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.
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."
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.