Talk:Poincaré conjecture

message: From the article:
Poincaré conjecture (/pwɛn.kɑːˈreɪ/ pwen-kar-AY;
Seriously???? There is only one way to pronounce that name. I can't see myself putting a bad pronounciation on an English name in a French article. How is that relevant?  — Preceding unsigned comment added by 82.244.149.143 (talk) 08:34, 2 May 2014 (UTC)
thread_title:  Pronounciation 

message: I agree with the above request... I would be very grateful if someone could write a "simplified overview" of this article for readers who are not mathematical experts.  I am reasonably well educated, but the content of the article is WAAAAY over my head.  I guess this could be taken as a compliment to the author, but for 99% of the world population - including young people who may just be developing an interest in mathematics - the article is far too scholarly.  I am not asking that the article be 'dumbed down', but rather that a new section be added that summarizes the article such that a non-mathematician can comprehend what the general concept is.  —Preceding unsigned comment added by 24.108.14.221 (talk) 06:03, 9 July 2010 (UTC)
replies: text: I got a better idea: stop acting like somebody owes you something. I bet that there's something YOU understand that not everyone else here does. Why aren't you spilling it, elitist? 68.121.164.157 18:44, 23 August 2006 (UTC)

text: Not to be cheeky? Please! Such insincerity gets you no love. 68.121.164.157 18:44, 23 August 2006 (UTC)

text: Hi 68.121.164.157, is that your real name? Perhaps you should address the clearly legitimate commentaries made above instead of throwing the toys out of the pram. This is after all a general interest encyclopedia and as someone with a small amount of mathematics in my history I don't understand this article! If you have no interest in writing an article that is accessible to the general public then your edits have no place on Wikipedia. Mglovesfun 17:41, 27 August 2006 (UTC)

text: why not do it for the sake of DOING IT Confront (talk) 02:56, 6 March 2009 (UTC)
thread_title:  Please explain to the layperson why this is such a big deal 

message: I found a very interesting link related to the Poincare's conjecture: . However I don't know if it is a hoax or not. Can someone verify their proof? --Matikkapoika 19:59, 4 June 2006 (UTC)
replies: text: This is the same thing I responded to in the previous section.  No hoax.  Just, well, a very interesting point of view that I think would not be universally agreed to.  It's an even worse article than the previous one mentioned...the quotes are kind of misleading, and I wonder if the journalist did a very selective job of quoting.  Both articles do not do a good job of explaining the different contributions (and kind of contributions).  One particularly bad thing is that this article's emphasis on Cao and Zhu's contributions comes at the expense of  lessening Perelman's contributions; however, it is clear that is is really Perelman's work that is significant, not theirs.  Of course, they have done something important here, which is to clarify Perelman's work...but other groups of people have and are doing this.  This team was apparently just one of the first to complete the task.  Perelman will probably win a Fields medal for what he did.  --C S (Talk) 22:19, 4 June 2006 (UTC)
thread_title:  Interesting link 

message: According to slashdot, it's been proven. To a certain degree anyways. Current tag up. --Rake 08:51, 5 June 2006 (UTC)
replies: text: This is the same link that has already been posted above. Read Chan-Ho's reply there. --Zundark 09:08, 5 June 2006 (UTC)
replies: text: Despite it being on slashdot, this isn't really news, and major editing is not needed.  -lethe talk [ +] 09:10, 5 June 2006 (UTC)
thread_title: major editing needed

message: I believe it is quite wrong to give undue emphasis to their work by mentioning them in the introduction.  They are mentioned in the main body of the article, which is quite enough, given that their work is not developed in isolation, but relies on other teams of mathematicians who have worked out the details of Perelman's work.  See also my previous comments in the prior sections.  --C S (Talk) 02:08, 6 June 2006 (UTC)
thread_title:  Mentioning Cao and Zhu in intro 

message: Somebody has asked that a citation be given for the claim in the lead that a consensus of experts has concluded Perelman's proof proves the Poincare conjecture.  In response to this, Jitse has included .  I didn't find this completely satisfactory, as it, in isolation, only indicates that experts are very very confident, but nobody has stuck their necks out saying it is correct.  So I replaced the link with this one .  This is an announcement by the ICM organizers that they expect Hamilton and Morgan to announce in their talks that the conjecture is proven.  Clearly, they would not say this unless they know there is a strong consensus on the correctness of Perelman's work.  Not only that, but at the end of the announcement, there is a quote from an expert explaining that experts have verified enough of Perelman's work to establish the Poincare conjecture.  
This is all old news in a way, as people have been saying this a while; in fact, Morgan has already stated that Perelman's proof of PC is correct at a conference I attended last October.  He stated this at the end of a talk, and even said he had verified much of it (except for standard well-known stuff) himself.  So I'm confident that Morgan will just reiterate this at the ICM.  In any case, I think the ICM article (plus the Cao-Zhu paper which has been vetted by Yau) is certainly sufficient justification for the challenged statement.  We will definitely have much better sources after the ICM, but we have enough for now.  --C S (Talk) 11:58, 11 June 2006 (UTC)
thread_title:  Upcoming announcements at ICM 2006 

message: A little while ago, I placed a request for peer review of this article.  One clear problem is that people are not able to understand the article.  This is already quite clear from comments made on Slashdot whenever PC gets in the news.  I think the most fundamental question is, what is the intended audience?  Once that is resolved, it should be much easier to know what should be included or not.
Also, I think it should be quite feasible to include short description (modulo the technical details) of how Perelman's proof works.  Should the article include this?
When I get a chance, I will create a proposal version at Poincaré_conjecture/rewrite; people are welcome to beat me to it.  :-)  Until then, I would like to open up a discussion here and see what your thoughts are on how this article should look. --C S (Talk) 12:40, 11 June 2006 (UTC)
replies: text: Well I can say that it's shameful that the article does not contain a quick-n-dirty description of what it means for a space to have trivial fundamental group before it states the conjecture. -lethe talk [ +] 16:10, 11 June 2006 (UTC)

text: As to the question of who the indended audience is, I'm afraid the inconvinient answer is, just about everyone. Paul August ☎ 16:40, 11 June 2006 (UTC)

text: Also it should include, probably in the first sentence, something like:  "The only bounded three-dimensional space without holes is "essentially" a sphere." ( see  for a good intuitive description of the conjecture. Paul August ☎ 16:54, 11 June 2006 (UTC)
replies: text:  I edited the intro in an attempt to make it a bit more accessible to non-technical audiences.--agr 19:54, 11 June 2006 (UTC)

text: If you guys are going to rewrite it, and just in general, please watch your grammar and sentence layout as I've noticed several implications which are not correct - for example due to paragraph layout the suggestion that Perelman has refused anything from the Clay people (fixed).  Unfortunately while I have done highschool and limited Uni maths I am still at a bit of a loss to understand this article, even after reading other background pages, so I have been a bit worried about correcting things.  --eps 1143, 23rd August, 2006 UTC
This article is nearly impossible to understand without a familiarity with rather advanced mathematics. Following the links tends to turn up other articles on math topics that are equally difficult to grasp. It needs to be translated for the layperson; as it's written now it's only of use to those who already know the lingo. 74.99.167.47 07:01, 23 December 2006 (UTC)
thread_title:  Peer review 

message: What do people have against including a pronunciation that can be understood by people who do not understand IPA? If someone wants to know how to pronounce it, and doesn't know IPA, then chances are they aren't going to take the time to learn IPA, they will just pronounce it incorrectly or look somewhere else. One person said that it is ulgy -- that must be their own personal view, I think many people would find the IPA pronunciation with its "funny looking" characters ulgy. If it is of "dubious quality" then improve it, but even in the form it was in it is better than nothing (if the person doesn't know IPA, then there is no pronunciation information in the article for them). Qutezuce 00:32, 20 June 2006 (UTC)
replies: text: IPA is standard on Wikipedia.  Silly rhyming pronunciation guides are also somewhat standard, but I don't think we need to have every different pronunciation guide in this article.  People who want to learn more about Henri (including other transcriptions of pronunciation) should view his article.  -lethe talk [ +] 00:42, 20 June 2006 (UTC)
replies: text: Maybe I'm missing it, but I see the same pronunciation guides at Henri Poincaré as I do in this article. Qutezuce 01:17, 20 June 2006 (UTC)
thread_title: Non-IPA pronunciation

message: The article states that "the case of n=1 is easy", but isn't n=1 actually totally different?  The homotopy group of n=1 is Z, not 1, so it's not really the same thing you're proving, right?
MGolden 06:47, 16 August 2006 (UTC)
thread_title: Case of n=1

message: The BBC just had someone on that explained it this way.
If you have a rubberband and you make the rubberband smaller and smaller then if the rubber band becomes a point then the space is a sphere. Not exactly what we have in the article. --Gbleem 07:40, 16 August 2006 (UTC)
replies: text: Maybe BBC should read Wikipedia more often. Nature does. I got some emails from them when they were preparing for an article in the issue that appeared earlier this month. --Francis Schonken 07:48, 16 August 2006 (UTC)
thread_title:  bbc 

message: Does the solving of this conjecture have any practical applications beyond the world of topology? I know that Fermat's Last Theorem was more of a mathematical novelty than a serious problem, and I'm not clear whether this issue is any different. It's great that someone solved it, but what does it mean to folks outside the world of abstract mathematics? I think the article could really use a section on this topic. | Mr. Darcy talk 01:32, 23 August 2006 (UTC)
replies: text: It doesn't have immediate applications. As with the Fermat theorem , it says no counterexamples exist, when we already knew that they would be hard-to-find. Charles Matthews 09:24, 23 August 2006 (UTC)
replies: text: Thanks. Then in my opinion, adding something to the introduction that says that the solution has no practical applications would be worthwhile. I think that's going to be the primary question of any lay reader who comes across this page. | Mr. Darcy talk 15:19, 23 August 2006 (UTC)

text: We would end up adding that to 95% of mathematics pages. Not a great idea, and also not 'encyclopedic', either. Mathematics is unreasonably effective, as Wigner says; but not if you throw out everything that doesn't have immediate paybacks. Charles Matthews 19:14, 23 August 2006 (UTC)

text: It's also important to remember that many results in mathematics are not applied practically for decades.  The oft-cited example of Riemannian geometry is a case in point; it was instumental in Einstein's formulation of general relativity, but was developed by Riemann a half-century before. Just because Perelman's proof has no immediate practical applications does not mean it will not in the future. Yill577 02:25, 29 August 2006 (UTC)
thread_title: Application or meaning?

message: "Perelman's achievement has been to solve the Poincare Conjecture, which, says Wikipedia, has been one of the most well-known - and most difficult - open problems in mathematics since it was first posed by Frenchman Henri Poincare in 1904. "
:Katherine Kizilos (August 26, 2006). "When being a genius just doesn't add up". Sydney Morning Herald.
Ta bu shi da yu 14:51, 26 August 2006 (UTC)
thread_title:  The Sydney Morning Herald referenced us! 

message: :Moved here from Article page by Francis Schonken 11:56, 11 October 2006 (UTC)
thread_title:  Comment by Sukumaran (203.115.13.78) 

message: Instead of reverting eachother, let's have a discussion about whether to include the sentence
:"The article [Manifold Destiny] implies that Yau was intent on being associated, directly or indirectly, with the proof, and pressured the journal's editors to accept Zhu and Cao's paper on unusually short notice."
It seems to me that, if this article include a section on Manifold Destiny, then it should give a summary of Manifold Destiny and the above sentence is a fair summary. So I believe that either the sentence should go in, or (if it is decided that the New Yorker article is not a very relevant or reliable source for the purposes of this Wikipedia article) the section should be removed or reduced to one sentence. Removing only this one sentence seems to be a bit inconsistent. -- Jitse Niesen (talk) 13:24, 17 October 2006 (UTC)
replies: text: The trouble with getting into details about Yau here, is that essentially Yau is irrelevant to the Poincaré conjecture. He may not be irrelevant to discussion of the controversy, but the controversy is not about proving the main question in geometric topology, it is about academic politics and (really) about mathematicians being naive and trusting when talking to journalists. Charles Matthews 16:56, 17 October 2006 (UTC)
replies: text: I agree, but in that case I think that Manifold Destiny gets too much attention. So I reduced it. -- Jitse Niesen (talk) 15:40, 26 October 2006 (UTC)

text: Removing all that irrelevant drivel was a big improvement. R.e.b. 15:26, 29 October 2006 (UTC)
thread_title:  "The article implies that ..." 

message: I've moved the other dimensions to another article, as they are very different.
Nbarth 22:38, 20 December 2006 (UTC)
thread_title:  Moved other dimensions to GPC article 

message: I thinks you mean it has a well defined boundry. —Preceding unsigned comment added by 193.136.128.7 (talk • contribs) 
:No.  --C S (Talk) 17:49, 22 December 2006 (UTC)
thread_title:  from the article: lacks any boundary (a closed 3-manifold). 

message: Although I support not moving the article, the beginning still states "In mathematics, the Poincaré conjecture (IPA: [pwɛ̃kaˈʀe])[1] is a conjecture...". Surely the end of that sentence should now be 'theorem'? Just wanted to check whether there was a reason why this hadn't already been changed. Also, the third paragraph seems to indicate his proof hasn't been verified, but if Perelman has been offered the Fields' medal, doesn't that mean it's been verified? DavidHouse 21:31, 26 December 2006 (UTC)
replies: text: Proof writen 2003, verified 2006. I think some paragraphs are not up-to-date. Barraki 00:03, 24 January 2007 (UTC)
thread_title:  Conjecture vs. Theorem -- not about moving 

message: The caption under the picture of homotopying a loop in the two-sphere in the beginning of the article is misleading. Of course, we do not know that the manifold in question is a three-sphere (that's the whole point of the conjecture), I think it could be very confusing. Arcfrk 05:43, 4 May 2007 (UTC)
replies: text: I concur, it's wrong!24.58.63.18 (talk) 04:55, 16 March 2009 (UTC)
thread_title:  Misleading caption 

message: the popular book - mentioned in the article - is entitled "Poincare's Prize" (not Perelman's Prize). Could someone correct that?
--89.139.118.120
:I've corrected it. --Zundark 08:50, 2 July 2007 (UTC)
thread_title:  Book by Szpiro 

message: "Hamilton's program was started in his 1982 paper in which he introduced the Ricci flow on a (...)" ist that date correct?  —Preceding unsigned comment added by 201.62.193.100 (talk) 06:18, 26 May 2008 (UTC)
thread_title:  Hamilton's program 

message: I removed a cover image of Science from this article. In general we avoid using non-free images in articles, by setting high standards for their use. In particular, WP:NFCC#1 and WP:NFCC#8 are relevant here. #1 asks, "Could the subject be adequately conveyed by text without using the non-free content at all?". I think that the answer is yes – the only point of the image was to show that this was a cover story on Science, a fact which can be conveyed via text without the image. In fact this was already in the article's text. — Carl (CBM · talk) 21:15, 29 December 2009 (UTC)
replies: text: I disagree. It also provides a nice illustration of the main idea of the proof. So I'm returning it. Maxal (talk) 15:25, 30 December 2009 (UTC)
replies: text:  We could create a free image to illustrate the main idea of the proof; see WP:NFCC#1. I don't see any argument why we need to use a non-free image here, and the policy on non-free images (WP:NFCC) is intended to be very restrictive. — Carl (CBM · talk) 15:59, 30 December 2009 (UTC)

text: The policy is restrictive but this image well satisfies the fair-use policy of using non-free images and perfectly fits the context of the article (both the image and text on the cover is very relevant to the article). So, I don't see why there is a need to avoid using it. Second, there is no suitable equivalent (simple and nice) illustration at the moment. Maxal (talk) 16:11, 30 December 2009 (UTC)
replies: text: The problem is that the Science cover does not satisfy the WP:NFCC policy; fair use is not a relevant consideration. Just because a non-free image fits into the overall context of the article is not a sufficient criterion for using it. In any case, I created an image of Ricci flow and replaced the cover with that. However, the pre-existence of a replacement is not relevant to NFCC; what matters is whether a free illustration could be created. — Carl (CBM · talk) 17:21, 30 December 2009 (UTC)
thread_title:  Science cover image 

message: Section from wiki article is incorrect.
Perelman's work survived review and was confirmed in 2006, leading to his being offered a Fields Medal, which he declined. Perelman was awarded the Millennium Prize on 18 March, 2010[2]  but declined the prize money stating, "I'm not interested in money or fame. I don't want to be on display like an animal in a zoo."[3]
This italicized quote - was made in 2006 in reference to the Fields Award, not in reference to the 2010 Millennium prize.
He still hasn't decided on the Milennium Prize.
NEW INFORMATION 7/1/2010  The Clay Mathematics Institute (awarding body for the Millennium Prize) made the following announcement:
"Dr. Perelman has subsequently informed us that he has decided not to accept the one million dollar prize. In the fall of 2010, CMI will make an announcement of how the prize money will be used to benefit mathematics."
http://www.claymath.org/  —Preceding unsigned comment added by Abter1 (talk • contribs) 16:09, 1 July 2010 (UTC)
thread_title:  Declining millenium prize 

message: Isn't this just a variant of the old joke about how topologists can't tell the difference between a coffee cup and a doughnut .. with the Poincare conjecture applying to any shape that is topologically simpler than a coffee cup or doughnut? Zaphraud (talk) 15:06, 2 July 2010 (UTC)
replies: text: A "coffee cup" is not simply connected, and so the Poincaré conjecture has nothing to say about it. Moreover, a "coffee cup" in three-space is a three-manifold with boundary, and so the Poincaré conjecture has nothing to say about it. (Every point has a neighbourhood that is either homeomorphic to an open ball, i.e. \{ (x,y,z) \in \R^3 : x^2 + y^2 + z^2 < 1\} or to an upper half-space, i.e. \{ (x,y,z) \in \R^3 : z \ge 0 \}.) The Poincaré conjecture relates to abstract manifolds, as well as submanifolds. It's a very general and powerful piece of kit. All it talks about is simply connected, closed 3-manifolds. If the space you have does not meet all of these hypotheses, e.g. a "coffee cup" or a doughnut, then the Poincaré conjecture has nothing to say. Please see the article about necessary and sufficient conditions. — Fly by Night (talk) 01:24, 29 July 2011 (UTC)
thread_title:  Coffee Cup / Doughnut problem? 

message: I propose merging (re-merging?) Solution of the Poincaré conjecture here because more than half of that article consists of statement of the problem (in more detail than this article has!), and what remains is not much longer than this article's "Solution" section. —Tamfang (talk) 04:15, 7 February 2011 (UTC)
replies: text: I absolutely agree with Tamfang. As with other articles in Wikipedia, the same article is composed of both the statement of the problem and its respective solution. If that means that the article might be a bit longer, so be it. An example, not an mathematical article, but an historical one, is the Cuban Missile Crisis article. And if you think about it, telling the problem and its solution is telling its history (intro, development, and conclusion). So, sysop, merge solution with the article, and make solution redirect to the article. Mrmagoo2006 (talk) 01:47, 15 April 2011 (UTC)
replies: text:  It's not a job for a "sysop", it's a job for us editors, assuming that there are no serious objections to such a move. —Tamfang (talk) 03:17, 15 April 2011 (UTC)

text: I just wanted to mention that I really like the explanation of the conjecture's requirements at Solution of the Poincaré conjecture, which in general seems to be written at about the correct level of accessibility. They're generally well-written and gloss over just enough (though perhaps "homeomorphism" could be recast in terms of limits--points getting closer to a fixed point on the first object get closer to the corresponding point on the second object, and vice versa, with the typical example of something that's not a homeomorphism, f(x) = (cos x, sin x) for 0 <= x < 2pi). 24.220.188.43 (talk) 00:08, 28 April 2011 (UTC)

text: I found the task not as easy as I imagined. —Tamfang (talk) 07:57, 22 August 2011 (UTC)
thread_title:  why a separate "Solution" article? 

message: There's a new book published about the Russian mathematician that has solved this conjecture entitled
"Perfect Rigour: A Genius and the Mathematical Breakthrough of the Century"
Perhaps this should be added as a reference to this article?  —Preceding unsigned comment added by 217.154.240.195 (talk) 13:18, 21 March 2011 (UTC)
thread_title:  new book published 

message: Didn't there use to be a section in this article that explained what the terms in the formulation of the conjecture mean? Simply connected, manifold, homeomorphism... Why was it removed? Jack Daw (talk) 04:27, 31 January 2012 (UTC)
replies: text: The "history" tool would let you look up previous versions. Could you give a link to the version you are talking about? — Carl (CBM · talk) 12:02, 31 January 2012 (UTC)
replies: text: Never mind 'homeomorphism'; I struggled with 'sphere'.  According to ordinary dictionary definitions, and Euclid, a sphere is a solid 3-dimensional figure.  So I was puzzled by the sentence in the current article saying 'The Poincaré conjecture claims that if such a space has the additional property that each loop in the space can be continuously tightened to a point, then it is necessarily a three-dimensional sphere'.  I first assumed that this meant a sphere in the ordinary sense, like (approximately) a tennis ball, but this didn't seem right.  (I would add that it is grammatically ambiguous whether in the quoted sentence 'it' is the 'space' or the 'loop' referred to in the preceding clause, but that is another matter.)  On following the various links to other articles I think I established that in the article the word 'sphere' does not have its ordinary meaning as a solid figure, but as the two-dimensional curved surface of such a figure, and that a 'three-dimensional sphere' is the analogue of such a surface in 4-dimensional space, which encloses the 3-dimensional figure called a 'ball'.  If so, it might be clearer if the article consistently used the term '3-sphere' and not 'three-dimensional sphere', which would at least warn the reader that it is a technical term.86.178.146.101 (talk) 13:57, 11 June 2019 (UTC)
thread_title:  Explanation of terms 

message: This section reads for me in a somewhat unenyclopaedic manner. Specific examples being the phrase "something called", which is totally unnecessary, and the explanation of eignvalues, rather than merely linking to the article.
In the explanation of shape of the singularities, it says "essentially three-dimensional cylinders made out of spheres stretched out along a line". "essentially" seems unnecessary. Would a sphere stretched along a line, in this context, be four dimensional, rather than three? The whole article appears to be about the four dimensional 3-sphere.
--Atomic Fusion (talk) 04:42, 25 October 2013 (UTC)
thread_title:  Solution Section 

message: Do you really believe that conjecture is a theorem? МетаСкептик12 (talk) 13:58, 19 August 2015 (UTC)
replies: text: It should really say "the Poincaré Conjecture is a theorem", the capitalization making it clear that Poincaré Conjecture is a proper noun. The statement would then be no more contradictory than "the Chicago Bears are humans". But Wikipedia's convention for capitalization of theorem names was established long ago, and there's little chance of getting it changed. --Zundark (talk) 15:26, 19 August 2015 (UTC)
replies: text: If it should say, then  say, I cite what I see now. However, if you want to say that Poincaré Conjecture is not a conjecture, I am afraid, you are not right. МетаСкептик12 (talk) 16:29, 19 August 2015 (UTC)
replies: text: Also: it's old hat, boring, and irrelevant. See #Consider renaming this article above.  Also see WP:SHOUT. Choor monster (talk) 15:29, 19 August 2015 (UTC)

text: I have fixed the Conjecture article, so that it uses the correct name.  (Thank you for bringing this to our attention.)  Also, it's not an issue restricted to English.  Check out ru:Гипотеза Пуанкаре, and note that someone asked the same question on the Talk page there.  Choor monster (talk) 18:39, 19 August 2015 (UTC)
thread_title:  ...the Poincaré conjecture is a [[theorem]]... 

message: This article Colin P. Rourke has a nice link to a 1986 New York Times piece on Rourke and a colleague claiming to have solved the problem but no further information about how it was disproved. I wonder if that's worth following up on and adding to this article. I found it just reading random articles so I have no idea about how to include it or fix his article. Thanks. JonathanPlaster 14:22, 4 October 2015 (UTC)
replies: text: If I remember correctly, Rourke-Rego wsa widely disbelieved at the time (no new ideas that would bypass known difficulties) and Rourke gave an informal seminar at UCB where his mistake was identified.  It's probably extremely UNDUE to bother. Choor monster (talk) 20:32, 4 October 2015 (UTC)
replies: text: Thanks. JonathanPlaster 11:50, 5 October 2015 (UTC)
replies: text: I found a reference, and expanded the Rourke page. Choor monster (talk) 18:43, 7 October 2015 (UTC)
thread_title:  Colin P. Rourke article disproved  

message: Substituted at 02:29, 5 May 2016 (UTC)
thread_title: Assessment comment

message: There's no audio file. May i help, as a french citizen ? 
Is yes, how ? How to upload mp3 files of me saying it ?  — Preceding unsigned comment added by BeKowz (talk • contribs) 15:04, 18 January 2017 (UTC)
replies: text: You can upload an audio file to Wikimedia Commons (your Wikipedia username and password will work there). Then it will be available for use in Wikipedia. But you can't upload MP3, as it's not an allowed format (Ogg Vorbis is usual). --Zundark (talk) 19:02, 18 January 2017 (UTC)
thread_title:  Audio file for Poincaré 

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thread_title:  External links modified 

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thread_title:  External links modified 

message: Doesn't the formulation of the conjecture at the top of the article need the additional condition of compactness, which appears in the section "Poincaré's question"?  In fact, isn't Euclidean 3-space a simply connected, closed 3-manifold, not homeomorphic to the sphere? AmirOnWiki (talk) 12:33, 14 October 2019 (UTC)
thread_title:  Compactness 

message: I have revised this section. The previous version said
 Huai-Dong Cao and Xi-Ping Zhu published a paper in the June 2006 issue of the Asian Journal of Mathematics with an exposition of the complete proof of the Poincaré and geometrization conjectures.[23] They initially implied the proof was their own achievement based on the "Hamilton–Perelman theory", but later retracted the original version of their paper, and posted a revised version, in which they referred to their work as the more modest "exposition of Hamilton–Perelman's proof".[24] They also published an erratum disclosing that they had forgotten to cite properly the previous work of Kleiner and Lott published in 2003. In the same issue, the AJM editorial board issued an apology for what it called "incautions" in the Cao–Zhu paper.
I find the writer's objective use of "they initially implied" to be remarkable, given Cao-Zhu's very clearly stated opening paragraph - which I have inserted, to let the reader judge for themselves. I also clarified what the AJM editorial board was apologizing for, and the nature of their lack of citation of Kleiner-Lott. I believe that my revision gives a much clearer picture than the somewhat murky previous lines.
I have also added the relatively recently-noticed errors in Kleiner-Lott and Morgan-Tian's expositions, since (beyond being directly relevant) it should clarify for the general reader why it is important to have so many expositions of such a technically demanding result.  — Preceding unsigned comment added by Gumshoe2 (talk • contribs) 07:46, 11 May 2020 (UTC)
thread_title:  The discussion of Cao-Zhu and the other expositions 

message: In this section: https://en.wikipedia.org/wiki/Differential_structure#Differential_structures_on_spheres_of_dimension_1_to_20 , the following is mentioned:
It is not currently known how many smooth types the topological 4-sphere S4 has, except that there is at least one. There may be one, a finite number, or an infinite number. The claim that there is just one is known as the smooth Poincaré conjecture (see generalized Poincaré conjecture). Most mathematicians believe that this conjecture is false, i.e. that S4 has more than one smooth type. The problem is connected with the existence of more than one smooth type of the topological 4-disk (or 4-ball).
My feedback:
I'm pretty sure that the Poincaré conjecture already got proved by that funny Russian dude who turned down the millenium prize.
It's even mentioned in the introductory paragraphs on: https://en.wikipedia.org/wiki/Poincar%C3%A9_conjecture  — Preceding unsigned comment added by Sacha1618 (talk • contribs) 00:45, 23 December 2020 (UTC)
replies: text: Perelman and Hamilton's work is about the three-dimensional problem, the discussion there (as indicated by the link to the "generalized Poincare conjecture" page) is about the four-dimensional problem. Gumshoe2 (talk) 01:27, 23 December 2020 (UTC)
thread_title: New section

message: Since the then Henri Poincaré conjecture [or hypothesis] was demonstrated by the russian mathematician Grigori Perelman on November 13, 2002, it is no longer a conjecture [or hypothesis], so the name of this article should be Poincaré's Theorem.
Aainitio (talk) 23:25, 31 July 2021 (UTC)
replies: text: It would normally only be called Poincaré's Theorem if Poincaré proved it.  It would instead be more proper to call it Perelman's theorem.  But, I think it was such a famous conjecture for so long that it is still generally called the Poincaré conjecture even though it is no longer a conjecture.  2602:24A:DE47:B8E0:1B43:29FD:A863:33CA (talk) 06:35, 12 September 2021 (UTC)
replies: text: Support for name change：I object to the use of the so-called "universality" instead of "reasonableness". This page should have been renamed 17 years ago, but for some reason it is still using the wrong and misleading name.——WMLO (talk) 11:57, 28 July 2023 (UTC)
replies: text: I support the name change as well, but considering what Perelman said about the contributions of Richard S. Hamilton, I’d suggest using the name Poincaré–Smale–Freedman–Hamilton–Perelman theorem. Smale and Freedman are also included because Smale proved the conjecture for higher dimensions, and Freedman proved the conjecture for the 4 dimensional space.—-EPN-001GF IZEN བཀྲ་ཤིས་བདེ་ལེགས།  — Preceding undated comment added 15:28, 12 January 2024 (UTC)

text: It is still all but universally referred to as the Poincaré conjecture, and not as the Poincaré theorem or Perelman theorem or Poincaré-Smale-Freedman-Hamilton-Perelman theorem. So wikipedia has to call it as such. Same as how Fermat's last theorem isn't called "Wiles theorem" and the Weil conjectures aren't called "Dwork-Grothendieck-Deligne theorem." Gumshoe2 (talk) 22:57, 12 January 2024 (UTC)

text: Just to strongly support what Gumshoe said. Until there are clear sources showing that everyone now calls it something different, it should not be changed. Imaginatorium (talk) 03:12, 13 January 2024 (UTC)
thread_title:  Poincaré's theorem, no more conjecture or hypothesis...