Wikipedia:Peer review/Poincaré conjecture/archive1

Poincaré conjecture

This is a mathematical problem that is considered quite important and has garnered much interest in major newspapers and scientific periodicals over the last several years, due to the recent work by Grigori Perelman. It appears to be somewhat back in the news. Since this page has mostly been edited by math-focused editors, I thought it would be good to get feedback from a wide cross-section of Wikipedians, particularly those not fluent with mathematics. I would also encourage those with some science background, but not strictly in mathematics, per se, to respond and make comments. --C S (Talk) 03:03, 5 June 2006 (UTC)

Honestly, I think the explaination could be clearer. I think the Clay Mathematics Institute's description of the problem is a little easier to understand though I like that this article talks about 3-spheres where as the Clay article just talks about points (though I understand that the point and 3-sphere are homeomorphic).

I think the "loosely speaking" explaination is so vague when it talks about the 3-manifold being "sufficiently like" a sphere it would not help anyone to understand the problem. I think one of the ways to improve the explaination, is to explain homeomorphism as the article on homeomorphism explains it. That is, "intuitively, a homeomorphism maps points in the first object that are close together to points in the second object that are close together, and points in the first object that are not close together to points in the second object that are not close together." I think neither this article nor the Clay's article did that well.

I think more analogies would be helpful. The donut case in the Clay's article wasn't bad - though I think some people would fail to understand why a donut cannot be shrunk to a point but an apple can (hence the need to clearly explain homeomorphism).

I was really surprised to see that the conjecture was not actually stated in the lead especially since its standard form is so concise. I think doing so will benefit most readers — especially those who come to the article with an understanding of manifolds and homeomorphism.

Cedars 01:22, 6 June 2006 (UTC)