A leading Chinese mathematician Yang Le said Sunday that the successful unraveling of one of the world's toughest puzzles is an outstanding job.
Two Chinese mathematicians, Zhu Xiping and Cao Huaidong, have put the final pieces together in the solution to the puzzle that has perplexed scientists around the globe for more than a century.
The pair have published a paper in the latest US-based Asian Journal of Mathematics, providing complete proof of the Poincare Conjecture promulgated by French mathematician Henri Poincare in 1904.
A Columbia professor Richard Hamilton and a Russian mathematician Grigori Perelman have laid foundation on the latest endeavors made by the two Chinese. Prof. Hamilton completed the majority of the program and the geometrization conjecture.
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.
"Guidelines are totally different to complete proof of theories," Yang said.
Xinhua correspondents contacted Prof. Cao for many times and finally got a telephone interview. Prof. Cao said, "Under the guidance of Prof. (Shing-Tung) Yau, Xiping and I worked for the conjecture in more than two years."
"The latest find will be good for out future work," Prof. Cao said.
Harvard mathematics professor Shing-Tung Yau, winner of the Fields Prize, said the excellent job done by Zhu and Cao was the final strike on a global collaborative work for a complete proof.
Prof. Yau, co-editor-in-chief of the Asian Journal of Mathematics, said, "All the 31 members of our editorial board are meticulously critical, and we must have consensus on any articles which will appear in our publication."
Zhu and Cao were invited last September by the Harvard Mathematics Department to conduct academic exchange at Harvard. In the following half year, they spent three hours every week to explain their work to five Harvard mathematicians.
Yau rated the conjecture as one of the major mathematical puzzles of the 20th Century.
"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 said.
By the end of the 1970s, US mathematician William P. Thurston had produced partial proof of Poincar's Conjecture on geometric structure, and was awarded the Fields Prize for the achievement.
"The findings would help scientists to further understand three-manifolds geometrization and heavily influence the development of physics and engineering," said Yau, who will himself explain the methodology of proving the Poincare Conjecture to the 2006 International Conference on String Theory, which is expected in late June in Beijing.
(Xinhua News Agency June 5, 2006)
