Talk:Solution of the Poincaré conjecture

Compact?
The explanation of "Compact" doesn't seem quite right. In a metric space, it's "closed + bounded", but the definition given appears to give bounded twice and not closed: "A compact manifold is bounded and does not extend to infinity.".

I'm not sure of the best way to explain "closed" in layman's terms either, though.

--Rupertsw 14:26, 23 June 2007 (UTC)


 * "closed" maybe: if you move through the manifold, or what we would call in the 2-dim case "on it", you never need to stop or change your direction abuptly, i.e. there is no boundary. —Preceding unsigned comment added by 91.19.111.154 (talk • contribs) 21:33, 10 September 2007 (UTC)

And...
...the images? —kiddo 22:06, 7 July 2007 (UTC)


 * Yes, what happened to all the images I uploaded? They were graphics I made myself and were free for common use.  Now the only images left were made by someone else. —Preceding unsigned comment added by 208.120.19.3 (talk • contribs) 07:27, 9 August 2007 (UTC)


 * The images were deleted because you didn't specify which license you want your pictures to fall under. When uploading a picture, you should label it with one of the Image copyright tags.
 * Now, you don't have to go through the whole process again. If you tell me what license you want to use (look in the "For image creators" section for some possibilities), I can retrieve your images and do the tagging for you. — Jitse Niesen (talk) 03:14, 12 August 2007 (UTC)

Image of 3-sphere
The illustration in "What is a 3-dimensional Sphere" is very misguiding. I won't edit as I don't have an account. The whole point in this paragraph is: the 3-dim. sphere is one dimension more than what we usually call sphere. Then this picture comes with a map of the world as an example of 2-dim, and continues to call the 2-sphere 3-sphere, confusing everyone for whom this paragraph is intended. Delete it please. —Preceding unsigned comment added by 91.19.111.154 (talk) 21:33, 10 September 2007 (UTC)


 * Update: edited it. but it goes on like that. Whoever mad these illustration did not understand the 3-sphere at all. Please change it. —Preceding unsigned comment added by 91.19.111.154 (talk) 21:41, 10 September 2007 (UTC)

Need Professional Writing
Alright. Please find a mathematician who is willing to bring sense into this mess. I'm not going to. There is a lot of good information in the other articles, maybe delete this one. Believe me, whoever is responsible for this article: almost everything is incorrect, find someone who knows this stuff. I don't have time. —Preceding unsigned comment added by 91.19.111.154 (talk) 21:50, 10 September 2007 (UTC)


 * Actually, I believe that this page was started by a mathematician, so that's not the problem. The problem is that trying to explain such an advanced topic to a layperson audience in such a short article is impossible without taking many liberties with mathematical precision.  In any case, I am doubtful that a layperson (or even a math major) can learn much from this article as written.  The ideal solution would be to refer to other articles that describe the mathematical concepts involved in a way that is understandable to a layperson, but sadly these "other articles" do not exist.  The next best solution would be to rewrite this article as a much longer article that that explains the relevant mathematical concepts from scratch.  I hope to find time to do this one day.  —Preceding unsigned comment added by 146.96.107.32 (talk) 19:00, 16 April 2009 (UTC)

Use of differing symbols and terminology in Wikipedia's mathematics (it usually leans towards the more and unnecessarily complex symbols and terminology) has made it often useless to me as a student, why should this article be any different? We need best someone who is not only intelligent in mathematics, but English as well before this information is usable. Inthend9 (talk) 04:42, 21 March 2010 (UTC)

Definition of manifold is not well-explained
The definition given of a manifold uses the unnecessarily technical term charts — but then goes ahead and gives a wrong example (the 2-sphere built from two disks glued only at their boundaries) to supposedly illustrate this concept. Nowhere is the essential concept of "locally Euclidean" either mentioned or implied. —Daqu (talk) 20:51, 8 December 2007 (UTC)


 * Yes, that's a problem. This whole article violates WP:NOTPAPER, WP:MTAA, etc. but I can accept that, as long as you explain it in the section that is supposed to be a non-specialist's explanation in words that a non-specialist can understand.


 * Fortunately somebody on Slashdot responded to that very complaint about this article in words that I can understand (I took a few college math courses years ago but I'm not a mathematician). I'm inserting them into the article. If somebody sees a plagiarism problem they can rephrase it, or substitute better language, but don't just delete a simple explanation. --Nbauman (talk) 18:02, 20 March 2010 (UTC)


 * OK, I did it. It's not even a copyvio since I had to rewrite the Slashdotter's generally excellent explanation http://science.slashdot.org/comments.pl?sid=1588180&cid=31535100 a little bit to fit it into encyclopedic style.


 * Now I don't care if somebody comes along and rewrites it to make it more accurate or easier for the non-specialist to understand. I would mind if somebody, in the name of precision, pedantically rewrote it to make it harder for the non-specialist to understand (again).


 * There are few times in life when a writer has a reader from his target audience come back and say that the reader can't understand a paragraph. When you get that useful feedback, there's no question. You have to simplify it.


 * And don't forget, under WP:NOTPAPER, you can't just include a word your reader won't understand and link to a more detailed discussion about that word in another article. --Nbauman (talk) 18:28, 20 March 2010 (UTC)

Inappropriate attribution of solution to Hamilton
If two mathematicians jointly or independently solve a problem, that is when it is appropriate to attribute both their names to the solution(s). But unless this be the case, mathematicians do not list as solvers all historical contributors to the mathematics used in the solution. As is well-known, Hamilton did develop mathematical ideas that were later used by Perelman to solve the problem. But Hamilton did not solve the problem.

Especially since Hamilton wasn't even willing to meet with Perelman to discuss the latter's ideas that led to the solution of the Poincaré conjecture, it would be a particularly cruel miscarriage of fairness to attribute the proof to Hamilton. (No one would deny that Perelman's proof makes crucial use of mathematics developed by Hamilton about two decades earlier. It also makes crucial use of ideas developed by Riemann and Poincaré and many other mathematicians as well.) — Daqu (talk) 21:07, 8 December 2007 (UTC)


 * What are you referring to specifically?  If you're referring to the title "Hamilton-Perelman solution....", it's because the title is not only giving attribution to the person who completed the proof of Poincare.  That's not the point of the title.  The point is to explain the proof, and the macroscopic aspects of the proof, the "big picture" is largely due to Hamilton.  If you don't mention his name you would be misleading the audience into thinking Perelman devised the Ricci flow approach all on his own.  It's not the job of the page title to give a full and complete attribution to who solved the problem.  The point is the big picture.  The complete attribution you look for inside the article.  —Rybu (talk) 23:53, 8 December 2007 (UTC)

annoying ignorant layman stickler for detail
Unless I am told otherwise, I will think a manifold is a space, and a space is not necessarily a manifold. —Preceding unsigned comment added by 74.170.68.234 (talk) 16:13, 16 April 2008 (UTC)


 * ...and you would be correct. —Preceding unsigned comment added by 146.96.107.32 (talk) 18:50, 16 April 2009 (UTC)

confusing definition of dimension
First, I'll say I'm not a mathematician... but isn't a circle described by (x^2 + y^2 = r^2) two dimensional and a sphere given by (x^2 + y^2 + z^2 = r^2 )3-dimensional? Why are they described as 1- and 2- dimensional, respectively? Is this really true? --Dru007 (talk) 05:07, 16 August 2008 (UTC)


 * See the Dimension page. This is not an issue of `truth' it's the issue of what does the word dimension means. —Rybu (talk) 19:18, 16 August 2008 (UTC)


 * Yes! so according to the dimension page I'm correct, and the article needs to be changed! But since I'm no mathematician, I'm not going to touch it... —Dru007 (talk) 01:59, 17 August 2008 (UTC)


 * You might want to spend more time reading the dimension page, because you're still not understanding the way the word dimension is used in mathematics. —Rybu (talk) 04:00, 18 August 2008 (UTC)

Organization?
This page isn't like any of the other articles. There should be a seperate, more advanced article. Most of the other pages do not put it in layman's terms; this does not follow the guidelines. —Preceding unsigned comment added by 69.248.30.100 (talk) 00:40, 24 May 2009 (UTC)

Homeomorphism must be mentioned
I can't beleive this article doesn't even mention the concept of homeomorphism. Furthermore, it currently defines the 3-ball in metric terms. This way, the statement of the conjecture becomes false. We need to explain that bodies that objects that normally wouldnät be called "balls" are included under the term. —Rain74 (talk) 19:22, 10 September 2009 (UTC)


 * Went on and added a paragraph about it. —Rain74 (talk) 19:37, 10 September 2009 (UTC)


 * I suspect it was deliberately left-out in an attempt to make the article sound less formal. —Rybu (talk) 18:26, 12 September 2009 (UTC)


 * Perhaps, but totally omitting it makes it wrong in my opinion. I would be fine with omitting the explanation of what a homeomorphism is, but it must be mentioned that "is a sphere" means "is homeomorphic to a sphere", with a link to homeomorphism.
 * —Rain74 (talk) 15:16, 13 September 2009 (UTC)

Nicely Done
Thank you to the people who put so much effort into this article. I was curious about the topic after reading about the prize and was delighted to find such a readable article about a complex topic. --Gomi no sensei (talk) 13:46, 19 March 2010 (UTC)
 * This article was a pleasure to read, so I am astonished that the discussion page doesn't list this as being part of any article or having any kind of status. Is there a math project that could adopt this an nominate it for GA status?  Clearly it needs a bit more work before becoming a Good Article, but the groundwork is laid. 146.139.144.220 (talk) 18:20, 19 March 2010 (UTC)
 * WikiProject Mathematics would seem to fit. I have no idea why this article isn't marked as being part of it. 86.136.255.51 (talk) 16:40, 24 March 2010 (UTC)

why "solution"?
Why isn't this article titled Proof of the Poincaré conjecture? One doesn't solve a conjecture, one proves it or disproves it. —Tamfang (talk) 00:29, 21 September 2010 (UTC)


 * Resolution maybe? —Tamfang (talk) 23:14, 9 July 2023 (UTC)

Removal
Half of the article had a patchwork of explanations of concepts for which we already have articles; articles which explain the concepts in greater depth and detail than the patchwork of explanations. As such, I have removed several unnecessary pages of text and replaced them with wiki-links. — Fly by Night  ( talk )  20:30, 14 June 2011 (UTC)

Merge
See Talk:Poincaré_conjecture about the merge. Looked like rough consensus for it to me. --Izno (talk) 03:32, 4 October 2011 (UTC)