Poincare Conjecture (#151, Topic I)

The top story in 6/5/06's People's Daily Overseas Edition, received yesterday, is on two Chinese professors' solving a century-old math problem in topology, known as the Poincare Conjecture. With a headline covering 3 of 4 columns, on two lines, 龐加萊猜想獲得完全証明 中国數学家破解世界百年難題, along with a photo of the two (Zhu Xi-ping 朱熹平 of Zhongshan University, Quangdong, and Cao Huai-dong 曹怀東 of Lehigh University, PA), the story accorded academicians the deserved recognition I have never seen in US newspapers in my 56 years in this country -- not even to Nobel laureates. Curious, though a rank layman, I nevertheless did a Google search, which brought me to an abstract of this 334-page paper. (How does one do a Google search in English, when the subject is given in Chinese? Good question.) The paper in its entirety is in the June 2006 issue of Asian Journal of Mathematics, pp. 165-498. Another link led me to a 6/6/06 essay, in Guardian Unlimited; the author poohpoohes the two professors' accomplishments. Another link, mathworld, has an entry dated 2004. (Late last evening, I sent its editors an e-mail asking for their reaction to the Zhu-Cao paper.) Another link, by the Clay Mathematics Institute, also in 2004, notes that, as to its earlier offer of $1 million to the solver of this conjecture (there are 6 other million-dollar prizes to 6 other math problems), Grisha Perelman seems to have "substantially" solved it. According to PD's side-bar, the conjecture, proposed by a French mathematician, Henri Poincare, in 1904, states that, in a closed 3-dimensional space, as each curved line is reduced to a point, the empty space must necessarily be a sphere. (My translation; a formal description is in the mathword webpage.) The PD article ends with the following, quoting another Chinese mathematician, Yang Le 楊樂: "If contributions are allocated on a percentage basis, US mathematician Richard Hamilton's is more than 50%; Russian mathematician Grisha Perelman's, about 25%; and Chiu Cheng-dong 丘成桐 [Cao's dissertation supervisor], Zhu Xi-ping, Cao Huao-dong, and others', about 30%." (The sum of these three percentage figures is more than 100%. Oh, well.)