Wikipedia talk:WikiProject Mathematics/Archive/2008/Oct

Tangent between two circles proposed for deletion

See Wikipedia:Articles_for_deletion/Tangent_between_two_circles. VG ☎ 13:37, 29 September 2008 (UTC)

The article has been re-named as Tangent lines to circles and updated. Everyone here is encouraged to contribute! :) Willow (talk) 18:52, 30 September 2008 (UTC)

2008 Wikipedia for Schools

The 2008/9 Schools Wikipedia is now available for browsing and feedback is welcome. Downloads start in two weeks so final improvements are possible; this is a big project with millions of users so it is worth doing well. The list of maths topics included is here. We have also included the Maths Portal. The subject list is quite a long list but feedback on what should be included or left out would be good. Also ideally if someone could split the 270 articles into two of three sub lists (preferably Pure Maths, Applied Maths and Statistics or something like that) it would help. See Wikipedia:Wikipedia CD Selection. --BozMo talk 13:09, 30 September 2008 (UTC)

Edit war on the article Non-Newtonian calculus

Please help to resolve this dispute. The articles Non-Newtonian calculus and Multiplicative calculus have come under sustained attack for including references to a self-published work which the opposing editors consider to be invalid as a reference.

The reference concerned is: Grossman and Katz. Non-Newtonian Calculus, ISBN 0912938013, Lee Press, 1972.

Points against:

• The work is self-published.

Points for:

• The work is cited and used as a basis for the peer-reviewed journal articles:

• • Meginniss. "Non-Newtonian calculus applied to probability, utility, and Bayesian analysis", Proceedings of the American Statistical Association: Business and Economics Statistics, 1980.

• • Bashirov, Misirli Kurpinar, and Ozyapici. "Multiplicative calculus and its applications", Journal of Mathematical Analysis and Applications, 2008.

• The article Non-Newtonian calculus is based mainly on this work. To remove its main reference is equivalent to destroying the article.

• The page WP:SPS says "a reliable self-published source on a given subject is likely to have been cited on that subject as authoritative by a reliable source." The papers above might not specifically use the word "authoritative" but why would they? The papers were not written for the purpose of conforming to the language of wikipedia's guidelines. Let's not be pedantic here - this is not about the precise words that the papers use. This is about the meaning that the papers convey. It's clear that these papers are based on the work Non-Newtonian Calculus. The work Non-Newtonian Calculus should therefore be valid as a reference.Delaszk (talk) 16:10, 30 September 2008 (UTC)

• Please read the entire relevant paragraph; I've been quoting the first sentence, while the inclusionists have quoting the last (except for the explanatory phrase, which makes deprecates it.)

Self-published material may, in some circumstances, be acceptable when produced by an established expert on the topic of the article whose work in the relevant field has previously been published by reliable third-party publications. However, caution should be exercised when using such sources: if the information in question is really worth reporting, someone else is likely to have done so. For example, a reliable self-published source on a given subject is likely to have been cited on that subject as authoritative by a reliable source.

• — Arthur Rubin (talk) 17:09, 30 September 2008 (UTC)
• And the appropriate venue is probably WP:RSN or WT:RS, rather than here or the article talk page. — Arthur Rubin (talk) 17:18, 30 September 2008 (UTC)

Well WP:RSN suggests using the talk page of a wikiproject, so here we are.

Another point in favour of allowing Non-Newtonian calculus as a reference is that it is a very short book, it doesn't actually say all that much, there is not much there to verify in the first place and as such the above papers should be ample verification of its reliabilty.Delaszk (talk) 19:16, 30 September 2008 (UTC)

I personally would not accept a self published article or book. If it is worthy of being a peer reviewed publication then why isn't it one? I could write a book on why the moon is made of cheese, and then publish it. Before you could say "hang on a minute" all the moon landing conspiracy theorists would be saying "The landings could not have taken place for the moon is made of cheese and could never support the weight of a landing module." Self published work is non-reviewed original research! As for Delaszk's point that "it is a very short book", if my book consisted of the line "The moon is made of cheese. QED" would that make it more reliable? Maybe I missing something here... if I am then please tell me.  Declan Davis   (talk)  20:19, 30 September 2008 (UTC)

"The moon is made of cheese. QED" - is this backed by third party journal articles? Answer -No. The answer is no, so why did you even ask the question? Hmm ? It is hard to assume good faith on your part when you say things like that. Your misdirection is just an underhanded trick.

"The moon is made of cheese. QED" - is this backed by third party journal articles? Answer -No.

Non-Newtonian calculus - is this backed by third party journal articles? Answer -Yes!

User:Declan Davis overlooks what I said in my previous post in favour of making jokes. Those jokes are engaging in misdirection. The comments are completely overlooking the main fact which is that the two papers above that cite and are based on the book, are in peer reviewed journals. ""The moon is made of cheese. QED" would that make it more reliable?"" - yes if a peer-reviewed journal agreed with that statement. Of course not that any journal article would and yet journal articles were based on Non-Newtonian calculus, so your mooncheese is a complete misdirection. You say: "Self published work is non-reviewed original research!" - actually no it's not - it's not original research if there are peer-reviewed journal articles based on it.

The wikipedia editors who are arguing against inclusion are being absurd with their anti-selfpublishing hysteria, that completely ignores this case, in favour of unthinking, dogmatic, indiscriminate application of guidelines regardless of the particular situation.Delaszk (talk) 21:21, 30 September 2008 (UTC)

I think Delaszk is taking things too seriously. I could have replaced "the moon is made with cheese" with any other non-humorous yet equally incorrect statement. I just thought that the moon comment might shed light upon the rediculous things that can, and will, be self-published. Okay, so I didn't agree with one of Delaszk's points. That doesn't mean I attacked him, or was disrespectful to him. This is a democracy, people have freedom of speech. It's nothing personal! My point was that anyone can write anything and have it published themselves. As for third party journals, well someone sees that something's been published and they think "well, there's a reliable source". How many people check if a book has been self published or not? In my opinion it's a cyclical argument. I thinkDelaszk may need to relax a little. His unfriendly reply doesn't help anyone. It makes him angry and me sad. You get my point. If you don't agree with it then please don't be so heavy handed in your replies. This is the problem with Wikipedia, as I have been discovering. I think I'll leave it at that. All the best.  Declan Davis   (talk)  22:11, 30 September 2008 (UTC)

p.s. Self published work is non-reviewed original research! The third party journals based on that work are not original. But the original work is, ermm, original.  Declan Davis   (talk)  22:33, 30 September 2008 (UTC)

p.p.s. There may be a conflict of interests with Delaszk commenting on this discussion. He sites the non-Newtonian article as one of his favorites. (Again, nothing personal .Delaszk, just being objective).  Declan Davis   (talk)  22:47, 30 September 2008 (UTC)

If you are being completely objective then you will stick to arguing the merits or otherwise of the case rather than bringing my interest into the discussion. If you don't want to get personal then argue the case, not the person.Delaszk (talk) 22:55, 30 September 2008 (UTC)

Please read the COI guidelines, and replace "article" with "discussion page". You are clearly a big fan of the article and as such will fight tooth and nail to keep it, and its sources, standing. This, for me, offeres a conflict of interest with respect to the discussion. Sorry. Declan Davis   (talk)  22:59, 30 September 2008 (UTC)

You are seeking to prevent me from discussing this article, rather than engage the arguments. Shame on you. Back to the discussion - All research is original when it is originally made otherwise it wouldn't be research. It ceases to breach WP:OR when third-parties take up the baton.Delaszk (talk) 23:19, 30 September 2008 (UTC)

P.S. Since you say I'm clearly a big fan - it should be noted that I have bent over backwards to be neutral over this article. It was me who put the "Criticism" section into the article. It was me who included references to Volterra and others rather than letting it appear Grossman and Katz were the first to think of multiplicative calculus. Similarly I spun-off multiplicative calculus into its own separate article rather than have it appear multiplicative calculus was developed purely as a result of Grossman and Katz's work. I may be interested in it but I have been neutral.Delaszk (talk) 00:15, 1 October 2008 (UTC)

I started of making my point about the edit war: please scroll up. That was what got you so annoyed. I had to stray from the point in an effort to calm you down in the hope you would take any offence.  Declan Davis   (talk)  15:39, 1 October 2008 (UTC)

Your point was that you would not accept a self-published source. You also made the point that being short was not a reason for accepting it, as if this was in response to what I had said. This is a misdirection, because shortness of itself being a reason is not what I said. I responded to this misdirection in a forceful manner in order to clearly highlight that the example given was not comparable to the self-published source under discussion. I was not offended by your point, I was arguing against it. The rest of my reply that you called 'heavy handed' was my assessment of the discussion as a whole that has taken place on the article talk pages over the last few weeks.Delaszk (talk) 17:38, 1 October 2008 (UTC)

How I wish my AfD had succeeded! I assumed that obscure nonsense was obviously non-notable...

Delaszk, if there is an edit war, you ought to be able to point to the problematic edits. I've been following the article and commenting on the talk page, and I've seen no evidence at all of an edit war (which, I'm sure you know, has a precise meaning on Wikipedia). I do not believe there is one; if you disagree, please point out the edits! Ozob (talk) 23:45, 30 September 2008 (UTC)

When I said edit war I was referring to the insertion of verifiability tags on every occurrence in the article of the reference to the book "Non-Newtonian calculus", followed by deletion of those tags, followed by reinsertion of those tags, followed by accusations of vandalism. If this does not qualify as an edit war as such, then it still qualifies as a dispute. To continue in the efforts to be neutral I have rewritten the opening sentence of the article to make it clear that this is a phrase used by GandK rather than a commonly used term. The article is now mainly about GandK's work and as such the book is the main reference.Delaszk (talk) 00:15, 1 October 2008 (UTC)

A bigger issue with the article is that it doesn't conform to WP:FRINGE. This is clearly a fringe theory, which has been roundly rejected by the mainstream mathematical community, despite the best efforts of its closest adherents to promote it by the continual publication of monographs on the subject. The article, however, approaches the subject as though it were a legitimate area of mathematical research. This is clearly assigning undue weight to fringe views, and so is a violation of the neutral point of view policy. Most of the mathematical material in the article needs to get the chop, and the remainder of the article should be devoted to explaining how and why this was rejected. siℓℓy rabbit (talk) 13:10, 1 October 2008 (UTC)

I'm entirely in agreement with making sure the article takes a neutral approach.Delaszk (talk) 18:04, 1 October 2008 (UTC)

"Dubious reference" at Graph isomorphism

See Wikipedia:ANI#.22dubious_reference_....22.3F. VG ☎ 23:27, 30 September 2008 (UTC)

User Míkka said "The fact that it is repeated in some obscure articles by persons with little credentials in graph theory bears little weight" about the following persons:

1)M. I. Trofimov 2)E. A. Smolenskii 3)V. N. Zemlyachenko 4)N. M. Korneenko 5)R. I. Tyshkevich 6)R. T. Faizullin

7)A. V. Prolubnikov 8)Jitse Niesen 9)David Eppstein 10)Corneil 11)Gotlieb

!!!--Tim32 (talk) 19:16, 1 October 2008 (UTC)

Lambda calculus and friends

Over at WP:CS, I'm wondering what to do about various forms of the lambda calculus...please do drop by and chime in! --mgreenbe (talk) 13:04, 1 October 2008 (UTC)

math question

How much is 85 billion divided by 200 million?

Is it 425000 or 42500? —Preceding unsigned comment added by 24.2.200.144 (talk) 11:34, 2 October 2008 (UTC)

In general, math questions such as this should go to Wikipedia:Reference desk/Mathematics. But you should be able to answer this one with any calculator. —David Eppstein (talk) 13:56, 2 October 2008 (UTC)

At least once you've decided how big a billion is. Algebraist 15:47, 2 October 2008 (UTC)

There are two conventions. An American billion is one thousand million, i.e. 10⁹. An old British billion was one million million, i.e. 10¹². Nowadays we use 10⁹ as one billion in the UK. Although I believe some European counties, such as Spain, still use 10¹² for one billion.  Δεκλαν Δαφισ   (talk)  15:54, 2 October 2008 (UTC)

And, the answer is 425 - as in $425 for every adult American, rather than the $425,000 that is being circulated around the Internet for the AIG bailout.  Frank  |  talk  17:58, 2 October 2008 (UTC)

The response "...the answer is..." is missing something. Are you using the short scale or the long scale? That seems to have been the point of the question.  Δεκλαν Δαφισ   (talk)  18:09, 2 October 2008 (UTC)

The short scale; the question clearly relates to the ridiculous email circulating that states the US Government should, instead of bailing out AIG, give every adult American the equivalent amount of money ($425,000). The math doesn't work, since in the United States, a billion is always 10⁹, so the correct amount would be a relatively paltry $425.  Frank  |  talk  18:14, 2 October 2008 (UTC)

I would love to see the inflation that would result from giving every American nearly half a million dollars! --Tango (talk) 18:36, 2 October 2008 (UTC)

As one of the many non-American English speaking editors here on Wikipedia the question, for me, did not clearly relate to the said email.  Δεκλαν Δαφισ   (talk)  19:27, 2 October 2008 (UTC)

I realized any number of readers might have been in that situation, which is why I put in the specific reference to AIG in my response. You can find details over here at snopes. 19:32, 2 October 2008 (UTC)

Article Help

Would appreciate neutral eyes on Esquisse d' un Programme, which has been deleted under WP:CSD#A1 by two different administrators (including myself). I am inclined to delete it again but I am interested in others' opinions first.  Frank  |  talk  18:00, 2 October 2008 (UTC)

Some people seem to think that Alexander Grothendieck is a genius, but I have seen nothing which justifies that belief. JRSpriggs (talk) 06:14, 3 October 2008 (UTC)

LOL? Probably comments like that are best ignored, but I have to ask: are you so arrogant to think that anybody cares about your opinion of Grothendieck? My memory of your previous contributions do not include a habit of going around giving unsolicited opinions of mathematical greats. --C S (talk) 06:29, 3 October 2008 (UTC)

The point is that the article in question is only important, if one thinks that Grothendieck himself is important. As if it were notes that Albert Einstein had written on his intentions to develop relativity. JRSpriggs (talk) 07:37, 3 October 2008 (UTC) P.S. There is at least as much reason to care about my opinion of Grothendieck as there is to care about your opinion of me.

An important distinction here is that I don't think anybody gives a rat's ass what I say to you here in response to your ridiculous comment. On the other hand, I really want to know why you would think anybody cares at all about your opinion of Grothendieck, or why you would think your opinion is in the slightest informed. --C S (talk) 08:47, 3 October 2008 (UTC)

Hey, peaceful!

I think it is fair to say that Grothendieck is in the very first row of mathematicians. He revolutionized algebraic geometry and many related fields, both by introducing groundbreaking notions and ideas and emphasizing a top-to-down and structural viewpoint. I personally think it is due to him that algebra is much more conceptual in flavor than other areas of mathematics, which often seem to rely on methods instead of structures. As for the article on Esquisse d'un programme (notice that in French there is no space after the '), I think it would be good to merge this into his own article. This "belief" is, for example, detailed in the introduction to the Grothendieck Festschrift. Jakob.scholbach (talk) 08:17, 3 October 2008 (UTC)

Looks like this discussion is now moot, following the rapid and conclusive consensus in the AfD discussion that the topic of the article is definitely notable. Gandalf61 (talk) 09:53, 3 October 2008 (UTC)

"Balloon calculus"

user:Espressobongo has been installing external links to something called "balloon calculus", which claims to be a novel approach to some aspects of calculus (see Special:Contributions/Espressobongo). When you go to the web site, it turns out that (as far as I can tell) you can't find out what it's all about unless you download their software. Opinions? Michael Hardy (talk) 18:59, 2 October 2008 (UTC)

I think you need to report this to WP:ANI. IIRC, there is a bot that automatically removes spammy links (but it must be configured). VG ☎ 19:09, 2 October 2008 (UTC)

I reported it to WP:RSPAM. VG ☎ 19:19, 2 October 2008 (UTC)

And reverted all of the links (hopefully). It's clearly spam based on the guidelines. VG ☎ 19:32, 2 October 2008 (UTC)

I can't see a link on the contributions page. There's one to calculus but that's about it. Is that because the article has been deleted?  Δεκλαν Δαφισ   (talk)  19:52, 2 October 2008 (UTC)

He/she inserted external links, not Wikipedia links. (There are no deleted contributions (admin only).) — Arthur Rubin (talk) 20:02, 2 October 2008 (UTC)

I think reporting this to WP:ANI and WP:SPAM was ill-advised. Persons knowledgeable in the subject matter had already dealt with it without newbie-biting. If people who've never heard of mathematics but who work daily on WP:SPAM start dealing with it, I expect they will tell me that since I am knowledgeable in the subject matter I am scum who should meekly obey them while they kick me. That's what they do. If a link constitutes spam, that's not necessarily because the page's owner intended it that way, and it is possible that the page's owner can alter it in such a way that the link has value, and we are better qualified to judge that sort of thing than are admins who've never heard of mathematics and who believe we should obey them because of it. Michael Hardy (talk) 19:08, 3 October 2008 (UTC)

No offense, but I think you're blowing it way out of proportion. Nobody told him he was scum. I gave him a polite, albeit automated, level 1 warning (see User_talk:Espressobongo). Adding the same website link indiscriminately to many pages (Quotient_rule, Chain_rule, Product_rule, Antiderivative, Integration_by_parts, etc.) meets the Wikipedia definition of spam. He gave no indication how his site is germane to the articles he linked to, and the site itself is raised a big "huh" from me and another editor above. When I reported him to WP:RSPAM I had no idea if he was going to stop or not, and my report was intended to prevent further disruption and clean-up work. Hindsight is 20/20 I hear. VG ☎ 20:36, 3 October 2008 (UTC)

I didn't mean they told the alleged spammer he was scum; I meant those who are in the habit of enforcing rules against spam are sometimes gratuitously disrespectful, not to alleged spammers, but to subject-matter experts whose interest is in the topics of the articles on which alleged or suspected spam is posted. Michael Hardy (talk) 01:07, 4 October 2008 (UTC)

Vandalism: Julia Sets

Resolved

I've just found this upon reading the article on Julia Sets:

"It is commonly believed that Julia sets are named in honor of Gaston Julia, the celebrated French mathematician. Unfortunately, this is a vicious lie perpetrated by sexist mathematical historians seeking to remove every last trace of female influence from the annals of the numerical arts. The true namesake of these sets is Julia Gaston, the renowned Amazon.com customer whose lofty literary tastes (Vonnegut, Bradbury) are counterbalanced by her low-brow DVD selections (Desperate Housewives) and silly video game preferences (Lego Indiana Jones, Karaoke Revolution). Also, she appears to like cooking. See for yourself.

Fun facts about Julia Gaston:

• She was born on Christmas.
• She likes fun, stuff, and fun stuff.
• She hails from Wichita, Kansas, that beacon of light on the banks of the mighty Arkansas.
• One day, while waiting for UPS to deliver the Mama's Family DVDs she purchased from Amazon.com, she had a breathtaking mathematical insight that led to the discovery of Julia sets, whose eponymous title has since been misattributed to Gaston Julia.

"

I'm not to experienced, and can't find who added this rubbish. But can an admin get on the case and block the fool?

I've deleted most of this so that it simply reads "It is commonly believed that Julia sets are named in honor of Gaston Julia, the celebrated French mathematician."

This sentence may need to be rewritten: Is it names after him, or is it believed to be named after him?  Δεκλαν Δαφισ   (talk)  15:50, 3 October 2008 (UTC)

Checking the page history can reveal who did what. You may also find it easier to use the undo link there, which ensures all traces of the vandalism are gone. WP:POPUPS is another useful tool. --Salix (talk): 16:09, 3 October 2008 (UTC)

Do we have a rule about rounding numbers from sources?

Sorry for asking a question that isn't directly relevant to any maths articles, but I think this is one of the few places where I don't have to explain what the problem is. Many population numbers in Wikipedia look like "19,297,729 (2007 est.)". I consider this very embarassing, wondering (only rhetorically, of course) why we never see decimal points in this context. Do we have guidelines for or against reasonable rounding when our sources pretend some preposterous precision? --Hans Adler (talk) 22:46, 3 October 2008 (UTC)

Usually these population figures come from surveys or consensuses. For example, in the UK we have a national consensus every ten years that it manditory: if you're on the governemnt's radar and you don't complete it then they'll take you to court. As such we get figures with similar levels of accuracy. Of course there are people that aren't on the governement's radar, and this might cause a problem. An easier way might be to say that the official population was around 19.3m in 2007.  Δεκλαν Δαφισ   (talk)  23:15, 3 October 2008 (UTC)

I read "est." as "estimated" and "2007" as "at some undisclosed time on some undisclosed day in the year 2007". These numbers are probably produced by bureaucrats who are afraid of decisions (such as how, exactly, to round). They run some software that gives them a number like 19,297,728.72954 ± 119.30673, and they invariably round up or down to the next integer rather than to a round number that reflects the actual precision. In the case of a census it makes a bit more sense, but even then I think we should round. I don't think we should ever have more than 3 non-zero digits in a population number. --Hans Adler (talk) 23:29, 3 October 2008 (UTC)

From Wikipedia:Manual of Style (dates and numbers):

Avoid overly precise values where they are unlikely to be stable or accurate, or where the precision is unnecessary in the context (The speed of light in a vacuum is 299,792,458 metres per second is probably appropriate, but The distance from the Earth to the Sun is 149,014,769 kilometres and The population of Cape Town is 2,968,790 would usually not be, because both values are unstable at that level of precision, and readers are unlikely to care in the context.

Of course, this advice may be controversial, and there may be other rules contradicting / clarifying this, so it would be dangerous to storm ahead and change this in thousands of articles. -- Jitse Niesen (talk) 12:24, 4 October 2008 (UTC)

A security guard at a museum told a visitor that a dinosaur skeleton displayed there was 70,000,006 years old. When asked how he could be sure of so precise a value, he explained that it was seventy-million years old when he started working there, six years earlier. Michael Hardy (talk) 04:12, 6 October 2008 (UTC)

Thanks a lot, that's exactly what I was looking for. I suppose one of the reasons it's not being followed is because it doesn't give clear instructions what to do (i.e. how to round, exactly), and only says what not to do. I'll try to look through the MOSNUM talk page archives. These issues must have been discussed before, and that looks like a better place for doing it. --Hans Adler (talk) 13:02, 4 October 2008 (UTC)

conversions of tables to orbit diagrams

A discussion at Talk:Gliese 581 c revolves around the OR-ness of converting data tables to diagrams of orbits. This might be of interest to you. 70.51.8.75 (talk) 08:56, 6 October 2008 (UTC)

Is TeX broken?

When I went to put in some new formulas, such as

$J^{\alpha }=4\,,$

they are not being formatted. Can anyone help? JRSpriggs (talk) 14:08, 6 October 2008 (UTC)

It's just extremely slow, for some reason; the image has loaded now for me. I'll sign on and point it out to the site admins. This sort of thing note might be better on the technical village pump. — Carl (CBM · talk) 14:16, 6 October 2008 (UTC)

Which web browser do you have? Some of the security updates for older versions of Windows have caused this to happen. Certain icons are downloaded by the browser, and these were being used to transfer viruses etc. Some of the Windows patches stopped the browser from downloading these icons. When I use Explorer I can't see the LaTeX, it just shows the raw code. I have to use Firefox to be able to see it.  Δεκλαν Δαφισ   (talk)  14:22, 6 October 2008 (UTC)

I pointed it out to Domas on IRC, he did some voodoo behind a curtain and says it is fixed now. Some problem with the image servers, I don't know any details. — Carl (CBM · talk) 14:24, 6 October 2008 (UTC)

Yes, it seems to have cleared up now. Thank you and Domas. By the way I am using Firefox. JRSpriggs (talk) 14:50, 6 October 2008 (UTC)

Locally connected space

I just reviewed one of the first articles that I have ever edited and I was wondering what criteria it needs to satisfy in order to be a feature article. I have already read the Wikipedia page on feature articles. At the moment, the article looks fine to me and the only problem is that the article seems to lack references. If I fix this, can I nominate it for a featured article (the mathematical correctness seems alright, I don't think further information can be added to the article either)? Or at least a good article? It does not seem so but if someone could tell me what criteria (specifically) that the article must satisfy I could fix that up.

Topology Expert (talk) 15:33, 6 October 2008 (UTC)

Lots of references are certainly required. You should probably also add something about the history of the concept and any other non-technical stuff you can think of that's relevant. At the moment the article is extremely technical, but there is only so much you can do about that for such a technical subject. The criteria for FAs and GAs are at Wikipedia:Featured article criteria and Wikipedia:Good article criteria. You can get more detailed advice on how to improve an article by submitting it to Wikipedia:Peer review. --Tango (talk) 16:22, 6 October 2008 (UTC)

The article would need quite a big restructuring. It seems to follow a maths textbook format with a theorem-proof, theorem-proof style so a rethink in style would be necessary. Whether wikipedia should contain proofs is whole other question see Wikipedia talk:WikiProject Mathematics/Proofs, at least the proof should contain a reference to satisfy WP:V. An image or two would also help. Have a look WP:WPM#Assessment of mathematics articles for some examples of current maths GAs and FAs. --Salix (talk): 19:14, 6 October 2008 (UTC)

(ec) Yes, history and references are certainly needed. The article is also crying out for images to illustrate some of the concepts and (counter)examples.

Another substantial issue is the overall style. At the moment, while there's a lot of great content, it is written more in a textbook than an encyclopedia style. There are more detailed arguments and proofs than are appropriate for an encyclopedia article. There are a lot of sentences beginning "To see this..." Also, try to avoid self-references ("this article", "In the next section...") and the first person plural (the latter is not forbidden, but a phrase like "which we shall prove imminently" is not encyclopedic). The article itself is supposed to be invisible, if you see what I mean, whereas a textbook advertises itself to the reader. The article also has quite a few lists. Wikipedia tends to prefer prose as much as possible, to provide connections between things. Speaking of connections, it looks as if more wikilinks would be helpful.

A good place to start might be the lead section: this is supposed to be both a summary of the article, and a good introduction to the subject. At the moment it is a definition and one interesting fact. The definition probably needs to be expanded in its own section, while the lead itself needs to summarise (in about 3 paragraphs) other aspects of the article as well.

Changes along these lines would give you a good shot at GA level. As the content is thorough, the main issue with FA is the immense attention to detail required: references and citations need to be formatted consistently, dashes and spacing correctly used, the prose will need to be copyedited (e.g., in the sense of Strunk: "Omit needless words"),... see WP:MOS for a start.

One more suggestion: look at some existing maths and science GAs and FAs. I hope that helps. Geometry guy 19:17, 6 October 2008 (UTC)

I think that this article needs a lot of work to be a satisfactory article, let alone a GA or FA. I made (many) comments on Talk: Locally connected space. Plclark (talk) 20:00, 6 October 2008 (UTC)

I've left a couple of remarks at Talk: Locally connected space. Paul August ☎ 21:42, 6 October 2008 (UTC)

Thankyou all for your response. I appreciate it! I will try to make edits along those lines in the next couple of days and (hopefully) fix up the main problems.

Topology Expert (talk) 08:13, 7 October 2008 (UTC)

Compass and Midpoint Problem

Not sure if this should go here, but I encountered a problem related to geometry drawing, but did not find an article on it.

So basically, you have a compass. No ruler or anything else. This means you cannot draw a straight line. So given a line segment, use the compass to find the midpoint of it.

Anyways if there is any relevance in this, I thought it might be important to write an article related to geometry drawing? Any tips on the problem let me know ;). --electricRush (T C) 01:59, 7 October 2008 (UTC)

Try asking at Wikipedia:Reference desk/Mathematics. Ozob (talk) 02:44, 7 October 2008 (UTC)

Or look at the Mohr–Mascheroni theorem. Richard Pinch (talk) 05:28, 7 October 2008 (UTC)

Terminology proposal in topology: locally P

Ask yourself the following question: let P be a property of topological spaces. Is it then necessarily the case that the phrase "locally P" has an unambiguous meaning for you, or does it have to be defined separately depending on what P is?

I would like to propose the following definition of "locally P" in all cases: we say that a space is "locally P at a point x" if there exists a base of neighborhoods of x each having the property P, and a space is "locally P" if it is locally P at each of its points. Here I had better add that by a "N is a neighborhood of a point x" I mean that x lies in the interior of N but N is not necessarily itself open: this is the more common terminology on wikipedia and elsewhere, but it is not universal.

If you compare this to the various meanings that "locally P" has had historically for various important properties P, you will see that the phrase "locally P" has different meanings for different people. For instance, the current article locally compact space has a very clear discussion of this ambiguity, and you can see that I am advocating the third definition of locally compact, which is the one used by Willard. However, Willard defines "locally connected" to mean that every point has a base of open connected neighborhoods, which is an apparently stronger condition. (In fact he does not explicitly define "locally connected at x".) However, Engelking defines "locally connected" according to the general scheme above. Interestingly, the article locally connected space does define "local connectedness at x" according to the above scheme, but a careful reading indicates that probably the Willard definition is intended: on the one hand, an arbitrary neighborhood is denoted by U, suggesting that it is supposed to be open, and more significantly there is an entire section on "weakly locally connected" which gives, formally, the same definition as before but in langauge that makes clearer that non-open neighborhoods are allowed. The article does make nicely clear the fact that the two terms are equivalent when applied to an entire space, but not when applied to a single point.

As far as I know, my proposed definition of "locally P" agrees with at least one of the standard definitions in the primary sources wherever it is defined, and the fact that it has an intrinsic meaning seems to be a big expository and pedagogical advantage. I propose that there be an article on "local property (topological space)" which carefully explains this convention and that it be used (with explicit reference and all due explanation) in general topology articles.

As a subsidiary point, I would like "weakly locally P" to mean that there exists at least one neighborhood of every point which has property P, so that P itself implies weakly locally P but not necessarily locally P. But this is less critical and I don't wish to push it as strongly. Plclark (talk) 09:28, 7 October 2008 (UTC)

The definition sounds good to me since it satisfies:

• For every point x, and any open neighbourhood U of x, there is a neighbourhood V of X having the property P

Topology Expert (talk) 11:26, 7 October 2008 (UTC)

Unless you have a verifiable source for your definition of "locally P", it is original research and has no place in wikipedia. Each article about local properties should give NPOV description of the term giving all definitions in use due weight. (TimothyRias (talk) 09:49, 7 October 2008 (UTC))

I'm not sure whether I agree that a consolidation of cognate terminology is OR. In any case, I think that it is important for WP:WPM to have terminology which is standardized across articles, chosen so as to make cross-references as easy and efficient as possible, and easy for a reader of any given article to pick up. This particular terminology proposal is so natural that I'm sure that with some effort I can find a primary source for it. So let us assume that such a source can be found: then what do you think? Plclark (talk) 10:07, 7 October 2008 (UTC)

I have found at least one source giving a general definition of "locally ..." Alan Hatcher's Algebraic Topology (available online) does so on page 62. He however requires a base of open neighborhoods. (Clearly "locally compact" requires some extra explanation in this context) This is probably an issue you will find across different sources, namely that they won't agree exactly on the definition.

Standardizing the terminology across articles would 1)violate NPOV, we would basically proclaim one definition to be better than others. 2)Almost impossible to realize. 3)Undesirable in articles where in the relevant subfield there is a strong concensus on which definition to use.

Also, since having this ambiguity in the actual field of mathematics seems to cause very little trouble (the definition to use is usually clear from the context). I don't see why it should cause much trouble on WP. (TimothyRias (talk) 12:27, 7 October 2008 (UTC))

As a side note. Having a base of connected open neighborhoods is equivalent to have a base of connected neighborhoods. Every open neighborhood is clearly a neighborhood. The other way around, the connected component of the interior of neighborhood containing x is a connected open neighborhood of x. (TimothyRias (talk) 09:57, 7 October 2008 (UTC))

Your explanation in "The other way around" was not clear to me: what is the connected component of a possibly disconnected set? Note that the current article (which was not written by me, so I will want to look more carefully) purports to give a counterexample to this, namely the broom space. If you still think your argument is correct after reading the article, please comment at the talk page. Plclark (talk) 10:07, 7 October 2008 (UTC)

See also Exercises 3.6 and 3.7 on page 157 of K.D. Joshi's Introduction to General Topology, available on google books. Plclark (talk) 10:14, 7 October 2008 (UTC)

Nevermind, major brain fart on my part. The connected components of an open set, need not be open sets themselves. (This is true if there is only a finite number of components, but can fail if there are infinitely many components see rational number as example.) (TimothyRias (talk) 11:56, 7 October 2008 (UTC))

In fact, the page local property already exists, and includes both what I want to call "locally P" and "weakly locally P". It does not give references, but the fact that it exists certainly suggests that I will succeed in finding references. I am willing to flesh out this page, and then my proposal becomes that people either use the terminology "locally P" consistently with the way it is used on this page or explain that the terminology that they are using is not consistent with that page but they are using it anyway because XXX (e.g. because it is the terminology used in their primary source). Plclark (talk) 10:25, 7 October 2008 (UTC)

It's better if each article simply explains what each of its terms means (perhaps very briefly). Even if we have a convention, (1) many readers will not be familiar with it and (2) some readers will assume it's a different convention than it is. The nature of Wikipedia is that any article might be an entry point for a reader coming from a search engine; we don't have the luxury of a textbook of defining our conventions up front. — Carl (CBM · talk) 12:45, 7 October 2008 (UTC)

Agree. Paul August ☎ 20:53, 7 October 2008 (UTC)

Here is a reference for a general definition of "local property": [1], starting at the first complete sentence on the page. Ozob (talk) 22:22, 7 October 2008 (UTC)

Stokes' theorem

I moved this article from the strange name "Stokes's theorem" just now. If anyone objects to this, let's talk at Talk:Stokes' theorem. Apparently Skewes' number has also been moved to "Skewes's number" and back recently. — Carl (CBM · talk) 02:12, 6 October 2008 (UTC)

It is fine with me, as long as Stokes’s theorem works as well. --Yecril (talk) 11:46, 8 October 2008 (UTC)

Different style of wiki math formatting

User:Yecril has been advocating a different format of writing mathematics using several templates and the <var> tag. Personally, I find it somewhat cumbersome, and don't see advantages that outweigh the difficulty in editing. Here are some examples:

[2] [3] [4]

I don't think these unilateral changes (which are not mentioned in the edit summaries) are a good idea. I want to get a sense of what other people think. — Carl (CBM · talk) 13:01, 7 October 2008 (UTC)

I strongly dislike this blowing up the (already cumbersome) notations we have to deal with, without or almost without any positive effect. If other's agree, as you seem to, I suggest we as a Wikiproject communicate this somewhat in unison to the people setting up these guidelines and stuff to tell them that we are not happy (to say the least) with this development. Jakob.scholbach (talk) 13:08, 7 October 2008 (UTC)

There hasn't been any change in the manual of style, as far as I can tell. There was a discussion about using <var here but it didn't get consensus, and has been idle since Sep. 30. I don't think there has been a thorough discussion of the new templates, like {{{math}}. — Carl (CBM · talk) 13:29, 7 October 2008 (UTC)

You should take an other look at those edits. They all involve articles that use <code><math></code> tags. In order to get the same styling on the other math expressions they need the <code>{{math}}</code> template and <code><var></code> tags (although the later could be replaced by any other way of acieving italics.) So, at least the <code>{{math}}</code> templates were absolutely necessary to obtain uniform formatting. The use of var tags is debatable but anybody should be free to use them if they want to. (TimothyRias (talk))

I don't believe there is any establish practice of using the {{math}} template, so claiming it is "required" is somewhat odd. Indeed, the math template was created by Yecril himself in June [5]. The last time I checked, it was only used on a few articles Yecril had edited.

The underlying issue is the unilateral change of articles from the established style to this new, undiscussed, unagreed style. This seems to violate our established rule not to make style changes unless there is strong agreement behind them. — Carl (CBM · talk) 13:29, 7 October 2008 (UTC)

"required" in the sense that it is the easiest way of recreating the formatting used by the < math> tag. The template simply assigns the same CSS style to the expression as is applied to HTML output produced by the TeX processor. (At moment this only changes the font to serif, but it should also make the spaces non-breaking). I wasn't implying that there was any guideline requiring this. (guidelines can't require anything by definition) (TimothyRias (talk) 14:21, 7 October 2008 (UTC))

@Timothy: I'm talking about replacing ''s'' by {{math|<VAR >s</VAR >}}. It seems to me to be a gigantic overkill replacing 5 characters by 23. I also disagree that anybody should use the markup he wants. Simplicity in editing is a key point for WP's success. Markup changes as above seem to torpedo this aim. Jakob.scholbach (talk) 13:34, 7 October 2008 (UTC)

Well, {{math|}} is a lot shorter than the <code><span style="font-family:serif"> </span></code>, which would be needed to obtain uniform formatting of formulas in those articles. I sort of agree with your point about <var>, though. (TimothyRias (talk) 14:21, 7 October 2008 (UTC))

Timothy, could you please be a bit more specific about the articles already using <math> ? When I look for instance at the first example given by CBM, the only <math> tags I can see are rendered as PNG. Are these the ones you are referring to, or did I not look carefully enough? I would think that the styling of PNGs are so different from the styling of HTML that it does not matter whether the HTML is serifed or not. -- Jitse Niesen (talk) 15:43, 7 October 2008 (UTC)

The advantages of using wikicode for formulas:

1. There are no images involved.
2. HTML constucts are available (bookmarks, titles, hyperlinks, borders, frames).
3. If we decide do typeset something in a different way, e.g. that the imaginary unit should be upright, we can do it by modifying the corresponding template (instead of modifying the code on the pages).
4. User preferences regarding styling of mathematical formulae are applicable.
5. The styling of the text rendered is more consistent.
6. Full power of wikicode is available inside formulae.
7. You can actually copy the equation as displayed and paste it into a HTML document, such as an e-mail message, without attachments.
8. We do not depend on the developers of Mediawiki to change something that does not work as expected.
9. Formulae do not break unless instructed with <BR >.
10. We can manipulate word spacing (which may be smaller from word spacing in English text).

The ultimate goal is to ask the texvc engine to do the same so that the output is identical to what comes out from the math island.

The reason the templates are not mentioned in edit summaries is that I never touch text that is readable and not problematic, so the summaries reflect the problem I was trying to address.

I am aware of the formula length problem, although using templates makes this a bit less drastic. My POV is that when you write down these things, you actually think about them using words, e.g. integral of exponent of minus x from zero to plus infinity is 1. This translates to the templates you have to call:

{{math|{{minteg|0|+∞|{{mexp|−<VAR >x</VAR >}} d<VAR >x</VAR >}} {{=}} 1}}

to get ∫^+∞
₀e^−x dx = 1. The source is admittedly hard to read; TeX provides better visual clues. I can only repeat my argument about due dilligence: there are more readers than writers. More complicated formulae are usually better rendered stand-alone; I am not pushing for a wholesale replacement.

--Yecril (talk) 13:51, 7 October 2008 (UTC)

I strongly dislike this format, as much as I generally prefer semantic markup. This is seriously bloated.

Most of your advantages already apply to the current situation. TeX can be copied as plan text and doesn't break. User settings change how it's displayed, too -- if they want MathML they get MathML (though why anyone would want that is beyond me), if they want .png they get .png.

CRGreathouse (t | c) 13:58, 7 October 2008 (UTC)

TeX can be copied as plain text but it cannot be copied with formatting except as an image. With images you cannot even navigate to a section because the document scrolls away while the images load. And it takes forever on a slow connection. MathML is not part of contemporary browsers so you get nothing at a public kiosk.

And how do you want to get semantic markup without typing? Computers are rather dumb beasts; you have to talk to them in capital letters. --Yecril (talk) 11:23, 8 October 2008 (UTC)

To Yecril: a unformatted or badly formatted (as you would probably consider it) line such as $\int _{0}^{\infty }e^{-x}dx=1$ (<math>\int_0^\infty e^{-x}dx=1</math>) or ₀∫^∞ e^−xdx = 1 (₀∫^∞ e^−''x''dx = 1) is always better than a line of code, which is perfectly formatted but never written, or subsequently improved (because it's unreadable). "Due diligence" is a term I cannot accept in these circumstances. As far as I can see, this is just fooling around with what would be theoretically possible. Jakob.scholbach (talk) 15:55, 7 October 2008 (UTC)

I would say that {{minteg}} is much easier to read than its inline expansion. The difference is that you read what the author wanted to write, not the particular style he had to choose for his writing. I agree the letter "m" in the beginning is confusing, and there are templates that not use it, such as {{radic}}; however, I think that polluting the main namespace with mathematical templates would be a bad idea. It would be best if you could get context-dependent templates but MediaWiki does not support it at present.

And if a user like Gandalf wants his formulas to be bigger, or silver, or on a yellow background, or whatever, he has no way of getting that effect. --Yecril (talk) 10:49, 8 October 2008 (UTC)

About a month ago I had a lengthy discussion at Yecril's talk page about his unilateral markup changes to modular group. I suggested he should seek consensus here, but he was reluctant to do so. In the end I reverted his changes to modular group and triangle group. I continue to find his proposed markup cumbersome in use and poor in appearance. I suggest Yecril's unilateral markup changes should be reverted on sight unless and until he can obtain consensus here or at WP:MOSMATH. Gandalf61 (talk) 16:29, 7 October 2008 (UTC)

I was not reluctant; I just did not have enough information to handle all Gandalf’s problems, or anybody else’s, which is not solely my fault but the MediaWiki developers’ whose reaction time is a good example of silicon-based life. This idea is immature for asking consensus and requires thorough testing and consideration. --Yecril (talk) 10:36, 8 October 2008 (UTC)

Yecril - in that discussion on your talk page I suggested at least four times that you should bring your ideas here for discussion, but you didn't. That is clear reluctance in my book. If your new markup is still immature then you should not be trying it out in live articles - Wikipedia is not your personal sandbox ! Gandalf61 (talk) 10:57, 8 October 2008 (UTC)

And where are the dead articles I can try it on? --Yecril (talk) 11:32, 8 October 2008 (UTC)

It sounds like you don't know this, but you can copy over any articles to your userspace subpages and experiment there to your heart's desire. --C S (talk) 17:26, 8 October 2008 (UTC)

Now for what it's worth, I have no objection to having <math> incorporate some of these changes internally for users requesting HTML rather than a .png or MathML. But putting this directly in the pages is a bad idea. CRGreathouse (t | c) 17:33, 7 October 2008 (UTC)

I am afraid it is not be a simple task, for the following reasons:

1. We have to know how it should look (what is feasible) before we submit a request to implement it.
2. math islands do not support templates, styling, wikilinks and the like. (They do not even support macros.)
3. You cannot fix anything quickly in this setting.

--Yecril (talk) 11:40, 8 October 2008 (UTC)

This is a bad idea for a couple of reasons:

• For simple math formulas using plain italics for variables is a lot easier to type than the <var syntax.
• For complex math, the <math> LaTeX constructs can be translated by Wikipedia's servers to MathML as well (you can set this in your user preferences), which the preferred way to render it if you have proper fonts installed. MathML is a standard, and browser support is moving in that direction; PNGs are for backward compatibility. Also LaTeX markup is the de facto standard that most mathematicians already know. This new {{math markup is Wikipedia-only.

This message approved by: VG ☎ 17:54, 7 October 2008 (UTC)

So, should {{math}} and associated templates be put up for deletion? (If so, how. As an inline template, we can't include a TfD notice into the included text....) — Arthur Rubin (talk) 18:08, 7 October 2008 (UTC)

{{tfd-inline}} or {{tfd-tiny}}. Septentrionalis PMAnderson 04:45, 8 October 2008 (UTC)

Slight change of topic: The subscript 0 before the integral sign, in the above examples, looks purely awful. Is this notation actually used, anywhere? --Trovatore (talk) 19:34, 7 October 2008 (UTC)

I agree. Michael Hardy (talk) 20:11, 7 October 2008 (UTC)

There is an old-fashioned style with 0 under the integral sign, but this is not it. Septentrionalis PMAnderson 04:56, 8 October 2008 (UTC)

This is a compromise:

1. ∫₀¹ looks much worse, to the point of being unreadable;
2. ∫₀¹ needs different manual twiddling in each case;
3. ∫¹
   ₀, as it is implemented, may break older browsers;
4. ∫_{[0, 1]} is acceptable but rather surprising.

I also find this style appealing because of the similarity with [1…n]: from 0, integrate, to 1.

Also, if we decide to prefer one over the other, it would be as simple as changing {{minteg}} to that effect, except for syntax #2. No bots, no nonsense. --Yecril (talk) 12:03, 8 October 2008 (UTC)

OK, so first of all, I don't agree with you that #1 looks worse. The slight space between the top of the integral sign and the 1 is a mild aesthetic flaw, but to my eye looks much better than having the 0 come before the integral sign. More to the point, even if it didn't look better, it would still be the one we'd have to choose (if those two were our only choices), because I'm afraid the lower-limit-before thing is more or less your own invention (or at the very least has only a tiny diffusion in the literature), and that's not allowed here. WP does have outlets for your creativity but they're quite restricted and certainly don't extend to making up notation.

However, to give my opinion on the aesthetic question -- actually they all look quite horrible. Only the LaTeX PNG images look even decent. Probably we should adopt a guideline that one should never (well, hardly ever) write integrals inline -- they should always be in a displayed <math> environment. --Trovatore (talk) 08:04, 9 October 2008 (UTC)

Yecril formatting

Yecril (contribs) just added an entry in his style at the article Almost prime. This should be a good test: rather than existing code being quickly converted, this should be ideally suited to the style. Anyone want to post a side-by-side of this?

If anyone happens to edit the page, you can flesh out the source with a full citation:

Gérald Tenenbaum, Introduction To Analytic And Probabilistic Number Theory, Cambridge University Press (1995)

if desired. CRGreathouse (t | c) 21:02, 7 October 2008 (UTC)

On Firefox 3.0.3 on Mac OS X 10.5, this is what Yecril's version and the original TeX version look like:

Yecril version: File:Yecril.png

TeX version: File:Hardy.png

--C S (talk) 01:49, 8 October 2008 (UTC)

Thanks for the screen shots, I can see the same picture (MSIE7@MSWINXP). Please rename them somehow; [[:Image::Yecril.png]] is not a photo of me. --Yecril (talk) 10:25, 8 October 2008 (UTC)

What's the point? They'll be deleted soon when their role in the discussion is done. --C S (talk) 17:30, 8 October 2008 (UTC)

User:Michael Hardy has standardised the stand-alone formula in Yecril's addition to almost prime, and I have standardised Yecril's in-line expressions - I find that the font produced by Yecril's new markup is too small for readability.

As an aside, does anyone know whether the asymptotic formula at the end of the article is for numbers with at most k prime factors, not necessarily distinct (i.e. Ω(n)<=k) or for numbers with at most k distinct prime factors (i.e. ω(n)<=k). From the context of the rest of the article, I have assumed the former, but I am not certain. Gandalf61 (talk) 09:12, 8 October 2008 (UTC)

Gandalf61! It is for both, please check it up and revert. Your π does not resemble π at all. It is so sharp that I am afraid of getting hurt when I look at it.

Font too small? use

SPAN.texhtml { FONT-SIZE: LARGER }

That is the power of CSS. You do not have to cripple everyone else’s view because it is too small for you.

--Yecril (talk) 10:20, 8 October 2008 (UTC)

Yecril - not just me - see screen shots posted by C S above. I should not have to make bespoke changes in my style sheet to make your experimental markup readable. Gandalf61 (talk) 11:02, 8 October 2008 (UTC)

As I already noted, I already saw them, and it looks exactly the same at my place. That is all right with me although I cannot speak for everybody. If we agree it is wrong by default, we can put the relevant declarations into a common stylesheet. If I am reluctant to get published, you are reluctant to coöperate. --Yecril (talk) 11:32, 8 October 2008 (UTC)

Yecril, in this matter the only one reluctant to cooperate, in the sense of agreeing to common consenus (firmly (re)established by the posts of everybody above except you), is you. Note that not everybody or actually apparently nobody here is willing to change his style sheets, editing habits, writing habits (such as writing integral over [0, 1] instead of integral from 0 to 1) just because you propose it. Jakob.scholbach (talk) 12:29, 8 October 2008 (UTC)

Not willing is equivalent to reluctant. I did not propose writing integral over [0, 1]. --Yecril (talk) 13:15, 8 October 2008 (UTC)

Many people will read the articles without having WP accounts, and most of those who do have an account either don't know CSS, or are unaware that they can modify their monobook.css. This hardly qualify as reluctance. So the focus should be on what people see using the default style, even if experienced Wikipedians can edit their own stylesheet. (BTW, in the first screenshot above it's impossible to understand whether the last-but-one (k − 1) is an exponent of log log n or the numerator of the fraction, i.e., whether it's

${\frac {(\log \log n)^{(k-1)}}{(k-1)!}}$

or

$(\log \log n){\frac {(k-1)}{(k-1)!}}$. -- Army1987 (t — c) 23:46, 10 October 2008 (UTC)

Wow, CS's screenshot looks pretty nice. Here is what mine looks like in Konqueror 3.5.5. Methinks this has some accessibility issues for people using alternative browsers. siℓℓy rabbit (talk) 12:25, 8 October 2008 (UTC)

Here it is in emacs, my other browser of choice:

Cheers, siℓℓy rabbit (talk) 12:32, 8 October 2008 (UTC)

The current KDE release is 4. The argument to use File:Clubs.png instead of ♣ was rejected because ♣ is in the standard HTML character set. Of course, this case is rather more important. I am shocked and unable to help because I do not use KDE; however, Safari is built on the same engine and it does not have this problem. I think we would get better results even with Lynx; happy users of other retarded browsers, please report here.

And please please rename the images; I really do not look like that!

--Yecril (talk) 13:15, 8 October 2008 (UTC)

The Yercril version in Lynx looks like

The number p[k](n) of integers of at most k prime divisors from the
initial segment [1...n] is asymptotic to^[1]
            p[k](n) ?1 ^n/[(log n)] ╖ ^(log log n)^(k - 1)/[(k - 1)!]

while the current version looks like

The number p[k](n) of positive integers less than or equal to n with
at most k prime divisors (not necessarily distinct) is asymptotic
to^[1]
      \pi_k(n) \sim \left( \frac{n}{\log n} \right) \frac{(\log\log
      n)^{k-1}}{(k - 1)!},

Really, neither one is great; I can figure the LaTeX one out more easily (what's ╖? why the question mark? why is 1 raised to the power of n?), but Yecril's one looks nicer in plain text.

CRGreathouse (t | c) 20:26, 8 October 2008 (UTC)

Its worth distinguish three different places where mathematics is encountered

1. Isolated variables in text. Eg at most k prime divisors
2. Inline mathematical expression
3. Displayed maths equations

It seen clear to me that latex is best for display equations, he other two cases are less clear. Inline mathematics is tricky we have fairly inconstant usage of this through wikipedia,a mixture of some <math> tags, some awkward wikicode markup ''x''² and a smattering of template based code. Generally most inline equations look horrible, the fonts don't match those of display equation (serif vrs san-serif), latex inline don't line up with the surrounding text well there, font sizes don't match. Display of special characters is dependent on the user having a correct set of fonts and are frequently missing.

The distinction between isolated variables and longer equations follows a discussion on MOS (text formatting) on the case for the <var> tag, which is a html tag to indicate a variable. There seem to be case for semantic markup of isolated variables if for no other reason than making wp more accessible for screen readers: <var>x</var> indicates this is a variable, ''x'' just indicates its in a italics. The semantic case weakens for anything more complex than a single variable as a proper semantic markup get very verbose, better to just indicate that the whole equations is an expression.

Given that inline mathematics is currently broken what is to be done? ideally we should be pressing for better support in software rather than have to use a variety of workarounds. Maybe there is a case for an <inline-math> element to complement the <math> element (TeX has $$ and $ with different formatting rules). --Salix (talk): 15:22, 8 October 2008 (UTC)

The only difference between $$ and $ that's relevant for WP is that $$ starts in display style and $ starts in text style; you can switch between them manually using \displaystyle or \textstyle. Everything else is a matter of spacing with respect to the surrounding document; see the TeXbook, chapters 25, 26, and appendix G. There might still be a case for <inline-math> if you can think of some WP-specific formatting that would need to be done for inline equations. Ozob (talk) 18:11, 8 October 2008 (UTC)

Indeed but in the latex -> png conversion the surronding context is erased completely. Perhaps the difference between the two tag would be simply to use \displaystype for the maths one: $\displaystyle \int _{0}^{\infty }e^{-x}dx=1$ and \textstyle for inline: $\textstyle \int _{0}^{\infty }e^{-x}dx=1$--Salix (talk): 20:43, 8 October 2008 (UTC)

The main problem is not different font size or type, it is vertical alignment. In stuff such as $\textstyle {\vec {F}}$, $\textstyle j$, $\textstyle x^{2}$, $\textstyle x_{2}$, the baselines aren't at the same height as those of the remainder of the text or with each other. Also, some really trivial formulas including some TeX commands get rendered as PNG without any particular reason: $\mathbf {F} =m\mathbf {a}$, F = ma. For these reasons, I format inline formulas without TeX (e.g. ''x''<sup>2</sup>), and display formulas which cannot be decently formatted this way indented on their own lines.-- Army1987 (t — c) 00:06, 11 October 2008 (UTC)

I most definitely object to Yecril's characterization of my choice browser as "retarded". The problem is other browsers do exist, and something which may look ok to one set of users may definitely not look ok to another set. Even in Firefox, some of Yecril's earlier experimentations didn't look at all as advertised in his/her own screenshots. And before I upgrade to the "latest version of KDE", I assume that Yecril knows first-hand that this will *not* be an issue should I take the time to upgrade? siℓℓy rabbit (talk) 15:27, 8 October 2008 (UTC)

In fact, that does it. We are intended to be widely available to readers, who may have no choice what browsers they use. I think this discussion constitutes concensus to delete; if no-one other than Yecril has spoken up for his system in 24 hours, I will file a deletion request. Septentrionalis PMAnderson 18:57, 8 October 2008 (UTC)

Why must the templates be deleted? It seems to me that the system is not yet ready for use, and that it may never be. But if Yecril or others are interested in continuing to investigate it, why foreclose the possibility of learning something useful? -- Dominus (talk) 04:29, 9 October 2008 (UTC)

Yes. I don't expect anything good to come out of these templates, but I think they should be userfied, not deleted. --Hans Adler (talk) 11:38, 9 October 2008 (UTC)

If Yecril will consent to having them removed from the articles until there is consensus that they are an acceptable alternative, that will be satisfactory. Septentrionalis PMAnderson 14:59, 9 October 2008 (UTC)

A graph theory article proposed for deletion

See G127. Is this worth saving? Michael Hardy (talk) 20:19, 9 October 2008 (UTC)

If they proved their theorem, merge with Ramsey's theorem, where it belongs. I don't think we need the redirect; the name for the graph is unlikely to be of interest outside this one paper. Septentrionalis PMAnderson 02:56, 10 October 2008 (UTC)

Ramsey theory is a non-technical intro article to Ramsey's theorem. Is this wise? Will it produce good incoming links? Septentrionalis PMAnderson 03:10, 10 October 2008 (UTC)

Name suggestions at CfD

• Wikipedia:Categories_for_discussion/Log/2008_October_7#Category:Graphs_as_models_of_other_objects

Any additional ideas would be welcome. - jc37 06:58, 10 October 2008 (UTC)

Originator's explanation: see Category talk:Graphs#Subcategory suggestion, and please continue the discussion there. Twri (talk) 16:46, 10 October 2008 (UTC)

Riemann hypothesis

This article is, while in (IMO) mediocre state, rated A-class. Is there any particular processus to downgrade A-class articles like for GA and FA? Jakob.scholbach (talk) 21:01, 8 October 2008 (UTC)

There are a few A-class ratings from before the project's A-class review process was set up; this is one of them. The process to downgrade is the same as to assign a new rating. See Wikipedia:WikiProject_Mathematics/A-class_rating. If you start a review, I'm sure some improvements can be made. Otherwise, we may just want to remove the rating from all articles that did not go through the process; however, this is likely to be somewhat contentious and there should be consensus before any such action is taken. --C S (talk) 23:59, 8 October 2008 (UTC)

I wouldn't like to see that kind of mass removal. I'd prefer the individual review and downgrade option. CRGreathouse (t | c) 00:03, 9 October 2008 (UTC)

I remember that when the more recent discussion-based A-class system was introduced, there was a discussion of the existing A-class articles, people looked through them, and at that time there was agreement they were "good enough" not to demote them. So I'd rather see them removed on a case-by-case basis. Meanwhile, the A-class process has gone idle; was it too rigorous? — Carl (CBM · talk) 12:33, 9 October 2008 (UTC)

I've now put it up for review at Wikipedia:WikiProject Mathematics/A-class rating/Riemann hypothesis --Salix (talk): 14:15, 9 October 2008 (UTC)

@Carl: As an example, when working on group (mathematics) I skipped the A-class step, since I wanted to go for FA anyway. To me, it is not quite clear what the three-level organization of good and "better" articles gives us. Maybe the assessment scale is too fine? Jakob.scholbach (talk) 09:06, 13 October 2008 (UTC)

"On-Line Encyclopedia of Integer Sequences" - a reliable source?

See Wikipedia:Articles for deletion/Alexander R. Povolotsky's problem 1. Three articles by this author about his problems have been AfD'd as original research. He claims that the "On-Line Encyclopedia of Integer Sequences" where they have entries, is "managed/edited by renowned scientist - Neil Sloane, therefore OEIS reference is a Reliable Source!" I guess the key question is, to what extent are entries there vetted. Anyone know enough to confirm or deny? Opinions would be useful at the AfD. JohnCD (talk) 16:11, 11 October 2008 (UTC)

It may be reliable, but I would not think mere inclusion in the OEIS alone is enough to establish sufficient notability for a Wikipedia article. —Ilmari Karonen (talk) 16:35, 11 October 2008 (UTC)

There's some vetting. Enough that a specific claim in OEIS should be taken seriously. But most sequences in the OEIS simply aren't notable enough to have Wikipedia articles about them specifically. We certainly aren't going to have separate articles for every sequence that is describable as a binary quadratric form for example. JoshuaZ (talk) 16:45, 11 October 2008 (UTC)

It is certainly a respected source, but whether it's reliable is another question. As far as I've been able to verify various things I've found there, it's accurate. There is certainly some vetting, but that doesn't necessarily mean checking all the numbers in submissions. It does mean mathematicians have read the submissions and approved them. Michael Hardy (talk) 18:39, 11 October 2008 (UTC)

I would call it a reliable source (for WP purposes), certainly. But I agree with Ilmari Karonen that it does not establish notability. CRGreathouse (t | c) 01:23, 12 October 2008 (UTC)

Critical value

Hi everyone. I think the article should because become a disambiguation page because the meanings of critical value in differential topology and statistics are completely unrelated. It should be split into two different pages. What does everyone else think? Gizza^{Discuss ©} 07:41, 13 October 2008 (UTC)

If there were more information then certainly. These two articles are, at the moment, stubs. There's not much point spliting the arclices. If more work is done to these then they should be split.  Δεκλαν Δαφισ   (talk)  14:06, 13 October 2008 (UTC)

I agree that it should become a disambiguation page. An article is supposed to be about a topic, not about different topics that accidentally have the same name. Michael Hardy (talk) 19:14, 13 October 2008 (UTC)

Okay, great. Then there are a few articles that need to be changed. I have seen a few where a link basically links to a dictionary, i.e. def1, def2, etc. I guess the discussion page would be the place to post the discussion on those pages?  Δεκλαν Δαφισ   (talk)  20:29, 13 October 2008 (UTC)

Problem of Apollonius now featured

Just to let editors here know that there's a new mathematics featured article today. I know many project members have contributed to the article (and one is even cited!) so congratulations to all concerned! The main contributor to the article (by a large margin) is WillowW, so some of us are celebrating on her talk page. Geometry guy 20:26, 13 October 2008 (UTC)

Brian_Bowditch up for deletion

AfD here. VG ☎ 02:54, 15 October 2008 (UTC)

On this day...

From "On this day..." on the "main page:

• 1843 – William Rowan Hamilton first wrote down the fundamental formula for quaternions, carving the equation into the side of Broom Bridge (pictured) in Cabra, Dublin, Ireland.

Michael Hardy (talk) 04:56, 16 October 2008 (UTC)

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

Copy from archive of this page: "Dubious reference" at Graph isomorphism See Wikipedia:ANI#.22dubious_reference_....22.3F. VG ☎ 23:27, 30 September 2008 (UTC)

User Míkka said "The fact that it is repeated in some obscure articles by persons with little credentials in graph theory bears little weight" about the following persons: 1)M. I. Trofimov 2)E. A. Smolenskii 3)V. N. Zemlyachenko 4)N. M. Korneenko 5)R. I. Tyshkevich 6)R. T. Faizullin 7)A. V. Prolubnikov 8)Jitse Niesen 9)David Eppstein 10)Corneil 11)Gotlieb !!!--Tim32 (talk) 19:16, 1 October 2008 (UTC)

Sorry, but Míkka restarted this edit war!--Tim32 (talk) 00:08, 12 October 2008 (UTC)

In fact, Mikka reverted his own edit on 1 October to give you time to address his concerns. He then re-instated his edit on 11 October after you failed to do so. Calling this an edit war is a gross exageration. -- Jitse Niesen (talk) 19:58, 12 October 2008 (UTC)

It is not correct, "Sorry, I still don't have access to the article (ILL is proving slow on this one), so I cannot comment either way right now. VG ☎ 19:19, 12 October 2008 (UTC)" At the same time, I repeat again and again my reasons and links, but Míkka & Co is unable to understand the reasons, and did not answer my questions in generally. Recently, Arthur Rubin wrote:“I have trouble reading Mikka's English” and Míkka wrote to Arthur Rubin: “I have trouble in reading your English”. I think, this fact explains the situation -- my opponents have problems to read English. Also, I asked them to give me links to their publications about GI problem to understand their points of view better -- they have no, at the same time I have printed about 100 articles about GI, about Mathematical (Computer) chemistry, about computer sci. etc. It seems they dislike this fact as well. Is it envy? Sorry, but, for example, I can suppose that 4 students play game “2*2=5” vs me. --Tim32 (talk) 19:43, 16 October 2008 (UTC)

I don't have any trouble reading your English. I can see you haven't supported your statements. Any of them remaining in the article need to be removed until you can supply a reliable source. — Arthur Rubin (talk) 21:21, 16 October 2008 (UTC)

It is false! I supported my statements and put links to printed papers. It is your problem that you unable to understand these papers.--Tim32 (talk) 23:02, 16 October 2008 (UTC)

I haven't seen the papers. Those who have don't see any support for the statements you made in the article. — Arthur Rubin (talk) 23:44, 16 October 2008 (UTC)

And computational chemistry is not at all the same thing as mathematical chemistry, and neither is likely to have anything to do with graph isomorphisms, except possibly for graphs of valence (vertex degree) at most 6. — Arthur Rubin (talk) 23:51, 16 October 2008 (UTC)

Arthur Rubin wrote: "(vertex degree) at most 6." -- You are poor informed for example see Ferrocene -- vertex degree is 10 (For Fe). --Tim32 (talk) 19:15, 17 October 2008 (UTC)

Parallel postulate and Playfair's axiom

I'd like to ask someone who is already an expert in plane geometry to look at Parallel postulate and the question at Talk:Parallel_postulate#Equivalence. The issue is whether the parallel postulate is equivalent to Playfair's axiom, and which other axioms are required to prove this equivalence. I recently noticed edits to the article by an IP editor, which also should be double-checked by an expert. Unfortunately I managed to avoid plane geometry in school and know almost no details about it. — Carl (CBM · talk) 13:13, 16 October 2008 (UTC)

Mathworld says that "The parallel postulate is equivalent to the equidistance postulate, Playfair's axiom, Proclus' axiom, the triangle postulate, and the Pythagorean theorem."  Δεκλαν Δαφισ   (talk)  15:04, 16 October 2008 (UTC)

Some of the confusion here may be because it's not quite clear just what "parallel postulate" refers to. People often refer to Euclid's fifth postulate ("E5") as the "parallel postulate", but when they cite its content, they produce something much more like Playfair's axiom ("PA"). The equivocation of two unlike things, namely E5 and PA, produces an apparent tautology, that the "parallel postulate" is equivalent to PA.

However, E5 actually looks more like this:

"If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles."

Which makes clear that the equivalence with PA is not trivial. -- Dominus (talk) 15:09, 16 October 2008 (UTC)

This is the sense that I have as well, but I'm not at all familiar with the literature. If you could look at the article and fix any mistaken impressions there, it would be a great help. In particular, an IP editor pointed out in the article that the "great circle" model of elliptical geometry appears to satisfy E5 as you have stated it, since every pair of lines intersects regardless how they are cut by another line. — Carl (CBM · talk) 16:19, 16 October 2008 (UTC)

It does. Elliptical geometry violates Euclid's first postulate, that a line (segment) can always be extended. Septentrionalis PMAnderson 04:20, 17 October 2008 (UTC)

To CBM: Elliptic geometry violates Hilbert's axioms#II. Order in addition to violating Playfair's axiom. Notice that the article on elliptic geometry is ambiguous on whether it is the geometry of the hypersphere S³ or the result of identifying the antipodes of the hypersphere. If one uses the hypersphere, then it also fails to satisfy the requirement that there is only one line through two distinct points. JRSpriggs (talk) 08:08, 17 October 2008 (UTC)

So is it true that Playfair's axiom and E5 are equivalent just under the assumption of E1 + E2 + E3 + E4 ? Or are additional axioms (such as Hilbert's axioms without the parallel postulate) required to prove the equivalence? This is the point that ought to be clarified in the article. The fact that E5 and Playfair's axiom are not logically equivalent (provably equivalent with no extra assumptions) is hardly surprising, after all. — Carl (CBM · talk) 12:31, 17 October 2008 (UTC)

More on axiomatic Euclidean geometry

(See isosceles triangle theorem.)

• Could someone who has the book handy check that I've got the right theorem in this edit?
• Some famous person said (I'll see if I can find it) that it is an instance of the callousness of youth to think that a theorem is trivial because its proof is trivial. I think non-triviality can be found in the consequences rather than in the proof, and maybe elsewhere too. For example, look at the roles of Desargues theorem and Pappus' theorem in 20th-century research in projective geometry—all that stuff about coordinatizing the plane and non-Desarguean planes and the fact that that can't happen in more than two dimensions, and what it has to do with commutativity of division rings and "near-rings" or whatever they're called. So how does that apply to isosceles triangle theorem and the proposal to delete it on the grounds that it's trivial (I removed the "prod" template)? Michael Hardy (talk) 20:08, 16 October 2008 (UTC)

I would strip away all of the mention of youth and nature to leave the very true statement that

"A theorem is not necessarily trivial because its proof is trivial."

 Δεκλαν Δαφισ   (talk)  23:51, 16 October 2008 (UTC)

I wasn't thinking of putting that into the article. Michael Hardy (talk) 05:15, 17 October 2008 (UTC)

No, I know.  Δεκλαν Δαφισ   (talk)  11:49, 17 October 2008 (UTC)

Opinion requested on Kepler's laws

Could someone have a look at Kepler's laws? I think the article needs to be rigorously pruned in the amount of mathematical proofs, since they are not illuminating the concepts, but rather tediously proving concepts that are rather easy to visualize. But maybe i'm seeing it wrong. Please discuss on Talk:Kepler's laws of planetary motion. Han-Kwang (t) 20:56, 19 October 2008 (UTC)

Yes, I did. By the way, I have a much worse example of unneeded proof; I mean Tsirelson's bound. This one is really long, bad and boring. Boris Tsirelson (talk) 21:56, 19 October 2008 (UTC)

Integral expression

The new article integral expression defines the term as follows: "monomials and polynomials are collectively called to be integral expressions." I have my doubts about this. Can anybody confirm that this definition is correct, preferably by adding a reference? -- Jitse Niesen (talk) 13:47, 20 October 2008 (UTC)

I don't have a reference for this, but I know that quotients of polynomials are called "rational expressions". Since quotients of integers are called rational numbers, it at least seems to fit the pattern. And the fact that polynomials form a Euclidean ring seems to be a sort of basis for that analogy. Michael Hardy (talk) 15:51, 20 October 2008 (UTC)

Since every monomial is a polynomial, it's a rather useless term. That doesn't mean it hasn't been used in reliable sources, however. Algebraist 15:59, 20 October 2008 (UTC)

I don't think it is, though... it's just a redundant term, presumably due to translation issues. CRGreathouse (t | c) 16:06, 20 October 2008 (UTC)

No references have appeared, so the consensus on Talk:Integral expression seems to be that the article should be replaced by a disambiguation page. Gandalf61 (talk) 08:21, 21 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)

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 [6]:

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)

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)

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, |a_n - 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)

I favour major surgery on "Limit (mathematics)" as well. Move some stuff out of it to individual articles, and then give it a purpose as a short overview which directs people to all the different articles for details. Not just a list like the disambiguation page. Dmcq (talk) 11:04, 2 November 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)

This is caused by a bug in dvipng; see bugzilla:15777. Here is an example of the bad output, for those who haven't seen it. — Carl (CBM · talk) 02:45, 3 November 2008 (UTC)

Semiregular space, Locally regular space, Regular space

All of the articles mentioned are being discussed on the talk page of semiregular space (I proposed semiregular space for deletion and currently there is a proposal that semiregular space is merged with locally regular space). Please contribute if you have any opinions.

Topology Expert (talk) 09:42, 2 November 2008 (UTC)

Discussion has started here. --C S (talk) 10:01, 2 November 2008 (UTC)

What subtends and what gets subtended?

This dispute has sat there for months. Can the mathematical public help settle it? Michael Hardy (talk) 02:33, 3 November 2008 (UTC)