Wikipedia talk:WikiProject Mathematics

A Rant About Articles By Mathematicians On Mathematics

If one looks up many mathematical articles on wikipedia, a vast number of them would be good articles for a mathematical encyclopedia, but completely lousy ones for a general encyclopedia. Definitions are emphasised above illustration (no 's'), and definitions given are often precise, terse - excellent for a maths textbook, useless for the general encyclopedia.

I think this is inappropriate. We are writing for wikipedia, not mathworld - yet I think the articles on mathworld would be more useful to a non-mathematician.

Yes, I know that some mathematical concepts are difficult. Perhaps some even utterly defy explanation within the grasp of the intelligent layperson. But if we are contributing to a general-purpose encyclopedia, shouldn't we at least try?

mike40033 (talk) 01:21, 16 October 2008 (UTC)

This has been discussed at length already. I think the overall consensus is that many mathematics articles would benefit from more examples, more pictures, and more prose. However, the same is true of any other kind of article on Wikipedia, especially articles in scientific and technical fields. The fact is that it takes much less work to write an encyclopedia article on, say, a Star Trek episode than it does to write a good article on groups. Many mathematics articles are constantly being improved, but there are many articles, and few editors qualified to make the improvements, so progress is understandably slow. Another issue is time: many of us have extremely demanding lives outside of Wikipedia, so that, if we are lucky, we can get around to revamping maybe one article every couple of months. Bear in mind that there is no deadline, and on the whole progress will always be incremental and slow. siℓℓy rabbit (talk) 01:38, 16 October 2008 (UTC)

To Mike: "It is better to light a candle than to curse the darkness." Choose an article and improve it. JRSpriggs (talk) 07:39, 16 October 2008 (UTC)

I can't. I have (to quote) "[an] extremely demanding li[fe] outside of Wikipedia". Anyway, a partial inspiration for my rant is the gradual deterioration of my home-made candle from a featured article to a not-even-good article. Check the historical revisions and you'll see some awful edits. mike40033 (talk) 04:27, 22 October 2008 (UTC)

"Dubious reference at Graph isomorphism (2) - edit war restarted!!!" revisited

siℓℓy rabbit (talk) wrote: "I think the overall consensus is that many mathematics articles would benefit from more examples, more pictures, and more prose." May I add to this: more algorithms, more short listings and more applications? For example, this year I took part in Intel Threading Challenge Contest and in the forum (http://software.intel.com/en-us/forums/) we used mathematical articles from Wiki very intensive. But sometime some Wiki editors try to save "pure mathematical view", see for example Wikipedia talk:WikiProject Mathematics#"Dubious reference" at Graph isomorphism (2) - edit war restarted!!!: here a few persons want to delete an important link to GI chemical applications because it is link to chemical journal. At the same time I asked them "Can you find many sources about chemical applications in pure mathematical journals? For example, in J. of Graph Theory?" Of course, they could find nothing.I want to show that not only pure mathematical sources have to be used for mathematical articles.--Tim32 (talk) 20:12, 16 October 2008 (UTC)

As I said above, your assertions are clearly bogus. The field of the assertion is computational complexity theory, not applied chemistry; why should an applied chemistry journal have referees who understand the issue, much less are competent to review it? For what it's worth, I have a paper in graph theory (with Paul Erdos) which touches on computational complexity theory, which probably puts me one up on you. But perhaps you can improve chemistry articles.... — Arthur Rubin (talk) 21:28, 16 October 2008 (UTC)

I suggest that you are wrong. Graph theory has been extensively used by a small group of chemists and there are clearly people who, for example, publish in the Journal of mathematical chemistry who are experts on the subject. I think it is also true that some concepts in Graph theory were originally developed in the context of chemistry. The Coulson-Rushbrooke theorem comes to mind. That was developed by Charles Coulson who was Rouse Ball Professor of Applied Mathematics at Oxford University and then Professor of Theoretical Chemistry there. At one time he also held a chair in Physics. However his work throughout his career was chemistry based. --Bduke (Discussion) 21:45, 16 October 2008 (UTC)

Quite. Some chemists are experts in graph theory. Do we have any indication that these are, other than their own words? — Arthur Rubin (talk) 22:06, 16 October 2008 (UTC)

Well, I am not into the specific issue, but you seemed to be saying that no chemistry referee would have knowledge of the issue. I was querying that. --Bduke (Discussion) 22:11, 16 October 2008 (UTC)

Again, I should show mistake by Arthur Rubin, he wrote "applied chemistry journal". The journal is "fundamental" not "applied": "The Russian Chemical Bulletin is a mounthly jornal covering practically all areas of fundamental chemical research, published by Kluwer Academic/Plenum Publishers." http://www.russchembull.ru/index.php3?id=2 Sorry, that Mr Rubin does not understand this difference! Also, I am sorry that Mr Rubin & Co discuss my person rather than the articles I cited, it is personal attack... --Tim32 (talk) 22:54, 16 October 2008 (UTC)

I'm confused here. We started out on a discussion on making mathematics articles more accessible yet have somehow got distracted into a discussion as to whether an emprical result should be included in a specific article. My first thought is that the amount of time devoted to these very narrow discussions is actually distracting us from the task of improving accessibility. Rather than such discussions I'd much rather see the article on Chemical graph theory develop to more than a stub, it could certainly use some illustrations. But then maybe its easier to have a nice flame war than it is to work on articles. --Salix (talk): 23:30, 16 October 2008 (UTC)

It would be nice if Tim32 would stop vandalising articles, including this section. I have no objection to moving this discussion into the discussion above on the edit warring in Graph isomorphism, but Tim has not introduced anything helpful to this section. I shouldn't have responded here, though. — Arthur Rubin (talk) 23:43, 16 October 2008 (UTC)

Chemistry always has had a close relation with Graph Theory. Actually, the word "Graph" comes from a paper published in Nature. Shall I recall that most of the terminology of Graph Theory comes from chemistry, that the first paper dedicated to spectral graph theory (E. Hückel, Quantentheoretische Beitrage zum Benzolproblem, Z. Phys. 70(1931), 204-286) was about quantum chemistry, that some graph theorists still study subjects closely related to chemistry (like fullerenes and isomers)... I don't know if you would have the same kind of opposition if one would like to add a reference to Topological Graph Theory in the entry dedicated to Topology? —Preceding unsigned comment added by 86.198.117.189 (talk) 19:54, 28 October 2008 (UTC)

Check this edit

An anon added this paragraph to Mathematical notation [1]:

Unfortunately the notation in common use is quite ambiguous. For example, |x| may mean the absolute value of x, the cardinality of x, the determinant of x, and so on. The notation sin^-1x may mean to take the arcsine of x, to take the reciprocal of the sine of x, or to multiply s times i times n^-1 times x. Ambiguity is particularly common in calculus, where the notation such as ^dy/_dx is not normally meant to be interpreted as multiplication and division involving a variable d.

The content seems essentially fine but unpolished; I'm more concerned about the prominence of the addition. Any thoughts? I'm loathe to revert right now.

CRGreathouse (t | c) 04:52, 20 October 2008 (UTC)

This paragraph is overstating things. When does sin^-1x ever mean anything other than arcsin ? Everything needs to be taken in context. In this respect mathematics is no different from any other language. Delaszk (talk) 06:06, 20 October 2008 (UTC)

I agree with Delaszk.  Δεκλαν Δαφισ   (talk)  08:06, 20 October 2008 (UTC)

I also agree with Delaszk, and I have reverted the edit. Without a source that discusses the ambiguities of mathematical notation, this addition is just a POV assertion. Gandalf61 (talk) 08:39, 20 October 2008 (UTC)

There is a difference between

sin⁻¹ x

and

sin⁻¹x.

The latter may mean you're multiplying s, i, the reciprocal of n, and x. The former does not. Likewise there is a difference between

$\sin ^{-1}x$

and

$sin^{-1}x.\,$

And the part about determinants seems silly. Michael Hardy (talk) 15:56, 20 October 2008 (UTC)

This is overstating things even more. I'm afraid that most mathematicians would read sin⁻¹ x and sin⁻¹x to both mean the inverse sine of x. Any one with mathematics knowledge above that of a 14 year old would realise there was a clash of notation and would change their notation as not to have to write the product of s by i by n^-1 by x. Failing that they would write s · i · n^-1 · x. I'm sure you'll disagree but to almost all people that were to read sin⁻¹ x and sin⁻¹x there would be no difference, except for typographical pedantry.  Δεκλαν Δαφισ   (talk)  20:26, 21 October 2008 (UTC)

And, by the way, if it is handwritten on a board, could you make this distinction? Boris Tsirelson (talk) 20:32, 21 October 2008 (UTC)

Quite so!  Δεκλαν Δαφισ   (talk)  20:50, 21 October 2008 (UTC)

Interestingly, $\sin ^{n}x$ for n=-1 is not $\sin ^{-1}x$. Well, mathematical formulas are intended for humans only; expressions in a programming language are not. Boris Tsirelson (talk) 21:37, 21 October 2008 (UTC)

A related observation: about 90 percents of mathematicians of my generation hate programming. (Is it true for new generations?) I was initially puzzled to see it, but then I understood: they hate to be REALLY exact! They express exact relations in non-exact languages (and understand one another exactly). Boris Tsirelson (talk) 21:59, 21 October 2008 (UTC)

Please: don't write

n=-1

when you can write

n = −1.

Michael Hardy (talk) 23:23, 21 October 2008 (UTC)

OK, thanks. Boris Tsirelson (talk) —Preceding undated comment was added at 05:42, 22 October 2008 (UTC).

I've made an attempt to write a paragraph which puts things in better perspective. The Mathematical notation article now includes: "Depending on the context, the same symbol or notation can be used to represent different concepts, therefore to fullly understand a piece of mathematical writing it is important to first check the definitions that an author gives for the notations that they have used. This may be problematical if the author assumes the reader knows what they are talking about."Delaszk (talk) 07:28, 22 October 2008 (UTC)

Nice. You could also use your words: "In this respect mathematics is no different from any other language". Or better: from any natural language (in contrast to formal language). Boris Tsirelson (talk) 07:42, 22 October 2008 (UTC)

Let's move this to Talk:Mathematical_notation#Example_of_differing_notation. — Carl (CBM · talk) 13:14, 23 October 2008 (UTC)

I second it, Delaszk Bharath (talk) 07:57, 28 October 2008 (UTC)

Assessment of math articles

I just noticed that the criteria of article ratings given at Wikipedia:WikiProject_Mathematics/Wikipedia_1.0#Quality_grading_scheme does often not correspond to the status of given sample articles. For example, [Trigonometric functions from March 2007] is given as an example for FA, but was recently demoted. Likewise [this old revision of vector space] counts as B-class. Should we rediscuss the criteria or simply change the given examples? Jakob.scholbach (talk) 07:28, 24 October 2008 (UTC)

The reason the articles given as examples in the criteria are dated is because of the precise problem you've pointed out. One can't be changing the examples every day because of what the last person who messed up a page did. Just follow the links and you get your dated example. Another project I looked at a bit ago had some examples with the latest versions and undated - it was a real mess figuring out what they meant by a standard. How else would you do it? Dmcq (talk) 13:06, 25 October 2008 (UTC)

I see your point though looking at the dated articles. I don't think hat trigonometry one should have been a featured article. Perhaps standards have risen. Dmcq (talk) 13:10, 25 October 2008 (UTC)

Probably it's really that standards have risen. I have chosen some more recent examples, in particular where the current version of the article does not meet the standard anymore (simply by looking at the talk page assessment). Perhaps somebody wants to crosscheck... Jakob.scholbach (talk) 15:55, 25 October 2008 (UTC)

Algebraic number theory

Algebraic number theory is the current Mathematics COTM. A discussion has started at Talk:Algebraic number theory about how much introductory material the article should include, and whether a separate "Introduction to..." article is required for this topic. Wider participation in this discussion would be very welcome. Gandalf61 (talk) 10:33, 26 October 2008 (UTC)

groups "similar" to Emmy Noether?

I added a request to put the recently featured article about groups on the main page. This system is a bit complicated, and the article being showcased probably depends on whether groups are "similar" to Emmy Noether, which was displayed on the main page some weeks ago. If you are interested in having a mathematics article showcased (and not the (n+1)^st video game), please join in the discussion over there. Jakob.scholbach (talk) 17:34, 26 October 2008 (UTC)

I would hope that we have a good chance, mathematics FA's do seem to have a better than average chance of getting to the main page. --Salix (talk): 23:06, 26 October 2008 (UTC)

I hoped so, too, especially in view of the support uttered by many (thank you) and by the "rules" that are set up. But disappointingly the authorities chose something else, without much ado. It'd be interesting to know what it needs to get displayed at main page other than an accessible, well-written article, and community support. Perhaps a Futurama episode in the application section:)? Kafkaesque. Jakob.scholbach (talk) 22:43, 28 October 2008 (UTC)

Actually, after reading User:Raul654/Featured article thoughts I think it makes sense. While the "similarity" argument was of course nonsense, I think the article is at most borderline appropriate for the main page, since it is too abstract for most readers. With some patience, the article will eventually get there: see Raul's "resource starvation" remark. But the "underrepresented" credits are not for this type of mathematics article; they are for those with appeal to the layman. Short and somewhat imprecise version: We are much more likely to read about Emmy Noether in Time Magazine than about groups, and therefore Emmy Noether was featured faster. It was a journalistic decision not to feature the article now, and it's a wiki politics decision to make sure that an article of this kind will be featured eventually. --Hans Adler (talk) 23:31, 28 October 2008 (UTC)

Hm. I won't argue with Raul (and even less so with you, obviously), but it strikes me as very non-wiki-ish to have a process that tries to weigh advantages or disadvantages of some article being displayed or not, and then have one person override the result of that. If it is "borderline", it would/could/should have come to day at the discussion (which it did not). I also don't get your point "it will shown eventually". If it is worth showing it, it can be shown now (if somebody "applies" for it), if not, it should never be featured. (Btw, due to the number of featured articles, for numerical reasons there will be articles that are never shown [if new FA's come in as they do now]). Finally, you refer to the abstraction of the article. I agree it is not what many readers will (want to) read daily, but unless my vision is completely biased, it is something which can be appealing to a layman. (I did get positive response in this respect from lay readers at FAC). Indeed it was one of the main concerns in the later stages of the article development and in particular the FAC process to make it accessible, which, I believe, it is, to the amount that can be expected. If we only feature articles that are understandable/"appealing" to the last line for everybody, isn't that systemically biased? Jakob.scholbach (talk) 23:49, 28 October 2008 (UTC)

Seems like we made a couple of tactical errors. Nominating it too quickly after Noether and choosing the 29th rather than a later date which may have given it more time to gain Raul's attention. You live and learn. I still think there is a chance it will appear at Raul's discretion. --Salix (talk): 08:40, 29 October 2008 (UTC)

Into the memory hole?

So what happened to this discussion? It is evident from the queue that the article will not appear on October 29th, that date that was proposed, but what decision was made ought to be available somewhere. Maybe with some archive of the discussion. Do things like that exist, or does the whole thing vanish from all memory? Michael Hardy (talk) 01:22, 29 October 2008 (UTC)

...in fact, I now see that in the time zone used by Wikipedia, it's already October 29th. Michael Hardy (talk) 01:23, 29 October 2008 (UTC)

There does not seem to be an archive of discussions or a documentation why or how the chosen page was effectively chosen (Raul543's documentation alluded to above is little helpful in this respect -- it roughly says: "in the end, the decision is mine, I carry the burden, I have some pages I will never show, but won't tell which, but there are only a few of them"). What decision is taken is shown at Wikipedia:Today's featured article/October 2008. The relevant edit at the request page reads October 29 scheduled; one slot open. Jakob.scholbach (talk) 07:47, 29 October 2008 (UTC)

Limits

I recently initiated a merge discussion at limit of a function. Of the 4 editors seemed in favor of some type of merge, but one editor is very against. He made the reasonable point that "limit concept is one of the central ones in mathematics, drastic changes in the current configuration should be discussed at WPMath." So I thought I would bring it up here. The articles involved are limit of a function, limit of a sequence, (ε,_δ)-definition_of_limit, and limit (mathematics). Fresh input would be greatly appreciated. Thenub314 (talk) 21:22, 27 October 2008 (UTC)

Clearly, a limit is a general concept, and a limit of a function is one notable but particular example. The merger doesn't sound right to me. -- Taku (talk) 21:58, 27 October 2008 (UTC)

The main point of the (ε,_δ)-definition_of_limit is not quite the limit (and its definition), but rather (1) the problem of intuitive understanding of alternating quantifiers, and (2) comparison between analysis and nonstandard analysis. As for me, it is not (and should not be) a competitor to the other articles on limits. Boris Tsirelson (talk) 22:08, 27 October 2008 (UTC)

Moreover: why not split the (ε,_δ)-definition_of_limit in two articles, each to grow? Boris Tsirelson (talk) 22:11, 27 October 2008 (UTC)

Boris Tsirelson makes an interesting point. But if the article is about quantifier complexity and comparisons with nonstandard calculus, shouldn't the article have a different name? When I first visited this article I had thought it was an article whose primary purpose was explaining the (ε,δ)-definition of a limit. Thenub314 (talk) 03:35, 28 October 2008 (UTC)

We don't need four overlapping articles. Pointless and confusing. Merge into one. Gandalf61 (talk) 22:32, 27 October 2008 (UTC)

Tsirel makes a valid point on (ε,_δ)-definition of limit, but the other three should probably be merged. CRGreathouse (t | c) 02:59, 28 October 2008 (UTC)

There is a lengthy discussion of the issue at the talk page of limit of a function, please see there. My personal feeling is don't fix it if it ain't broke. Katzmik (talk) 08:35, 28 October 2008 (UTC)

I think there is good reason to have different articles for limit of a function and limit of a sequence. The methods applied to finding the limits of one are practically entirely disjoint from those for finding the other and they just look different. An overall page on the concept of a limit sounds right too and (ε,_δ) is very notable. I think the problem is more of removing too much duplication. Wiki is hyperlinked so important concepts can have a page to themselves and be linked to rather than trying to write a book under each heading. Dmcq (talk) 08:57, 28 October 2008 (UTC)

Hear, hear! Katzmik (talk) 09:01, 28 October 2008 (UTC)

There seems to be disagreement there for the need for an overall limit (mathematics) article. I think it is necessary to expand on the Limit disambiguation page so people who don't know very much can find what they want without looking through everything. The one liner information wouldn't be removed from the disambiguation page - just have another page which was mostly constructed of the header parts of the various different articles and structured into some hierarchic form. Most of the current information in Limit (mathematics) could be removed to the more specific articles. Dmcq (talk) 18:15, 28 October 2008 (UTC)

I do not have strong feelings, for or against, having separate articles for limit of a function and limit of a sequence. And I agree the the ε-δ definition of limit of a function is notable, as is the ε-N definition of a limit of a sequence. But I do think something is broken. There is a good discussion of ε-δ definitions in limit of a function and limit of a sequence. And has pointed out above the page (ε,_δ)-definition_of_limit (as written) is not about the limits or their definitions, but rather as a place to talk about quantifiers and comparisons with nonstandard calculus. I think if nothing else happens, this article should be merged. If we should include a discussion of quantifiers, and comparisons to the definitions of between standard and non-standard calculus, they should take place in the articles themselves. Thenub314 (talk) 09:24, 29 October 2008 (UTC)

I had a quick look, and it indeed appears that the (at least) four existing limit-related articles do not work well together. Starting from the most obvious, there should be no need for (ε,_δ)-definition_of_limit: part of that content belongs to the article that discusses limits on metric spaces (and more specific cases as suitable). If people really insist it should be searchable in WP, one could leave it as a redirect to a relevant section in the right article.

Second, Limit (mathematics) mainly discusses the limit concept in topology, primarily specializing in the "elementary" cases of sequences and functions defined on subsets of R or a more general metric space. Suitably enough Limit (category theory) is mentioned (linked away), while some other limits in mathematics (lim sup, homotopy limits) are not. It would make more sense to have Limit (mathematics) as a disambiguation page, which could use a paragraph or two to discuss the general "flavour" of concepts baptised limits in various parts of mathematics. The discussion of topological limits in their various guises (easily the most notable of these) should be in a separate article, where most of Limit (mathematics) should be moved; it would also be an opportunity to improve the exposition significantly - currently it is essentially left to the reader to work out which definitions are special cases of the more general ones. Limit (mathematical analysis) discussed on the article talk pages would be too specific for this article, where eventually limits of filters and nets should be discussed and linked to the more specialised definitions.

As for Limit of a function and Limit of a sequence, I would keep them as separate articles, link them to the more general limit in topology article and make it clear they are special cases. Some duplication (and more detailed discussion) in these articles would do not harm. But the logical structure of the article should be in line with the logic of the content, so some coordination is needed.

Finally, for whatever reason, much prominence is given in these articles to writing definitions that have just been presented adequatly in plain English again using quantifier´notation. Sometimes this is done as if writing more technical-looking formula (with shorthand that is really seldom used outside blackboard) would make the definition more precise or properly mathematical. If the intention is to make the definitions understandable this additional notational complexity is, at least in my view, not useful. Stca74 (talk) 12:06, 29 October 2008 (UTC)

Given the divergence of views regarding such surgeries, dramatic edits at these pages will cause more controversy than they are worth. As far as the quantifiers are concerned, perhaps a consensus can be reached about restricting their use to (ε,_δ)-definition_of_limit where the logical structure of these definitions is emphasized. Katzmik (talk) 12:28, 29 October 2008 (UTC)

The last paragraph of Stca74's comment is very apropos. I occasionally remove the repetitive formulas from other articles. The English definition of convergence is perfectly rigorous and formal:

(a_{n) converges to l if for all ε > 0 there exists an N such that for all n > N, |an - L| < ε}

The idea that a gain in formality or rigor can be obtained by using the symbols ∀ and ∃ is misguided.

On the other hand, the definition of convergence is widely regarded as difficult for students to learn, with the difficulty attributed to the large depth of nested quantifiers. So it may be worth including the formula

$\forall \epsilon >0\,\exists N\,\forall n\,(n>N\to |a_{n}-L|<\epsilon )$

simply to point out the quantifier structure. The claim to avoid is that this is somehow more formal than the English definition.

As to merging articles, I do think that the ε/δ article should be merged to the article on the limit of a function. And I think it would make perfect sense for Limit (mathematics) to just give pointers to other articles.— Carl (CBM · talk) 12:32, 29 October 2008 (UTC)

I am in agreement with Stca74, and Carl (CBM). How do people feel about just merging the ε/δ article and preforming some minor clean up on the others? Thenub314 (talk) 15:58, 30 October 2008 (UTC)

Nikolai Nikolaevich Nekhoroshev

Hello. The new article on Nikolai Nikolaevich Nekhoroshev used to say that he passed away on 19 October of this year. I removed it for the time being because I could not find a source for this, so you will have to look at a previous revision. Can anybody confirm his death? -- Jitse Niesen (talk) 09:43, 28 October 2008 (UTC)

I could not find a source for this either. The relevant departmental site on Moscow State University announces some recent deaths but not, as far as I can tell, Nekhoroshev's. His other host institution does not mention his death. I would expect some announcement on at least one of these sites, particularly the former. I searched for Нехорошев in the original and read a machine translation into English, but found nothing relevant. I can't read Russian, so please correct me if I missed something obvious. Aburov, the editor who created the article, has asserted that an obituary was posted locally, and Alex Bakharev has asked Aburov for a source. Michael Slone (talk) 03:22, 30 October 2008 (UTC)

Error on Cook-Levin theorem

There is what I believe to be an error on the page for the Cook-Levin theorem. I posted today, and I also found that Taejo had already noticed it. Vegasprof (talk) 16:11, 31 October 2008 (UTC)

I think we've determined what should be there (thanks for the invite, Vegasprof.) It's not resolved as of 1 1/2 hours ago, but we're on our way. — Arthur Rubin (talk) 18:26, 31 October 2008 (UTC)

Gamma function rendering

See Talk:Gamma function#Baffling rendering of definition, although there's a typo there. It appears that the lead definition is rendering as t^≈-1 instead of t^z-1, and I don't know why, either. — Arthur Rubin (talk) 18:29, 31 October 2008 (UTC)

Why it happens seems obvious. Or am I missing something? I've commented on the aforelinked talk page. Michael Hardy (talk) 18:50, 31 October 2008 (UTC)