Monday, June 05, 2006

Poincare conjecture solved

China news:
Professor Cao Huaidong, of Lehigh University in Pennsylvania, and Professor Zhu Xiping, of Zhongshan (Sun Yat-sen) University in south China's Guangdong Province, co-authored the paper, "A Complete Proof of the Poincare and Geometrization Conjectures - application of the Hamilton-Perelman theory of the Ricci flow", published in the June issue of the journal.

Cao and Zhu put the finishing touches to the complete proof of the Poincare Conjecture, which had puzzled mathematicians around the world, said Professor Shing-Tung Yau, a mathematician at Harvard University and one of the journal's editors-in-chief.

The conjecture was rated as one of the major mathematical puzzles of the 20th Century, said Yau.

"The conjecture is that if in a closed three-dimensional space, any closed curves can shrink to a point continuously, this space can be deformed to a sphere," he explained.
This is big news. The higher dimensional analogues had already been proved. Word of the proof has been around for a couple of years, but this is the first that I have heard that an expert journal editor is vouching for it. Yau is a genius in the field, and he would know. I expect that Grisha Perelman will get most of the credit. You can find his papers here.