Wikipedia talk:WikiProject Mathematics/Proofs/Archive 2

message: 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 significant 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/referenced 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)
replies: text: 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)
thread_title: Distinguishing between proofs in context and stand-alones

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

text: 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  that would indicate a proof was needed. Pdbailey 17:43, 1 April 2007 (UTC)
replies: text: 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)

text: 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)

text: 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)
thread_title: Let's just create articles that gather related proofs

message: 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)
replies: text: See []. Cheers--Shahab 18:11, 19 October 2007 (UTC)
thread_title: Suggestion

message: 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)
thread_title:  A student-mathematician's perspective 

message: 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)
thread_title: A guinea pig

message: 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)
replies: text: 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)
replies: text: 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)
replies: text: 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)
replies: text: 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)

text: Since you ask: you just put the  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)
replies: text: I changed the template to an infobox style. That should resolve the problem. CMummert · talk 22:39, 30 May 2007 (UTC)
replies: text: It does. Thanks! Magidin 18:48, 31 May 2007 (UTC)
thread_title:  What is Category:Proofs all about? 

message: The  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. --KSmrqT 20:03, 2 August 2007 (UTC)
replies: text: Looks good to me. --Zvika 07:34, 4 August 2007 (UTC)
thread_title:  Template text 

message: I am looking at Union of two regular languages right now, which is an expired PROD that I am keeping open for a few more minutes with , but which I will likely deprod as not an uncontroversial deletion.  There is a second type of solution to the introduction of proofs into Wikipedia other than subpages or moving to Wikibooks - I hope you've not discussed this previously - and that is to treat the proof as 'supporting information' and upload it as a PDF where it would be stored in the 'image' namespace.  As far as I know, there is no bar to taking that route, which is sorely overutilized by people uploading copyrighted images and underutilized by people uploading illustrative figures, data analyses (not bordering on WP:OR but little different from creating an image yourself for upload) and supporting information.  Thoughts? --User:Ceyockey (talk to me) 19:20, 27 December 2007 (UTC)
replies: text: What would be the advantage of this over having the proof in mainspace? I can think of several disadvantages (in terms of portability, for example). --Zvika (talk) 19:35, 27 December 2007 (UTC)
replies: text: The lack of opposition - the social factor. --User:Ceyockey (talk to me) 19:41, 27 December 2007 (UTC)

text: The other thing is that PDF need not be the format.  For instance, one could use wikimarkup and save the page into the image namespace ... I think ... or use some other form of portable mathematical markup. --User:Ceyockey (talk to me) 20:34, 27 December 2007 (UTC)
replies: text: Would that make the text editable like an ordinary wiki page? --Zvika (talk) 08:24, 28 December 2007 (UTC)
replies: text: Not sure - needs to be verified. --User:Ceyockey (talk to me) 15:18, 28 December 2007 (UTC)
thread_title: Proofs in Wikipedia - another approach?

message: Many of the "proof subpages" directly violate the wikipedia guideline WP:SP#Articles do not have sub-pages (main namespace). Every article in the encyclopedia should be self-standing (in form only, of course; not content wise. i.e. they should have a lead, headings, proper english, and other MoS type things) and titles shouldn't use slashes to indicate belonging to some parent page.  128.139.226.37 (talk) 11:33, 21 February 2008 (UTC)
replies: text: That is probably true. If you see a page such as "X/Proof", please move it to something like "Proof of X". --Zvika (talk) 13:40, 21 February 2008 (UTC)

text: The list below are the ones I know about. Please add if you see more, or remove if no longer there.  --Lambiam 16:55, 29 March 2008 (UTC)
thread_title: Incorrect use of subpages

message: I see in previous conversations on this /Proofs page above that there was a suggestion that hidden text or images might solve the problem, but neither seemed to have support.  Carl said that  might be useful.
I don't think anyone who's experienced in a subject, including academics, should self-censor in an attempt to be "encyclopedic", as long as what they want to say is important in their field.  Yes, Wikipedia has had phenomenal growth, I think we're up to 7th in the U.S. in number of hits, and yes, that suggests that we should have a certain respect for the principles that got us here, and some of those principles might be described as rules to keep the information from appearing too specialized or boring to a general audience.  But general arguments about keeping Wikipedia interesting must not be allowed to slide into non-scientific bias against any group or subject, including math.  The subject came up in the current WP:GAN for the Monty Hall problem that some of Marilyn Vos Savant's columns on math problems have attracted phenomenal response from readers of Parade, which is as general an audience as you can get.  Many people study graduate math, and proofs are almost always a large part of the curriculum.  The fact that proofs seem boring or irrelevant to some people is immaterial.  Articles should be as accessible as possible, given the material, but there's no rule that Wikipedia has to limit itself to articles that every 14-year-old can understand.  On the other hand, when, for whatever reason, material that we believe to be important and relevant doesn't survive in Wikipedia, I don't think we should miss the opportunity to keep the material in Wikibooks (if it's typical textbook material) and link it, from the right place in the Wikipedia text (and not just with a "more information is available in Wikibooks" graphic at the end, which sounds more like a disclaimer than like a true extension of the text). - Dan Dank55 (talk) 15:30, 31 March 2008 (UTC)
thread_title:  New discussion