View topic - [SEMI-OT] Poincar� Conjecture Proved

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Forum index » Archive » Archive: Perplex City » PXC: Questions/Meta

[SEMI-OT] Poincar� Conjecture Proved

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jbd
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Joined: 27 Jul 2004
Posts: 295

[SEMI-OT] Poincar� Conjecture Proved

From mathpuzzle.com:

Quote:

According to Harvard mathematics professor Shing-Tung Yau, winner of the Fields Prize in 1982, the global collaborative work for a proof of the Poincar� Conjecture is now complete.

In 1982, Columbia University mathematician Richard Hamilton showed that a compact manifold with positive Ricci curvature evolves toward a state of constant curvature. His paper gave an initial framework to prove Thurston’s geometrization conjecture, of which the celebrated Poincar� conjecture is a special case. (Willam P. Thurston won a 1982 Fields medal for this work.)

In 2003, Russian mathematician Dr. Grigori Perelman gave a series of public lectures at the Massachusetts Institute of Technology. These lectures, entitled "Ricci Flow and Geometrization of Three-Manifolds," were presented as part of the Simons Lecture Series at the MIT Department of Mathematics on April 7, 9, and 11 of that year. These widely acclaimed lectures made spectacular advances to the work of Hamilton, and led to MathWorld article Poincar� Conjecture Proved -- This Time for Real. The Perelman lectures gave a roughly 70 page guideline for a final proof.

In 2006, the 300-page paper "The Hamilton-Perelman Thoery of Ricci Flow-The Poincare and Geometization Conjecture," was was published in the June issue of Asian Journal of Mathematics. Zhu Xiping of Zhongshan University and Cao Huaidong of Lehigh University co-authored the paper, which finalized the earlier work of Thurston, Hamilton, and Perelmen.

Zhu and Cao spent two years writing their paper, under guidance from Shing-Tung Yau. Once completed, they then went to Harvard for half a year. Each week, they spent three hours explaining and defending their work to a team of Harvard mathematicians. After this long series of lectures and reviews, the 31 members on the editorial board of Asian Journal of Mathematics reached a unanimous consensus to publish the paper.

Why is this semi-on topic for Perplex City? Because this is one of the Clay Institute Millenium Problems. Yes, one of the 7 has fallen. (Although it still has to hold for 2 years before the Clay Institute makes their final declaration.)

Hence, there's still hope for Reimann yet.

Just keep in mind Perelman's work in this goes back to the mid-90s. Don't expect anything to go quickly, now.

Posted: Thu Jun 29, 2006 11:58 pm

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