{equiv} \approx K_{colon}$ (the added bar is no less conspicuous than the added two dots, and the discussion here showed that "≡" isn't that popular either). And

C e q u i v > 0

, because it includes at least me. ;-) — Sebastian (talk) 00:40, 28 October 2006 (UTC)

Speaking for the others, when they commented they may well have had the impression that you were requesting input on how to deal with this in WP:MSM, rather than attempting to press-gang them into a task force. As to your exercise in linear programming, aren't you overlooking the quantity

C c o l o n

D i f f e r e n c e = C e q u i v + K e q u i v - C c o l o n - K c o l o n

. You may say it isn't ambiguous, but there is also the meaning of assignment in Pascal and other programming languages. And I've seen it used for denoting substitutions. How many places are there where ≡ is actually ambiguous? In any case, I suggest that you do not ignore the judgement of several editors that := is not appropriate. --Lambiam ^Talk 01:25, 28 October 2006 (UTC)

I don't know how you come up with the accusation that I'm press-ganging anyone. In the contrary, I have been volunteering my time to fix something that bothers me. I would like to do this in a simple way, as described above. It is others who demand it to be done in a much more work intensive way, which practically makes it impossible for me to do it alone.

C c o l o n

: I assumed it to be 0, but it actually is less than 0. The connection with assignment is not confusing but helpful.

Re How many places are there where ≡ is actually ambiguous?: In every place, by definition. There are three contradicting definitions for "≡" (including "is identical"), and it takes always some extra bit of information to distinguish between them.

Re ":= is not appropriate": This is your same absolute statement again, where we need a relative comparison. We have to choose one option. If I understand you correctly, your preferred option seems to be to leave everything as is until we run out of "stub articles and other pages that have been flagged as needing attention" - which will be when pigs fly. I don't think that is any more "appropriate". — Sebastian (talk) 02:02, 28 October 2006 (UTC)

We've got someone who wants to make a productive contribution to Wikipedia mathematics articles. Can we not find a way to put that to good use? If substitution of ":=" for "\equiv" or "≡" is undesirable, which appears to be the consensus, then what task would be helpful? The claim that "we have over 300 articles with several occurrences each", if accurate, could be converted into a list of those articles. That list could be linked here. Interested parties could work through it, eliminating items as they are fixed. What I have found in working through a similar list, the blahtex problem article list, is that often an article that exhibits one dubious construction accompanies it with other problems. This is the wisdom behind the suggestion to fix things as we encounter them.

And please, help my frayed nerves and stop abusing TeX. It is wrong to write

$K_{equiv} \approx K_{colon} . \,\!$

A correct form is

$K_{\mathrm{equiv}} \approx K_{\mathrm{colon}} . \,\!$

This is not just a matter of italics; without proper markup TeX thinks you mean to multiply the single-letter variables c, o, l, o, n, and uses the wrong font and the wrong spacing. Compare

$fifty \,\!$

versus

$\mathit{fifty} \,\!$

for appearance. --KSmrq^T 03:15, 28 October 2006 (UTC)

Thank you, KSmrq! This list exists already: /equivlist (described in next section). After David Eppstein was busy again, today, we might just have touched 300. And I'll take your point about \mathrm. I found that it is already in Help:Math, but hidden in the Rendering section. I thought it was just used to define types. Maybe this could be written a bit more explicitly? — Sebastian (talk) 03:26, 28 October 2006 (UTC)

I also strongly agree that ":=" is awfully ugly, and that it should be always avoided in math. Oleg Alexandrov (talk) 03:27, 28 October 2006 (UTC)

To KSmrq: I have not used "\mathrm{...}" because I do not know what it means. What does it mean? I have used "\operatorname{...}" in some similar situations. JRSpriggs 06:04, 28 October 2006 (UTC)

operatorname and mathrm are different, IIRC because the former adjusts the spacing for operators (compare entering $|$ and $\mid$ into TeX), the other does not. Dysprosia 06:46, 28 October 2006 (UTC)

What? Could someone translate that into English, please. What does "IIRC" mean? What are "$|$" and "$\mid$"? JRSpriggs 07:13, 28 October 2006 (UTC)

IIRC means: "If I Recall/Remember Correctly". In TeX "$...$" means the same as "<math>...</math>" does here. In math mode, "|" and "\mid" produce the same symbol, but presumably with subtly different spacings. --Lambiam ^Talk 09:59, 28 October 2006 (UTC)

I very much appreciate the willingness to spend effort on improving a weak point in our maths articles, and I do not suggest (nor have I suggested) that one should wait till there are no more stubs, but, rather, that, following the "ant algorithm" embodying Wikipedia, they may be fixed as one runs into them. As to the concrete way of fixing them, here is an ordering of some ways of presenting a definition, ordered – according to my personal preferences – from most to least desirable:

The frobnitz ψ, defined by ψ = ∂u/∂v, forms a core.
The frobnitz ψ, defined as ∂u/∂v, forms a core.
The frobnitz ψ, defined by ψ ≡ ∂u/∂v, forms a core.
The frobnitz ψ, defined by ψ := ∂u/∂v, forms a core.
The frobnitz ψ = ∂u/∂v forms a core.
The frobnitz ψ ≡ ∂u/∂v forms a core.
The frobnitz ψ := ∂u/∂v forms a core.

Perhaps it explains why I am not entirely enthusiastic about addressing the issue by replacing \equivs by colon-equalses. --Lambiam ^Talk 10:40, 28 October 2006 (UTC)

Ah, that helps indeed! My list looks like this:

The frobnitz ψ, defined by ψ = ∂u/∂v, forms a core. (=d)
The frobnitz ψ, defined as ∂u/∂v, forms a core. (0d)
The frobnitz ψ, defined by ψ := ∂u/∂v, forms a core. (:d)
The frobnitz ψ := ∂u/∂v forms a core. (:0)
The frobnitz ψ = ∂u/∂v forms a core. (=0)
The frobnitz ψ, defined by ψ ≡ ∂u/∂v, forms a core. (≡d)
The frobnitz ψ ≡ ∂u/∂v forms a core. (≡0)

(For easier reference, I added a mnemonic after each. First character refers to the infix, second to the word "definition")

In short: Anything is better than using "≡" in the wrong place. This means: At least we agree that replacing every wrong "≡" with "=" would be an improvement. (This is what David Eppstein has been diligently doing in many instances. Accomplished mathematician that he is, I am not concerned about his edits. But if someone did it with search and replace then there will be cases where we lose information, which is why I prefer (:0).)

So may I ask why you prefer "≡" over ":=" despite its ambiguity? I thought I made it pretty clear above why this is really bad, and so far my reasoning has not been refuted. — Sebastian (talk) 18:13, 28 October 2006 (UTC)

Just a note here: I would characterize the bulk of my work in this direction, not as any kind of replacement, but as identifying the articles that use ≡ for modular congruences, Boolean equivalence, and other uses that have nothing to do with definition, and removing them from your list of targets for editing. But at this point it seems that a lot of what's left is physics or areas of math that I'm less familiar with, so I've stopped doing as much on this. —David Eppstein 18:19, 28 October 2006 (UTC)

Since the $\equiv$ symbol has reasonable uses for math articles, merely replacing them all with := won't work. If someone wants to replace only the equivs that are part of a definition with :=, that would be fine with me, because I think that both symbols are equally bad for definitions. At least := stands out more, making it more likely to be spotted by editors in the future. But it might require a lot of editing by hand to do the replacing. CMummert 14:04, 28 October 2006 (UTC)

Exactly! Disambiguating the uses by getting rid of the wrong use of "≡" for definitions is the whole point of what I'm trying to achieve! — Sebastian (talk) 18:13, 28 October 2006 (UTC)

Unless you are familiar with the article, it will in general take some time in each instance to understand the context in which the symbol is used and whether this is truly a definition. If it is immediately obvious that this is a definition, then it should be safe to replace \equiv by =, since that then introduces no possible misunderstanding. I consider all cases of the form "F(ψ), where ψ = ∂u/∂v", obviously definitions. Also, if the meaning of "frobnitz" is something that could not possibly be an equation (e.g., when it is a scalar, vector, or metric), then "the frobnitz ψ = ∂u/∂v ..." is quite unambiguous. If it takes some time to understand the situation so that you can be sure this use is a definition, it means that the article urgently needs some text like "defining the frobnitz ψ by". While it takes a few extra seconds to add that text, it is then a minor part of the undertaking.

I'm not the only one not in favour of ":=". The reason I prefer "≡" over ":=" is simply that I expect it will lead to less confusion or puzzlement among our readers who need this least. Does any physics textbook, or any commonly used mathematics textbook, use the notation ":="? --Lambiam ^Talk 21:15, 28 October 2006 (UTC)

For what it's worth, Wolfgang Rindler's excellent Relativity: Special, General and Cosmological uses the ":=" notation, without (as far as I can see) explicitly introducing it. It sometimes also turns the symbol around and says something like "... and thus we see the importance of ∂u/∂v =: ψ = the frobnitz" to define ψ and the word frobnitz in one go. No, I don't find that particularly readable, and prefer prose where disambiguation is needed. In contrast (and still for what it's worth) I can't remember ever seeing "≡" for definitions in a respectable source. Henning Makholm 21:33, 28 October 2006 (UTC)

Conclusion and /equivlist

Thanks Charles, Salix and Lambian – you make enough good points to elevate your preferred solution (of banning ":=") within my margin of error close to my preferred solution (of allowing it where it helps). The reason I'm not entirely swayed is that I absolutely disagree with Lambian’s last remark: It is precisely because our math articles are often hard to understand that readers need help. Even small things can provide a straw for struggling readers to cling to. But I acknowledge that there is a tradeoff, and which solution actually provides more help is a moot judgment call. — Sebastian (talk) 20:57, 21 October 2006 (UTC)

I'm slightly puzzled by your absolute disagreement with my last remark. I only meant to express dissatisfaction with the complete lack of understandability of several of our maths articles. While small things might make the difference of the proverbial straw for some articles, too many articles are like a heavy block of concrete dropped on the camel. So all this lamentation – which you should also see in light of my expressed opinion that ":=" is more problematic – is saying is this: I wish possible ambiguity of "=" was the worst problem we have. I don't think you want to claim that it is actually the worst, or that you wish for worse problems. --Lambiam ^Talk 03:09, 22 October 2006 (UTC)

No worries! If that statement wasn't meant as an argument against any small improvements then I agree with it, of course. — Sebastian (talk) 17:06, 22 October 2006 (UTC)

OK, now that we agree that we don't want to use \equiv for definitions, we need to do two things:

Add the policy to WP:MSM. I'm fine with the policy proposed by Charles, Salix and Lambian, but I wouldn't want to be the one who adds it to MSM.
Change "\equiv" to "=" where it means definition. Here's a list of all articles that contain "\equiv": /equivlist. Let's work with this together: Whoever cleared an article, just deletes its line from the list. I'll begin with articles that I understand. — Sebastian (talk) 17:06, 22 October 2006 (UTC)

Dang! I just realized that my original query yields far too few results. Unfortunately, searching for "math" does not, as I thought, yield all pages that contain the <math> tag, but only those that contain the word "math" in plain text - which are mostly entries like "J. Math. Pures Appl.". Replacing "math" in the query with "function" already yields 408 results. Does anyone have an idea how to filter all mathematical articles in a Google (or other) search? — Sebastian (talk) 18:05, 22 October 2006 (UTC)

I replaced the list with the result of this query, which gives us a few too many articles, but at least we won't miss any. — Sebastian (talk) 19:25, 22 October 2006 (UTC)

We can also simply fix such things as we encounter them. In terms of best use of time to increase the quality of maths articles, it is (in my opinion) more effective to work on some stub articles or other pages that have been flagged as needing attention. --Lambiam ^Talk 20:57, 22 October 2006 (UTC)

I just found out about this discussion, and I really need to register my strong objection to changing \equiv, :=, and = to $\stackrel{\mathrm{def}}{=}$ , for a number of reasons:

I have never (in my very broad reading of math and physics) even seen this before. We shouldn't make up new conventions.
The appearance of this word above the = sign is distracting to me, even when I know the equation perfectly well.
\equiv does mean that two things are identical, which they are when they are defined as such.
I see no problem with using a simple = sign when words to the effect of "defined as" appear nearby.
:= and \equiv are variously standard in various publications. Why can't we use them, if they're good enough for Cambridge University Press, Springer, etc? If a reader looks for related ideas in a book, these are what he/she will see. Consistency is good.

Again, most of objection relates to the concept that we shouldn't make up our own conventions. This is really starting to bug me. Also, I don't think you've taken a broad enough poll to be establishing this as convention, and the discussion above doesn't look like consensus to me. Please stop, at least until it is clear that a consensus among editors (not just people in this discussion) has been reached. --MOBle 19:46, 25 November 2006 (UTC)

This is a stale discussion, with decisions made and actions taken, so I'll keep my response brief. You raise legitimate concerns, but reach unsupported conclusions. We agree that we should stick to established conventions. How? Mathematicians and physicists and engineers can differ in their conventions, and among themselves. If I have seen a convention frequently, and you have never seen it at all, is it a convention? The equal sign with the letters "def" above it has a Unicode code point, U+225D, so the standards body thinks it important. Yet it is not enough to know that a symbol is used, we must also examine how it is used, and by whom. Most important is that our readers understand. The colon-equal is familiar in computer science, but with the meaning of assignment, not definition. The \equiv is familiar in mathematics, but often with the meaning of a congruence in modular arithmetic, not a definition. The equal-by-definition symbol has no such ambiguity, but is less widely used, and many readers will not have a font including it. The wisest course, and our consensus, is to prefer a plain equal sign accompanied by words and context to make clear that a definition is intended. --KSmrq^T 20:31, 25 November 2006 (UTC)

I agree with most of what you wrote, but I disagree about what the consensus was. In the discussion, we talked that there were over 300 articles with "\equiv", and no one was willing to go through all of them and write the appropriate, wise prose. So that course, while desirable, was just not viable. By contrast, there was consensus that =^def was better than \equiv, which is the replacement I did. — Sebastian (talk) 22:16, 25 November 2006 (UTC)

It is true that things are identical when they are defined to be, but the reverse implication does not hold: Things can be identical for other reasons than a definition. Therefore $\equiv$ is not a reliable way of indicating definitions. Neither $\equiv$ nor := are universally recognized as definition signs; therefore we should not assume that a reader knows them, and the only reliable way to point out that an equation is a definition is to say so in prose. Finally, discussions such as this one is the only way we have to gauge consensus. What do you suggest that we do otherwise - autopost messages on the talk pages of everybody who has ever edited a math article? Henning Makholm 20:07, 25 November 2006 (UTC)

I suggest we stop changing \equiv to something that is completely unrecognized, i.e. $\stackrel{\mathrm{def}}{=}$ . Either leave it alone, or write the prose. PAR 20:13, 25 November 2006 (UTC)

Also - Does anyone have a problem with \equiv as long as it is accompanied by prose? PAR 20:19, 25 November 2006 (UTC)

As you may guess, I fully agree with PAR. I don't think it would be reasonable to autopost messages. How about posting on some relevant main talk pages (e.g., General relativity)? Moreover, I don't think that the people who have commented agree with the =^def decision.

I have seen alternate usages for basically every form of equality symbol there is. It's unfortunate that there is no universal agreement on \equiv, or :=, or =^Delta... even ~, or \approx, etc. However, that's the way it is. Real authors and editors have to deal with this issue, and generally use =, :=, and \equiv anyways. My point is that we shouldn't go making up our own conventions. I have never seen =^def or =_def anywhere, and I have seen =, \equiv, and :=, so I really feel that we should stick to convention.

I ask that the changes be stopped at least until some sort of formal poll is taken and a reasonable number of editors have chimed in. There must be some standard thing, like "Request for Comment", or something? --MOBle 20:35, 25 November 2006 (UTC)

Sorry, I hadn't seen KSmrq's comment. I've still never seen =^def in any text, which is what should matter. Also, KSmrq seems to say that we should just use =, with accompanying prose. So why is everything being changed? --MOBle 20:38, 25 November 2006 (UTC)

What is the "everything" of which you speak, that is being changed? As far as I can read, the conclusion of this discussion was to use plain '=' and qualify in prose if it is not clear that a definition is taking place. You seem to be complaining against the fact that somebody once in an old discussion advocated using =^def instead. Can't you just let it be? Henning Makholm 20:52, 25 November 2006 (UTC)

Thank you, Henning, but I think there may be a minsunderstanding. The complaint was about my replacement of \equiv with =^def in all articles on /equivlist where it was used for a definition. — Sebastian (talk) 20:58, 25 November 2006 (UTC)

(edit conflict) OK, I'm stopping it till we reach an agreement. I'm sorry, I thought it was clear that nobody liked the ambiguity of $\equiv$ being used for several different purposes. (See discussion in the rest of this section.) Unfortunately, this is not a good place to stop since I'm three quarters through the list, so I'm hoping we can reach agreement soon.

Regarding MOBle's points:

This is not something any of us made up, but I agree that we should use symbols that are as widely understood as possible. This was actually part of my motivation for doing this: I think that $\stackrel{\mathrm{def}}{=}$ is easier understood than $\equiv$ .
I agree - I feel the same way.
I disagree, in addition to Henning Makholm's point: How are 2 and 7 (mod 5) any more identical than 2 and 2?
I agree. Please feel free to replace these cases when you see them.
I would love to use :=, but many people here felt it was not common enough.

In reply to PAR: I do have a problem if \equiv is used in places where it is not commonly agreed standard. I think we should avoid ambiguous symbols whenever reasonably possible. — Sebastian (talk) 20:57, 25 November 2006 (UTC)

Okay. I'm glad to learn that this was a misunderstanding.

As for Sebastian and number 3, I realized that \equiv has different uses, but this ambiguity is just something most authors live with. I wouldn't mind seeing :=, either, but I can see the point that it might not be common enough. I've honestly never understood why = and context are not enough, so I guess my vote is for a simple = with accompanying text saying that it is a definition. --MOBle 21:04, 25 November 2006 (UTC)

I've used and seen \equiv as a definition in the literature, but I have never researched the subject. The use of = with explanation is ok, I still think \equiv with explanation is better, but if, outside my experience, it is used ambiguously, then perhaps = with text is best. PAR 23:48, 25 November 2006 (UTC)

"=" and context can be enough, and of course, good explanations are best. This means, we need to take loving care for the context, which takes more time than a simple replacement. With 81 remaining articles on /equivlist and about 3-4 occurrences per article, we got around 300 contexts or explanations to care for. So, do we have any volunteers to do this? — Sebastian (talk) 00:08, 26 November 2006 (UTC)

I'll do some, but is there a list we can check off? PAR 02:58, 26 November 2006 (UTC)

Cool, thanks! The list is /equivlist - just delete the bullet points for articles you completed. — Sebastian (talk) 06:32, 26 November 2006 (UTC)

Adding my opinion based on lots of math experience... First a fact of math writing: The symbol \equiv has several common meanings in mathematics. Sometimes it means a definition, sometimes it means arithmetic congruence, sometimes it means equivalence under an equivalence relation. Probably it has other meanings. In a math paper or book, one has to see from context, or from an explicit explanation by the author (in words), what it means in each case. IMHO, that eliminates it as a standard Wikipedia conventional symbol for a definition. I don't have a strong opinion on := vs. other options, but I do think that when you define something, it always helps if you say that you're defining it, and then the = sign should be clear, and also := or =^def. (I have seen the latter used in print, though not often.) It comes down to the opinion expressed earlier, that if you want to be clear, you have to say what you mean in plain language, even if it's longer. End HO. Zaslav 06:11, 1 December 2006 (UTC)

For what it's worth, my late mother frequently used =_Df in her textbooks (especially in a mathematical logic book in which $A \equiv B =_{\mathrm{Df}} \ldots$ might make sense. I wouldn't recommend using it here even if it were standard in some fields of mathematics, because the what the... factor is higher. — Arthur Rubin | (talk) 17:42, 3 December 2006 (UTC)

The problem is not pure mathematics. The problem is physics, physical chemistry, engineering, etc. For a century, thermodyamicists have said things like "The Helmholtz free energy is defined to be $A\equiv U-TS$ " and you folks are now charging through ruining perfectly good articles with this jihad against a notation that has been in use as long as the field has existed. Stop. Just stop. End this hideous equals-with-a-def-over-it abomination. All fields of study are not the same, and I assure you that those who study statistical mechanics and other fields do not want you tramping in and changing the notation on the basis of a discussion among a small self-selected group of people. This discussion is not widely known. This so-called "consensus" is not the consensus of the bulk of the people editing and maintaining pages in twenty different subjects in physics, chemistry, engineering, etc. where \equiv is in wide use. This change to a notation used nowhere but Wikipedia is not something that is widely acceptable. I don't know how many ways to say "there is not a consensus". If you feel that the \equiv notation is not understandable to people outside the field, then the right thing to do is to explain it. Put in a brief notation that "the symbol $\equiv$ in this context means "is defined as"" or some such. If you change the notation, what will someone do when they go from the encyclopedia article to a textbook on thermodynamics and find the \equiv symbol and wonder about it -- have you done them any service, or have you just confused them more in your attempt to invent a notation used nowhere else in the field? Again, stop this silliness, reverse these ridiculous edits, and simply explain what \equiv means when it is appropriately used. --Pmetzger 18:51, 3 December 2006 (UTC)

But your article doesn't say "The Helmholtz free energy is defined to be $A\equiv U-TS$ ". It just says " $A\equiv U-TS$ ". That makes it difficult to read for people who are not already so familiar with that discipline that they recognize ≡ as a definition, instead of a logical equivalence, or an equivalence relation, or modular congruence, or... —David Eppstein 19:25, 3 December 2006 (UTC)

Then why not compromise and change the wording rather than the formula?

Introducing a notation unfamiliar in thermodynamics is at least as bad as keeping a notation that would mean something else in group theory; I don't expect Helmholtz free energy to suddenly begin talking about congruences, so I'm not sure that confusion is a real risk. Septentrionalis 20:52, 3 December 2006 (UTC)

I've repeatedly suggested what you are calling a "compromise". The rational thing to do is just explain what \equiv means in articles where it might cause confusion. The rational rule is "use the notation that is most commonly understood in a given field, explaining it if necessary", not "mindlessly adopt a consistent notation at the expense of clarity in fields that have traditionally used a different notation". The latter is a procrustean solution, acceptable only to those who do not understand the consequences. The proposed "compromise" is exactly what I've suggested, but it is claimed that we have "consensus" to do otherwise -- an incorrect claim, since clearly a lot of people are not agreeing. Meanwhile, people are altering articles that they have no business altering in the name of implementing said procrustean non-consensus, as though it was already a foregone conclusion. --Pmetzger 22:50, 3 December 2006 (UTC)

No, no, no! The rational thing is not to try to use any particular symbol with the meaning "defined" as, because no such symbol will be generally understood by all readers. Nobody is going to misunderstand "The Helmholtz free energy

A

is defined as

U - T S

", and that is the true compromise between adherents of different symbols. Henning Makholm 23:38, 3 December 2006 (UTC)

A similar usage in probability theory

The notation

$X \ \stackrel{\mathcal{L}}{=}\ Y.$

conventionally means that the two random variables X and Y both have the same probability distribution. The letter "L" stands for "law"; probability distributions are sometimes called "laws". Michael Hardy 04:11, 25 November 2006 (UTC)

Policy for WP:MSM

So, what exactly should we add to WP:MSM? How about the following:

For definitions, do not use "\equiv". If something is a definition try to say so in words. If that isn't possible, use ":=".

We could also recommend " $=_{def} \,$ " , as used in Implementation of mathematics in set theory. — Sebastian (talk) 23:18, 24 October 2006 (UTC)

That article specifically discusses how to "define" (actually "implement") things in terms of other things, and then you want these "definitions" to stand out. Because they aren't truly definitions in the usual sense, we should not take them as examples.

It is different when definitions are introduced in the course of a discursive account. There are many ways of doing this:

We denote g_1(x) + g_2(x) + ... + g_n(x) by f_n(x). Then the sum f(x) is the limit lim f_n(x).
Letting f_n(x) stand for g_1(x) + g_2(x) + ... + g_n(x), we now define the sum f(x) to be the limit lim f_n(x).
Define f_n(x) = g_1(x) + g_2(x) + ... + g_n(x). Then the sum f(x) is simply the limit lim f_n(x).
Let a sequence of functions f_n be defined by f_n(x) = g_1(x) + g_2(x) + ... + g_n(x). Then the sum f(x) is the limit lim f_n(x).
We can then define the sum f(x) by f(x) = lim f_n(x), the limit of a sequence of approximations, where f_n(x) = g_1(x) + g_2(x) + ... + g_n(x).

In most cases the problem is not so much the ambiguity of a form like X = Y by itself, but the lack of appropriate text connecting the formulas. I don't want to outlaw the use of =_def, but it shouldn't be encouraged by our style manual.

Perhaps we can collect some bad examples and show how to fix them. One candidate I'm nominating is in Geometric mean, where it is not obvious (I think) to the mathematically unwashed that in the first maths display the l.h.s. is not a definiend. Here no new symbol is being introduced. Contrast this with Polylogarithm. Here the opposite confusion might be possible: a reader stumbling upon the article might think that the two expressions connected by an equality sign are just two different, already understood, ways of saying the same thing. An easy fix is to amend the first line to read: "... is the special function Li_s that is defined by:". Or one could write: "The polylogarithm (also known as Jonquiere's function) Li_s is a special function that is defined by:". --Lambiam ^Talk 02:40, 25 October 2006 (UTC)

Good idea! Here's the seed for such a table, taken from my recent edits. I never claimed I was good at writing math prose, so I'm sure you'll have some ideas for improvements. Please don't hesitate to edit them directly in the table. I added a column "Found in" so we can easily take the improvement to the article. — Sebastian (talk) 20:24, 25 October 2006 (UTC)

Old version of table deleted - see new version below.

Hamilton's characteristic function <math>W</math> is often defined as... seems to mean that Hamilton's characteristic function has different definitions and that the often used one is ... This is not the same meaning as the initial sentence, which is that Hamilton's characteristic function, which is defined as ..., is also often used. Isnt't it right? pom 20:56, 25 October 2006 (UTC)

Good point! The word "often" is a bit overused in that article (and maybe Wikipedia in general) anyway. For the reader, much more relevant than how often something is used is what it's used for, and if it helps him/her solve his/her problem. I'll take a closer look at that article and see what I can do. — Sebastian (talk) 21:41, 25 October 2006 (UTC)

I suggest: "another action function, Hamilton's characteristic function

W

, is often introduced. It is defined as ...". I find LaTeX notation hard to read and have produced a typeset version below, in which I've tentatively applied this suggestion (but not in the actual article). By the way, all the examples use(d) \equiv, but many articles using = for definitions would also improve by similar changes. --Lambiam ^Talk 22:24, 25 October 2006 (UTC)

Yes, I like your proposed wording. But since I just rewrote the whole section it would doesn't fit exactly anymore. Please feel free to change as you see fit. I also prefer the typeset, so we don't need to keep my old table. I agree with your point that these changes have a wider applicability - all the more reason to put something like this table in the style guide. — Sebastian (talk) 22:45, 25 October 2006 (UTC)

Before	After	Found in	Comments
where $\mathbf{n} \equiv (n_1,n_2, \cdots, n_d)$	where we define $\mathbf{n}= (n_1, n_2, \cdots, n_d)$ and $\mathbf{k} = (k_1, k_2, \cdots, k_d)$	Discrete Fourier transform
where the division $\mathbf{n} / \mathbf{N} \equiv(n_1/N_1, \cdots, n_d/N_d)$ is performed element-wise	where the division $\mathbf{n} / \mathbf{N}$ is defined as $\mathbf{n} / \mathbf{N} = (n_1/N_1, \cdots, n_d/N_d)$ to be performed element-wise	Discrete Fourier transform
The action is defined as the integral of the Lagrangian $L$ for an input evolution between the two time points $\mathcal{S}[\mathbf{q}(t)]\equiv \int_{t_1}^{t_2} L[\mathbf{q}(t),\dot{\mathbf{q}}(t),t]\, \mathrm{d}t$	The action $\mathcal{S}[\mathbf{q}(t)]$ is defined as the integral of the Lagrangian $L$ for an input evolution between the two time points $\mathcal{S}[\mathbf{q}(t)] = \int_{t_1}^{t_2} L[\mathbf{q}(t),\dot{\mathbf{q}}(t),t]\, \mathrm{d}t$	Action (physics)	Copy defined term in sentence for clarity.
another action function is often defined:Hamilton's characteristic function $W\equiv S - Et$ .	another action function, Hamilton's characteristic function $W$ , is often introduced. It is defined as $W = S - E t$ .	Action (physics)	Move "defined" closer to equation.
the final and initial positions, $x_{1} \equiv x(t_{1})$ and $x_{2} \equiv x(t_{2})$ , are specified in advance.	the final and initial positions are specified in advance as $x 1 = x (t 1)$ and $x 2 = x (t 2)$ .	Action (physics)	use "specified ... as" to indicate definition.
The difference between these two evolutions is infinitesimally small at all times: $\varepsilon(t) \equiv x_{\mathrm{per}}(t) - x_{\mathrm{true}}(t)$	The difference between these two evolutions, which we will call $\varepsilon(t)$ , is infinitesimally small at all times: $\varepsilon(t)= x_{\mathrm{per}}(t) - x_{\mathrm{true}}(t)$	Action (physics)	The original equation served two purposes: Defining $\varepsilon(t)$ and showing which term is small. Explain these two verbatim.

Bugzilla

Added bug bugzilla:7753. _→AzaToth 21:45, 29 October 2006 (UTC)

Strong objection to ditching \equiv

I was just informed on the talk page for an article that I help maintain that some people here appear to believe that Wikipedia gets to revise a century of usage by ditching $\equiv$ , and that, indeed, said decision has "already been made".

Pardon my saying so, but no, that's not really Wikipedia's decision to make. $\equiv$ is in wide use in all sorts of places. Those who claim to have math degrees and to have never seen it before, well, I don't know what math classes you were taking, but there is a strong reason that Knuth put the character in TeX's math font, and it wasn't perversity.

I see that some believe this issue is "decided", but that's absurd. \equiv is not going from articles I edit, because it is there in all the references I use and all the papers I read. If you don't like it, the place to take it up is with organizations like the American Mathematical Society, and not in a Wikipedia project talk page. Abolishing it is the moral equivalent of Wikipedia deciding, as a matter of style, to rename Hydrogen "Element One" because that is "more logical". No, sorry, that's not what we get to do around here. Wikipedia is a reference, not a place to try to change the world's notational conventions. This is an encyclopedia, not a reform movement. If you don't like the way professionals in certain fields write their equations, take it up with them directly.

Repeating, in the specific case of particular pages I edit regularly, I've checked the standard notation in reference works, and it is \equiv (i.e. $\equiv$ ), and so that is how it should remain on those pages until such time as the textbooks and papers in the field change. Let me know when you have gotten all the textbooks revised. --Pmetzger 21:12, 2 December 2006 (UTC)

Sorry, but you do not own those pages. Regardless of what you believe, many readers will not understand without additional explanation that " $A\mbox{ }\equiv\mbox{ }U-TS = \mu n - PV$ " is supposed to mean: "

A

is defined by the equation

A = U - T S

, which, by the way, happens to be equal to

μ n - P V

." Why wouldn't it mean: "the proposition

A

is true if and only if the equality

U - T S = μ n - P V

holds"? Have you read the discussion on this page at all? --Lambiam ^Talk 21:57, 2 December 2006 (UTC)

First, I never claimed to "own" any pages. I'm just an editor like everyone else. Second, I've consulted several texts that discuss thermodynamics in the last few hours. Of them, only Fermi's treatment from the 1930s used

=

rather than $\equiv$ -- the rest use \equiv. If people don't know what $\equiv$ means, then I have no objection to explaining what it means. By all means, lets add annotations explaining what the symbol is for -- explaining things is, after all, the purpose of an encyclopedia. I do, however, object to our deviating from common notation. --Pmetzger 01:30, 3 December 2006 (UTC)

I agree with Lambiam. It seems odd that Pmetzger would come and post so vehemently right below a very long and, I believe, fruitful discussion addressing this issue. But to be fair, what are these textbooks that use \equiv to mean definition? Maybe this is a "field of study" issue. In pure mathematics, I have never seen it used, but that's not to say that other fields don't use it. If it can be demonstrated that there is a large number of textbooks in a well-established field of study that considers this usage a proper convention, then we may have no choice. It may be like the serial comma: something people have strong feelings about, but that ought not to be changed upon sight. VectorPosse 00:53, 3 December 2006 (UTC)

Even though there may be textbooks that use $\equiv$ for definitions, we certainly do have a choice as to whether to use this notation in our encyclopedia. At least, this discussion has demonstrated that some people would not understand it on sight, and it is not as if people who do understand it would not also understand a definition set out in prose. Henning Makholm 01:08, 3 December 2006 (UTC)

If people don't understand it on sight, then explain it. One would have to put prose in to explain that an equals sign was intended as a definition anyway, so there is no rational reason you can't instead explain what an \equiv symbol means. As for the vehemence of of my remarks, it is because there are a variety of areas of study and they have a variety of common notations and it is not our job to change them. If you want just one example of a book that uses $\equiv$ , have a look at Levine's "Physical Chemistry". I could find a dozen more examples, and if people insist I will keep enumerating them until the point is made. As for the discussion, I think the fact that most people who edit pages do not keep up with every discussion is likely why you haven't heard more objection. --Pmetzger 01:30, 3 December 2006 (UTC)

I agree with Pmetzger. The notion that ":=" would be better understood is also nonsense, and the "def" on top of an equal sign is even worse, something that is going to be totally strange to almost everybody. Gene Nygaard 01:37, 3 December 2006 (UTC)

For what it is worth, I should point out to readers here that using ≡ for definitions is very common in physics (much more common than := or alternatives). In fact, the first five textbooks I pulled off my shelf all use it. They are

Jose and Saletan, Classical Dynamics
Hassani, Mathematical Physics
Sakurai, Quantum Mechanics
Griffiths, Introduction to Electrodynamics
Callen, Thermodynamics and an Introduction to Thermostatistics

I agree that good prose is the best solution, but I wouldn't go so far as to banish ≡ from physics articles. It is, after all, a very standard notation in that field. -- Fropuff 01:38, 3 December 2006 (UTC)

That was my thought too; very common, and more likely to be understood than the alternatives. And the really incomprehensible thing about some of the discussion above is the notion that \equiv ( $\equiv$ ) is somehow different from &equiv; (≡) or ≡ ≡ or ≡ ≡ or just entering the ≡ character (by copy and paste or whatever). Gene Nygaard 01:53, 3 December 2006 (UTC)

So you think that alternative B below is more likely to be understood than A?

A. The second Chebyshev function $\psi(x)\,$ is defined by

$\psi(x) = \sum_{n \leq x} \Lambda(n).\,$

B. The second Chebyshev function

$\psi(x) \equiv \sum_{n \leq x} \Lambda(n).\,$

Somehow I find that unlikely. The use of "equiv" as meaning "is defined as" is definitely not usual in mathematical texts, and I doubt it will ever become so, because the symbol already has several meanings (equivalence, congruence), and overloading it thus is likely to create confusion. Just consider defining negation by "¬p ≡ p ≡ false", or the divisibility relation by "m|n ≡ n ≡ 0 (mod m)". Physics texts don't have this problem because they don't deal with logic or number theory. I'm fairly sure that most of our readers have never opened a physics textbook beyond the elementary level. In the texts on physics topics at wikiversity (e.g. [67]) I don't see the use of "equiv" for definitions. I also don't see it in any text I can easily get my hands on, which, I must confess, are all many decades old. In any case, as far as I can see from the above discussion the main issue most participants in the discussion have is not the use of "equals" versus "equiv" per se, but the use of these symbols for a definition without making it clear in the context that the symbol indicates a definition. --Lambiam ^Talk 08:10, 3 December 2006 (UTC)

It seems the obvious answer here is that physics represents a field where ≡ is both commonly used and unambiguous (while in mathematics it is not - to me in means congruence modulo something) and in that case it seems only reasonable to follow the publications in the field and use ≡ in the physics articles on subjects that traditionally use it. On the other hand I tend to agree with with the eventual consensus view here, at least for pure mathematics articles, that ≡ isn't the best option due to rarity and ambiguity of meaning, and that clear prose is the answer. Leland McInnes 09:38, 3 December 2006 (UTC)

Re the example given: why does it have to be the first versus the second? This is silly. Clearly the right thing is to say:

The second Chebyshev function $\psi(x)\,$ is defined by

$\psi(x) \equiv \sum_{n \leq x} \Lambda(n).\,$

and then the intent is quite clear. Say what the \equiv means, leave the equiv, all is well. However, I don't even see why this is necessary in the sense that the problem is not replacing all definitions with the use of \equiv but removing all uses of \equiv from contexts like thermodynamics, statistical mechanics, etc., where the use is traditional. If people want to leave pure math articles alone, fine -- different fields have different notations. However, people are now going through and replacing \equiv with the abomination equals-sign-with-def-over-it that was invented here only a few days ago for articles in areas where \equiv has been used forever. If people are confused about what \equiv means, just add an explanation (as above) to the prose and leave the \equiv -- which has been in use in these fields for decades if not a century -- alone! --Pmetzger 18:40, 3 December 2006 (UTC)

I hate to break it to you but equals with def over it is the common format in many fields of mathematics and has been in common use for quite some time (there's a reason there's a unicode character for it). I've also seen both ≔ and ≜ used reasonably frequently. The aim of the discussion here was to try and come to some agreement on a common notation for Wikipedia for the sake of consistency. If your field has a consistent common notation already then fine, use that in the articles on that field. The discussion and conclusions here are still valuable, and it seems to me that the only issue is that some people are pushing things a little too hard and a little too far outside the logical domain (let's be honest you are discussing physics articles and this is WikiProject Mathematics). -- Leland McInnes 20:28, 3 December 2006 (UTC)

I don't ask anyone to stop using what they are already using, but the same deference isn't being shown in both directions. You may say "lets be honest you are discussing physics articles and this is WikiProject Mathematics" but people are editing physics articles to remove the use of \equiv, and they're pointing us here for the reason why. I've said, repeatedly, articles should reflect usage common in the field, but then people have said "no, we have to be consistent and use one thing across the whole encyclopedia", and they've gone off to implement this madness. The only reasonable rule is "follow the notation commonly used in a field, and explain it if necessary". --Pmetzger 22:43, 3 December 2006 (UTC)

I agree with Pmetzger that people shouldn't go to physics pages (or even applied maths) and replace $\equiv$ with $\stackrel{\text{def}}{=}$ . I doubt the latter is clearer for people reading physics articles. However, I agree with others here that "The second Chebyshev function

ψ(x)

is defined by $\psi(x) = \ldots$ " is preferable to "The second Chebyshev function

ψ(x)

is defined by $\psi(x) \equiv \ldots$ ", even in physics pages, since I think former is clearer to everybody and in wider use (even better in my opinion would be "The second Chebyshev function

ψ

is defined by …", but that's a different matter). -- Jitse Niesen (talk) 00:54, 4 December 2006 (UTC)

Two misconceptions The most emotional statements seem to be caused by not knowing the following two facts:

This is not about "ditching \equiv". Nobody here denies that \equiv has legitimate uses.
Nobody here denies that adding prose is the best option.

Re #1: This is not a "jihad against symbols"[68]. It is an endeavor to disambiguate the different uses of \equiv (demonstrated so nicely by Lambiam above).
Re #2: It is the best, but it takes a lot of time. We're still at about 300 occurrences - if you really feel strongly about this, please help by editing the articles on /equivlist.

If this is not immediately obvous to you, please read the older parts of this section. I'm tired of hearing these misconceptions over and over again. — Sebastian (talk) 02:31, 4 December 2006 (UTC), amended 03:47, 4 December 2006 (UTC)

Maybe it is time you paid some attention to the objections. You might claim here that "this is not about ditching \equiv" but that quite clearly was the result of the previous discussions, with editors going on a rampage to delete it. You might claim now that "nobody here denies that \equiv has legitimate uses" but the fact of the matter is, until Pmetzger spoke up, most editors would reasonably have assumed that denial.

Why are all the people so worried about theoretical ambiguities not on a rampage against the "=" symbol? Gene Nygaard 11:45, 4 December 2006 (UTC)

Here is American Institute of Physics, AIP Style Manual,, 4th ed. 1990, Appendix F:Special symbols available for typesetting, p. 44:

R3 ≜ corresponds to
R4 ≡ identically equal to; equivalent to; triple bond
R5 ≢ not identically equal to; not equivalent to; not always equal to

Note that ≝ is nowhere to be found. Nor is :=, but that of course can be composed of two characters without a special typesetting symbol. Gene Nygaard 14:08, 4 December 2006 (UTC)

A general usage in physics books and articles certainly should be respected. However, the 'worry about theoretical ambiguities' has rather concrete grounds. Two points:

Pmetzger and Gene Nygaard, are you familiar with notation like $17 \equiv 33 \pmod 8\,$ , do you recognise what this means in 'ordinary mathematemathics', and do you understand that this is the by far most common usage of the ≡ symbol at least our math students meet in their courses? ('Our math students' here means 'The students at the Department of Mathematics of the University of Stockholm, except possibly at our section of mathemathical statistics', but I strongly suspect that the same is true for most places where physics and pure mathematics are taught at different departments. They might meet ≡ in the sense of implication, if they take a course in mathematical logic.) If you are not, you may reread Lambian's explanation supra.

Our students will in all probability not meet similarly widely different usages of the equality sign = ; except, possibly, in connection with a usage of the Ordo symbols. (However, some text books avoid this ambiguity by consistingly using words instead of the equality symbol in order contexts; ' f(x) is O(x²)' instead of ' f(x) = O(x²)').

I am 'old enough' to recognise the usage of ≡ in the meaning 'identically equivalent to' in calculus. (I have once or twice tried to convince some of our 'youngsters' (ph. d. students et cetera) that this usage is not an outright error of students, and that they actually may have met this alternative usage of the symbol at school.) However, while this usage is closer to the usage of ≡ in definitions, it does not quite coincide with it. Being indentically equivalent is a symmetric relation; you may as well write $g(x)^2 \equiv f(x)\,$ as $f(x) \equiv g(x)^2\,$ , since both formulations simply mean that are defined for the same values of x, and that $f(a)\,$ and $g(a)^2\,$ coincide for each such value a. A definition is assymetric, on the other hand.

In other words: There are real reasons for concern, and it should be recognised in articles which are not 'clearly mathematical' or 'clearly physical' but aiming at being understood from both sides. IMO, the Chebychev polynomials belong to this intersection of areas.

With this said, I agree with Pmetzger and Gene Nygaard, that mathematicians shouldn't try to force a certain usage onto 'pure physics' articles in the name of an encyclopaedian uniformity. I don't think you'll find such a far-reaching uniformity (going further than the main-stream scientists have achieved themselves) in other major encyclopaedia. What we could do, on the other hand, is to try to be more aware of the differences, and try to find some way to help students of both subjects translate notation and concepts from one area to the other. I've noticed other examples of such 'Babel language confusion'; e. g., when theoretical physicists suddenly chock pure mathematicians by employing the Einstein summation convention. Probably we are causing similar troubles for physicists, now and then. I think we should try together to identify such differences, and make some easily accessed pages explaining the differences. IMO, this could yield a tangible contribution to the wikipedia.--JoergenB 17:50, 4 December 2006 (UTC)

Perhaps this is a regional difference in addition to a field difference. As far as I know, the above modulo statement should be written with a standard '=' sign. These differences should be worked out, but I agree with Pmetzger that the "equals sign with def" should be avoided. Can ≡s be wiki-linked to Table of mathematical symbols, or is that unfeasible? johnpseudo 18:08, 4 December 2006 (UTC)

Unfortunately, linking doesn't work in mathematical formulas. — Sebastian (talk) 18:58, 4 December 2006 (UTC)

If everyone agrees that adding prose is the best option

Sebastian, I believe, claims that the beginning of this discussion shows that everyone agrees that adding prose, presumably such forms as "We define" and so forth, is the best option. This is not at all obvious to me; but if it is so, let's agree to go do it, as part of the slow improvement that is Wikipedia. It will take a long time; but so will lots of other important things. Septentrionalis 18:19, 4 December 2006 (UTC)

Yes, that's what I claimed. At least I'm not aware of anyone opposes it. But I do disagree that it will all just work out magically by the Wikipedia ant process. It hasn't done so in the past - in the contrary, we accumulated thousands of formulas where ≡ is used for definitions. This is a misleading deviation from approved standard.

As Gene Nygaard writes above, the American Institute of Physics defines "≡" as "identically equal to; equivalent to; triple bond". Using "≡" for "definition" is misleading. I was confused about it myself - which was in fact the reason why I started this whole thread with my initial question, and why I still believe we should eliminate this misleading wrong usage. — Sebastian (talk) 18:51, 4 December 2006 (UTC)

Here's a table with the options we have so far - please feel free to amend: — Sebastian (talk) 19:27, 4 December 2006 (UTC)

Option	Basis	Remaining effort (person hours)	Quality (A...F)	Certainty of outcome
Leave as is	haphazard	0	F (ambiguous)	certain (trivially)
Annotate as we go	consensus	30	A	unlikely (has not worked so far)
Annotate now	consensus	30	A	low (few volunteers)
repl \equiv with =^def	lesser evil	2	E (notation unfamiliar to some)	certain (already done for 75% of all articles on /equivlist)
Finish math \equiv replacements, revert all \equiv replacement made on non-math articles	Allow for field differences, avoid stepping on toes	10	B	50/50, sporadic

One question to all who believe that slow improvement (the "ant algorithm") fixes the problem: Why are you confident that it will improve formulas with \equiv signs, but not formulas with =^def signs? — Sebastian (talk) 19:41, 4 December 2006 (UTC)

Spelling out the definition in words will improve the readability of an article no matter which kind of symbolism it previously tried to use for "is defined as". Replacing one symbol with another symbol will not improve anything at all; it will just make the article look strange to a different set of people than it looked strange to previously. Your assertion that =^def is a "lesser evil" or "only a third as bad" as \equiv (as implied by the difference between B-A versus D-A) appears to be essentially unsupported by this discussion. Henning Makholm 21:46, 4 December 2006 (UTC)

It is the lesser evil because it is not ambiguous. This has been discussed ad nauseam already, and nobody ever countered this argument. — Sebastian (talk) 21:53, 4 December 2006 (UTC)

Each symbol is unfamiliar to some people. It ought to be clear to any reader of this discussions that there are people who understand \equive more readily than =^def (or at least they claim to, and why whould they lie?) The fact that \equiv has some other legitimate uses should not change the relative merits more than to, say: \equiv: F; =^def: E-; prose: A. Henning Makholm 22:06, 4 December 2006 (UTC)

I agree, and I changed the table accordingly. — Sebastian (talk) 22:16, 4 December 2006 (UTC)

I appreciate that this debate has very poor timing- a lot of work has already gone into this, and changing course now would certainly result in a lot of wasted man-hours. However, what does =^def add that ≡ doesn't have? While ≡ is a standard that people in most fields of science would understand, =^def is brand new, and it is just as confusing to the casual reader if it isn't clarified using prose. Wikipedia is just an encyclopedia, and for people inclined to get more in-depth understanding on these topics, developing non-standard mark-up will not help. johnpseudo 21:03, 4 December 2006 (UTC)

What it adds is DISAMBIGUATION. Sorry for shouting, but it sometimes is necessary to get heard. — Sebastian (talk) 21:53, 4 December 2006 (UTC)

Your assertion that "≡ is a standard that people in most fields of science would understand" is just plain wrong, as evidenced by this very discussion. Henning Makholm 21:48, 4 December 2006 (UTC)

I feel like this forum is not an accurate judge of the level of acceptance of ≡. This unfamiliarity with ≡ is a little foreign to me, so I'll see if I can do a little research. Re Sebastian: I'll listen, whether or not you shout :-) johnpseudo 23:08, 4 December 2006 (UTC)

OK, thanks. I know, it's hard to jump into a discussion that already is several pages long and understand what it's all about right away. It was just an excuse for me to draw attention to a point that many who join this discussion are not aware of. So, this is really not about unfamiliarity. I would really appreciate if you could confirm that the information that this is about disambiguation has reached you. — Sebastian (talk) 23:17, 4 December 2006 (UTC)

One of the goals here certainly is to disambiguate between equality and definition, but we must also keep in mind that non-standard symbols reduce the usefulness of an encyclopedia by forcing readers to learn extraneous information. The key here is to determine the proper balance between these two factors. johnpseudo 00:06, 5 December 2006 (UTC)

This is a very nice statement, but what does it mean in practice? If you have any idea for a concrete plan of action, please let us know and I'll be happy to list it in the table above. — Sebastian (talk) 17:50, 5 December 2006 (UTC)

Since we all agree that prose is what will distinguish between a clear article and an unclear one, perhaps we treat symbol terminology the same way we do dialects. As long as what the authors of the article have written is clear, they can use whatever symbol they feel is most appropriate. This may help with the problem of different fields using different terminology. Trying to reach some kind of consensus between all scientific fields here in this forum wouldn't work. Making grand, sweeping changes to every article that uses an /equiv should be avoided, but in articles in which the "definition" clarification is important, the symbol should be accompanied by good prose.

That doesn't really help us in our current situation though, because there have been grand, sweeping changes made already. I think the changes should be reverted to whatever terminology was used before. johnpseudo 18:20, 5 December 2006 (UTC)

Yes, it is very reasonable to change things back (for now at least) to the way they were before this thread. As I have already suggested in this discussion earlier, this is similar to many issues of punctuation and spelling on Wikipedia. We leave things the way the original editor had them insofar as they are correct for a large group of our readers. I hope to insist at least a little bit that pure math articles maintain the strong tradition of using = only (plus prose, of course). But I'm happy for physics articles--even ones that border on pure math--to use \equiv since it is widely accpepted in that community. And CS articles should use := if that is an established method of "assignment" in that field. I despise =_def and =^def and all variants thereof, but only because = is more common, more universally understood, and less obtrusive. Even at that, I would think twice before changing =^def to = in an article "just because". VectorPosse 19:30, 5 December 2006 (UTC)

You are both digressing. Your statements do not address disambiguation, which is the point of this initiative. — Sebastian (talk) 21:31, 5 December 2006 (UTC)

Disambiguation applies to articles. It is not necessary (or possible) to disambiguate each symbol from all other possible uses in Wikipedia as long as it is clear in context. Septentrionalis 21:39, 5 December 2006 (UTC)

No, disambiguation is a general term. It does not only apply to Wikipedia articles. Your second sentence is true, but your premise is not true: This particular symbol is not always clear in context. — Sebastian (talk) 21:57, 5 December 2006 (UTC)

And most editors here agree that the solution is to make the context clear when necessary. Septentrionalis 22:04, 5 December 2006 (UTC)

Yes. Actually, everybody agrees that it's the best solution, as the name of this subsection correctly states. But it is not feasible. — Sebastian (talk) 22:11, 5 December 2006 (UTC)

I do not believe it is a digression to request that the "fixes" which turn out not to be fixes and have upset people (especially in physics) be reverted until real consensus is formed. As for disambiguation, it is not our place to rewrite math notation to make it clearer in fields that already have well-established traditions. This has always been a problem in math. Clear exposition is the answer. There has been consensus on that much, but little else has been decided. (Just to be sure, I went back and read the whole thread one more time. Nobody agrees on anything else.) VectorPosse 22:15, 5 December 2006 (UTC)

To be clear about my point: the equal sign does not need disambiguation. If it did, the math community would have changed it a long time ago. VectorPosse 22:18, 5 December 2006 (UTC)

I'm not sure how you plan to revert the changes, since many of them were made by different people at different times. Could you give some examples of non-math articles where these changes were made? I thought that the discussion here was clearly only intended for math articles. It is certainly appropriate for the math editors to write a Wikipedia:Manual of style (mathematics), and the presentation of definitions could be covered there. CMummert 22:29, 5 December 2006 (UTC)

I don't know how to revert the changes. I thought Sebastian was keeping a list since he said earlier that 75% of the work was done. I figured someone was keeping track. If not, then I suppose there's not much that can be done. Also, I assumed that physics articles were affected due to the entrance in this thread of several editors crying foul about physics articles. I have no first-hand knowledge of which articles have been changed. VectorPosse 22:55, 5 December 2006 (UTC)

Thank you for rereading the whole thread. It's really a lot of work to go through all of this largely unstructured text. I'm starting to think that it might be better to start over in a more collaborative way, similar to a Wikipedia article.

Maybe the term "digression" was a bit harsh. What happened was that I had just reached an agreement with Johnpseudo that "One of the goals here certainly is to disambiguate", then he proposed a policy which did not disambiguate anything, and you followed up on the same tangent. — Sebastian (talk) 22:32, 5 December 2006 (UTC)

Way too serious. I mean, way way too serious about a format issue. As on some other points (e.g. spelling) if there is not going to be a settled consensus, just try not to annoy others on this. The wiki way isn't about six-week threads that settle nothing. Charles Matthews 22:35, 5 December 2006 (UTC)

Thank you! That's a good point which I hope everyone reads who considers this a mere format issue. I hope we can move to a rational discussion, where people who see this as a problem that impedes understanding, and who do the right thing by following "WP:SOFIXIT", are not held up by rants, many of which posted without care for what has been said in the discussion before. — Sebastian (talk) 23:52, 5 December 2006 (UTC)

I would like to address the issue that ≡ is "a standard that people in most fields of science would understand" while ≝ is "brand new". I think it's clear from discussion here that for a great many people ≡ means something other than definition - for most mathematicians it means congruence or a similar statement of identity or exact equivalence. Equally impotantly it needs to be recognised that ≝ is not "brand new", but is in fact quite common is many fields. That it is not new should be clear from the fact that there is a unicode character for it, U+225D: EQUAL TO BY DEFINITION. Indeed the only other equivalence relation character in Unicode to specify itself as being definitional is U+225C (≜) which is described as equal to by definition in the comment (though is named DELTA EQUAL TO). I have sympathy for the physicists who are having their toes trod on here, and would be more than happy to leave physics articles to use whatever notational convention they agree on. What I object to is the implication that, since people are apparently only familiar with their own field, their particular notation is "a standard that everyone understands" and anything else is just people making stuff up. -- Leland McInnes 22:41, 5 December 2006 (UTC)

I disagree with the idea that improving context is "not feasible". It may not be able to be done en-masse, with hundreds of edits in a week or two, but it is certainly feasible in the long term and will achieve the goal of disambiguation. I agree with Charles Matthews, CMummert, and VectorPosse, and I think that this change to =^def can serve math articles well but should be carefully kept out of other fields. johnpseudo 22:54, 5 December 2006 (UTC)

Of course it's feasible. Feasible does not mean "done by next week." We have the list of articles which use \equiv; and those of us who feel this is the most important thing thatWikipedia can do can work on that. The rest of us will remember to edit any definition we come across to say "definition." Septentrionalis 02:55, 6 December 2006 (UTC)

Well, maybe I've been impatient. I'd be happy to be proven wrong. I'll take another break from this for a month or two and we'll see how much the situation improves. If there still is no promising progress towards eliminating unnecessary misleading uses of \equiv, then I'll volunteer my easy 2-hour solution again. — Sebastian (talk) 07:47, 6 December 2006 (UTC)

Implementing proposal

I've created Wikipedia talk:WikiProject Mathematics/equivlistrevert for reverting non-math changes. Sebastian, you should finish the job you've done on /equivlist with math articles. johnpseudo 15:47, 6 December 2006 (UTC)

Hold on a second. As I've pointed out, there's no consensus that things should be changed even in math articles. Many of us have expressed that especially in pure math articles, the = should remain. Maybe I am misunderstading what you mean by the "job", but if by that you mean changing = to =_def (or something like that), then Sebastian should not finish the job but should still plan to take a month or two off like he suggested he would. Please correct me if I have misunderstood the thrust of your comment. VectorPosse 16:18, 6 December 2006 (UTC)

Never mind. I think you're saying to change \equiv to =^def and not = to =^def. Well, I still disagree with that, but since both \equiv and =^def are equally bad in my book (for pure math articles at least), I won't say anything either way about it. VectorPosse 16:46, 6 December 2006 (UTC)

I thought the agreed on change was "=...as a definition" and that sort of thing, which which no one, so far, has any problem. Septentrionalis 20:16, 6 December 2006 (UTC)

Euler reciprocity?

I did some edits to Euler reciprocity relationship. I agree with whoever put the "context" tag there: its opening sentence is horribly abrupt, not informing the reader that mathematics is what the article is to be about, etc. But I wonder if this article ought to exist. As nearly as I can understand it, it's another statement of what is called Clairaut's theorem. (If you tell me that it's obviously supposed to be Clairaut's theorem, that may be because I edited it to say what I guessed it was intended to say.) Michael Hardy 01:25, 17 November 2006 (UTC)

I also tried to find out what Euler reciprocity relationship is supposed to refer to, before you edited the article. As far as I could see, it's indeed the same as Clairout's theorem, but I wasn't certain because I found only a few references and none were very clear. I think a redirect is in order. By the way, symmetry of partial derivatives is also on that subject. -- Jitse Niesen (talk) 04:10, 17 November 2006 (UTC)

Now I've put "merge" tags on these three articles. Michael Hardy 04:13, 25 November 2006 (UTC)

This seems like yet another instance of "theorems are named after the first person after Euler or Gauss to re-discover them" -- Euler was indeed the first to discover this. By the way, in Thermodynamics, the relation is used a lot, for example to prove the Maxwell relations, and it is generally known as the Euler Reciprocity Relationship there. I would make sure that both names are featured prominently because people reading things like thermodynamics texts will be hunting for explanation under the name "Euler Reciprocity Relationship" and not "Clairaut's theorem" --Pmetzger 05:15, 3 December 2006 (UTC)

John L. Greenberg seems to claim that Clairaut had priority (in the 1730s, versus Euler in the 1740s) in a book review appearing in Annals of Science 41 (1984), 171–177. He refers to his (Greenberg's) prior article, in the same journal, volume 39 (1982), 1–36. Michael Slone (talk) 06:56, 3 December 2006 (UTC)

STIX Fonts

The STIX Fonts project will make the beta version of its fonts available for download in early December. This will be a great boon to all mathematics readers, and of special interest to the Wikipedia mathematics community. The fonts come with a generous license, and now would be a good time for experts here to review it to decide if it will cause any problems for us. For example, does item 2 apply if a Wikipedia page displays an equation as a PNG typeset with these fonts? (What is considered a "derivative work"?) --KSmrq^T 10:38, 20 November 2006 (UTC)

you could always stick text metadata in a chunk in a PNG. the text from the license is pretty small; it could be abbreviated and then compressed in the PNG, but it still might be a big price to pay for zillions of little PNGs. (200 bytes?) someone could write to the STIX project to ask if it's necessary for each image; that is, the Wikipedia as a whole could be the work. Lunch 19:47, 20 November 2006 (UTC)

What I'm hoping is that using the fonts in a document does not constitute a derivative work. Otherwise, anyone who typesets a paper using these fonts has the same problem. I'm hoping they mean something much more narrow, like a new font derived from these. --KSmrq^T 22:52, 20 November 2006 (UTC)

They seem very hazy on the how the fonts are published, in terms of what formats. They may be true-type fonts or similar which can be easily resized. Ideally we would of course use MathML for the output, in which case font selection would be left to the browser. In any case we'll need to sweet talk some of the MediaWiki developers, and probably file a bug when they are finally released. --Salix alba (talk) 23:59, 20 November 2006 (UTC)

Looking at item 3 of the licence: You may (a) convert the Fonts from one format to another (e.g., from TrueType to Postscript), nd (b) embed or include a subset of the Fonts in a document for the purposes of allowing users to read text in the document that utilizes the Fonts. So this seems to give explit permission for our needs. I guess we could probably just add the Stix Fonts to the general Wikipedia:Copyrights page, or link to it from that. I'm guessing a document that includes the fonts is not a derivative work, but a program which convert to PNG would be. --Salix alba (talk) 00:12, 21 November 2006 (UTC)

with regards to using the fonts to produce a document, copies of fonts included in PostScript and PDF files often have (short) copyright notices included/encoded with them (but not whole licenses). as to what's considered a "derivative work", that may be partly up to the copyright holder and what's set in law and court precedents in a given country; i dunno - ask an IP lawyer or the STIX project. if someone does approach the STIX project, they might also ask if the fonts could be released under the GFDL. MicroPress might not want to though. salix is right in thinking that we could punt on the whole issue if we used MathML and had the browsers worry about rendering... :) Lunch 20:16, 21 November 2006 (UTC)

Some of the legal issues with FOSS and font licenses are addressed in a February, 2006 article by Bruce Byfield. He mentions that the STIX license evolved in response to feedback.EdJohnston 17:32, 24 November 2006 (UTC)

Expert requests

Hey there folks. I've been sorting through the {{expert}} tags over the last few days and there are a couple requets in your pile. Could you take a look at Category:Pages needing expert attention from the Mathematics Portal? Don't be thrown by the word portal; It's pretty much just a category of math articles that requested expert help. Thanks much! --Brad Beattie ^(talk) 19:03, 20 November 2006 (UTC)

Category is defunct; now there is Category:Pages needing expert attention from Mathematics experts. And there is, of course, as always, Wikipedia:Pages needing attention/Mathematics/Lists. --Lambiam ^Talk 10:13, 23 November 2006 (UTC)

Thales' Theorem

Some of the interwiki links provided on this page describe another theorem, also credited to Thales of Miletus, proving that parallel lines intersecting a pair of intersecting lines create similar triangles. (See the featured article on the French wikipedia, fr:Théorème de Thalès for probably the best explanation). What is this theorem called in English, and is there an article here about it? (There should be.) Rigadoun (talk) 16:22, 22 November 2006 (UTC)

After exploring a little, I believe that two fundamentally different theorems are tied to Thales' name. The French article picked one; we picked the other. Each has some importance, but each can also be seen as a simple corollary of something more basic. --KSmrq^T 05:21, 24 November 2006 (UTC)

Corrections to inverse trigonometric functions

I made a number of corrections to the article Inverse trigonometric function, in particular to the section Definitions as integrals, which was riddled with errors (about as many as it has formulas). It would be a good idea if someone who has access to a textbook with such formulas, or Abramowitz & Stegun, checked this, and if possible perhaps also the other formulas in the article. --Lambiam ^Talk 17:15, 22 November 2006 (UTC)

I have checked and reformatted the series and integral sections. The advent of "align" is a boon.

A general note: do not set the "d" in "dx" as roman; it should be italic. Thus, for example,

$\int_a^b x^2\,dx$

not

$\int_a^b x^2\,\mathrm{d}x$

should be used. --KSmrq^T 03:20, 25 November 2006 (UTC)

I hadn't noticed we now have "align"---thanks for mentioning this. Using \begin{matrix}, etc., for this produced some really ugly results in many cases. Michael Hardy 03:44, 25 November 2006 (UTC)

Several people worked on the article, most recently myself, and I think that it is substantially better now. However, I still feel uncomfortable with the section Inverse trigonometric function#Logarithmic forms. Specifically with distinguishing the principal branchs of the complex functions and making sure that the branch cuts are in the right place. JRSpriggs 06:25, 7 December 2006 (UTC)

Long-range dependency and heavy-tailed distribution

These were formerly a single article, which conflated LRD processes with long-tailed distributions as if the presence of a long-tailed distribution only ever arose as a result of LRD, and vice versa, and that they were, in effect, two aspects of a single concept. Terms like "memoryless distribution" were used...

I've tried to separate the two, but I'm no expert, and I'm pretty sure the result is still a mess. Can anyone with some probability/statistics/queueing theory knowledge help tidy these up and proofread them for errors? -- The Anome 00:03, 24 November 2006 (UTC)

Dǎnuţ Marcu

I just made an article on a serial plagiarist Dǎnuţ Marcu. The hope is that "contributions" of this person become better known. Please take a look and contribute to make the article adherent to WP style. Also, keep an eye on it - I am afriad there might be a "speedy deletion" move by the Marcu himself. Mhym 02:29, 24 November 2006 (UTC)

You must be very careful. You are stating that actual plagiarism has taken place. That is not the proper, neutral form of statement. You must state all claims and counter-claims. What you have posted is in effect an attack piece. In order to survive speedy deletion by administrators, you must rewrite it in a neutral style. Charles Matthews 17:38, 24 November 2006 (UTC)

The article seems quite okay to me, with the possible exception of the second sentence ("best known for a long series of plagiarised papers"). I was not able to find any counterclaim, and the evidence is clear that plagiarism has taken place. In my opinion stating that actual plagiarism has taken place is the proper and neutral form of statement. -- Jitse Niesen (talk) 04:20, 25 November 2006 (UTC)

That second sentence is clearly unsourced and a violation of WP:BLP, and so I removed it. Unfortunately, mhym, whom I'm sure is familiar with the policy, has re-added it. I suggest people watch the article to make sure these violations are not re-added. --C S (Talk) 04:10, 26 November 2006 (UTC)

For interested parties, a discussion between me and mhym has started at Talk:Dǎnuţ Marcu. --C S (Talk) 04:28, 26 November 2006 (UTC)

Dec 2006

This is the archive file "Wikipedia talk:WikiProject Mathematics/Archive20". It is for December 2006.

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

Equations gone

Any one know what is up with the equations on WP? I recently browsed one of my pet articles (Kt/V)-- and all the equations are gone despite that there were no edits. The equations in Navier-Stokes equations are also gone. Interestingly, the equations in Standardized Kt/V are still there. It looks like there's some error with the equation interpreter-- perhaps due to recent changes discussed above? Nephron T|C 20:40, 25 November 2006 (UTC)

Strange... no sooner had I posted the above and they re-appear. Nephron T|C 20:43, 25 November 2006 (UTC)

Stablepedia

Beginning cross-post.

See Wikipedia talk:Version 1.0 Editorial Team#Stablepedia. If you wish to comment, please comment there. ★TWO YEARS OF MESSED ROCKER★ 03:47, 26 November 2006 (UTC)

End cross-post. Please do not comment more in this section.

completing the square

An edit-warrior, wishing to give his arguments ONLY in edit summaries, has twice deleted a new section I added to completing the square. He says

“

Incidental mathematics, although clever, is not relevant. The wording ('this may be considered completigng the square') shows this.

”

Could we have some third (and fourth...) opinions? Michael Hardy 03:50, 26 November 2006 (UTC)

Here's the new section, with a typo fixed (I should have said "equal to −2"): Michael Hardy 03:54, 26 November 2006 (UTC)

A variation on the theme: the middle term

By writing

$x + {1 \over x}$

$= \left(x - 2 + {1 \over x}\right) + 2$

$= \left(\sqrt{x} - {1 \over \sqrt{x}}\right)^2 + 2$

one sees that the sum of a positive number x and its reciprocal is always greater than or equal to 2, with equality only when the last parenthesized expression vanishes. That happens if and only if x = 1. By adding the middle term, equal to −2, one gets a perfect square; thus this may be considered a sort of completion of the square.

I do not want an edit war. I would like additions like this to be supported by consensus before they are added. This addition is not directly related to the point of the article. Broadness is fine. Math with no apparent purpose is not. I don't think the addition adds anything of substance to the article, and it makes the article more confusing (at least to me). IF there were consensus, I would not object. Michael, thank you for putting out the request. Michaelbusch 03:58, 26 November 2006 (UTC)

It seems to me that Michael Hardy's example is no more and no less valid as the other examples in the article. And demanding that all additions to articles are first discussed on a talk page is just not how the wiki idea works. However, I would be concerned that there are too many examples in that article already − seeing such a density of formulas might give a newcomer the mistaken impression that there is something deep and complex going on here, which is not true. Henning Makholm 04:37, 26 November 2006 (UTC)

One of the guidelines for good writing is to focus on a clear purpose. Reading over this article and the proposed addition, I see one benefit, and a problem or two.

The new section points out that we can complete a square in a second way, which might be good to know. However, the "middle term" will be a constant only when the outer terms are reciprocals. That is, if we are given x²+y², the completion will add 2xy. Frankly, the "at least two" proof is too special-case to be motivating. Any other use steps out into more general algebraic manipulation. If that's where we want to go, then we need another example.

Meanwhile, the article needs a face lift; the formatting could be much nicer with the new "align" ability. --KSmrq^T 04:59, 26 November 2006 (UTC)

User:Michaelbusch is in the wrong here. Reasonable people can disagree about quite how many examples an article such as this should contain. But such disagreements should not be carried out by deletions: the Talk page is for such discussions. Charles Matthews 07:49, 26 November 2006 (UTC)

Lest there be any confusion, my previous remarks were not meant to say Michaelbusch did the right thing. On a more positive note, I took the opportunity to reformat, reword, and reduce the article. Maybe the proposed addition will fit more comfortably now. --KSmrq^T 09:20, 26 November 2006 (UTC)

I apologize for jumping the gun. I've probably been reverting too much vandalism and developed bad habits. Michaelbusch 01:08, 27 November 2006 (UTC)

OK, since the issue's been raised: can anyone contribute some good examples besides the one I used? Michael Hardy 00:47, 27 November 2006 (UTC)

I've put the new section, somewhat revised, back into the article.
Some decent additional examples could help. Michael Hardy 01:35, 29 November 2006 (UTC)

In case anyone cares: I've now added another example to the article: factoring the simple quartic polynomial.

$x^4 + 4.\,$

We get

$(x^4 + 4x^2 + 4) - 4x^2 = (x^2 + 2)^2 - (2x)^2,\,$

and this factors as a difference of two squares to get

$(x^2 - 2x + 2)(x^2 + 2x +2).\,$ Michael Hardy 20:18, 30 November 2006 (UTC)

I care, and I like it. My only suggestion is to use a constant term other than 4, to more clearly separate the contributions of different pieces. With that in mind, I replaced the 4 with 25. I also removed extra blank lines in the multiline equation; to my eye they space the lines too far apart. --KSmrq^T 01:40, 1 December 2006 (UTC)

Geometry portal

Flarn2005 has created a Geometry portal. At the moment is a bit bare bones-ish, so it would be useful if people could contribute to it. Tompw 00:08, 27 November 2006 (UTC)

Scientific citation guidelines

Discussion of the proposed Scientific citation guidelines seems to have simmered down. I suspect the guidelines have consensus among math and physics editors. If you have strong feelings about the guidelines, please comment on the talk page. CMummert 01:50, 1 December 2006 (UTC)

templates at ω-consistent theory and related

Need mediation at these articles (the other party is Gene Nygaard). I think the {{lowercase}} and {{wrongtitle}} templates are frequently misused, but this is one case where they are genuinely important. Using the Latinizations is wrong; the articles clearly should start with the Greek letter ω, but starting them with Ω would be worse, as that could be interpreted as being related to Ω-logic. --Trovatore 01:48, 25 November 2006 (UTC)

What is the exact controversy? Do you yourself prefer {{wrongtitle|ω-consistent theory}} or {{lowercase|ω-consistent theory}}? You believe that Gene Nygaard opposes the use of both of these templates? EdJohnston 02:05, 25 November 2006 (UTC)

Yes, I think he's against both of them. I guess {{wrongtitle}} is more precise for that one. Many of the disputed articles are actually redirects, where I have to admit it's a pretty puny issue, but I still think the templates should be there for tracking purposes. I feel strongly that, while there are decent arguments for automatically uppercasing titles that are in the Latin alphabet, there are no good arguments for automatically uppercasing titles that start with a non-Latin character. When that restriction is lifted, as it should be, we should have a way of finding these redirects and correcting them. --Trovatore 02:09, 25 November 2006 (UTC)

I understand that you want to use {{lowercase}} in redirects. I do see evidence of an edit war on the [Ω-consistent theory] redirect. So I went to Template:lowercase and did 'What links here', but did not see any pages listed with Greek initial letters. So:

Do we know that the Javascript-lowercasing trick works with Greek letters?
Do redirects show up in a 'What links here' request? Unless at least one of these is true, I'm not sure what the benefit is. EdJohnston 05:35, 25 November 2006 (UTC)

Redirects do show up in "what links here". Probably you didn't look far enough down the page. (There used to be a category for articles including this template; that seems to have been deleted, which I thought was a bit unfortunate.)
Redirect titles also show up at the top of the page, showing you from where you've been redirected. That, unfortunately for these articles, is automatically uppercased.
I haven't looked into the javascript thing. Personally I'm not happy with any solution that requires having javascript turned on in the user's browser (turning it off is the more secure practice). I really think we should agitate to remove the automatic uppercasing in the case of titles that start with non-Latin characters; I see no justification for uppercasing Greek letters. --Trovatore 05:49, 25 November 2006 (UTC)

Oh, now I see what you mean. I hadn't realized the javascript thing was automatic. Given that, I think we should move omega-consistent theory to ω-consistent theory and use {{lowercase}} (which does seem to work with Greek letters). It's not as good a solution as removing the auto-uppercasing for non-Latin letters, but it's probably the best available now. Unfortunately ω-consistent theory has too much of an edit history and won't permit a move on top of it, so I guess I'll need some help on that. --Trovatore 06:27, 25 November 2006 (UTC)

I used my magic stick to move the page. -- Jitse Niesen (talk) 08:27, 25 November 2006 (UTC)

Thanks, Jitse. "Your kung foo is the best." But it really is a seriously imperfect solution; I hope you'll support my proposal to remove auto-uppercasing for articles that start with non-Latin (or at least Greek) letters. (See section below.) --Trovatore 08:33, 25 November 2006 (UTC)

Is that magic stick a "three foot black rod with a rusty star on an end"? I used to have one of those, but I dropped it in a twisty passage and could never find it again. --KSmrq^T 09:14, 25 November 2006 (UTC)

It shouldn't have been moved anyway. There is nothing improper about the title as it existed, and it did not need any "wrongtitle" tags. Having them there was just plain flat-out wrong, and moving it so that it can be justified on the basis of the usage of a Greek letter as the initial letter of the article name is even worse nonsense. Gene Nygaard 01:56, 3 December 2006 (UTC)

And it most certainly didn't need the "lowercase" template, which is the one which it had and the one I removed. Gene Nygaard 02:04, 3 December 2006 (UTC)

And, lest anybody is dumb enough to be fooled by the Java-script shenanigans with the display on this articles page, just go follow the links to the one real non-stub category in which this article can be found, and come back and tell us exactly what sort of nonsense you see when you get there. Not only what you see for the article name, but also what letter you find it listed under.

Just where the fuck do you find it, anyway? Off in oblivion, somewhere after the Z.

I'll hold off on fixing the sort key properly until at least a few of you get a chance to see how you are squirreling away this information, hiding it so that is is unfindable.

If you aren't competent enough to deal with those templates and fix the problems they cause, then just stop using them. Gene Nygaard 02:16, 3 December 2006 (UTC)

The move was certainly not intended to justify the template. Rather, the javascript trick made it possible to put the article at the correct title. The title with Latin "omega" was flat-out wrong; you won't find that in the literature, except possibly in some popularization somewhere.

As for the sort key -- frankly, I can't see why the article shouldn't appear after Z. It's no more "unfindable" there than any other article not on the first page of the category listing. Where else ought it to appear, exactly? --Trovatore 02:46, 3 December 2006 (UTC)

It's not just the sort key; it appears in the cat as Ω-consistent theory. (I'm using an IE machine. Septentrionalis 03:10, 3 December 2006 (UTC)

Yeah, I know, and probably in watchlists too and who knows what else. It's not an ideal solution, but IMHO it's way better than "Omega-consistent theory". Brion Vibbers was not at all receptive to the idea of distinguishing between Latin and Greek letters for the purpose of case sensitivity (well, I was trying to give him extra work after all; I'm a programmer myself and know how that goes), but he did say that eventually we'll be able to mark articles as starting with lowercase. Presumably then the categories and so on will respect that. --Trovatore 03:14, 3 December 2006 (UTC)

New MathSciNet template

I just created a new template, {{MathSciNet}}. Hope you all find this helpful! —David Eppstein 06:34, 1 December 2006 (UTC)

Looks awesome. Well done! --King Bee 19:50, 2 December 2006 (UTC)

Good idea! But could you briefly explain the difference between the two kinds of id numbers, the one that's merely an integer, and the one that begins with 96f:....? For the WP reader, is there any advantage of one over the other? Also, I notice you recently updated the Leonidas Alaoglu article's references with the new template, and you explicitly added a JSTOR link to each entry there. Will this continue to be needed? Certainly getting the first page from JSTOR is beneficial for those readers who don't have an institutional subscription to MathSciNet. Also, for post-1995 articles, should we still be trying to find a DOI as well, even when an MR link is present? Reply on my Talk page if this question is too specific for the project Talk. EdJohnston 20:27, 2 December 2006 (UTC)

The 96f:etc numbering is an older style of MR identification, that lets one determine the year and MSC classification from the id. They've switched to a newer system involving meaningless integer ids. Both work equally well in terms of creating a working link to mathscinet, but perhaps the new system should be preferred as it's the way records on the system identify themselves when you view them. One can often get the jstor or doi link from the mr link (even without a subscription to mathscinet) but I think if a direct link is possible it should be included as well so that WP's content is more self-contained. I am only planning to include mr links for papers that have an actual review available at that link; I don't see the point in linking to mr for the ones that say "no review of this item is planned" and then just send you on to the article itself. —David Eppstein 20:33, 2 December 2006 (UTC)

Uppercasing again

The javascript thing is sort of nice, but not sufficient to allow different articles on Ω-logic and ω-logic, which we really ought to be able to have. I've left a note at Wikipedia:Village pump (technical)#Uppercasing of non-Latin letters (including references for the two logics that should be treated, or at least treatable, distinctively). See what you think. --Trovatore 07:32, 25 November 2006 (UTC)

We can't solve all the world's problems, including the foibles of some of the terminology used. Assuming that there are distinguishable concepts there, how do the fools who are silly enough to try to make a distinction of two concepts on the basis of the capitalization of a Greek letter used as a symbol deal with disambiguating them in speech? That might give us a clue as to whether it is a problem even worth our attention, and how to deal with it if it is. Gene Nygaard 11:53, 4 December 2006 (UTC)

Complete lattices (and Boolean algebras) and varieties

This comprises a few questions related to the concept of κ-complete lattices and Boolean algebras (where κ is an arbitrary cardinal number), and universal algebras with infinitary (or proper class) signatures.

Where should statements about κ-complete lattices appear? -complete lattice? A section of complete lattice? A section of lattice (order)? Something else?
In my Ph.D. thesis, I note that κ-complete Boolean algebras can be looked as as a variety (universal algebra) with respect to an infinitary signature. (I know of no other source, but I've never been contacted to say that it was in error. A reference in my thesis does apply universal algebra to infinitary algebras, but I don't know if I kept a copy of the reference.) Where (and if) should this information appear in Wikipedia. (I'll have to go over my thesis to see if I mentioned κ-complete lattices. I think it's in there, although it may only be for κ-complete κ-distributive lattices.)
Also in my thesis, I noted that complete Boolean algebras can be thought of as a variety with the signature being a proper class. (I'm almost certain no one else has dealt with that, but not absolutely certain).
Also in my thesis, I extended the concept of free algebra to those with a proper class of operations, and noting that the free complete Boolean algebra on an infinite set of generators does exist in that sense, but is a proper class.

What to do, what to do? I don't want to violate WP:OR or the extension of WP:AUTO to my work, but my thesis is a WP:RS, I suppose. — Arthur Rubin | (talk) 15:56, 4 December 2006 (UTC)

It's an important principal point. The WP:OR sums up Articles may not contain any unpublished arguments, ideas, data, or theories; or any unpublished analysis or synthesis of published arguments, ideas, data, or theories that serves to advance a position.; and in the fuller explanations states This policy does not prohibit editors with specialist knowledge from adding their knowledge to Wikipedia, but it does prohibit them from drawing on their personal knowledge without citing their sources. If an editor has published the results of his or her research in a reliable publication, then s/he may cite that source while writing in the third person and complying with our NPOV policy. I do not at all this excludes you from citing your own thesis; or any other to write about their own work (if it does fulfil the WP:RS guidelines and is of encyclopedian intetrest). Perhaps, we should be a little extra careful about our own work, because (a) we may risk to exaggerate its general interest, and (b) we may underestimate the troubles for others to follow the exposition of ideas. Apart from that, I find the 'who do you think you are' attitude extremely distasteful, and rather counterproductive. (I noticed you've had an attac of that kind on your talk page; you have my deepest sympathy and support in this matter.) The researchers also often do have experience of explaining their ideas to wider auditoria, and putting them into context. IMO, it would be an extremely stupid waste not to accept contributions of this kind.

Concretely, if you are asking 'Is κ-completeness of sufficient interest for the WP?', my personal answer is yes. However, I'd not like it to be written as parts of articles such as Complete lattice, since as far as I understand a complete lattice is κ-complete for 'each' κ (excuse my usage of 'naïve set theory'), not the other way around; and since I think at least one important result is not extendable from the theory of complete lattices to the κ-complete ones. (Namely, a complete semilattice is a lattice; but does this hold for e.g. $\alef_0$ -complete semilattices?) So, I'd prefer separate articles. I also think giving the basic definitions and a few main properties should be enough; and sensible links and categorisations.--JoergenB 18:41, 4 December 2006 (UTC)

Technical point; it's clear that an ℵ₁-complete semilattice is not necessarily an ℵ₁-complete lattice, even if it is a lattice. But there's still the naming problem to deal with. There is a PlanetMath article at κ-complete, but that's just wrong for a name. (Being ℵ₀ complete is trivial, under those definitions, which I believe are standard.

Possible vandalism in Taylor series

This article contains the text

Third, the (truncated) series can be used to compute function values approximately (often by recasting the polynomial into the Chlemloid's form and evaluating it with the Chlemshaw's algorithm).

I cannot find any Google hits for Chlemloid's form or Chlemshaw's algorithm anywhere but in this article or its mirrors. Could this be sneaky vandalism? -- 80.168.226.41 02:45, 6 December 2006 (UTC)

Zipping back many, many edits finds an older version of this text:

Third, the (truncated) series can be used to compute function values approximately (often by recasting in the polynomial into the Chebyshev form and evaluating it with the Clenshaw algorithm).

I've reverted to this version of that sentence: it looks at least plausible, given the context. -- 80.168.226.41 02:50, 6 December 2006 (UTC)

New "undo" function

From Wikipedia:Wikipedia Signpost/2006-11-27/Technology report:

It is also now possible to undo edits other than the last one, provided that no intermediate changes conflict with the edit to be undone. The interface used is more akin to "manual revert" than rollback: on diff pages, an "undo" link should appear next to the "edit" link on the right-hand revision. When this link is clicked, the software will attempt to undo the change while preserving any changes since then, and will add the result to the edit box to be reviewed or saved. (Andrew Garrett, r17935–r17938, bug 6925)

There is a new button labelled "(undo)" which appears on the right under the edit summary when you look at the diff in a vandal's contributions. This allows you to remove a change without disturbing subsequent changes to the same page. I just found out about it. Have not had an occassion to try it yet. JRSpriggs 10:18, 29 November 2006 (UTC)

By the way, the author of this feature, Andrew Garrett, is perhaps better known as User:Werdna who also created User:Werdnabot. JRSpriggs 12:22, 3 December 2006 (UTC)

Correction, I should have said:

There is a new button labelled "(undo)" which appears on the right on the top line, e.g. "Revision as of 17:15, 5 December 2006 (edit) (undo)", when you look at the diff. This allows you to remove a change without disturbing subsequent changes to the same page.

I have used it now and it is very convenient. Try it out! JRSpriggs 06:36, 7 December 2006 (UTC)

Wikipedia:Release Version 0.7

The next round of nominations for the Wikipedia:Release Version is now open, these are articles which are to go on a CD-release of wikipedia. I've nominated 19 new mathematics articles.

Number - Pythagorean theorem - Eigenvalue, eigenvector and eigenspace - Fermat's Last Theorem - Polar coordinate system - Euclidean geometry - Derivative - Integral - Regular polytope - Cartesian coordinate system - Chaos theory - Circle - Real number - Complex number - Decimal - Infinity - Polynomial - Statistics - Gottfried Leibniz

which are generally our higher importance topics and of at least B+ status. I guess most of these could do with some a bit of love and care. There may be other articles I've missed which others think should also be nominated. --Salix alba (talk) 11:09, 2 December 2006 (UTC)

I'm curious, what work do you think the derivative page needs? It's already a GA. --King Bee 22:33, 4 December 2006 (UTC)

So good that someone just vandalized it to say that the derivative is "defined as the poopie of a cow." Isn't anonymous public editing fun! For as appalling as such vandalism is, I have to tell the truth and say that this particular expression got a chuckle out of that corner of my brain where my junior high self still lives. (BTW, how does one go about reverting a change without messing up other edits that have taken place later? I was hesitant to try it myself since I figure someone out there knows how to do it better than I do. But I'd really like to know if there's some fancy trick for it.) VectorPosse 23:09, 4 December 2006 (UTC)

Never mind. I figured it out. This new "undo" feature is the bomb! VectorPosse 23:23, 4 December 2006 (UTC)

Actually, that is kind of funny that you checked it right after my comment. =) --King Bee 00:18, 5 December 2006 (UTC)

As you asked, compare the German version de:Differentialrechnung which is an FA. History is very brief, the critical points min/max could do with an illustration, only one application, taylors theorem could do with expansion, week on functions which fails to be continuous, no mention of C-infinity fuctions. Newton-Raphson methods missing (as an example of why derivatives are useful). The generisations section is written at too high a level, using a lot of technical terms the lay reader would not understand, a simple example of a function of more than one variable would help. Week on referencing. Differential equations could do with a mention. Generally OK as a how-to for single valued case, but peters out towards the end. Theres some more comments on Talk:Derivative#GA_Review and Wikipedia:Good_articles/Disputes/Archive_7#Derivative. --Salix alba (talk) 20:35, 6 December 2006 (UTC)

Continued fractions

I want to add some new articles about particular varieties of continued fractions to Wikipedia (S-fractions, J-fractions, the continued fraction of Gauss, etc). Unfortunately the definition given in the basic article is so restrictive that the mathematical objects I want to discuss have been defined right out of existence! There are already some 250 links to the existing article, so renaming it is probably out of the question. My plan is to rewrite the existing definition and tweak the rest of the article so it's still logically consistent. Here's the definition I'm working with right now.

In mathematics, a continued fraction is an expression of the form

$x = b_0 + \cfrac{a_1}{b_1 + \cfrac{a_2}{b_2 + \cfrac{a_3}{b_3+\,\cdots}}}$

where the a_i and the b_i are numbers. The a_i are the partial numerators of the continued fraction x. The b_i are the partial denominators, and the ratios a_i / b_i are the partial quotients.

If all the partial numerators are 1 and all the partial denominators (except b₀) are positive integers, the continued fraction is a simple continued fraction, expressed in canonical form. Most of this article is devoted to simple continued fractions – see this related article for a more general discussion.

I'm posting this for comment. Is this definition sufficiently general? I suppose I could define a continued fraction as the composition of a (possibly infinite) sequence of Möbius transformations, but that wouldn't be very accessible, for the general reader.

Oh -- I also have a question. I'm not an expert on TeX. The ellipsis in the formula above is not quite right – it really should be replaced with three dots that descend to the right. Does anybody know the name for one of those?

Your feedback is welcome. I'll check back here regularly, or you can contact me on my talk page. DavidCBryant 16:13, 30 November 2006 (UTC)

Why don't you just add a section on Generalizations? The "absurdly narrow" definition includes all real numbers, which is broad enough to start with. Septentrionalis 17:50, 30 November 2006 (UTC)

Well, I thought of that, but then I looked at generalized continued fraction, where I read:

In mathematics, a generalized continued fraction is a generalization of the concept of continued fraction in which the numerators are allowed to differ from unity. They are useful in the theory of infinite summation of series.

A generalized continued fraction is an expression such as:

$x = \cfrac{b_1}{a_1\pm\cfrac{b_2}{a_2\pm\cfrac{b_3}{a_3+\,\cdots}}}$

where all symbols are integers. [emphasis added]

So I can't even write about "generalized" continued fractions unless I change this definition. Opening up a "generalization of generalized continued fractions" seems like a bad idea for some reason, and if I'm stuck with cleaning up a bad definition, I might as well go whole hog.

Call me cranky if you like, but the existing definition of a cf on Wikipedia does not reflect the way mathematicians use this term. DavidCBryant 18:18, 30 November 2006 (UTC)

It seems to me like the correct thing to do would be to modify the generalized continued fraction article to fit your definition and discuss the various special cases there. The definition given at continued fraction seems to be the most common one and should probably remain the same. -- Fropuff 19:00, 30 November 2006 (UTC)

And why stop at numbers? There are extremely useful continued fractions where the coefficients are functions; most of the useful generalizations are proven by evaluating these. But do please leave the basic definition at the head of continued fractions; the urge to plunge into the greatest possible generality immediately should be resisted for the sake of comprehensibility. Septentrionalis 20:17, 30 November 2006 (UTC)

I proposed stopping at numbers because that's what most people think of when they think of addition and multiplication. I do understand that continued fractions of functions can be formed. And it's certainly possible to define continued fractions with differential operators, and with a whole lot of other objects that are the elements of a field, or even of a division ring. I'm not sure how useful such things would be ... that kind of stuff is not my bag. Anyway, I'm clearly a minority of one at the moment ... I read some other talk pages where others raised similar concerns, but they've apparently been driven away from Wikipedia. One poor guy named q analogue apparently tried to work on this before I did, without much success. Another guy, Hillman, apparently took some abuse from somebody -- I can't tell easily because his user page has been protected.

Arithmonic is apparently still around, but he seems to be keeping a low profile at the moment. I looked at his web site; he has written a book about generalized continued fractions and claims to have found periodic representations of cubic irrationalities. That's a pretty amazing advance, if he's right. LaGrange proved the bit about periodic continued fractions and quadratic irrationals about 200 years ago. So here's a guy who maybe made this huge advance in number theory, and you guys apparently don't even want to talk to him. "Original research", I suppose. (This is part of a message signed by User:DavidCBryant 01:07, 6 December 2006 (UTC) -- the original signature appears below, after some interpolated comments.)

No, sheer fantasy, like most "original research" around here; all periodic continued fractions are quadratic. The proof is in Hardy and Wright; briefly, if x is the value of the whole continued fraction, and r the value of the tail.

$x=\frac{h_nr+h_{n-1}}{k_nr+k_{n-1}}\,$

and by comparing this equation for n and m a period apart, and solving each for r, we get a quadratic equation for x. Septentrionalis 03:10, 6 December 2006 (UTC)

I'm familiar with the proof that an infinite periodic continued fraction in the traditional form (where each element of the cf is just a complex number) converges to a root of some quadratic polynomial if it converges at all. Not every infinite periodic cf is going to converge, though ... it's pretty easy to build [0; z, z, z, z, ...] and see that it's divergent for certain complex z, all of which lie on an open segment of the imaginary axis from −2i to 2i. For instance, just plugging in i for z generates a periodic sequence of convergents with a period of 3, and every third convergent is the point at infinity. You can get similar "orbits" of any length by plugging in other (pure imaginary) values of z. That's not what Arithmonic is talking about on his web site.

Arithmonic has devised a generalized continued fraction (a "fractal fraction") in which each partial numerator and partial denominator is itself a ratio between a finite continued fraction and one of those Engel expansion things. He has a whole lot of "1"s appearing as numerators, and positive integers as denominators. Anyway, his doodad looks sort of like a Christmas tree of integers arranged in a very complicated pattern, so it's only a "continued fraction" in a very general sense. I really don't think the proof mentioned above applies to Arithmonic's Christmas tree, because the recurrence relations he mentions involve the preceding 3 convergents, not just the previous 2. You _can_ get a third-degree polynomial out of a longer recurrence relation like that.

I haven't really figured out how that Christmas-tree-like structure works. But I did see his claim, which is that when you plug a "3" into this thing -- that's it, just a "3" everywhere a denominator occurs -- it converges to the (real) cube root of 2. I can't really say if he's right or not ... the web site doesn't provide enough detail for me to follow exactly what's going on. And I'm not ready to buy his book and try to plow through it right now. But I'm not ready to dismiss his claim as "sheer fantasy". I've looked at his stuff closely enough to understand that there just might be something unusual hidden inside the "fractal fractions" he's talking about. DavidCBryant 17:10, 6 December 2006 (UTC)

Anyway, I know when I'm licked. If you want to read any more about what I really think, try this link. DavidCBryant 01:07, 6 December 2006 (UTC)

What DCB really thinks is that

We should include

$\pi=3 + \cfrac{1}{6 + \cfrac{9}{6 + \cfrac{25}{6 + \cfrac{49}{6 + \cfrac{81}{6 + \cfrac{121}{\ddots\,}}}}}}$

in continued fraction

That we are preventing this by advising him to leave the definition there as that of "simple continued fractions".

He never said this; I'm going to surprise him. I agree that we should include it; I disagree that we need to fiddle with the definition. Septentrionalis 03:19, 6 December 2006 (UTC)

Well, thanks for reading my rant, PMA. That's nice of you. I do appreciate it. But your solution doesn't make a lot of sense to me, because now you've displayed an object in the article that is not one of the objects the article defines at the outset. I think some readers might find it confusing, the way it stands. But hey, what's a little inconsistency here or there? After all, the article about complex analysis says that a function of a complex number is itself a real number. Set of all sets, here we come! (Or was that "Bertrand Russell, here we come!" I forget now.)

Anyway, I'm tired of arguing about the difference between a "continued fraction" and a "simple" or "regular" continued fraction. I'm going to concentrate on some other topics for a while. DavidCBryant 17:10, 6 December 2006 (UTC)

I've just added the continued fraction for π given above to the List of formulae involving π (so I hope it's correct!). Michael Hardy 00:36, 8 December 2006 (UTC)

Thanks, Michael. The formula is already in the article about Pi, in the "Continued Fractions" subheading. So you're not on the hook, if it's wrong. It is correct, though. It doesn't converge very quickly ... it's reminiscent of Wallis' continued product for Pi, in a quaint sort of way. Anyway, just to allay any concerns you may have, the first 12 convergents are 3/1, 19/6, 141/45, 1321/420, 14835/4725, 196011/62370, 2971101/945945, 50952465/16216200, 974212515/310134825, 20570537475/6547290750, 475113942765/151242416325, and 11922290683065/3794809718700. (I know that numerical evidence does not constitute a proof. But at least you can see that this thing is tending in the right direction ... 3, 3.167, 3.133, 3.14524, 3.13968, 3.1427, 3.14088, 3.14207, 3.14125, 3.14184, 3.14141, 3.14174, ...) DavidCBryant 03:55, 8 December 2006 (UTC)

Sylvester's sequence listed as Good Article

Sylvester's sequence has been listed as a Good Article, thanks to a proposal by User:Anton Mravcek and a review by User:Twinxor. I'm a little surprised, given its low density of inline citations and our recent experiences with GA reviews, but pleasantly surprised. —David Eppstein 16:32, 6 December 2006 (UTC)

Happy news. Light and reason have pushed back dark and chaos, at least for a day. Another positive sign is that Wikipedia:Scientific citation guidelines has elevated status.

I'm sure the illustration helps. (People like pretty pictures, even if they don't understand them.) The topic will be unfamiliar to almost all readers; curiously, that can help. (Every day or so our geometry article is vandalized.)

One weakness that catches my eye is the lack of ISBNs. For the second edition of Concrete Mathematics, we should have

ISBN-10: 0-201-55802-5; ISBN-13: 978-0-201-55802-9; Published: 1994-02-28.

(I don't know if the exercise cited has changed from the first edition.) For Computational Recreations in Mathematica, we should have

ISBN-10: 0-201-52989-0; ISBN-13: 978-0-201-52989-0; Published: April 1991.

A reminder: We are but three weeks away from the big ISBN switch. From ISBN.org:

On January 1, 2007, the book industry will begin using 13 digit ISBNs to identify all books in supply chain.

However, any ISBN is better than none. (The online converter is handy for hyphenation, validation, and conversion.) A quick way to find a number if the book is not in front of you is to do a web search with the title in double quotation marks and 'ISBN'. Example: '"Concrete Mathematics" ISBN' (without the single quotation marks). Usually the top hits are Amazon and AbeBooks; often the ISBN is visible in the list of search results without clicking further.

We could also use ISSN ids. These are harder to find, but an AMS site can help with this, and with expanding abbreviated journal names. Thus we find

Acta Arith. is Acta Arithmetica; Polish Acad. Sci., Warsaw; ISSN 0065-1036.
Amer. J. Math. is American Journal of Mathematics; Johns Hopkins Univ. Press, Baltimore, MD; ISSN 0002-9327.
Enseign. Math. is Enseignement des Mathématiques (The Teaching of Mathematics); Masson, Paris; ISSN 1269-7842.
Enseign. Math. (2) is L'Enseignement Mathématique. Revue Internationale. IIe Série.; Enseignement Math., Geneva; ISSN 0013-8584.

I'm guessing that the second series is intended for the Erdős and Graham article.

Quibbles aside, it's nice to see a small technical article appreciated. --KSmrq^T 08:09, 7 December 2006 (UTC)

Good to see the guidelines have a greater status. I've now started a thread on Wikipedia talk:What is a good article? discussing the issue. At least some of the GA people are quite supportive of changing the criteia as soons as the agidelines have been accepted.

Nice to see Sylvester's sequence get through. The one point I'd make is that the caption could be expanded. I'd probably turn it round by 90 degrees and add a labels for 0 and 1, so its more obvious that the things are summing to 1. --Salix alba (talk) 14:02, 7 December 2006 (UTC)

Thanks for the quibbles; I added the ISBN-10's and a longer caption. To my mind ISSN's do not belong on individual article references but rather the reference should wikilink the journal name (as the ones in this article already do) and the ISSN should go into the article about the journal. If I had a DOI link I'd include that, though. —David Eppstein 16:19, 7 December 2006 (UTC)

Slashdot of previously deleted transreal number

FYI, slashdot.org has evoked transreal number which is a recreate of a previously deleted article. I think its an prime example of mathematical illiteracy. Oh well. Afd, fix or delete. linas 19:46, 7 December 2006 (UTC)

For the morbidly curious, the Slashdot article is here. Perspex machine has been AFDed, too; I prodded James Anderson (mathematician). Lunch 23:30, 7 December 2006 (UTC)

Template:Calculus footer

A new {{Calculus footer}} has been created. A discussion about it is going on at Talk:Calculus#Re: Addition of Template:Calculus footer. Oleg Alexandrov (talk) 17:30, 9 December 2006 (UTC)

A new article about continued fractions

Hi, all!

I just put a new article out in the big namespace. Please take a look at it and tell me what you think -- either here, or on my user talk page.

Thanks! DavidCBryant 02:10, 12 December 2006 (UTC)

Or the article talk page. Septentrionalis PMAnderson 04:03, 13 December 2006 (UTC)

Simple Introduction

Some science articles are starting to produce introductory versions of themselves to make them more accessible to the average encyclopedia reader. You can see what has been done so far at special relativity, general relativity and evolution, all of which now have special introduction articles. These are intermediate between the very simple articles on Simple Wikipedia and the regular encyclopedia articles. They serve a valuable function in producing something that is useful for getting someone up to speed so that they can then tackle the real article. Those who want even simpler explanations can drop down to Simple Wikipedia. What do you think?--Filll 22:55, 12 December 2006 (UTC)

I am completely sympathetic with the need to have good pedagogical material. At the same time these articles seem out of place in what is supposed to be an encyclopedia. An encyclopedia should be a reference work that provides a succinct overview of a given topic, not a textbook from which to learn. It also seems detrimental to divide the effort of editors amongst multiple articles on the same topic. In my view it would be more appropriate to move the introductions you mention and others like them to Wikibooks. We can and should provide links to that material from Wikipedia. -- Fropuff 04:17, 13 December 2006 (UTC)

I find the introductory versions for the physics articles refreshing and worthwhile. I can agree with many of the points made by Fropuff, especially about dividing up editors' efforts, but I do believe there is a place in an encyclopedia for such material. I have expressed the opinion here in this forum before--and perhaps I am in a minority here--that we ought to be flexible about what is "allowed" or "disallowed" instead of being too dogmatic about what is "encyclopedic". In other words, I believe good pedagogy can be a guiding principle and not a secondary consideration. VectorPosse 05:19, 13 December 2006 (UTC)

I can appreciate the need not to divide the efforts of a few editors. However, I have a few comments:

this is not a zero sum game. There are more editors joining all the time. There are roughly 30,000 editors now on Wikipedia and more will come if things continue
providing accessible materials will actually enable more editors to contribute in areas in which they are not specialists but can come up to speed, increasing the number of available editors
Encyclopediae are only useful if they can be used with a minimum of hassle. If I look in some subject I am not an expert in and it is too much trouble to even read the introduction/lead of the article, I will probably give up and look someplace else
Encyclopedia Britannica provides something of a gold standard in encyclopedias. Encyclopedia Britannica has multiple articles on many subjects at different levels of sophistication:
- "Britannica Discovery Library" for preschool children
- "My First Britannica" encyclopedia for 6 to 12 year olds
- the single volume Britannica Concise Encyclopædia
- macropedia
- micropedia
- ready reference volumes

and this does not include the propedia. So Britannica might have 6 or more articles at different levels aimed at different audiences. I am not suggesting that Wikipedia attempt to equal their efforts, but 2 or 3 does not seem excessive when the most famous competitor has recognized the need for 6 or more. And the criteria they have is utility, because if it is not useful, they cannot sell encyclopediae.

I have no objection to Wikibooks, but that seems like the wrong format for shorter articles that are somewhat focused.
The lead parts of many articles on Wikipedia are completely unhelpful to nonspecialists. In real print encyclopediae, I do not find this to be the case. They pay more attention to accessibility, and we should too. An introductory article is just an extended lead article, or primer that can be used as an aid to reading the regular article.
Succinct and terse is a great goal, but it is not one I have noticed being met here on Wikipedia often enough. That still does not preclude the requirement of the material being accessible.--Filll 05:47, 13 December 2006 (UTC)

I don't know if I agree that simple intro articles are out of place. But I do think the concern of dividing up effort is a very valid one. I would agree that editing is not a "zero sum game", but I think that's the wrong thing to bring up. I think what Fropuff was referring to is the dividing up of expertise. Sure there are editors joining everyday, and if somebody puts in less effort, people will join who will pick up the slack. Unfortunately, that doesn't really address expertise. When one person, expert on a particular topic, stops editing, progress in that area may stop for a very long time (and errors start creeping in). It's not like there's a uniform distribution of experts joining, let alone a uniform distribution of expertise in the different areas.

I find it doubtful that even doing an incredible job would significantly increase the expertise level of editors. To really gain significant expertise takes considerable effort and dedication. People with that desire will want to study the material out of books. What Wikipedia offers is a useful synthesis of materials. I don't think a scenario where someone learns exclusively off Wikipedia is viable, even assuming a radical improvement.

One thing I want to point out about Brittanica and paper encyclopedias is that they really do a careful job of selection. By doing so, they can focus on fewer articles and ones in which it is much simpler to write well. Wikipedia does not have this advantage. Its strength is in large coverage. So it's really unfair and unrealistic to compare.

Since I got on this soapbox, I do want to say one thing about accessibility however. A common refrain is "Only a specialist can understand it and why would he or she need to read this?" This is wrong. The mistaken assumption is that because the reader did not understand it, the article is esoteric and cannot be understood by anyone other than an "expert". This leads to the tagging of numerous mathematical articles as being too technical. Of course, in reality, there are many people and many levels of expertise and many levels of mathematical maturity. A person adept in one technical subject can often learn something in another because of a high degree of maturity and understanding of how to cull the main ideas out.

Being too technical is an issue that we should be concerned about, but probably if there was less of what I just described, math editors would probably take these concerns more seriously. We try nonetheless.

Having said that, this concern has been raised before, again and again. There's been more of a focus on improving what we have, rather than extending it. People, with the desire, have improved articles such as mathematics and manifold. It took a great deal of effort and time. Right now I've been working on a rewrite of knot theory. It's taking a lot of time, and I certainly can't put in that much time regularly. There are also a few things I promised, but never got done. So the spirit is willing, but the flesh, as usual, is often weak. --C S (Talk) 18:57, 13 December 2006 (UTC)

Chan-Ho raises some good points about how best to split our time, the sheare quantity of mathematical articles can be intimidating. levels of expertise can also be intermidating, when an undergraduate user joins the project, he is greated with a big list of very experiences mathematicians, which may give the feeling of "what can I contribute". The answer is plenty, we have a lot of articles which don't require PhD's to edit, indeed these are often our most visited articles.

Its just occured to me that it might be worthwhile to set up a /High school mathematics work group and /Degree level mathematics workgroup where those with those levels of qualifications could congrigate. The workgroups could have their own list of articles to work on and possible participants lists. It might help in setting up some sub communities where people feel more able to contribute.

Also Wikipedia:WikiProject Mathematics/Participants could do with a prune. Many of the people who are listed there are no longer active. I had a start at this at User:Salix alba/Sandbox2, moving those who had not contributed in the last three months to a hall of fame section.

We do have a good recruiting oportunity at the moment, the Wikipedia:Articles for deletion/Transreal number‎ and related debates have seen a lot of new people, maybe some of these could be encouraged to work on some of the mathematics article. --Salix alba (talk) 20:02, 13 December 2006 (UTC)

Things like knot theory and category theory are not places for amateurs. I would agree completely with that. However, if you do have a lot of editors with lower skill levels, I hope you can employ them in constructive ways.

Another value of having things as accessible as possible is that many scientists actually visit Wikipedia as one of their starting places when doing research on an unfamiliar topic. And many people interested in applications regularly try to mine mathematics for ideas and machinery to use in applied disciplines. These people might have an impressive level of sophistication in some other area, but need a helping hand or even a guide to the literature to help them get started. This is a function that Wikipedia can fill. --Filll 20:25, 13 December 2006 (UTC)

I've now created a Hall of Fame section in /Participants for users how have not editted in the last three months. There were some who had not edited since 2004. A reasuring number on the participants list are still active editors which is encouraging. --Salix alba (talk) 23:32, 13 December 2006 (UTC)

Actually, I think knot theory is a good field for amateurs. That's why I picked knot theory to improve, since I expect it's an article that can be widely read and digested. Mentioning it in the same breath as category theory is kind of misleading, although of course, some very advanced aspects of knot theory are very abstract and even category theoretical. There have been several editors with an "amateur" interest in knot theory that have made big contributions to the knot theory portion of Wikipedia. But some left, one passed away, and it's difficult to replace dedicated editors in general.

The goal of accessibility is a good one, and I hope some of Richard's proposed mechanisms will help that along. More direction would be beneficial, I think. ---C S (Talk) 04:52, 14 December 2006 (UTC)

Area of a disk

The article area of a disk could use some work. It may be the only Wikipedia article justifying the familiar πr² expression, so it wouldn't hurt to bring it up to civilized standards. Michael Hardy 01:09, 13 December 2006 (UTC)

I've reproduced the proof by Archimedes on the talk page. (But without the obvious figures.) The article page scares me! Maybe later. --KSmrq^T 00:22, 14 December 2006 (UTC)

Proofs of trigonometric identities

Proofs of trigonometric identities is, in its present form, a horrible mess. Please help clean it up. Michael Hardy 19:12, 13 December 2006 (UTC)

I slapped it into Category:Article proofs, which, by definition, only allows messy, horrible articles. :-) linas 02:55, 14 December 2006 (UTC)

"Big" articles

I'm encountering some concern about the size of the article Areas of mathematics. I saw a reference to a 64K (= 65,536 byte) limit in somebody's message (Oleg's?) recently.

Anyway, I want to learn more about that. Does anyone know where to look it up? Does the limit apply to the wiki markup file that an author/editor can access? Or does it apply to the XML file (sans images) that the server serves up? I'm certain the 64K limit doesn't count graphics ... I tried to load the Mandelbrot set article the other day, and my poor little box choked on it somewhere between 1.0 and 2.0 Mbytes. :(

Thanks for the help! DavidCBryant 20:53, 13 December 2006 (UTC)

Wikipedia:Article size is the relavant guideline. AoM is less than 64K, so I think its probably OK. As this is a list type article much of the guideline is not really relavant, and the problems with older browsers has mostly disapeared. Mandelbrot is one if the most image rich pages about, but I am suprised that your prowser chocked. You must have quite an old machine. --Salix alba (talk) 22:18, 13 December 2006 (UTC)

AMD K6, 300 MHz. Dial-up connection. I paid $50 for it, OS and all. I'm a Neanderthal. ;^> Thanks for the reference! DavidCBryant 11:45, 14 December 2006 (UTC)

I agree that AoM is not a place to enforce teh article size rule, unless it gets truley huge, and its very nature should make that avoidable. (I have a Cerelon 333, an even worse processor. However, even with broadband, info arrives at the computer slow enough for my ancient computer to deal with it... internet connections are far slower than internal data transfer - even the original IDE standard from 1994 ran at 3.3MB/sec = 26.4Mb/sec, over three times faster than the most turbo-charged broadband around in the UK today) Tompw (talk) 13:30, 14 December 2006 (UTC)

Problems at exponentiation and empty product

Yes, it's the infamous 0⁰ debate again, and from many aspects I regret that I stepped in it, because it's really kind of a silly argument that doesn't matter much. However it does matter, at least a little, that the two mentioned articles asserted a consensus that does not exist.

(Precis of my position, which is not really the point, but just so you know where I'm coming from: The arguments for 0⁰=1 make perfect sense for exponentiation as defined on the naturals, or even when the base is ineterpreted as a real and the exponent as a natural, because then we are indeed discussing an empty product. However they cease to convince in the context of real-number-to-real-number exponentiation. The natural number 0 and the real number 0.0 are distinct kinds of thing, and there is no reason 0.0^0.0 must be defined, merely because 0⁰ is.)

Anyway as I say my position is beside the point. The point is that there are editors (well, one in particular, a difficult fellow whom some of you have encountered in the past) who want to preserve the articles in a state where they assert a consensus that does not in fact exist among mathematicians. I think you'll all agree that's wrong, whatever your views on the underlying "issue", if we can dignify it with that name. Please come and work on a broader-based approach. --Trovatore 17:06, 15 December 2006 (UTC)

Isn't 0⁰ an indeterminate form; i.e., I can make it equal to whatever I like if it shows up in a limit? How does it make sense to define 0⁰ = 1? --King Bee 17:20, 15 December 2006 (UTC)

Please, let's take discussion on the merits somewhere else -- this talk page would quickly become unusable. (See talk:empty product, for example -- my fault, I concede, but let's not repeat the problem here.) --Trovatore 17:25, 15 December 2006 (UTC)

Agreed. --King Bee 17:32, 15 December 2006 (UTC)

I left a comment to Bo Jacoby on the talk page of empty product. I encourage others to come and make a comment. --C S (Talk) 11:39, 16 December 2006

For reference, some of the previous problems with this editor (Bo Jacoby) are recorded at Wikipedia talk:WikiProject Mathematics/Archive16#Problem editor. Editors dealing with him should be aware that he has a history of wanting to use Wikipedia to promote his own (invented) notations and preferred conventions, and no amount of editors or argument has been able to convince him otherwise. —Steven G. Johnson 17:28, 18 December 2006 (UTC)

Bullying

Judging by this and other past "wars" with Bo Jacoby, it seems that he is really nothing more than a big bully. (And I don't feel like I'm resorting to an ad hominem attack when I say so. The evidence speaks for itself.) I worry about editors leaving the project over such things. I know I, for one, refuse to play into his specious and tangential arguments, since he seems to thrive on getting impassioned responses to his silliness. But if we all ignore him and choose to leave the debate, it seems he gets his way. Is there no recourse for dealing with bullying like this? VectorPosse 20:31, 16 December 2006 (UTC)

So far, it appears that nothing has happened except for a vigorous discussion on two talk pages. All that needs to happen to correct the articles is for someone to rewrite the appropriate parts with a neutral viewpoint, using pedantic references that leave no stone unturned. Many editors will recognize quality writing and complain if it is reverted. CMummert 22:13, 16 December 2006 (UTC)

Fair enough, although I was refering to repeated problems in the past by Bo Jacoby, not just this particular discussion. I'd have to do a little research to find all the past problems--I'm relying a little on memory here. But my question is more general anyway. I have read of people leaving the project over this kind of thing before; editors willing to shout louder and longer than anyone else can be quite discouraging. At what point does this vigorous discussion become inappropriate and problematic? It may not have crossed that line in this case, but if there's a history of such aggression.... Anyway, your point about watching for POV reverts and then complaining is well-taken. VectorPosse 01:06, 17 December 2006 (UTC)

If you feel impelled to it - and I can't say his manners appeal to me -, it will be more useful at WP:RfC, the section on user conduct, not here. Do tell us so we can all chime in on the mathematical points though. Septentrionalis PMAnderson 01:14, 17 December 2006 (UTC)

Bo Jacoby has already been reported here as a problem editor. In past episodes one recurring passion was "improving" notation. Just revert as much as you need after leaving one brief comment on the talk page. If you have 3RR concerns, feel free to ask here for other editors to join in. I'd recommend against extended talk page engagements with Bo; he seems to feed on that.

The American Heritage Dictionary of the English Language defines ad hominem as

"Appealing to personal considerations rather than to logic or reason",

and includes in its usage note the observation that

"[T]he homo of ad hominem was originally the person to whom an argument was addressed, not its subject. The phrase denoted an argument designed to appeal to the listener's emotions rather than to reason. … The phrase now chiefly describes an argument based on the failings of an adversary rather than on the merits of the case"

It is perfectly acceptable to object to how someone behaves at Wikipedia, and it is also acceptable to question the content of edits. We do want to be careful about confusing the two, as in "Johnny doesn't play nicely with others, so what he just said is wrong." By contrast, it's OK to say, "Johnny doesn't play nicely so I don't want to play with him", or "Most of Johnny's edits contain nonsense and this one looks like more of the same."

Within Wikipedia, as in the real world, the real challenge with problem people is to decide how we will respond. Suppose, for example, Melchoir does something unhelpful and annoying, again. (Substitute the "problem person" of your choice — me, if you like!) Can we rewire his brain? Can we correct his sense of humor? Can we bring him to his senses? No, no, and probably not. The only person we might control is ourselves, and even that is uncertain. I cannot offer a sure recipe; I can offer quotations:

Never attempt to teach a pig to sing; it wastes your time and annoys the pig. — Robert A. Heinlein
One ought never to turn one's back on a threatened danger and try to run away from it. If you do that, you will double the danger. But if you meet it promptly and without flinching, you will reduce the danger by half. — Winston Churchill
I learned long ago never to wrestle with a pig. You get dirty, and besides, the pig likes it. — George Bernard Shaw
I like pigs. Dogs look up to us. Cats look down on us. Pigs treat us as equals. — Winston Churchill
Don't be too hard on me. Everyone has to sacrifice at the altar of stupidity from time to time, to please the Deity and the human race. — Albert Einstein
It is a dear and lovely disposition, and a most valuable one, that can brush away indignities and discourtesies and seek and find the pleasanter features of an experience. … It is a feature that was left out of me at birth. And, at seventy, I have not yet acquired it. — Mark Twain
Always look on the bright side of life. — Eric Idle

Draw your own conclusions! :-D --KSmrq^T 04:06, 17 December 2006 (UTC)

When I saw this subsection start up, I knew it was only a matter of time. I simply don't deserve this. Please show some decency. Melchoir 05:04, 17 December 2006 (UTC)

Don't be so hard on yourself; you do deserve a good laugh. I don't know how many banana peels must be sacrificed, but it will be worth it. Try reading the Eric Idle quotation in full; it's bound to cheer you up! --KSmrq^T 06:12, 17 December 2006 (UTC)

Okay, ha ha ha! What a card that KSmrq is; when he calls me unhelpful and annoying I know it's all in good fun and he doesn't mean it. He wouldn't embark on a campaign to tarnish my name on every forum available to him if he thought he might actually influence anyone's opinion. And since it's implicitly understood that he respects me as a human being, there's certainly no need for him to act like it. It's all a joke! Whee, I pass the test! Everybody in a three-parsec radius gets a cookie! Melchoir 06:59, 17 December 2006 (UTC)

Thanks Melchoir. Paul August ☎ 18:43, 17 December 2006 (UTC)

I'm here all week — try the veal. Melchoir 19:02, 17 December 2006 (UTC)

It's distressing that somehow this section on "bullying" actually contains some. --C S (Talk) 10:32, 17 December 2006 (UTC)

I'm curious how many cookies you passed out, Melchoir. Surely not as many as $\aleph_0$ , but probably quite a few. How fast were they moving when you let fly (to cover a 3-parsec radius, I mean)? Is your arm sore? And why didn't I get one? ;^> DavidCBryant 12:17, 17 December 2006 (UTC)

I'm missing all the jokes here, but in any case if Melchoir is on non-standard time, and cranks out one cookie at every 1/N second, he/she can crank out N cookies p/second. For N non-standard, the standard cardinality of the hyperinteger interval 1..., N is $2^{\aleph_0}$ . —The preceding ~~unsigned comment was added by CSTAR (talk • contribs) 17:38, 18 December 2006 (UTC).~~

Oops forgot to sign--CSTAR 17:42, 18 December 2006 (UTC)

At that rate, Melchoir's not only going to have a sore arm; he'll be falling-down dizzy in nothing flat, to boot. And what a windmill! Katrina was just a baby zephyr. This wind will blow the atmosphere right off the planet, along with most of the houses! ;^> DavidCBryant 19:44, 18 December 2006 (UTC)

How is it that the disputes in Mathematics are so much more civilized than those in the rest of Wikipedia? I am somewhat stunned to realize how much cooler and calmer things are after reading a bit. Especially when I think about some of the Mathematicians I know in real life...--Filll 14:08, 17 December 2006 (UTC)

Sorry, I only cranked out a couple dozen before running out of butter. (Really!) Who knew there'd be such a rush? Melchoir 17:29, 17 December 2006 (UTC)

Why "disputes in Mathematics are so much more civilized"? Because there is no reason to care at all about mathematics unless you care about getting things right (as opposed to getting your own way, say). This shared dedication to the standard of truth and esthetic beauty keeps us from fighting each other too seriously. JRSpriggs 07:15, 18 December 2006 (UTC)

Manifold Destiny

A well-meaning, new editor has been making some additions to this article. I don't believe these follow NPOV, but I no longer have the energy to talk to this person. I tried explaining NPOV doesn't mean putting out one argument followed by counterargument, but somehow this person doesn't seem to understand and takes everything as an accusation of some type. His/her grasp of the facts and circumstances also seems tenuous. --C S (Talk) 23:57, 18 December 2006 (UTC)

Need advice

I need an advice on how to group entries in List of operators. Any thoughts?--Planemo 13:26, 10 December 2006 (UTC)

This is a little out of my area, but I feel that you need more explanation of these transformations. What do the variables mean? What is the transformation used for? It is good that you have pointers to articles for some of them, but every one of them should have a pointer (even if it is a red-link). You described them as "This list includes the most widespread transformations of analytical functions of one argument.". In what sense are they "analytical"? If you mean that they are defined on the complex plane and have complex derivatives everywhere, then you should put them in a category that deals with complex numbers. JRSpriggs 04:56, 11 December 2006 (UTC)

I added some boilerplate and various links that perhaps addresses JRSpriggs' comments. A merge with list of transforms might be contemplated. There are some generic transforms that don't easily fit in this list. linas 06:44, 11 December 2006 (UTC)

I would strongly recommend the merge. List of operators is where I would look for unary and binary operators (+,- *,/, absolute value). Septentrionalis PMAnderson 16:00, 11 December 2006 (UTC)

They are functions, not operators and already covered in "left composition" entry ( $f\circ y \,$ )--Planemo 17:32, 11 December 2006 (UTC)

And these are functionals; so? Septentrionalis PMAnderson 18:48, 11 December 2006 (UTC)

No they all are particular cases of left composition operator.--Planemo 18:52, 11 December 2006 (UTC)

The question is how to group the entries better: by properties (i.e. linearity) or by branch of mathematics where they are used? But where to place such operators as composition or derivative then? Should the functionals be separated or not? Or to create a special section for binary operations such as composition, convolution and inner product? Or maybe group by type of coordinates/parametrization?--Planemo 11:39, 11 December 2006 (UTC)

IMHO, having such a "list" is not that good an idea. the term "operator" is used in a hell of a lotta places in mathematics, making a comprehensive listing difficult and somewhat pointless. and having an incomplete list, as that article is right now, is misleading, unless one is very specific about the context and what is meant by an "operator". right now it looks rather like an ungainly collection. for instance, an operator theorist would find few items on that list to be of interest; in any case, they are well-covered elsewhere. i am sure such examples abound from other fields, say the boundary operator from homology. also, some entries in the list seem rather funny, e.g. taking the inverse of a function is listed, so is the arc-length of a curve and the L^2 norm. sure one can use whatever terminology one wants, but calling every trivial thing an "operator" doesn't help the credibility or the utility of the "list". Mct mht 18:25, 11 December 2006 (UTC)

I agree the term is too broad, but the list is dedicated to the certain meaning. And what's wrong with arc-length or inverse function? Maybe that they are not liner while most "specialists in operators" work with linear ones?--Planemo 18:47, 11 December 2006 (UTC)

What's wrong with the non-linear operators is that there are just about zero operator-theoretic results, theorems or facts about them. Taking some random thing and calling it "an operator" seems pointless to me, as it does not suddenly offer new insight, nor does it allow some general theorem to be applied to obtain new results. By contrast, the linear opers have a rich theory and many general theorems that can be applied. Thus, I'd recommend discarding the entire non-linear section. But perhaps this discussion should be taken to the article talk page. linas 03:24, 14 December 2006 (UTC)

in light of the fact that the article has undergone further edits. i would like to state again that, if one insists on having such a list, one must be very specific about what's meant by an operator, in what particular context(s). right now it's a rather incoherent collection, including the see also links. a case might be made that an article listing all common integral transforms has a place in WP. but calling, say, the L² norm an "operator" is not a good idea. i doubt there's single piece of literature that uses that terminology. there are quite a few such misleading examples in that list right now. Mct mht 12:23, 20 December 2006 (UTC)

Representing probability

I need to represent the following probability mathematically using the correct wikicode/syntax.

A person is presented with 7 questions and 7 answers. What are the odds of them correctly pairing off 4 of them?

perfectblue 09:15, 19 December 2006 (UTC)

I'm not sure I understand your request. You've already stated the problem without needing any special syntax. The answer will, of course, be a number, also not requiring anything special. Are you saying that you need to know how to type up the solution to the problem using proper mathematical notation? Are you intending to put this in some article? In that case, maybe you could post what you have in the article and then someone could help you format it properly. Otherwise, this forum isn't really in the business of solving math problems, especially since we have no way of knowing if this is a question on a take-home exam or something like that. (Not to suggest that you're cheating on an exam or anything; I'm just pointing out a reason why it might not be a good idea for people in this forum to solve other people's math problems without knowing what they're for.) VectorPosse 09:31, 19 December 2006 (UTC)

The problem needs a bit more in order to be stated unambiguously. To define the probability of the outcome, we need to know more about the process by which the outcome is produced. If you ask a bunch of mathematicians seven questions like 24+13 = ?, 11+58 = ?, ..., and you give them the seven answers, like 37, 69, ..., but in some different order, then almost all will get all seven correctly paired off. At the other extreme is when people would not have a clue, like you give them seven phone numbers picked at random from the white pages of the Manhattan telephone directory, and the names of the subscribers, and you ask them to pair them off. To avoid a possible accidental bias, you randomize each time the order in which these items are presented to the subjects. Then the pairings will, on the average, have 1 correct pair and 6 incorrect pairs. So let us assume that the process is that the pairing is picked at random out of the 7! = 5040 possible pairings, each with equal probability of 1/5040. Letting p_c stand for the probability of having exactly c correct pairs, we have then: p₀ = 1854/5040; p₁ = 1855/5040; p₂ = 924/5040; p₃ = 315/5040; p₄ = 70/5040; p₅ = 21/5040; p₆ = 0/5040 = 0; p₇ = 1/5040. So the probability of having exactly 4 correct pairs is 70/5040, which is about 1.39%. The probability of having at least 4 correct pairs is p₄ + p₅ + p₆ + p₇ = (70+21+0+1)/5040 = 92/5040, which is about 1.83%. --Lambiam ^Talk 12:13, 19 December 2006 (UTC)

It's for a wiki entry the I'm drafting about the paranormal (User:Perfectblue97/Natasha Demkina), and I don't know how to write it up properly as I am neither a mathematician, nor a regular user of wikisyntax.

A woman is given 7 cards each bearing 1 person's medical record, and is sat before 7 people (1 card per person). She is asked to use her paranormal powers to match each card to the correct person. She does this correctly 4 times. The odds of her doing this (4 matches out of 7) by pure chance are about 1 in 50 (2%).

I would like to know how to write this up in the form of a mathematical formula using wiki syntax (so that it comes up like an image, rather than as written text).

perfectblue 12:18, 19 December 2006 (UTC)

There is no truly standardized way of doing this. After having explained that C denotes the random variable that gives the number of correct pairings for a pairing drawn from a uniform distribution (discrete) on all 7! possible pairings, you could write:

$\Pr(C \geq 4) = \frac{23}{1260}.$

However, this does not add any weight or credibility beyond the statement in plain English that the probability of getting at least 4 correct pairings by pure chance is 23/1260, which is less than 2%, and you introduce the risk that readers who understand the formulation in natural language might not understand the mathematical formula. --Lambiam ^Talk 14:57, 19 December 2006 (UTC)

<math>\Pr(C \geq 4) = \frac{23}{1260}?</math>

I don't know why, but I thought that there was a way of doing this where you fed in the data and the equation, and it calculated it on the server and presented it to the user.

perfectblue 15:20, 19 December 2006 (UTC)

That would be cool: a computer algebra system integrated with Wikipedia. In this case I don't know a formula, and rather than deriving one it was easier to (let a simple program) enumerate all 5040 possibilities. --Lambiam ^Talk 17:22, 19 December 2006 (UTC)

You should not consider a random process for comparaison but rather the results obtained in average by people choosen at random. As soon as one can see the people and have (even a short) look at the records, the pairing is far from being random. pom 15:32, 19 December 2006 (UTC)

Do you mean Cold reading? That was something that was determined best dealt with by setting a margin for success on the outcome based on Bayesian inference (or so I'm told). In this case, the margin was determined to be 5 out of 7. Significantly higher than could reasonably be expected through either random chance or educated guessing. Needless to say that some people have accused the margin of being set too high.

perfectblue 15:47, 19 December 2006 (UTC)

It really depends on what the hypothesis is you are testing. If the hypothesis is that the subject did better than purely random, and we had picked a moderately strict value of 2% for the size of the test, then we should conclude that the null hypothesis ("not better than random") is to be rejected. If, however, the hypothesis is that the subject does better than a control group of comparable (same age group, same background) but otherwise randomly selected people, then the necessary data for hypothesis testing is simply not there. (It might still be possible to acquire such data if the test conditions can be recreated.) In this specific case, it would actually have been more relevant to take a control group of general practitioners, and I don't understand why that was not done – it would have been easy enough to organise. If the aim was to potentially support an extraordinary claim, then I must say that 7 for the length of the run is rather low. --Lambiam ^Talk 17:22, 19 December 2006 (UTC)

Unfortunately, we're not talking about a fully fledged experiment carried out by serious scientists. All they did was to get two statisticians to decide that 5 out of 7 was a good score based on Bayesian inference, and then they ran the experiment with that. There was no null hypothesis (the only criteria were that 5,6 or 7 were good and any lower number might as well be 0 because they determined that 4 or less represented chance or cold reading), no control group, and no attempt to take the experiment any further. It wasn't exactly good science, but then it was conducted fro a TV documentary by SCICOP.

perfectblue 18:43, 19 December 2006 (UTC)

Without knowing the experiment, your characterization surprises me. The former CSICOP (correct spelling), now CSI, used (according to your writeup) the likes of Persi Diaconis — who surely understands statistics, and Ray Hyman — who is thoroughly familiar with proper experiments and controls involving human subjects. Unless the organization and these two minds have rapidly deteriorated in recent years, I would expect them to get their statistics right for a documentary they produced. --KSmrq^T 18:31, 20 December 2006 (UTC)

If all 5040 permutations of the seven answers are equally probable, then the answer is given in the article titled rencontres numbers as 70/5040 = 1/72. Michael Hardy 20:38, 19 December 2006 (UTC)

Michael Hardy's answer is correct for a purely random choice of a permutation of 7. But this is far from random. Medical records contain an enormous amount of identifying information which the woman could use (asside from the name), such as: age, sex, race, weight, height, medical conditions which have obvious effects on a person's appearance, etc.. Perhaps we should be amazed that she only got four of them right instead of all seven. And 1/72 = 0.0138888... . JRSpriggs 07:10, 20 December 2006 (UTC)

P.S. Also one should probably calculate the probability of getting at least four correct, rather than exactly four. Or perhaps another value. But I do not know enough about statistics to know for sure which is the correct probability to use. JRSpriggs 07:15, 20 December 2006 (UTC)

The relevant criterion should be of the form at least C correct, for some predetermined value C. --Lambiam ^Talk 12:15, 20 December 2006 (UTC)

The 1/72 for exactly four and the value for at least four were already given above by Lambiam. Actually, it seems that in this experiment she did not have medical records, but had to identify each of 7 medical conditions (including "none", the "control") with the correct person. This is less information than a medical record, but still not random. I don't know anything about how the 5/7 threshold was determined, but saying that statisticians had decided that and used it hardly shows that it wasn't carried out by serious scientists. The only question is whether there is an argument for saying that 4 or less could be chance/cold reading, and so a "failure". Since the aim was to determine whether or not further study was worthwhile, it is hardly surprising that a "failure" resulted in no attempts to take it further. JPD (talk) 11:05, 20 December 2006 (UTC)

To Lambiam: I am sorry that I did not notice that you had got the answer first. If you are correct about using a predetermined value, then presumably that would be the five correct that the "experts" called for. Then the probability would be, using your figures, (21+0+1)/5040 = 22/5040. However, then she failed the test, so I do not know how relevant that probability is in the case of failure. JRSpriggs 12:25, 20 December 2006 (UTC)

I haven't studied the rationale for picking the number 5. In general the criterion should depend on the hypothesis tested, which I don't know for this case. But it is indeed a matter of statistical hygiene to determine in advance the criterion for what shall and what shall not be deemed significant. Otherwise the temptation to pick the criterion afterwards that best supports your favourite hypothesis may prove irresistable. If you are to guess my telephone number and you tell me you can probably get the last two digits right, well, by pure chance that is 1 on 100, so if you then manage to pull that off, it is like wow (or you must have spotted it on a label on one of my suitcases). If instead you get the last one right, as well as the first digit, while the one-but-last is only off by 1, well, the probability of just that happening is actually less, but if you offer that as a replacement criterion afterwards I'm not going to go for it. The relevance, if any, of 22/5040 is that it is a pretty small (although not impossibly small) probability for some pre-agreed remarkable event to come about by pure chance. --Lambiam ^Talk 13:00, 20 December 2006 (UTC)

Luigi Fantappiè

Luigi Fantappiè could stand a cleanup job. It seems a touch heavy on the uncritical adoration. Anville 23:49, 19 December 2006 (UTC)

Symbol for differential

Lseixas (talk · contribs) has been going around changing the symbol for differential, e.g. "dt" to "\mathrm{d}t" inside Tex expressions at General relativity and elsewhere. If I remember correctly, KSmrq (talk · contribs) told us to do the exact opposite. Is there an agreed standard symbol for the differential? JRSpriggs 09:59, 20 December 2006 (UTC)

I have not seen this. The closest thing I know of is that sometimes "\mathbf{dx}" is used for vector quantities, as in:

$\mathbf{dx} = ( dx_{1}, dx_{2}, dx_{3} ).$

But this seems not to be the case here. VectorPosse 10:18, 20 December 2006 (UTC)

The d signs in ∫x³dx and dy/dx are primarily syntactic operators, like the λ in the lambda expression λx.x². Rendering them in the same font as normal variables may be confusing (what is the derivative of of sin(ωd) w.r.t. d). Therefore a good case can be made for using a distinctive font for this syntactic operator, and if we were to redesign the current hodgepodge of mathematical notation in a more rational way I'd be all in favour of that. The fact is, however, that this operator is conventionally rendered in italics, just like Euler's constant e and the imaginary unit i. This makes it impossible, for example, to use i as the summation variable in $\sum_{k=0}^{n-1} e^{2 \pi i k/n}$ . Oh well, such is mathematical life. In any case, it is not up to us Wikipedians to redesign mathematical notation, however irrational. We should stick to the conventional common use: italic d operators. --Lambiam ^Talk 12:36, 20 December 2006 (UTC)

In one of my papers, the publisher changed my italic d 's to roman d's in expressions like $\frac{\mathrm{d}}{\mathrm{d}t}\Big|_{t=0} f(t)$ and $\int f(t)\mathrm{d} t$ . I also own some books that follow this "roman d" convention (less than 10% of my total books, though, most seem to use italic), so the usage of italic d's is not universal. Kusma (討論) 13:10, 20 December 2006 (UTC)

This has been discussed before. I'm behind a dial-up connection now, so I won't look for it, but it's somewhere in the archives (the most extensive discussion was mostly about roman versus italic i for the imaginary unit). As Kusma says, roman d does definitely exist, mostly in Europe, but italic d is used more often. The previous discussion led to the conclusion of treating this the same as the difference between American and British English: articles should be consistent and the first contributor gets to decide which convention to use. For the record, I like the roman convention. -- Jitse Niesen (talk) 14:10, 20 December 2006 (UTC)

Believe it or not, but there's actually an ISO standard for this: a roman "d". See, for example, Beccari's article in TUGBoat (Volume 18, Issue 1, pp39--48, 1997). But mathematics articles and monographs haven't ever really followed the standard... My two cents, Lunch 21:01, 20 December 2006 (UTC)

The most recent comment I made was on the mathematics reference desk, where I recommended using the italic "d" when writing articles. We have a never-ending struggle with the variations in mathematical conventions. As Jitse says, there are parallels to the differences between American and British English. Our "offical" page of mathematical conventions is mute on this topic, though it has been briefly discussed on its talk page. Perhaps we should move this dialog there, for the benefit of future editors.

Those who have mostly seen basic calculus may not realize all the different roles dx can play. Some examples (not exhaustive):

Part of a differential operator, such as ^d⁄_dx f.
The variable of integration, such as ∫ f(x) dx.
A total derivative, such as ^d⁄_dx(f+g) = ^df⁄_dx+^dg⁄_dx.
In differential geometry, a vector in the cotangent bundle, such as 3dx+2dy.
In exterior algebra, part of a differential form, such as dx∧dy.
An exterior derivative operator acting on a differential form, such as ddx = 0.
In algebraic geometry, a boundary operator acting on a chain complex, such as d_n : A_n→A_n−1.

Those familiar with these applications will appreciate the important connections between them, so the parallel notation is not totally capricious. Yet each use is formally different.

In some of these cases dx is best considered a "diphthong", not a d acting on an x. For example, Herbert Goldstein, in Classical Mechanics, 2/e (Addison-Wesley, 1980, ISBN 978-0-201-02918-5), has a footnote (p.169) saying

“It cannot be emphasized too strongly that dΩ is not the differential of a vector. The combination dΩ stands for a differential vector, i.e., a vector of differential magnitude. Unfortunately, notational convention results in having the vector characteristic applied only to Ω, but it should be clear to the reader there is no vector of which dΩ represents a differential. As we have seen, a finite rotation cannot be represented by a single vector.”

Similarly, William L. Burke dedicates Applied differential geometry (Cambridge University Press, 1985, ISBN 978-0-521-26929-2) “[t]o all those who, like me, have wondered how in hell you can change $\dot{q}\,\!$ without changing $q\,\!$ .” (This also serves to remind us of the contrasting conventions of Newton and Leibniz.)

I am not bold enough to demand a universal convention, nor even a case-by-case dissection. However, I would highly recommend that the first two instances, which are elementary calculus, use the italic "d". This is partly because it seems to be the most common convention, partly to respect the diphthong, and partly because it frees up other typographical variations for the other cases. It is especially important to have variants available when describing connections, to avoid wild confusion. --KSmrq^T 21:35, 20 December 2006 (UTC)

If there's a controversy about this subject, including verifiable sources such as the ISO convention mentioned above, shouldn't something of the history of this controversy be mentioned in Leibniz's notation for differentiation? And why is that article separate from Leibniz notation, and why do those two articles use two different versions of the convention? —David Eppstein 21:47, 20 December 2006 (UTC)

With regards to the ISO standard, I think it's mostly meant to be applied to physics and engineering. I think IUPAC chimed in at one point or another with a similar standard for chemistry. On the other hand, like I mentioned above, mathematicians have never really gone along with all of it. ( So ppppppthtthhthththth! ;) Lunch 22:15, 20 December 2006 (UTC)

It seems that there are strong references for roman d: CBE manual (Scientific Style and Format 6ed 1994 CUP cf p208) and Swanson's Math into Type. pom 23:22, 20 December 2006 (UTC)

Those who would like to read the 1997 TUGBoat article about the ISO and IPU conventions can find it online. Please note that the introduction says

“I will discuss here those few tricks that physicists and engineers, not mathematicians, must know in order to satisfy the international regulations and to distinguish similar symbols with different meanings and, ultimately, in order to cope with the ISO regulations and the recommendations issued by the International Union of Pure and Applied Physics (IPU).”

(His emphasis!) He later says

“The house style of the majority of publishing companies, where the differential operator is a common italic ‘d’, was evidently set up under the influence of the tradition of pure mathematical typesetting before the ISO regulations were published; … while the modern world is so attentive to international standards, this particular one is almost completely neglected.”

The only other significant comment on d occurs on page 8, in regards to spacing. It has been almost a decade since the article was published; I do not know how standards and practices have changed in that interval.

Beccari spends most of the article dealing with constants and physical quantities, and that context explains the desire of the standards to distinguish the "e" indicating an electron from the "e" indicating the base of natural logarithms, or the "d" indicating crystal lattice plane spacing from the "d" indicating a differential. The needs of pure mathematics articles are rather different, though we cannot completely separate ourselves.

Consider a discussion of the electrical field surrounding an electron. A mathematician would confine the charge in a sphere and use the observation of Gauss that we can substitute an integral over the boundary for an integral over the interior. We would consider this a special case of the generalized Stokes' theorem, which concerns itself with differential forms.

$\int_M \mathrm{d}\omega = \int_{\partial M} \omega.\!\,$

Thus we see this as integrating a form, either ω or dω, over either a manifold, M, or its boundary, ∂M. Here the roman "d" indicates an operator, the exterior derivative, on forms. But if we consider a planar variant of this situation, where this theorem specializes to Green's theorem, we would use dx and dy, with italic "d", not roman. For example, suppose we wish to find the center of mass of a uniform density simple polygon region, R, with border P. Its coordinates are merely the average x and average y positions.

$\begin{align} \bar{x} &{}= \frac{1}{A}\iint_R x \, dx\,dy & \qquad \bar{y} &{}= \frac{1}{A}\iint_R y \, dx\,dy \\ A &{}= \iint_R dx\,dy \end{align}$

We can compute each of these three integrals using the theorem, which here we would write

$\iint_R \left( \frac{\part F}{\part x} - \frac{\part G}{\part y} \right) \, dx\,dy = \int_P G\,dx + \int_P F\,dy ,$

where F = F(x,y), G = G(x,y). In this context dx and dy should be viewed as parts of a differential form, because we are concerned with the broader theorem, which is stated in those terms. (Readers not familiar with this method are urged to discover the beautifully efficient computations in term of the polygon vertices for themselves. For example, to find the area integral we can let F(x,y) = x, G(x,y) = 0. The integral along P is the sum of the integrals along each of the edges.)

In this example, we would prefer not to use a roman "d" with two entirely different meanings. --KSmrq^T 03:38, 21 December 2006 (UTC)

If I may put this in cultural terms: it appears that WP engineering and some undergrad level physics articles prefer the roman d, while the math and especially the postgrad math articles prefer the italic. I beleive tha this is because the engineering/physics textbook authors are taking considereable pains to distinguish vectors from scalars, and differentials from derivatives, and all of those issues undergrads struggle with, and are placing that emphasis on the notation. Thus, undergrads are exposed to this meticulousness, and will edit on WP in this fashion. The (pure) mathematicians have "gotten over it", and have a different way of dealing with such issues ('by abuse of notation'), and are thus happier with the italic d, as it is visually prettier on the page: it doesn't screem out "look at me, I'm important" like the roman d does. linas 00:20, 21 December 2006 (UTC)

This "cultural" analysis is right on. I'm a pure math guy, and the expression $\int f(t)\mathrm{d} t$ screams at my eyeballs! :) VectorPosse 00:48, 21 December 2006 (UTC)

Mine too. Let's try a variation:

$\int f(t)\,\mathrm{d} t$

That looks a little bit better, but still

$\int f(t)\,dt$

is what I'm accustomed to and is what I see in most books, every day. If one must use the Roman "d", one should still have the space between "f(t)" and "dt". Thus: \int f(t)\,dt. Michael Hardy 01:16, 21 December 2006 (UTC)

Well, Lseixas (talk · contribs) did about 75 edits on 19 December 2006 alone, almost all of which were changing the italic form to the roman form (often many formulas in a single edit). JRSpriggs 05:29, 21 December 2006 (UTC)

I very much prefer the plain dx notation to \mathrm{d} t, and either way, I think mass conversions are a bad idea. I reverted a bunch of them. Oleg Alexandrov (talk) 20:47, 21 December 2006 (UTC)

Word problem (mathematics education)

There's a really interesting discussion going on about this article. The main problem seems to be that it is very difficult to explain what this is. Unfortunately, currently the article reads something like a diatribe on how the notion of "word problem" is nonsense. This article seems to have been in this kind of state for over three years. --C S (Talk) 19:57, 20 December 2006 (UTC)

Polar coordinate system

I'm thinking of putting this article as a FAC, but before I do so, I would love the opinion of a few math editors, so I can get the article even better before letting it be the subject of the scrutiny of the rest of the Wikipedia community. As I've never been through the featured article process before (nor have I been involved in it), any comments/help with the article would be greatly appreciated. —Mets501 (talk) 21:50, 20 December 2006 (UTC)

It looks good to me, I could not see any specific flaws on a brief scan. Much improved from a couple on months ago. --Salix alba (talk) 23:23, 20 December 2006 (UTC)

Great! Michael Hardy has done some nice cleanup, so I think I'll give others a chance to input here and then I'll submit it. —Mets501 (talk) 23:57, 20 December 2006 (UTC)

I see many tiny problems, but no big ones. The worst problem is that it is never made clear what subset of R×R the polar coordinates (r,θ) are supposed to range over, and the difficulties at r = 0 are completely ignored. Then there are many statements that are just not quite right; for example in the lead: "For many types of curves, a polar equation is the simplest means of representation; for others, it is the only such means." (my emphasis). The last part is indefensible. If a curve is given by a polar equation F(r,θ) = 0, then we can also describe the curve by a Cartesian equation G(x,y) = 0, where G(x,y) is defined by G(x,y) = F(radius(x,y), angle(x,y)) for suitable functions radius and angle. Finally, several of the citations are to sources that have no authoritative value. At some time there used to be a maths article of the week improvement drive or something like that; perhaps that could be revived. --Lambiam ^Talk 00:27, 21 December 2006 (UTC)

I left some comments at Talk:Polar coordinate system. -- Fropuff 00:51, 21 December 2006 (UTC)

Wikipedia:What is a good article?

This is being revised, especially the infamous section 2b about inline citation. It seems to me that even the edits I did not do are in a sensible direction; after some jumping up and down at Wikipedia:Good articles/Review#Johann Sebastian Bach (where it is perhaps clearer than on mathematical articles what sort of points are at issue), some mutual understanding may have been attained. Please come help. Septentrionalis PMAnderson 04:40, 21 December 2006 (UTC)

Renaming Exclusive disjunction Exclusive or

If you have an opinion about whether the article should be named "Exclusive or" or "Exclusive disjunction", come on down to Talk:Exclusive disjunction and share your opinion. Samboy 09:09, 21 December 2006 (UTC)

Vector Notation

Recently the vector notation on a huge number of pages was changed from bold style ( $\mathbf{B}$ ) to arrow style ( $\vec{B}$ ), in an effort to make notation on wikipedia more homogeneous. In paticular the Maxwell's Equations section has been changed.

Is this such a good idea? To begin with, mathematical notation is not in fact consistent, with different persons, groups, countries and even continents often using quite different notation. What is more appropriate to some may be less aprropriate to others. Notation vary's across fields as well. It doesn't seem wise to impose a single notation for all of Wikipedia when no over all consensus exits. ObsessiveMathsFreak 15:18, 21 December 2006 (UTC)

Wide sweeping changes to alter notation are generally frowned upon (and often reverted). There are numerous such notational issues which have been argued to death on this page (see above and almost any archive page). The upshot always is as long as an article is consistent in its notation don't change it simply because you prefer an alternative notation. We treat differences in spellings (British vs. American) the same way. In Wikipedia, as in life, we need to respect our differences. -- Fropuff 18:00, 21 December 2006 (UTC)

The latter is nice for one reason: It uses semantic markup. However, in the physics, math, and engineering I've seen, bold is more widely used. Perhaps a high-level admin could redefine \vec to produce bold, leaving \overrightarrow to produce $\overrightarrow{B}$ ? —Ben FrantzDale 18:21, 21 December 2006 (UTC)

Calculus footer

I find the {{Calculus footer}} template to be rather ugly, either with stuff hidden or stuff shown. I would suggest that it be rewritten keeping only the most relevant calculus topics, instead of the huge amalgam of links, whether they show up or are hidden. Comments? Oleg Alexandrov (talk) 20:32, 21 December 2006 (UTC)

I personally like it. It is well-organized and quite comprehensive. Relegating it to the end of the article keeps it from being obtrusive. Making it more attractive is worthwhile, but I wouldnt delete any content. - grubber 20:48, 21 December 2006 (UTC)

This template is very nicely put together, kudos to the editors. It is non-obtrusive in any way to the articals, and doesn't force people to scroll through links and links, looking for what they are looking for; This is much better than having to look in a page of links for what you are looking for. Just one click on the side for a list of pages with your topic. It is very nice, useful, and complete; it is good to have that much information organized that way. - 'Lord Nikon' --00:37, 22 December 2006 (UTC)

Just like the roman d vs. italic d discussion above, I will insist that footers are another cultural thing. I vaguely remember discovering "cheat sheets" for the first time in high-school, and they seemed to be brilliant way of organizing knowledge. Years later, entering grad school we had to pass "comprehensives", and we were allowed one page of notes. The top-of-the-class, all-grade-A honors student, a girl, came in with the most tightly packed, carefully designed cheat-sheet I'd ever seen, and ace'd the thing, of course (I myself couldn't remember the formula for coriolis forces). There is a debate going on now at WP:physics about a cheat-sheet arrangement of (nasty ugly) collection of thermodynamics formulas; in defense of this ugliness is the argument that the CRC does it this way too. So while I know that the overwhelming majority of mathematicians here absolutely deplore and despise these footers and nav-bars (as I do), I think that, perhaps, in a certain class of articles, these footers are an aid to understanding, and should be allowed instead of being busted down. Live & let live. linas 03:44, 22 December 2006 (UTC)

Nevertheless the purpose of these footers is different from crib sheets. I support the suggestion of keeping such navigation aids focussed on the most relevant topics. The people who need such navigation aids most are not served by an indiscriminate collection of links to vaguely related articles; before you know it they need a metanavigation aid to navigate the footer. That is simply a matter of being bold: if a link offend thee, pluck it out, and cast it from the template. What would bother me is if such a template gets plastered over all articles involving some calculus, but that isn't the case yet and will hopefully remain so. --Lambiam ^Talk 09:52, 22 December 2006 (UTC)

Featured article Regular polytope up for review

Hi. I have nominated the FA Regular polytope to be review to see if it still complies with the featured article criterias. You are welcome to comment at Wikipedia:Featured article review/Regular polytope.

Fred -Chess 22:57, 21 December 2006 (UTC)

Regular polytope has been nominated for a featured article review. Articles are typically reviewed for two weeks. Please leave your comments and help us to return the article to featured quality. If concerns are not addressed during the review period, articles are moved onto the Featured Article Removal Candidates list for a further period, where editors may declare "Keep" or "Remove" the article from featured status. The instructions for the review process are here. Reviewers' concerns are here. Sandy (Talk) 23:27, 21 December 2006 (UTC)

User:WAREL again?

this change at Perfect number by Chikushi (talk · contribs) looks a lot like User:WAREL. It's his first edit, and the formula is byte-for-byte identical to this edit by MIYAJ (talk · contribs), blocked as a sock puppet of User:WAREL. Did I do right in reverting it? — Arthur Rubin | (talk) 20:41, 13 December 2006 (UTC)

Definately. Well spotted! :-) Tompw (talk) 01:01, 15 December 2006 (UTC)

There have also been a sequence of WAREL-like edits to perfect number recently by Sugakusha (talk · contribs), Kotobakarihakirai (talk · contribs), Goodboy Johnny (talk · contribs), and InterCommunication (talk · contribs). Each of those names is a new account that only has edits to perfect number. The first one has been blocked and marked as a suspected sock but the other three have not yet. Given this repeated abuse, and evasion of repeated blocks, would protection for perfect number be in order? —David Eppstein 18:22, 23 December 2006 (UTC)

All blocked. Perhaps semi-protection is in order? -- Jitse Niesen (talk) 20:20, 23 December 2006 (UTC)

I agree that semi-protection makes more sense than full protection. —David Eppstein 20:57, 23 December 2006 (UTC)

Done. -- Jitse Niesen (talk) 15:20, 24 December 2006 (UTC)

Dispersive PDE Wiki

bumped into the above article, apparently on AfD for non-notable, and thought maybe it should be brought to attention here. if that Terrence Tao is indeed a (sufficiently regular) contributor, as claimed, seems to me it is very possible that the website is well-known or becoming so, among specialists. if that's the case, non-notability certainly gets disqualified as a reason for AfD, in my opinion. Mct mht 05:37, 17 December 2006 (UTC)

hm I just browsed a few articles there, looks like Terrence Tao is indeed a substantial contributor. some pages are written entirely by him. credibility is certainly not in question here. seems to me that whether that article is notable or nor should be decided by specialists from the PDE community. the first few votes seem to indicate that's not the case. Mct mht 05:45, 17 December 2006 (UTC)

more follow up, i don't mean to be harsh but the AfD is carelessly brought about. first a bot tags as an article related to Wikipedia:WikiProject Physics, which it is not really. then the bot's owner proposes AfD. the AfD debate is not categorized as mathematics but as (Web or internet), circumventing proper attention. Mct mht 05:57, 17 December 2006 (UTC)

~~I'll go add it to Wikipedia:WikiProject Mathematics/Current activity~~, although in fact the AfD listing is as much notice as most AfDs get. Septentrionalis PMAnderson 20:43, 17 December 2006 (UTC)

The bot got it; not a problem. Septentrionalis PMAnderson 20:48, 17 December 2006 (UTC)

The result of the AfD was keep (no consensus).

For follow on, those who visited the wiki seemed impressed with the quality and extent of its content, so I have a thought. I don't work on PDEs; perhaps someone who does would like to entice participation in an exchange program, like that with PlanetMath. This could both improve our PDE content, and help allay the concerns of those who felt the wiki was insufficiently notable to deserve an article. --KSmrq^T 07:13, 26 December 2006 (UTC)

GurchBot 2 messed up our archives! But I have repaired them.

GurchBot 2 (talk · contribs) moved all archives with non-standard names to standarized names. E.g. changing "Archive12" to "Archive 12" and leaving a redirect behind. By so doing, GurchBot 2 has messed up the archives at Wikipedia talk:WikiProject Mathematics and Wikipedia talk:WikiProject Physics and probably many others which use Werdnabot to archive their talk pages. It did not change the Werdnabot invocations to show the new file name for the current archive so Werdnabot added the archived material to the redirects which were left behind. Also, a minor point, GurchBot 2 did not change the archive lists to point at the new file names so they are now all going thru the redirects. This is a real mess. JRSpriggs 03:58, 26 December 2006 (UTC)

I have repaired this problem for the Mathematics Project and intend to do so for the Physics Project, but the others will have to fend for themselves. I adjusted our Werdnbot invocation and list of archive file names to reflect the new names given to the files by GurchBot 2. JRSpriggs 04:28, 26 December 2006 (UTC)

Apologies to everyone in this WikiProject for messing up your archives. I intended to change the archive lists and werndabot instructions soon after running the bot, but Christmas got in the way. If anyone notices any other pages that are wrong, feel free to fix them; I will try to find time later today to fix things and everything should be OK within 24 hours – Gurch 12:59, 26 December 2006 (UTC)

Writing about math

I am working on a guideline, Wikipedia:Writing about math. Can you people please look at it? --Ineffable3000 23:33, 25 December 2006 (UTC)

I changed a bunch of "it's"s to "its"s. It's pretty ironic to have grammatical errors in an article about how to write math; you should check for more of this. Ryan Reich 23:52, 25 December 2006 (UTC)

Thanks. Math is not english though. --Ineffable3000 02:21, 26 December 2006 (UTC)

"Each mathematics article should have an esoteric explanation." Really? --Lambiam ^Talk 00:53, 26 December 2006 (UTC)

You wouldn't want to write an article about continuity just saying "continuity is when you can draw a line without lifting the pencil". You would want to talk about "open ball in Domain --> open ball in range", etc.. In my opinion, a simple explanation is necessary too for the noobs. --Ineffable3000 02:21, 26 December 2006 (UTC)

"Each article about a proven theorem or lemma should contain a proof." Also for the Four-colour Theorem and the Poincaré conjecture? --Lambiam ^Talk 01:11, 26 December 2006 (UTC)

I said proven theorem. There is no analytical proof for the Four-colour theorem. The Poincare conjecture is a conjecture not a theorem. --Ineffable3000 02:21, 26 December 2006 (UTC)

No, they are both proven. Lambiam's point is that the proofs of these are generally considered fairly complicated and would take a lot of space. This is not an uncommon aspect of proofs of major theorems. --C S (Talk) 01:49, 27 December 2006 (UTC)

I don't see what the problem is! It's easy enough to include a proof by intimidation for each of your examples. --C S (Talk) 01:35, 26 December 2006 (UTC)

That would work. Proof by algorithm / computer-proofs are proofs also and should be included. A link to a script (if available) would be good. --Ineffable3000 02:21, 26 December 2006 (UTC)

I think you missed my joke entirely. --C S (Talk) 01:49, 27 December 2006 (UTC)

Comments should be added at Wikipedia_talk:Writing_about_math. I have my own doubts about all this, which I added there. --C S (Talk) 01:39, 26 December 2006 (UTC)

Are you aware that we already have written guidelines? (See WP:MSM.) Also, I have posted some tips here in the last few months. I suggest instead of writing your own guide, you study existing ones. --KSmrq^T 01:42, 26 December 2006 (UTC)

I did read over WP:MSM and I am proposing that we merge some of my ideas into there as a result of this discussion. --Ineffable3000 02:21, 26 December 2006 (UTC)

Lobachevsky Article

I think that the Nikolai Ivanovich Lobachevsky article should be switched from the scope of wikiproject Russian history to wikiproject mathematics since his importance is in the history of mathematics not the history of Russia. NikolaiLobachevsky 06:35:01 12/26/2006 (UTC)

It can be in both; I'm adding it to WP Mathematics. grendel|khan 16:20, 26 December 2006 (UTC)

Where do graph theory articles go?

There are a number of graph theory articles that I was going to put a {{maths rating}} template on, but I couldn't find the right category. Does it go under topology? I couldn't find any graph theory articles already tagged. grendel|khan 16:11, 26 December 2006 (UTC)

Category:Graph theory or its subcategories. —David Eppstein 16:33, 26 December 2006 (UTC)

No, no, I mean the field parameter of {{maths rating}}; which field are graph theory articles in? grendel|khan 22:36, 26 December 2006 (UTC)

Oh, that. "discrete". Wikipedia:WikiProject Mathematics/Wikipedia 1.0/Discrete mathematics. —David Eppstein 23:07, 26 December 2006 (UTC)

Thanks! grendel|khan 07:27, 27 December 2006 (UTC)

Writing about math (2)

This post recently appeared on the "Portal:Mathematics" talk page. I've taken the liberty of copying it over to this page, where it will probably get more attention. DavidCBryant 17:08, 26 December 2006 (UTC)

I am working on a guideline, Wikipedia:Writing about math. Can you people please look at it? --Ineffable3000 23:35, 25 December 2006 (UTC)

It is also on this page, 4 sections up. --Lambiam ^Talk 18:55, 26 December 2006 (UTC)

Congratulations to Paul August

Paul August, with enthusiastic support, has found a seat on the Wikipedia Arbitrary Committee. (Did I spell that right? ;-D) He joins Charles Matthews, another mathematician. (Why these two fine editors would prefer to settle squabbles rather than write mathematics articles, I cannot imagine.) I congratulate Paul on his success, and look forward to many excellent, even-handed decisions. --KSmrq^T 22:20, 26 December 2006 (UTC)

I did ask Paul why he was standing ... congratulations to him on his fine showing. Charles Matthews 11:19, 27 December 2006 (UTC)

I tried to call, but all I got was this recorded message telling me to rotate my phone by 90 degrees. ;0) Anyway, congratulations Paul! capitalist 06:26, 28 December 2006 (UTC)

Articles with the greek letter mu in their titles

Duja (talk · contribs) has just moved "Mu-operator" to "μ-operator". This is the third (or is it the fourth?) time someone has done this; on the earlier occasions the move was reversed. My understanding was that we had an agreement to keep the Latinized spelling of the Greek letters in the titles of mathematics articles. Please someone (an administrator) reverse this. JRSpriggs 10:55, 29 December 2006 (UTC)

Actually, I even suspect he wrote “µ operator” (with a MICRO SIGN), not “μ operator” (with a GREEK SMALL LETTER MU), and that Wikipedia normalizes Unicode strings in KC form. If this conjecture is true, this would make the letter μ particularly vulnerable to this sort of zealousness, because the symbol µ is generally simple to type and most people aren't aware of the difference (especially if KC normalization will, indeed, render them identical!). --Gro-Tsen 16:51, 29 December 2006 (UTC)

Wikipedia Day Awards

Hello, all. It was initially my hope to try to have this done as part of Esperanza's proposal for an appreciation week to end on Wikipedia Day, January 15. However, several people have once again proposed the entirety of Esperanza for deletion, so that might not work. It was the intention of the Appreciation Week proposal to set aside a given time when the various individuals who have made significant, valuable contributions to the encyclopedia would be recognized and honored. I believe that, with some effort, this could still be done. My proposal is to, with luck, try to organize the various WikiProjects and other entities of wikipedia to take part in a larger celebrartion of its contributors to take place in January, probably beginning January 15, 2007. I have created yet another new subpage for myself (a weakness of mine, I'm afraid) at User talk:Badbilltucker/Appreciation Week where I would greatly appreciate any indications from the members of this project as to whether and how they might be willing and/or able to assist in recognizing the contributions of our editors. Thank you for your attention. Badbilltucker 18:18, 30 December 2006 (UTC)

Categories: Wikipedia talk archives

\vartriangle\triangledown\lozenge\circledS\measuredangle\nexists\Bbbk\backprime\blacktriangle\blacktriangledown	$\vartriangle\triangledown\lozenge\circledS\measuredangle\nexists\Bbbk\backprime\blacktriangle\blacktriangledown$
\blacksquare\blacklozenge\bigstar\sphericalangle\diagup\diagdown\dotplus\Cap\Cup\barwedge	$\blacksquare\blacklozenge\bigstar\sphericalangle\diagup\diagdown\dotplus\Cap\Cup\barwedge$
\veebar\doublebarwedge\boxminus\boxtimes\boxdot\boxplus\divideontimes\ltimes\rtimes\leftthreetimes	$\veebar\doublebarwedge\boxminus\boxtimes\boxdot\boxplus\divideontimes\ltimes\rtimes\leftthreetimes$
\rightthreetimes\curlywedge\curlyvee\circleddash\circledast\circledcirc\centerdot\intercal\leqq\leqslant	$\rightthreetimes\curlywedge\curlyvee\circleddash\circledast\circledcirc\centerdot\intercal\leqq\leqslant$
\eqslantless\lessapprox\approxeq\lessdot\lll\lessgtr\lesseqgtr\lesseqqgtr\doteqdot\risingdotseq	$\eqslantless\lessapprox\approxeq\lessdot\lll\lessgtr\lesseqgtr\lesseqqgtr\doteqdot\risingdotseq$
\fallingdotseq\backsim\backsimeq\subseteqq\Subset\preccurlyeq\curlyeqprec\precsim\precapprox\vartriangleleft	$\fallingdotseq\backsim\backsimeq\subseteqq\Subset\preccurlyeq\curlyeqprec\precsim\precapprox\vartriangleleft$
\Vvdash\bumpeq\Bumpeq\geqq\geqslant\eqslantgtr\gtrsim\gtrapprox\eqsim\gtrdot	$\Vvdash\bumpeq\Bumpeq\geqq\geqslant\eqslantgtr\gtrsim\gtrapprox\eqsim\gtrdot$
\ggg\gtrless\gtreqless\gtreqqless\eqcirc\circeq\triangleq\thicksim\thickapprox\supseteqq	$\ggg\gtrless\gtreqless\gtreqqless\eqcirc\circeq\triangleq\thicksim\thickapprox\supseteqq$
\Supset\succcurlyeq\curlyeqsucc\succsim\succapprox\vartriangleright\shortmid\shortparallel\between\pitchfork	$\Supset\succcurlyeq\curlyeqsucc\succsim\succapprox\vartriangleright\shortmid\shortparallel\between\pitchfork$
\varpropto\blacktriangleleft\therefore\backepsilon\blacktriangleright\because\nleqslant\nleqq\lneq\lneqq	$\varpropto\blacktriangleleft\therefore\backepsilon\blacktriangleright\because\nleqslant\nleqq\lneq\lneqq$
\lvertneqq\lnsim\lnapprox\nprec\npreceq\precneqq\precnsim\precnapprox\nsim\nshortmid	$\lvertneqq\lnsim\lnapprox\nprec\npreceq\precneqq\precnsim\precnapprox\nsim\nshortmid$
\nvdash\nVdash\ntriangleleft\ntrianglelefteq\nsubseteq\nsubseteqq\varsubsetneq\subsetneqq\varsubsetneqq\ngtr	$\nvdash\nVdash\ntriangleleft\ntrianglelefteq\nsubseteq\nsubseteqq\varsubsetneq\subsetneqq\varsubsetneqq\ngtr$
\ngeqslant\ngeqq\gneq\gneqq\gvertneqq\gnsim\gnapprox\nsucc\nsucceq\succneqq	$\ngeqslant\ngeqq\gneq\gneqq\gvertneqq\gnsim\gnapprox\nsucc\nsucceq\succneqq$
\succnsim\succnapprox\ncong\nshortparallel\nparallel\nvDash\nVDash\ntriangleright\ntrianglerighteq\nsupseteq	$\succnsim\succnapprox\ncong\nshortparallel\nparallel\nvDash\nVDash\ntriangleright\ntrianglerighteq\nsupseteq$
\nsupseteqq\varsupsetneq\supsetneqq\varsupsetneqq\leftleftarrows\leftrightarrows\Lleftarrow\leftarrowtail\looparrowleft\leftrightharpoons	$\nsupseteqq\varsupsetneq\supsetneqq\varsupsetneqq\leftleftarrows\leftrightarrows\Lleftarrow\leftarrowtail\looparrowleft\leftrightharpoons$
\curvearrowleft\circlearrowleft\Lsh\upuparrows\rightrightarrows\rightleftarrows\Rrightarrow\rightarrowtail\looparrowright\curvearrowright	$\curvearrowleft\circlearrowleft\Lsh\upuparrows\rightrightarrows\rightleftarrows\Rrightarrow\rightarrowtail\looparrowright\curvearrowright$
\circlearrowright\Rsh\downdownarrows\multimap\leftrightsquigarrow\rightsquigarrow\nLeftarrow\nleftrightarrow\nRightarrow\nLeftrightarrow	$\circlearrowright\Rsh\downdownarrows\multimap\leftrightsquigarrow\rightsquigarrow\nLeftarrow\nleftrightarrow\nRightarrow\nLeftrightarrow$

Wikipedia talk:WikiProject Mathematics/Archive2006

From Wikipedia, the free encyclopedia

Contents

Jan 2006 – Feb 2006

Help with Simple harmonic motion

Tensor wars

Articles listed at Articles for deletion

Math Collaboration of the Week

A new project idea

Mathematics Portal

Multivariable calculus help

Formal calculation

Red links

70.22.128.220

Math Will Rock Your World

History of Science WikiProject being formed

List of decimal expansions

Areas of mathematics article

Subset notation

Chaos theory needs help

Editors need help at function (mathematics)

Shape or set?

Real projective line

Functions, partial, pre-, proto-, total, etc.

Notation for positive infinity

Division by zero

Sets of sets

Lethe for admin

Mediation needed in big dispute at relation (mathematics)

Proposed changes to mathematics

Question about bases

another problematic article

Appeal to clean up the page on "list of paradoxes"

Article intro text

Does the Wikipedia model really work for mathematics?

GSL GFDL Copvio problem.

Another small step towards MathML support in MediaWiki

Definition of "computational mathematics"

Differentiation of functions of matrices with respect to matrix

Functions of matrices

History of manifold

Template for deletion

Copula (statistics)

New stub cat (topology)

Proofs and derivations

I think I have nothing to do here

blahtex 0.4.1 released

Blahtex Compatibility Project — seeking volunteers

Carathéodory theorem

blahtex 0.4.2

AfD: Foundational status of arithmetic

Trigonometric and hyperbolic functions: create separate articles?

Multi-variable articles

PROD (Proposed deletion): Empty Summation Equations

Revert war at Real number

Possibly not notable articles

Good articles list

Archives

can't remember the name of something

blahtex compatibility update

Real, again

Frivolous articles on little-used geometric terms

Lists of PRNGs

A question about differential equations

combined set theory

blahtex 0.4.3

Compatibility project update

Ruud for admin

what's happened to planetmath?

Mar 2006

recategorizing recreational mathematics

Category:Mathematicians by religion

french spelling

Location of "elementary function" article

Definition of General Linear Group

LaTeX

Most linked to and least linked to maths articles

Endashes

WAREL

Articles for the Wikipedia 1.0 project