World top mathematician Richard Hamilton has recognized the work of Chinese mathematicians on giving a complete proof of the century-old puzzle of Poincare Conjecture.

Foreign member of the Chinese Acadamy of Sciences, Professor Shing-Tung Yau (2nd R) from Harvard University introduce the Poincare Conjecture to journalists in Beijing, capital of China, June 3, 2006. [Xinhua]

"Chinese mathematicians have played a very important part in this development," Prof. Hamilton at Princeton University said in a video talk recorded two weeks ago in Beijing when he discussed the proof with Prof. Cao Huaidong, one investigator who unraveled the conjecture.

"It's very nice to have such an account written by two outstanding people in the field of Ricci flow. They also introduced ideas of their own which makes the proof easier to understand," Prof. Hamilton said in the video that for the first time went to public at the ongoing International Conference on String Theory 2006.

"All Chinese can be proud of the achievements of their mathematicians in differential geometry and their contributions to the completion of the proof of Poincare Conjecture," he said.

Together with Prof. Cao, Prof. Zhu Xiping at Zhongshan University in Guangzhou, Guangdong Province, has put the final pieces together in the solution to the puzzle that has perplexed scientists in the world for more than a century.

The pair has published a paper in the latest issue of the U.S.-based Asian Journal of Mathematics, providing complete proof of the Poincare Conjecture promulgated by French mathematician Henri Poincare in 1904.

The work done by Zhu and Cao has given a new proof for the uniqueness of solutions on complete manifolds, a different idea for doing the backwards blowup in time and a proof of the canonical neighborhood theorem, Prof. Hamilton said.

He said he will further discuss details of the proof next week with a few prominent mathematicians in Zurich, Switzerland.

"We want to be complete certain that everything in the proof is beyond question before making a formal announcement, because many researchers will base their work on it," he said.

Prof. Hamilton, member of the U.S. National Academy of Sciences, is recognized as "the father of Ricci flow", who introduced the Ricci flow equation and his development of it into one of the most powerful tools in geometry and topology.

Hamilton's video talk was shown by Shing-Tung Yau, a Harvard mathematics professor and a Fields Medalist. His audience included legendary astrophysicist Stephen Hawking and 2004 Nobel physics laureate David Gross.

"I'm very positive about Zhu and Cao's work," Prof. Yau said when he elaborated the proof to the audience.

"Chinese mathematicians should have every reason to be proud of such a big success in completely solving the puzzle," Prof. Yau said.

In his wheelchair, Prof. Hawking listened to the lecture of Yau. Prof. Hawking combines physical theories and mathematical methods to explore cosmic origins and black holes.

"Professor Hawking's attendance at the lecture indicates that this is a very important work," Prof. Yau said.