Manifold Destiny

Book excerpt: On the evening of June 20th [2006], several hundred physicists, including a Nobel laureate, assembled in an auditorium at the Friendship Hotel in Beijing for a lecture by the Chinese mathematician Shing-Tung Yau. In the late nineteen-seventies, when Yau was in his twenties, he had made a series of breakthroughs that helped launch the string-theory revolution in physics and earned him, in addition to a Fields Medal - the most coveted award in mathematics - a reputation in both disciplines as a thinker of unrivalled technical power. Yau had since become a professor of mathematics at Harvard and the director of mathematics institutes in Beijing and Hong Kong, dividing his time between the United States and China. His lecture at the Friendship Hotel was part of an international conference on string theory, which he had organized with the support of the Chinese government, in part to promote the country's recent advances in theoretical physics. (More than six thousand students attended the keynote address, which was delivered by Yau's close friend Stephen Hawking, in the Great Hall of the People.) The subject of Yau's talk was something that few in his audience knew much about: the Poincaré conjecture, a century-old conundrum about the characteristics of three-dimensional spheres, which, because it has important implications for mathematics and cosmology and because it has eluded all attempts at solution, is regarded by mathematicians as a holy grail. Yau, a stocky man of fifty-seven, stood at a lectern in shirtsleeves and black-rimmed glasses and, with his hands in his pockets, described how two of his students, Xi-Ping Zhu and Huai-Dong Cao, had completed a proof of the Poincaré conjecture a few weeks earlier. 'I'm very positive about Zhu and Cao's work, ' Yau said. 'Chinese mathematicians should have every reason to be proud of such a big success in completely solving the puzzle.' He said that Zhu and Cao were indebted to his longtime American collaborator Richard Hamilton, who deserved most of the credit for solving the Poincaré. He also mentioned Grigory Perelman, a Russian mathematician who, he acknowledged, had made an important contribution. Nevertheless, Yau said, 'in Perelman's work, spectacular as it is, many key ideas of the proofs are sketched or outlined, and complete details are often missing.' He added, 'We would like to get Perelman to make comments. But Perelman resides in St. Petersburg and refuses to communicate with other people.'