Poincare conjecture proved by Chinese/Russian/American mathematician

Chinese mathematician, Zhu Xiping, of Sun Yatsen University in Guangzhou, collaborating with Chinese American Cao Huiadong of LeHigh University at Pennsylvania, have finished the last steps to prove the Poincare Conjecture, one of the 7 problems of this millenium (This is only the 7th year into the millenium). Earlier works has been done by many others, including Russian Perelman, American Hamilton and Thurston. So these two mathematicians are among the people who did the job and they finished the final remaining pieces of bricks. Arguably Russian Perelman made the greatest breakthrough in the effort by showing a scheme that has been widely believed to be the right path. It was said that there are a few major gaps in Perelman's scheme. So filling in these gaps are great accomplishments in itself.

This is the most important milestone since Fermat's Last Theorem was proved by Andrew Wiles of Princeton (Cao HD also received his PhD from Princeton in 1986, a student of Yau Shingtung). Both proofs were done with hundreds of pages of paper.Chinese mathematician Yang Le was forced to quantify the contribution by reporters. He gave a very rough estimate, Hamilton 50%, Perelman 25%, Zhu/Cao/Yau(ST) 25-30%. (Such division should not be taken too seriously)

Poincare conjectured that a simply connect space is essentially a sphere, topologically. i.e. you can squeeze and mould (without inducing or splitting hole or gaps) to change any objects that are "simple connected" to become a sphere.See Ming Pao, Google news for report. For more technical introduction and historical (insider) notes see this blog (in Chinese). As usual, blog is at least 2 weeks ahead of MSM.

Zhu did not publish for 4-5 years when he switched from PDE to Geometric Analysis about 10 years ago. His employer, Sun Yatsen University did not attempt to pressure him. ZYS Chancellor Huang said, his school tried not to exert pressure on professors who have already proved themselves. He added, for these people, research is their lives. If this report is true and such policy is widely (and effectively) implemented in China, we may expect to see major transformation in China's academic developement. (According to Yau, Zhu refused a professorship from MIT and said he preferred to stay at SYSU)

Cao HD is already 46 year old. Zhu is 44
. Unfortunately, they are not "young enough" (under 40) to be become the first Fields Medal for a Chinese (doing his research in China). Still, enormous achievement. This is the Peaceful Development, the development that pentagon worried so much about.

1) Thurston had received his Fields Medal already in 1982 (same year when Yau Shingtong got his).
2) Freedman got his in 1986 for proving the case in 4-dimensional space.
3) Smale the case of dimension larger than and equal to 4 and got his in 1966.
4) Fields Medal is awarded every 4 years to mathemticians who are under 40 year old. Typically there are 3-5 receivers.



Sun Bin said...

see all Guardian tech blog

Sun Bin said...

More detailed coverage (in Chinese) here.

Sun Bin said...

more by jacky peng

Sun Bin said...

a good insider's review from thurston to perelman. the poster also believed that hamilton+perelman did 90% of the work.