Seven years after the Clay Institute announced its challenge, the century-old Poincaré Conjecture, one of the thorniest of the millennium problems, is thought to have been solved. Ever since French mathematician Henri Poincaré posed the conjecture in 1904, at least a half-dozen eminent mathematicians—and many lesser ones—have tried and failed to crack the problem. But a series of papers on the conjecture posted online in 2002 and 2003 by Russian Grigory Perelman have successfully withstood intense scrutiny by the mathematical community for the past four years—twice the number of years of public examination required by the Clay Institute. Poincaré’s Conjecture deals with the branch of math called topology, which is the study of shapes, spaces, and surfaces. The Clay Institute offers this deceptively friendly-sounding doughnut-and-apple explication of the bedeviling problem: The resolution of Poincaré’s Conjecture would have enormous implications for our understanding of relativity and the shape of space. But while mathematicians are hailing this as potentially the biggest breakthrough since Andrew Wiles solved Fermat’s Last Theorem in 1994, Grigory Perelman himself has taken a decidedly standoffish attitude to his accomplishment. He has shown no interest in collecting the million-dollar prize, and instead of publishing his solution in a “refereed mathematics publication of worldwide repute,” as the Clay Institute requires, he simply published his papers online. His proof never even mentions Poincaré by name and is presented in such a sketchy and elliptical fashion that it resembles guidelines for proving the conjecture more than an actual proof. Once having answered the problem to his own satisfaction, one can only speculate, Perelman considered public validation superfluous. In June 2006, however, two Chinese mathematicians, Zhu Xiping and Cao Huaidong, published a 329-page article in the Asian Journal of Mathematics that fills in the blanks left by Perelman, supplying a complete proof of his solution. This has led to the question of whether Perelman, the Chinese mathematicians, or both should receive the credit. James Carlson, president of the Clay Institute, admits that “it’s definitely an unusual situation, but what’s important is that the person who made the breakthrough put it out there so the community could scrutinize and analyze it.” Fact Monster/Information Please® Database, © 2005 Pearson Education, Inc. All rights reserved.
