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Manifold Destiny Sylvia Nasar, David Gruber 1 1 34 NAW 5/8 nr. 1 maart 2007 Manifold Destiny Sylvia Nasar, David Gruber Sylvia Nasar, David Gruber The New Yorker 4 Times Square, New York, NY 10036 www.newyorker.com Manifold Destiny A legendary problem and the battle over who solved it In het tijdschrift ‘The New Yorker’ van 21 augustus 2006 is een uitgebreid verslag verschenen described how two of his students, Xi-Ping van de zoektocht naar het bewijs van het vermoeden van Poincaré. In dit vermoeden wordt Zhu and Huai-Dong Cao, had completed a gesteld dat een compacte variëteit homotoop is aan de eenheidssfeer dan en slechts dan als proof of the Poincaré conjecture a few weeks deze variëteit homeomorf is aan de eenheidssfeer. Tot 2003 was het vermoeden bewezen earlier. “I’m very positive about Zhu and voor alle dimensies behalve dimensie drie. In deze heroïsche zoektocht spelen de wiskundi- Cao’s work,” Yau said. “Chinese mathemati- gen Grigory Perelman en Shing-Tung Yau een hoofdrol. Perelman bewees uiteindelijk in 2003 cians should have every reason to be proud het Thurston-geometrisatievermoeden. Hiervan is het Poincarévermoeden een speciaal geval. of such a big success in completely solving Hem werd een Fieldsmedal toegekend; een prijs die hij vervolgens niet accepteerde. Yau vond the puzzle.” He said that Zhu and Cao were echter dat hij en niet Perelman het precies uitgewerkte bewijs had geleverd. Hoe zit het werke- indebted to his longtime American collabo- lijk in elkaar? Wat bewoog Perelman tot het weigeren van de meest prestigieuze prijs in de rator Richard Hamilton, who deserved most wiskunde? Sylvia Nasar, bekend van het boek ‘A beautiful Mind’ en David Gruber, wetenschap- of the credit for solving the Poincaré. He also sjournalist reisden naar China en naar Rusland om het werkelijke verhaal te achterhalen. Hun mentioned Grigory Perelman, a Russian math- artikel gaf aanleiding tot nogal wat tumult: Yau voelde zich in zijn eer aangetast en dreigde de ematician who, he acknowledged, had made auteurs met een rechtszaak. Een gang naar de rechter is er echter nog niet van gekomen. Na an important contribution. Nevertheless, Yau dit artikel zal meetkundige Jozef Steenbrink kort ingaan op deze controverse. said, “in Perelman’s work, spectacular as it is, many key ideas of the proofs are sketched On the evening of June 20th, several hun- ference on string theory, which he had or- or outlined, and complete details are often dred physicists, including a Nobel laureate, ganized with the support of the Chinese missing.” He added, “We would like to get assembled in an auditorium at the Friend- government, in part to promote the coun- Perelman to make comments. But Perelman ship Hotel in Beijing for a lecture by the Chi- try’s recent advances in theoretical physics. resides in St. Petersburg and refuses to com- nese mathematician Shing-Tung Yau. In the (More than six thousand students attended municate with other people.” late nineteen-seventies, when Yau was in his the keynote address, which was delivered by For ninety minutes, Yau discussed some twenties, he had made a series of break- Yau’s close friend Stephen Hawking, in the of the technical details of his students’ proof. throughs that helped launch the string-theory Great Hall of the People.) The subject of Yau’s When he was finished, no one asked any revolution in physics and earned him, in ad- talk was something that few in his audience questions. That night, however, a Brazilian dition to a Fields Medal — the most coveted knew much about: the Poincaré conjecture, a physicist posted a report of the lecture on his award in mathematics — a reputation in both century-old conundrum about the characteris- blog. “Looks like China soon will take the lead disciplines as a thinker of unrivalled technical tics of three-dimensional spheres, which, be- also in mathematics,” he wrote. power. cause it has important implications for math- Grigory Perelman is indeed reclusive. He Yau had since become a professor of math- ematics and cosmology and because it has left his job as a researcher at the Steklov In- ematics at Harvard and the director of math- eluded all attempts at solution, is regarded stitute of Mathematics, in St. Petersburg, ematics institutes in Beijing and Hong Kong, by mathematicians as a holy grail. last December; he has few friends; and he ship Hotel was part of an international con- Yau, a stocky man of fifty-seven, stood at lives with his mother in an apartment on the dividing his time between the United a lectern in shirtsleeves and black-rimmed outskirts of the city. Although he had never States and China. His lecture at the Friend- glasses and, with his hands in his pockets, granted an interview before, he was cordial 1 1 2 2 Sylvia Nasar, David Gruber Manifold Destiny NAW 5/8 nr. 1 maart 2007 35 , kopergravure, 1514, The Metropolitan Museum of Art, New York Melencolia I Dürer: 2 2 3 3 36 NAW 5/8 nr. 1 maart 2007 Manifold Destiny Sylvia Nasar, David Gruber and frank when we visited him, in late June, by peer-reviewed journals; to insure fairness, er: “He proposed to me three alternatives: shortly after Yau’s conference in Beijing, tak- reviewers are supposed to be carefully cho- accept and come; accept and don’t come, and ing us on a long walking tour of the city. “I’m sen by journal editors, and the identity of a we will send you the medal later; third, I don’t looking for some friends, and they don’t have scholar whose paper is under consideration is accept the prize. From the very beginning, I to be mathematicians,” he said. The week kept secret. Publication implies that a proof told him I have chosen the third one.” The before the conference, Perelman had spent is complete, correct, and original. Fields Medal held no interest for him, Perel- hours discussing the Poincaré conjecture with By these standards, Perelman’s proof was man explained. “It was completely irrelevant Sir John M. Ball, the fifty-eight-year-old presi- unorthodox. It was astonishingly brief for for me,” he said. “Everybody understood that dent of the International Mathematical Union such an ambitious piece of work; logic se- if the proof is correct then no other recognition (IMU), the discipline’s influential profession- quences that could have been elaborated is needed.” al association. The meeting, which took place over many pages were often severely com- Proofs of the Poincaré have been an- at a conference center in a stately mansion pressed. Moreover, the proof made no direct nounced nearly every year since the conjec- overlooking the Neva River, was highly un- mention of the Poincaré and included many ture was formulated, by Henri Poincaré, more usual. At the end of May, a committee of elegant results that were irrelevant to the cen- than a hundred years ago. Poincaré was a nine prominent mathematicians had voted to tral argument. But, four years later, at least cousin of Raymond Poincaré, the President of award Perelman a Fields Medal for his work two teams of experts had vetted the proof and France during the First World War, and one on the Poincaré, and Ball had gone to St. Pe- had found no significant gaps or errors in it. of the most creative mathematicians of the tersburg to persuade him to accept the prize A consensus was emerging in the math com- nineteenth century. Slight, myopic, and no- in a public ceremony at the IMU’s quadrennial munity: Perelman had solved the Poincaré. toriously absent-minded, he conceived his fa- congress, in Madrid, on August 22nd. Even so, the proof’s complexity — and Perel- mous problem in 1904, eight years before he The Fields Medal, like the Nobel Prize, man’s use of shorthand in making some of his died, and tucked it as an offhand question grew, in part, out of a desire to elevate sci- most important claims — made it vulnerable into the end of a sixty-five-page paper. ence above national animosities. German to challenge. Few mathematicians had the Poincaré didn’t make much progress on mathematicians were excluded from the first expertise necessary to evaluate and defend proving the conjecture. ‘Cette question nous IMU congress, in 1924, and, though the ban it. entraînerait trop loin” (“This question would was lifted before the next one, the trauma it After giving a series of lectures on the proof take us too far”), he wrote. He was a founder caused led, in 1936, to the establishment of in the United States in 2003, Perelman re- of topology, also known as ‘rubber-sheet ge- the Fields, a prize intended to be “as purely turned to St. Petersburg. Since then, al- ometry’, for its focus on the intrinsic prop- international and impersonal as possible.” though he had continued to answer queries erties of spaces. From a topologist’s per- However, the Fields Medal, which is award- about it by e-mail, he had had minimal con- spective, there is no difference between a ed every four years, to between two and four tact with colleagues and, for reasons no one bagel and a coffee cup with a handle. Each mathematicians, is supposed not only to re- understood, had not tried to publish it. Still, has a single hole and can be manipulated ward past achievements but also to stimulate there was little doubt that Perelman, who to resemble the other without being torn or future research; for this reason, it is given on- turned forty on June 13th, deserved a Fields cut.
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