According to Mingpao News, two Chinese mathematicians have successfully completed the proof of the Poincaré Conjecture, which has been one of the great unsolved mathematical puzzles since 1904.
Professor Qiu Chengtong (Shing-Tung Yau) of Harvard University, a world renowned Chinese mathematician who has won the Fields prize, announced at the Morning Star Institute of Mathematics, Chinese Academy of Sciences in Beijing, on June 3, that based on the theoretical foundation laid by American and Russian scientists, Professor Zhu Xiping at Zhongshan University in Guangzhou City, and Professor Cao Huaidong at Lehigh University in Pennsylvania, who is also a visiting Professor at Beijing's Qinghua University, have completely proved this conjecture.
Professor Qiu said this achievement is far more important than the Goldbach Conjecture. The mathematician Yang Le said that, as a result of the outstanding mathematical work, it is the first time that a complete proof of the Poincaré conjecture has been published in an international journal of mathematics.
In the June issue of the U.S.-based Asian Journal of Mathematics, the two scientists published a 334-page paper, "A Complete Proof of the Poincaré and Geometrization Conjectures - application of the Hamilton-Perelman theory of the Ricci flow."
The Poincaré Conjecture, first stated by French mathematician Henri Poincaré in 1904, is that, in topology, if in a closed three-dimensional space, any closed curves can shrink to a point, this space is topologically equivalent to the three-dimensional sphere. Like the Riemann Hypothesis, the Hodge Conjecture and the Yang-Mills Existence and Mass Gap, the Poincaré Conjecture has been rated as one of the seven "Millennium Prize problems"for proofs of which the Clay Mathematics Institute of Cambridge, Massachusetts was offering prizes of US$1,000,000 each, in May 2000.
By the end of the 1970s, U.S. mathematician William P. Thurston had produced partial proof of Poincaré Conjecture on geometric structure, and was awarded the Fields Prize for the achievement. Fellow American Richard Hamilton completed the majority of the program and the geometrization conjecture. In 2003, Russian mathematician Grigory Perelman made key new contributions.
Utilizing the Hamilton-Perelman theory of Ricci flow, Zhu and Cao have successfully provided the complete proof of the Poincaré Conjecture in the paper.
Zhu and Cao were invited by Harvard University to give a three-hour lecture every week, between last September and March, to five mathematicians, including the head of Harvard's Mathematics Department.
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