Wikipedia:WikiProject Mathematics/A-class rating/Poincaré conjecture

The following discussion is preserved as an archive. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this page.

Poincaré conjecture

Result: Promoted to A class. The only outstanding criticism is the rather vague "the prose could also be made a bit tighter". No comments have been made for quite some time, so I have to make a decision, and this discussion leads me to the conclusion that the article is not quite FA class but close. -- Jitse Niesen (talk) 11:27, 18 May 2007 (UTC)[reply]

This article has made it through a period of tumultuous change and currently reads very nicely. The lede has been much improved, and there is a well-written section on Perelman and Ricci flow worked on by R.e.b. and others. I believe concerns about readability and accessibility have been addressed as much as can be reasonably expected. Perhaps some improvements to the exposition could be made, e.g. analogy to heat equation in the Ricci flow section, and so forth, but I figure people can use this review to make such improvements.

Since accessibility has been a frequent complaint, let me made one more remark: the statement of the Poincare conjecture is actually much harder to understand than problems like P vs. NP (probably the easiest of the Millennium problems to explain). Even compared to something like the Riemann hypothesis – after all, more people are familiar with basic complex analysis (or advanced calculus) than manifolds and geometric topology. So I hope this discussion doesn't focus on accessibility, although I will agree that this is an issue we need to be concerned with in relation to this article. --C S (Talk) 01:57, 4 May 2007 (UTC)[reply]

oppose while good I don't think its A-class yet. I think the section on higher dimensions could be expanded a little as it adds context to the 3 dimensional case. The section Hamilton's Program and Perelman's solution has a lot of full references in the text, these could be better presented with a shorter title in the text and a reference/footnote. The prose could also be made a bit tighter. Reading through the Ricci flow section I came across ... as all constant curvature manifolds are well understood, which provoced my interest wanting to find out more about this, but alas no link. --Salix alba (talk) 08:00, 5 May 2007 (UTC)[reply]
- I expanded the higher dimensions part and made a couple other changes like the caption for the lede image. Also, that interesting sentence you quote isn't so good. Hyperbolic 3-manifolds aren't nowhere nearly as well understood as spherical 3-manifold or flat 3-manifolds (see these links to satisfy your curiosity ^.^). In this context where you have some restriction on the fundamental group (simple connectivity, and later in the section, free products of finite groups and infinite cyclic groups), the hyperbolic case doesn't have to be worried about. Anyway, I think the point is that in this context, the only constant curvature guys will be spherical ones, and the only simply-connected spherical 3-manifold is a 3-sphere; I made the appropriate modification.--C S (Talk) 11:32, 6 May 2007 (UTC)[reply]

I had a go at the formatting of the references and the "External links" section, which seemed a bit excessive. I agree with Salix alba that the section on higher dimensions should have a bit more. I'm also wondering whether the term "three-dimensional sphere" in the first paragraph should be explained: I fear that most people would think that it refers to the 2-sphere. And perhaps the article needs more motivation. Why is the conjecture so important? -- Jitse Niesen (talk) 14:16, 5 May 2007 (UTC)[reply]

- Hopefully the new caption should help. As for your question, that's hard to answer. For a long time, like Fermat's Last Theorem, it wasn't really important, just tricky, so gained a big reputation. To a large degree, topologists just worked around it and managed just fine. Later on, the conjecture fit into Thurston's picture of what a classification should look like, but even then, if that part of the geometrization conjecture had been shown false, I don't think it would have been too devastating. Right now the lede says it is considered one of the "most important" conjectures in topology; I've never been too happy with that. I think it's always been more famous than important. Thurston said once in one of his papers that his hope for the geometrization conjecture is that it would be a more productive conjecture to tackle than the Poincare conjecture. So I would say its importance, such as it is, comes from other important conjectures, rather than on its own. Another take on this is that the Poincare conjecture really is a truly basic question about 3-manifold topology. Can there be other simply-connected 3-manifolds other than the 3-sphere? It's an intriguing question, which is undoubtedly why so many have gotten "Poincaritis". --C S (Talk) 11:32, 6 May 2007 (UTC)[reply]

Hey guys, I am on a unassessed article journey and I am going to give the article a B until you decided on this issue.--Cronholm144 01:02, 12 May 2007 (UTC)[reply]

The above discussion is preserved as an archive. Please do not modify it. Subsequent comments should be made on the appropriate discussion page, such as the current discussion page. No further edits should be made to this page.