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.

• Yang, member of the Chinese Academy of Sciences, said in an interview with Xinhua, "All the American, Russian and Chinese mathematicians have made indispensable contribution to the complete proof."

  Prof. Zhu at Guangzhou-based Zhongshan University and Prof. Cao at Lehigh University in Pennsylvania co-authored the 300-page paper, "The Hamilton-Perelman Thoery of Ricci Flow-The Poincare and Geometization Conjecture," which was published in the June issue of the journal.

  "The total length of Perelman's work on the conjecture by the end of 2002 was about 70 pages," said Yang, citing that Perelman raised guidelines for proving the conjecture but not specifically pointed out how to unravel the puzzle.

• According to Huang Daren (Chancellor of Sun Yatsen University), Zhu said, "This is international team work, Russian made great contribution. We progressed step-by-step, I was lucky to be at at the right place to finish the goal with Cao Huaidong, taking the ball passed by our international colleagues."
• 中山大学校长黄达人转述朱熹平的话说：“其实国际上很多团队都在做这个事情，做出了很大的贡献，特别是俄国数学家，这个猜想的完成，是国际数学界的同行们你一步我一步，共同做出来的。我只是比较幸运，由我和曹怀东完成了临门一脚。”

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.

p.s.
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.

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