Wikipedia talk:WikiProject Mathematics/Proofs/Archive 2

This is a discussion page for WikiProject Mathematics

This page is devoted to discussions of when and how to include proofs in mathematics articles. The main discussion page should be used for other issues.

Please add new topics at the bottom of the page and sign your posts.

Distinguishing between proofs in context and stand-alones

This thread has produced many good ideas for proofs which exist mainly to support an article. In my opinion though, there are some proofs which are deserving of their own article. If the proof is only in existance to support a specific concept, one of the ideas outlined above would be appropriate, but some proofs have signifigant backgrounds of their own. Proofs with histories, versitile applications, and context in the development of math may well be worth their own article. I think most mathmaticians would agree that the classec 'proof' of the 4 color theorem, for example, is worth discussing on its own, seperately from the theorem itself because it has a long history, complex solution, and has had a noteworthy response from the mathematical community. Alternately though, we could likely come to a consensus that, for example, the double angle theorem proofs are not worthy of their own article but should be explained/refrenced as a part of the theorems' article because the proofs are relatively trivial and did not mark a signifigant point in the development of math. 48v 05:36, 13 July 2006 (UTC)

I believe that consensus already exists. Culturally/historically important proofs deserve their own stand-alone articles. The somewhat open question is what to do about "relatively trivial" proofs that "do not mark a significant point in the development of math.". At the moment, the latter are allowed, but shunted into the ghetto called Category:Article proofs. NB. this latter category has been growing at the rate of one article proof per month; there is no particular demand. In important ways, Planetmath is a more suitable place for article proofs. linas 19:46, 10 December 2006 (UTC)

Let's just create articles that gather related proofs

I already started one, Proofs of trigonometric identities. --Ķĩřβȳ♥;ŤįɱéØ 11:32, 20 October 2006 (UTC)

I agree, Wikipedia should include 'naive' definitions etc for the general public, but there is no reason why we should try to exclude proofs. If we can somehow group proofs into sensible collections and then have links to the appropriate pages on an article then that would stop a proof/more rigour slowing the flow, whilst allowing the more 'expert' reader to delve into the subject deeper. --TM-77 11:57, 28 October 2006 (UTC)

Proofs of trigonometric identities is, in its present form, a horrible mess. Please help clean it up. Michael Hardy 19:11, 13 December 2006 (UTC)

How does it look now? --Ķĩřβȳ♥ŤįɱéØ 22:03, 18 December 2006 (UTC)

/Proof subpages

Proposition: Create a /Proofs subpage with mathematical articles, listing proofs of theorems and statements made in that article. For example, the page Linear_Algebra contains a section Some useful theorems, the proofs of which could be given on Linear_Algebra/Proofs.

Arguments: (Here is my argumentation, including many points made above) As a mathematician I often read statements and theorems on Wikipedia pages of which the proof would interest me. Often, proofs are omitted though. One could argue that Wikipedia is a general encyclopedia and not a compilation of mathematical theorems and that therefore, proofs do not belong in it. Also, they would make pages unnecessarily cluttered and harder to read for the general public, and those just trying to grasp an idea without getting caught up in the details. On the other hand, one may as well argue that Wikipedia is (and is becoming more and more) a compilation of knowledge and should actually contain as much information as possible. Therefore, I'd propose to include proofs, but separated from the main article. To do this in a uniform way, a subpage of the article should be created: when one sees a statement on a mathematical page, one simply appends /Proofs to the page name to verify it. This would keep the page clean and readable, make the details available in an extremely easy (and uniform!) way for anyone interested and would have the advantage that proofs can be verified and corrected by anyone that can read them. A cite-like reference to the /Proofs page could be added to the statements of which the proof is available.

For an example, see Addition_of_natural_numbers/proofs; I'm talking about generalizing this concept.

CompuChip 10:28, 12 November 2006 (UTC)

This is a wonderful idea. I stopped editing and reading Wikipedia articles related to math when I saw that proofs are, by policy, not to be included in the Wikipedia. Reason being that I have no idea if a mathematical statement is correct without seeing the proof and have been burned too many times by taking a text book or author's word for something. If wikipedia is going to store real mathematical knowledge and be credible, it needs to store the proofs. This is the same as referencing a politics piece to a newspaper. None of the knowledge in Wikipedia regarding math is worthwhile without the proofs or references to them, and there is no reason not to include them on a separate page, allowing interested parties to see them and less interested parties to skip them. For recent mathematics knowledge, I see no reason a link to relevant articles can be used instead, but most of the stuff in Wikipedia is over 100 years old and I think including proofs is a worthwhile venture. I would also suggest a markup similar to {{fact}} that would indicate a proof was needed. Pdbailey 17:43, 1 April 2007 (UTC)

Although this discussiion seems to be a bit old, I find it very relevant. Proofs are such a vital part of mathematics that I think we MUST find a way to include them for the interested reader. This proposal seems to be a good solution. I'm new to editing Wikipedia but I'm already tired of the same things as the poster above. Is there any way to give this debate more attention among the mathematics editors as I think it is very vital to the mathematics articles. JKBlock 17:31, 18 June 2007 (UTC)

A very good proposal! To support it and let us gain some experience with it, I've started a new example, which proves a relation in the main article that was questioned on the Talk page. I could not find a proof for this relation in the literature, so could not simply add a reference to the proof. Even if we did have a reference, it might be hard to come by and check (the reference). --RainerBlome 10:29, 5 July 2007 (UTC)

Interesting idea. However I think it is very important, that at least one reference is made in the main article to the proofs page if one such is made. Otherwise one would never guess that the article has a proofs subpage. Apart from people not being able to find what they are looking for, we risk duplication of material. Also the main article might be moved, with the proofs page staying behind. I'm not sure where best to put a reference to the proofs page (I think it should be placed prominently), but under See Also may be a start. Aenar 03:46, 23 September 2007 (UTC)

A lay perspective?

I do not know whether my comments are welcome here, as I am a very new contributor to WP. Anyhow, here goes. I am all for proofs, both complex and elementary. I agree that they cannot all appear in the main article on a subject, but I feel strongly that they should appear somewhere.

Is there any reason why WP cannot be a both an encyclopedia for lay people and an encyclopedia of mathematics. This would allow people who are interested in a subject to start out as a lay person and (assuming accurate articles meaningful interpretation) progress to higher levels of understanding. It is often mentioned in the long discussion about proofs, that they can be found in any mathematics textbook, yet how many lay people have mathematics textbooks in the bookcase at home? And how many people have more than one mathematics textbook? When i was studying, I had the vast library on campus to turn to for alternate proofs when the one my textbooks gave was above my understanding. I am no longer a student and without those reference works I am lost.

I don't work in the field of mathematics, but mathematics is the human construct that I find most fascinating. I also love asking Why?. I feel that if a person asks why? or thinks that cannot be right when reading an article, the answer or proof should be readily availible.

I could go on, but this page is quite long enough as it is ;-)

I support the inclusion of proofs in WP, either as a subpage or as a separate article --payxystaxna 22:00, 27 November 2006 (UTC)

Obviously (see my above post) so do I. The question is where to place this to reach consensus on it and get it implemented. I can start adding proofs to pages now (well, actually in a few days when I have time) using the /Proofs subpages I proposed, but I'd rather wait until it's made "official" and I'm sure everything is done correctly the first time. --CompuChip 15:34, 28 November 2006 (UTC)

The problem with proofs is this. To simply state every theorem in every textbook on mathematics, it would increase the number of WP math articles by a hundred-fold. I have, for example, entire shelves of math books which are currently summarized in WP by a handful of mostly small articles. So, just to recap the content would require an explosive growth. Now, as proofs are typically 3 to 100 times longer than the statement of a theorem, this would require another explosion in the quantity of content. Even if the explosion occurred, simply protecting it against vandalism would be a task.

Thus, I argue that the appropriate thing to do is to focus on providing missing content, rather than providing proofs. I would also like to suggest that a better repository for proofs might be Planetmath, which does have a charter for this, and already has hundreds if not thousands of proofs. By contrast, we have only seventeen in Category:Article proofs so far, and this cat is growing at the rate of one a month. linas 20:05, 10 December 2006 (UTC)

I have long been taught that there are three kinds of proofs - those that establish a result, those that illuminate a result, and those that expand a result. That is to say, there are proofs that are simply a way to get from point A to B - they don't really generalize, and there isn't much that can be learned from a close analysis of them. The second class of proofs are proofs that, in doing them (or seeing them) one realizes something more fundamental, or important, about the thing being proved. The last class is the type of proof where the method of proof, or construction used, is more important than the result found - like, say, Euclid's Method in a proof involving congruences. It seems that the latter two are the most important for our purposes - and, especially the second, should be included in an article. The first should be 'sourced', but probably not included. Most mathematicians have an learned sense of what class a given proof falls into - and one will note that it is independent of the difficulty of the proof given. In addition, length seems to be totally separate, as a consideration. To relate to what you said - we should focus on adding content - however, we should not omit, or overlook, the fact that in many cases a proof 'is' content, and just as important for understanding. Haemo 09:01, 19 December 2006 (UTC)

Experience shows that explosive growth of Wikipedia happens anyway, proofs or not, so it will be dealt with anyway. Mathematics is just one area in Wikipedia, and adding proofs will not make a big difference in volume, I believe. The question to me is not "do we want growth?", but "what kind of growth do we want?" You suggest to focus on missing content. Proofs are content to me, and I and others miss them, and I and others want to add them. PlanetMath has the disadvantage of not being a public Wiki, with all the associated advantages and disadvantages. In particular, PlanetMath's potential growth speed is limited. My personal experience is that Wikipedia's quality is high enough for my needs. --RainerBlome 10:18, 5 July 2007 (UTC)

Suggestion

Have you considered creating a Mathematical proof book in Wikibooks? That seems to be a natural place for a chunk load of proofs. or Wikitext. CommandoGuard 22:27, 19 December 2006 (UTC)

A student-mathematician's perspective

I am currently a student who loves Mathematics, especially the abstract kind. So of course I would like to have easy access to formal treatment in proofs of theorems. On the other hand there must be a sort of outline of the proof in layman terms for the general public. Thus I suggest that both be accomodated as far as possible.

Firstly, the main article should consist of the background and mathematical content relevant to the users who find and read it. This means that it should have in my opinion intuitive explanations rather than strict proofs, so that everyone can grasp the concepts involved in as little time as possible. Even for myself, I sometimes avoid reading long proofs or skip certain sections, and get confused further down, in the end realising that I had missed out something in the middle of the "chunk". So it would help everyone if there was a intuitive and preferably short explanation of the truth of the mathematical content discussed.

Secondly, those who are really interested in the rigorous mathematical establishment of claims and theorems would surely want an easily obtainable form. This could be placed apart from the main article either through the dynamic "Click to reveal hidden content" or a "Proof" link to a separate dedicated article. I do have an inclination for the former method, because I think that it might be a bit cumbersome if a separate webpage has to be accessed for every proper proof.

Lastly, I believe it would be neater if proofs were written out one mathematical statement per line, because it may otherwise be harder to see the development of the proof. One example is Approximation_theory/proofs. I do not intend to be critical, but it is at least to me quite hard to read as every statement is concatenated into one paragraph, which is then at the mercy of word-wrap. Also the formal proofs themselves should have a complete formal statement of the result to be proven. In this example it was and still is not clear to me what exactly the first sentence means in formal terms, especially "is optimal". When I referred to the main article in question, I found a circular reference, which should be avoided as well.

Thus I too recommend that those who author the proofs check for readability and minimize referencing necessary. In other words the "proof" page/section should be ideally stand-alone, so that readers from mathematical background could if they wish look at only those and nothing else, while other readers could if they wish look only at the intuitive interpretation and explanation of the mathematical results. And both groups of people should be satisfied with whatever they choose to read, without having to struggle with what they do not want to read.

Lim Wei Quan 10:19, 30 December 2006 (UTC)

A guinea pig

I have mainly been editing pages on sporadic simple groups. In my study of them I work out proofs as I go, but have not tried to post any on Wikipedia. There are many statements about simple groups that few could hope to prove. Certainly it would be formidable (and voluminous) to include a proof of the classification theorem.

I added a definition to the article on the Higman–Sims graph. Someone else then posted a colorful diagram of the graph. I have since worked out a proof that the graph is strongly regular. The proof is pretty simple, but there are some presuppositions based on properties of Mathieu groups. THe proof really ought to be accessible from another article, on the Higman–Sims group Scott Tillinghast, Houston TX 03:41, 10 April 2007 (UTC)

Originality of proofs

Some might consider an original proof to be original research. On the other hand, an unoriginal proof could violate a copyright. I would hope that a contributor would rework any existing proof.

I have not seen anyone's proof that the Himan-Sims graph is strongly regular. Nevertheless I did what almost any mathematican would probably do after reading this result on the Wikipedia page. Scott Tillinghast, Houston TX 04:05, 10 April 2007 (UTC)

I don't really see the relevance whether a proof is original research or not. My main objection against original research is that it is in general hard to verify, an objection that vanishes here. I think in most cases copyright is not an issue, since proofs should be as straightforward as possible and will not involve creative work by one author. In most cases, there will be one or only a few ways to approach a proof - when any mathematician would logically take some path I think it's safe to consider the proof... what do you call it, common, standard, ...?

Only in rare cases a proof will involve sufficiently creative work that copyright may pose a problem, but then usually the proof will be exciting enough to provide a reference (and if not, it's not worth it anyway, is it).

But I think most proofs -- at least I can't think of any proof I've seen up until now, and after three years of studying mathematics full-time, that's quite a lot -- can be considered general enough not to have copyright, are old enough for the copyright to have expired, and probably a lot of modern proofs will be too complicated / specialized to show anyway. --CompuChip 16:01, 10 April 2007 (UTC) Note I used the words often and probably a lot in my reply, to allow for exceptions. Of course, there could be cases in which the copyright is relevant, but what I'm basically saying is: in general I think there's no problem, if it is an issue it can be viewed case by case.

If a proof can be included in the wikipedia with some fruit (i.e. if anyone can understand it) it will be over 70 years old. About the most recent proof of interest I can think of would be that of the Banach–Tarski paradox (over 80 years old as of now). Also, I would argue that original proofs that other editors agree are correct are just fine. Pdbailey 20:51, 11 April 2007 (UTC)

I think this isn't true at all. Much of discrete mathematics is more recent: see Bellman-Ford algorithm, for an example that is less than 50 years old. I agree that you probably can't copyright a proof though. -137.222.10.58 23:05, 20 May 2007 (UTC)

My understanding is: You cannot copyright the idea of a proof, that is, the general method used. But you can copyright a specific sequence of words or symbols which implement that idea, if the author made enough personal choices to make it something which someone else would not have created without copying him. So you should be OK, if you read a proof and then rewrite it in your own words, not quoting the text. That is, do not follow the original too closely, use different variables, et cetera. JRSpriggs 07:01, 24 May 2007 (UTC)

What is Category:Proofs all about?

Does anybody know what Category:Proofs is about? Most of the articles there seem to be just math articles which also happen to have a proof (e.g. König's lemma, Pythagorean theorem). Others are articles that contain nothing but a proof of a theorem (Pythagorean theorem proof (rational trigonometry)). Others are topics about proofs (Q.E.D., Reductio ad absurdum). What is the true/original purpose of this category? --Zvika 16:28, 23 May 2007 (UTC) (Copied from here, hoping to get a response)

I believe the intention is not so much for "WP customers", but for us, the people on the proofs project, to have a place where we can find all the pages that would be affected. That way, when someone makes a proposal ("proofs should be banned", "proofs should be footnotes to the main article", "proofs should avoid original research", ....) the proposal can be evaluated in the light of the existing body of WP proofs. William Ackerman 20:00, 23 May 2007 (UTC)

In other words, your understanding is that the category should contain pages with actual proofs? Rather than pages like Q.E.D.? In that case, shouldn't Q.E.D. and the like be removed? --Zvika 21:04, 23 May 2007 (UTC)

I'd lean toward being inclusive -- "Anything that a person working in the general area of how proofs should be handled in WP ought to be aware of." In that sense, Q.E.D. ought to be included. Remember, it's for our own use. William Ackerman 00:27, 25 May 2007 (UTC)

This still doesn't make sense to me. Sure, if someone is interested in any article related to proofs, they can find it here. But I think it would make more sense to split this up at least to two subcategories: one for articles about proofs and one for articles containing proofs. It seems to me that there are very different uses for these categories. For instance, someone might be interested in the philosophy of proof, but really doesn't care that an article with a proof of Pythagoras' theorem exists. The Category:Article proofs is a step in this direction, I think. --Zvika 06:22, 25 May 2007 (UTC)

Well. Since there seem to be no further comments, I am planning on organizing this category as follows:

• Articles containing only a proof or proofs will be moved to ArticleName/Proof or ArticleName/Proofs (where ArticleName is the article which contains the statements being proved) and given the template {{proof}}, which will place them in the (already existing) Category:Article proofs.
• Ordinary articles which also contain proofs will be moved to a new Category:Articles containing proofs, which will be a subcategory of Category:Proofs.
• Articles like Q.E.D. will remain in Category:Proofs.

Feel free to suggest, complain, or help out.. --Zvika 19:58, 28 May 2007 (UTC)

Since you ask: you just put the {{proof}} template in Proofs of Fermat's theorem on sums of two squares. I notice that after the preamble that indicates what this experiment is all about, the article immediately begins without starting a new line. Thus, the text of the article begins in the indented italic paragraph that is provided by the template. I think the template should be fixed so that this does not happen, and the body of the article begins in a new, unindented, line. Magidin 18:21, 30 May 2007 (UTC)

I changed the template to an infobox style. That should resolve the problem. CMummert · talk 22:39, 30 May 2007 (UTC)

It does. Thanks! Magidin 18:48, 31 May 2007 (UTC)

Template text

The {{proof}} template says, in part,

• This article is "experimental" in the sense that it is a test of one way we may be able to incorporate more detailed proofs in Wikipedia.

In my view the "experiment" has long since ended, in success. I see no reason to mention it in the template any further. Therefore I am revising the template, trimming it to the essentials. --KSmrq^T 20:03, 2 August 2007 (UTC)

Looks good to me. --Zvika 07:34, 4 August 2007 (UTC)

An argument against detailed proofs

I would in fact like to see fewer proofs on wikipedia. Let me explain my reasoning:

(i) Every proof which appears on wikipedia is either original to the author or not. To argue by cases:

(ia) If the proof is original to the author, there are issues about posting it on the internet for all to read. Namely, in mathematics we have a refereeing process whereby a specific person or persons takes (some) responsbility for checking the correctness of the argument. This is not the case on wikipedia, and moreover the wikipedist "everyone makes small modifications as they like" philosophy is not conducive to writing a correct proof.

(ib) If the proof is not original to the author, then (obviously) the author is taking the proof from some other source. I am not worried about copyright issues per se (I do not believe proofs are copyrightable), but there is a scholarship problem. Namely, I think that an encylopedia of mathematics has more of a duty to getting the history, influences and attributions correct and explicit than a mathematics textbook (though I have come to wish that e.g. mid-level undergraduate texts were also more scholarly in this sense).

(ii) It is more likely that an imitative attempt by a wikipedist (or a good faith effort by a student of the subject to gain understanding by working through the proof) will come out worse (pedagogically and/or logically) than the best of the treatments to be found in carefully refereed original sources. It is also tedious to write proofs in html. Because of this many proofs seem to come out with a rushed, breathless quality to them.

(iii) Someone above wrote that they do not have access to the original sources in which the proofs appear. I have all sympathy for this, but this is a swiftly changing situation. I would submit that at the present time a large percentage of proofs of important theorems (and at any rate, the theorems discussed here!) are available SOMEWHERE online. Rather than seeing a proof typed up on the fly, I would much rather see (a) a careful reference to the _first_ published proof (and a discussion of priority, where appropriate), and (b) references to one or more (but not too many; choose the best!) webpages which contain the proof in question. (Sufficiently) many professional mathematicians put their cutting edge papers as well as their lecture notes available on the web as a matter of course. There is no reason to rehash a proof if someone else has already done it better, and they usually have.

(iv) Writing proofs is a time-consuming effort which in many cases reduplicates efforts made by (more qualified) others. In particular it takes away energy from the other things I expect to find in an encyclopedia article, namely historical information, synthesis, intellectual impacts and so forth.

(v) As an example of this, I rewrote the page on Tychonoff's theorem because the previous version spent too much time copying the proof of Munkres. It was not said that Munkres' proof is a (nicely done) reworking of the proof of Cartan-Bourbaki. It seemed clear that the author was more interested in demonstrating his own personal understanding of the proof of Tychonoff's theorem than in sorting through the history of the result and all the various proofs using different ideas. My rewrite does not claim to prove the theorem even once, but it discusses the historical and intellectual interrelationships between five different proofs. There is no shortage of proofs of Tychonoff's theorem available on the internet. (However, my rewrite is not perfect or even complete: I have not yet had time to add enough references. But I can find half a dozen online proofs of Tychonoff's theorem with no trouble at all.)

Plclark 01:52, 18 September 2007 (UTC)Plclark

Plclark. Also I am new here at Wikipedia (trying to figure out whether I belong here or not …). I have read the contributions above on this page, and I essentially agree with them all. I agree mostly with your opinion, too. But there is one catch in it I would like you to comment on. If you would allow me.

You say

”If the proof is not original to the author, then (obviously) the author is taking the proof from some other source”

I have a concrete example, that MIGHT have slipped your attention as a principle example of ”proof without any other source than the author”: In prevalent literature, nuclear physics, an already well known approximation formula for nuclear radiuses is partly used and partly experimentally proven ”approximately OK” as the so called (my name) cube graph r = r0(A^1/3). But, as far as I know (despite some Internet research and other), there is no corresponding ”mathematical deduction” to this seemingly simple and direct expression. However, there is, nevertheless, a simple way to EXPLAIN a WHY and HOW, a simple mathematical deduction with the same basic preferences as those used by the water drop model presumptions of ”homogeneous substance density” and which leads to the actual expression

r = r0(A^1/3). Just a single line, really. No extensive work. (See example at talk page on Nuclear size).

The author (in the exemplified talk page) do not know whether (such) an already existent (published) proof already exists. So, the author MIGHT be a unique source here to that particular proof (although it is not likely he is — with respect to the relatively long history of nuclear physics). IF that is the case, it would be an example that slipped out of your observation. Meaning: we cannot categorize (exactly) according to your explained paragraphs. There are (categories of) exceptions to take account of.

Meaning in general: Clarifying descriptive explanations (proofs) should be added to, or incorporated with, or given as appendix or footnote or other available context to any main article where it so has come to a consensus between the collaborators (additional proofs MUST have consensus, not by vote but by argumentation in accord with already deducible mathematical laws, in order to exclude hazard or ”MathWacko-communities”). I think this is (approximately) what (nearly all of) the above contributors already have proposed. Question is only: how organize it? Or am I missing something, Plclark? --85.89.80.140 17:20, 20 September 2007 (UTC)

By way of response: first, your example has something to do with physics, whereas I was thinking only about mathematical articles (and the heading of this page explicitly restricts to mathematics). More than that, I'm afraid I didn't quite understand what you said. But if you are saying that it is possible for an author to independently come up with a proof which is not in fact "original" in that it someone else, unbeknownst to the author, already came up with it, then I agree. I don't think this has much effect on what I was saying about writing wikipedia articles though, except that if you find your own proof because you thought there wasn't one already in the literature you are committing a(n understandable, and forgivable) scholarly error. Plclark 06:08, 23 September 2007 (UTC)Plclark

Plclark. Thanks for the response. I was trying to exemplify what this project page exposes,

”This page is devoted to discussions of when and how to include proofs in mathematics articles.”,

in the light of an obvious conflict with Wikipedia’s already stated No Original Research

in trying to give a concrete example that ”mathematics articles”, really, not easily can be distinguished from articles in general containing mathematical descriptions: I was trying to convince you, perhaps by an odd example, that descriptive and explanatory novels in Wikipedia inevitably appears spontaneously IF the Wikipedia aim is to let also (type) not high school educated people get a glimpse, an idea, of a specific subject. Meaning: original research in Wikipedia already exists, it is already established and launched — through mathematically connected articles. We cannot stop it. It is already here. Mathematical novelty is already working at full in Wikipedia, and we find it in pure mathematical articles as well as in mathematical physics articles.

Example (the best at present, my opinion): Planck radiation law. Without the contributed novel in the example, explaining the details, only readers with a (type) high school education in mathematics would be able to read the stuff. Or as it is stated by the actual contributor:

”I gave a self-contained derivation suitable for wikipedia. You won't find this derivation anywhere in the literature, because textbooks usually assume that the student knows the basic stuff and they'll proceed from there. Giving the standard derivation that you can find in textbooks serves no purpose, because the people who can follow that are precisely the ones who already know it. What I did here was to imagine that the reader knows nothing except what he/she can find on wikipedia. He/she must, of course, have some basic mathematical skills. So, perhaps a sentence needs to be included at the start of the derivation saying that we give a self contained derivation and that other derivations can be found in books such as.... Count Iblis 16:29, 3 October 2006 (UTC) ”

@INTERNET Wikipedia, Talk:Planck’s law, references

All mathematics. Excellent generalized example of the project core quest on this page, my opinion.

My quest to you Plclark was just: do you object to such a stand alone mathematical novelty in Wikipedia, by principle? It shouldn’t be there (you say?). Remove it (you say?). Is that what you say?

Please, give your opinion to clarify on the Planck math example as a core example, if you approve.--85.89.80.140 16:50, 23 September 2007 (UTC)

Addendum

To sum up the previous long post: when I look up "Theorem X" on wikipedia, I would like to find:

(i) a careful, reliable statement of the theorem in question (reliability ensured by references both online and otherwise).

(ii) information which complements, rather than duplicates, the complete proof I would find by looking in one of these references. Plclark 01:57, 18 September 2007 (UTC)Plclark

These are legitimate things to look for in an article on "Theorem X". It also seems to me, in many cases, legitimate to look for a proof (if it is short) or a commented proof skeleton. In many cases this helps understanding or exemplifies a general proof method. In the end, I guess it depends on the situation: I think the article on the Euclidean algorithm would be deficient without the proof, whereas obviously we aren't going to include the proof of Fermat's last theorem.

As for Wikipedians not being the right kind of people for writing proofs, five years ago I would have thought the same about writing any serious math article, yet fortunately I was proven wrong. Why not give us a chance? --Zvika 18:32, 20 September 2007 (UTC)

I agree that some discussion of the proof is often helpful or integral. If the proof is really easy enough, then yes, I agree that giving it in the context of the article probably makes for easier reading than referring the reader to an external source. The Euclidean algorithm is a good example of this. What I am saying is that if it is much harder than that I would prefer not to see a proof.

Regarding your second paragraph: when I look through wikipedia math articles I see some lovely ones (that I, as a mathematician in a different field, can use as my first reference) and some that are deficient in various distressing ways. (The article on number theory is an embarrassment to me, to the extent that I nominated it for deletion, but unsurprisingly that didn't work.) I should admit that I have not seen a proof on wikipedia that I thought was wrong, only proofs that I thought were not as good as the ones found in standard, easily accessible sources. Again though, my point is this: an encyclopedia article is a work of scholarship. It is not the same kind of scholarship as a technical book or article in mathematics, but it is not lesser or less important for this. Most math books and articles provide too little in the way of "encyclopedic scholarship", so there is a lot of work to do in most encyclopedia articles in mathematics. When there is so much work to be done, why try to reinvent the wheel? Plclark 06:08, 23 September 2007 (UTC)Plclark

It sounds like we can pretty much agree that proofs or proof skeletons are sometimes useful in an article, and sometimes unnecessary. It also sounds like you know a lot about many of the subjects here and have a clear vision of how they could be improved. Certainly you know more than me in these matters; I am not even a mathematician. That being the case, might I suggest that you be bold and improve articles as you see fit -- not by nominating core articles for deletion, but by adding what knowledge you have to them. Please keep in mind that Wikipedia is a work in progress, so some articles -- even important ones -- are bound to be deficient. The thinking in our community should not be "delete anything that contains serious flaws" but rather "fix the flaws, one by one." That is how we got to where we are today. Hopefully, with the help of people like you and me, we will improve articles like Number theory and get them to the level of articles like Game theory. --Zvika 07:12, 23 September 2007 (UTC)

Comments on some articles in "Category: Article proofs"

Perhaps it will be helpful if I comment specifically on some of the proof pages.

Addition of natural numbers: There are no references given. Presumably these facts were proven in Peano's original paper, which should be cited, along with a more contemporary reference.

Approximation theory: a mess. Here we have a proof without a precisely stated theorem. (The parent page is not very good either.)

Bertrand's postulate: this is nicely done. My only complaint is that it gives a proof and says "the gist" of it is due to Erdos. This isn't very clear. Also, the reference to Erdos paper should be given.

Boy's surface: There is no reference to Bryant's paper. Also, what is the significance of all this? In what sense do the results of Morin and Bryant improve upon Boy's original construction? Did Boy want an explicit paramterization but not have one? It is an instance where the (simple enough) proof is being given instead of other more interesting information.

Cardiod: again, too little context is provided. Why do we care about this curve? Do we, in fact, still care about it? Plclark 06:37, 23 September 2007 (UTC)Plclark