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下面英文的完整译文见30、31楼。是否准确，请达人来分析吧。呵呵。8越30日更新。
http://www.wangf.net/vbb/showthr ... &threadid=22278
云中君
丘成桐先生严厉批评大陆学术风气的报导在华人世界可谓甚嚣尘上。当然大陆目前的学风的确很有问题，所以很多人只要一看这样的批评便鼓掌称快，我自己原本也倾向于此。但是我最近从三个完全不同的渠道听到对丘先生议论的背景的评价。这三个不同的渠道对丘先生都有非常负面的评价。所以使我开始觉得我们对任何事都不能臆断。果不其然，这最新一期的《纽约客》（New Yorker），登了一很长的有关庞加莱猜想被解决的报导，作者不是别人，正是当年写纳什传记的Sylvia Nasar，她现在是普大新闻系的讲座教授，也是目前美国有关科学方面的报告文学最受尊敬的作家之一。她的这篇文章中有不少关于丘成桐先生的报导。涉及各种方面，尤其是丘先生对田刚等人的批评的背景等等。她引述了美国数学界不少重要的数学家的看法，对丘先生的动机和学霸作风有很负面的批评，这基本印证了我前些时候所听到的个人意见。全文很长，我没有可能去翻译，但其中对丘先生的最致命的一句评价就是：
Many mathematicians view Yau’s conduct over the Poincaré as a violation of this basic ethic, and worry about the damage it has caused the profession.
（许多数学家认为丘在庞加莱猜想上的所做所为违反了科学研究上的这种基本伦理，他们为这种做法对这个领域所造成的伤害而感到忧虑。）
这种基本伦理特指数学研究上的合作精神和不埋没他人成绩的伦理。西方的评论家，尤其像Nasar 这样身份的人一般在批评科学界名人时用词会比较含蓄。而上面的那句评价基本上就是负面评价的极限了。相对之下，Nasar 的文字高度赞扬了为解决庞加莱猜想的证明工作作出了真正关键成绩而又拒绝领菲而兹奖的俄国数学家Perelmen 。我现在将英文全文转载如下。以供各位参考。
MANIFOLD DESTINY
by SYLVIA NASAR AND DAVID GRUBER
A legendary problem and the battle over who solved it.
Issue of 2006-08-28
Posted 2006-08-21
On the evening of June 20th, several hundred physicists, including a Nobel laureate, assembled in an auditorium at the Friendship Hotel i Beijing for a lecture by the Chinese mathematician Shing-Tung Yau. In the late nineteen-seventies, when Yau was in his twenties, he ha made a series of breakthroughs that helped launch the string-theory revolution in physics and earned him, in addition to a Fields Medal—th 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.”
For ninety minutes, Yau discussed some of the technical details of his students’ proof. When he was finished, no one asked any questions. That night, however, a Brazilian physicist posted a report of the lecture on his blog. “Looks like China soon will take the lead also in mathematics,” he wrote.
Grigory Perelman is indeed reclusive. He left his job as a researcher at the Steklov Institute of Mathematics, in St. Petersburg, las December; he has few friends; and he lives with his mother in an apartment on the outskirts of the city. Although he had never granted a interview before, he was cordial and frank when we visited him, in late June, shortly after Yau’s conference in Beijing, taking us on a lon walking tour of the city. “I’m looking for some friends, and they don’t have to be mathematicians,” he said. The week before the conference Perelman had spent hours discussing the Poincaré conjecture with Sir John M. Ball, the fifty-eight-year-old president of the Internationa Mathematical Union, the discipline’s influential professional association. The meeting, which took place at a conference center in a statel mansion overlooking the Neva River, was highly unusual. At the end of May, a committee of nine prominent mathematicians had voted t award Perelman a Fields Medal for his work on the Poincaré, and Ball had gone to St. Petersburg to persuade him to accept the prize in public ceremony at the I.M.U.’s quadrennial congress, in Madrid, on August 22nd
The Fields Medal, like the Nobel Prize, grew, in part, out of a desire to elevate science above national animosities. German mathematicians were excluded from the first I.M.U. congress, in 1924, and, though the ban was lifted before the next one, the trauma it caused led, in 1936, to the establishment of the Fields, a prize intended to be “as purely international and impersonal as possible.”
However, the Fields Medal, which is awarded every four years, to between two and four mathematicians, is supposed not only to reward past achievements but also to stimulate future research; for this reason, it is given only to mathematicians aged forty and younger. In recent decades, as the number of professional mathematicians has grown, the Fields Medal has become increasingly prestigious. Only forty-four medals have been awarded in nearly seventy years—including three for work closely related to the Poincaré conjecture—and no mathematician has ever refused the prize. Nevertheless, Perelman told Ball that he had no intention of accepting it. “I refuse,” he said simply.
Over a period of eight months, beginning in November, 2002, Perelman posted a proof of the Poincaré on the Internet in three installments. Like a sonnet or an aria, a mathematical proof has a distinct form and set of conventions. It begins with axioms, or accepted truths, and employs a series of logical statements to arrive at a conclusion. If the logic is deemed to be watertight, then the result is a theorem. Unlike proof in law or science, which is based on evidence and therefore subject to qualification and revision, a proof of a theorem is definitive. Judgments about the accuracy of a proof are mediated by peer-reviewed journals; to insure fairness, reviewers are supposed to be carefully chosen by journal editors, and the identity of a scholar whose pa-per is under consideration is kept secret. Publication implies that a proof is complete, correct, and original.
By these standards, Perelman’s proof was unorthodox. It was astonishingly brief for such an ambitious piece of work; logic sequences that could have been elaborated over many pages were often severely compressed. Moreover, the proof made no direct mention of the Poincaré and included many elegant results that were irrelevant to the central argument. But, four years later, at least two teams of experts had vetted the proof and had found no significant gaps or errors in it. A consensus was emerging in the math community: Perelman had solved the Poincaré. Even so, the proof’s complexity—and Perelman’s use of shorthand in making some of his most important claims—made it vulnerable to challenge. Few mathematicians had the expertise necessary to evaluate and defend it.
After giving a series of lectures on the proof in the United States in 2003, Perelman returned to St. Petersburg. Since then, although he had continued to answer queries about it by e-mail, he had had minimal contact with colleagues and, for reasons no one understood, had not tried to publish it. Still, there was little doubt that Perelman, who turned forty on June 13th, deserved a Fields Medal. As Ball planned the I.M.U.’s 2006 congress, he began to conceive of it as a historic event. More than three thousand mathematicians would be attending, and King Juan Carlos of Spain had agreed to preside over the awards ceremony. The I.M.U.’s newsletter predicted that the congress would be remembered as “the occasion when this conjecture became a theorem.” Ball, determined to make sure that Perelman would be there, decided to go to St. Petersburg.
Ball wanted to keep his visit a secret—the names of Fields Medal recipients are announced officially at the awards ceremony—and the conference center where he met with Perelman was deserted. For ten hours over two days, he tried to persuade Perelman to agree to accept the prize. Perelman, a slender, balding man with a curly beard, bushy eyebrows, and blue-green eyes, listened politely. He had not spoken English for three years, but he fluently parried Ball’s entreaties, at one point taking Ball on a long walk—one of Perelman’s favorite activities. As he summed up the conversation two weeks later: “He proposed to me three alternatives: accept and come; accept and don’t come, and we will send you the medal later; third, I don’t accept the prize. From the very beginning, I told him I have chosen the third one.” The Fields Medal held no interest for him, Perelman explained. “It was completely irrelevant for me,” he said. “Everybody understood that if the proof is correct then no other recognition is needed.”
Proofs of the Poincaré have been announced nearly every year since the conjecture was formulated, by Henri Poincaré, more than hundred years ago. Poincaré was a cousin of Raymond Poincaré, the President of France during the First World War, and one of the mos creative mathematicians of the nineteenth century. Slight, myopic, and notoriously absent-minded, he conceived his famous problem in 1904 eight years before he died, and tucked it as an offhand question into the end of a sixty-five-page paper
Poincaré didn’t make much progress on proving the conjecture. “Cette question nous entra?nerait trop loin” (“This question would take us too far”), he wrote. He was a founder of topology, also known as “rubber-sheet geometry,” for its focus on the intrinsic properties of spaces. From a topologist’s perspective, there is no difference between a bagel and a coffee cup with a handle. Each has a single hole and can be manipulated to resemble the other without being torn or cut. Poincaré used the term “manifold” to describe such an abstract topological space. The simplest possible two-dimensional manifold is the surface of a soccer ball, which, to a topologist, is a sphere—even when it is stomped on, stretched, or crumpled. The proof that an object is a so-called two-sphere, since it can take on any number of shapes, is that it is “simply connected,” meaning that no holes puncture it. Unlike a soccer ball, a bagel is not a true sphere. If you tie a slipknot around a soccer ball, you can easily pull the slipknot closed by sliding it along the surface of the ball. But if you tie a slipknot around a bagel through the hole in its middle you cannot pull the slipknot closed without tearing the bagel.
Two-dimensional manifolds were well understood by the mid-nineteenth century. But it remained unclear whether what was true for two dimensions was also true for three. Poincaré proposed that all closed, simply connected, three-dimensional manifolds—those which lack holes and are of finite extent—were spheres. The conjecture was potentially important for scientists studying the largest known three-dimensional manifold: the universe. Proving it mathematically, however, was far from easy. Most attempts were merely embarrassing, but some led to important mathematical discoveries, including proofs of Dehn’s Lemma, the Sphere Theorem, and the Loop Theorem, which are now fundamental concepts in topology.
By the nineteen-sixties, topology had become one of the most productive areas of mathematics, and young topologists were launching regular attacks on the Poincaré. To the astonishment of most mathematicians, it turned out that manifolds of the fourth, fifth, and higher dimensions were more tractable than those of the third dimension. By 1982, Poincaré’s conjecture had been proved in all dimensions except the third. In 2000, the Clay Mathematics Institute, a private foundation that promotes mathematical research, named the Poincaré one of the seven most important outstanding problems in mathematics and offered a million dollars to anyone who could prove it.
“My whole life as a mathematician has been dominated by the Poincaré conjecture,” John Morgan, the head of the mathematics department at Columbia University, said. “I never thought I’d see a solution. I thought nobody could touch it.”
Grigory Perelman did not plan to become a mathematician. “There was never a decision point,” he said when we met. We were outside th apartment building where he lives, in Kupchino, a neighborhood of drab high-rises. Perelman’s father, who was an electrical engineer encouraged his interest in math. “He gave me logical and other math problems to think about,” Perelman said. “He got a lot of books for m to read. He taught me how to play chess. He was proud of me.” Among the books his father gave him was a copy of “Physics fo Entertainment,” which had been a best-seller in the Soviet Union in the nineteen-thirties. In the foreword, the book’s author describes th contents as “conundrums, brain-teasers, entertaining anecdotes, and unexpected comparisons,” adding, “I have quoted extensively from Jule Verne, H. G. Wells, Mark Twain and other writers, because, besides providing entertainment, the fantastic experiments these writers describ may well serve as instructive illustrations at physics classes.” The book’s topics included how to jump from a moving car, and why, “according to the law of buoyancy, we would never drown in the Dead Sea.
The notion that Russian society considered worthwhile what Perelman did for pleasure came as a surprise. By the time he was fourteen, he was the star performer of a local math club. In 1982, the year that Shing-Tung Yau won a Fields Medal, Perelman earned a perfect score and the gold medal at the International Mathematical Olympiad, in Budapest. He was friendly with his teammates but not close—“I had no close friends,” he said. He was one of two or three Jews in his grade, and he had a passion for opera, which also set him apart from his peers. His mother, a math teacher at a technical college, played the violin and began taking him to the opera when he was six. By the time Perelman was fifteen, he was spending his pocket money on records. He was thrilled to own a recording of a famous 1946 performance of “La Traviata,” featuring Licia Albanese as Violetta. “Her voice was very good,” he said.
At Leningrad University, which Perelman entered in 1982, at the age of sixteen, he took advanced classes in geometry and solved a problem posed by Yuri Burago, a mathematician at the Steklov Institute, who later became his Ph.D. adviser. “There are a lot of students of high ability who speak before thinking,” Burago said. “Grisha was different. He thought deeply. His answers were always correct. He always checked very, very carefully.” Burago added, “He was not fast. Speed means nothing. Math doesn’t depend on speed. It is about deep.”
At the Steklov in the early nineties, Perelman became an expert on the geometry of Riemannian and Alexandrov spaces—extensions of traditional Euclidean geometry—and began to publish articles in the leading Russian and American mathematics journals. In 1992, Perelman was invited to spend a semester each at New York University and Stony Brook University. By the time he left for the United States, that fall, the Russian economy had collapsed. Dan Stroock, a mathematician at M.I.T., recalls smuggling wads of dollars into the country to deliver to a retired mathematician at the Steklov, who, like many of his colleagues, had become destitute.
Perelman was pleased to be in the United States, the capital of the international mathematics community. He wore the same brown corduroy jacket every day and told friends at N.Y.U. that he lived on a diet of bread, cheese, and milk. He liked to walk to Brooklyn, where he had relatives and could buy traditional Russian brown bread. Some of his colleagues were taken aback by his fingernails, which were several inches long. “If they grow, why wouldn’t I let them grow?” he would say when someone asked why he didn’t cut them. Once a week, he and a young Chinese mathematician named Gang Tian drove to Princeton, to attend a seminar at the Institute for Advanced Study.
For several decades, the institute and nearby Princeton University had been centers of topological research. In the late seventies, William Thurston, a Princeton mathematician who liked to test out his ideas using scissors and construction paper, proposed a taxonomy for classifying manifolds of three dimensions. He argued that, while the manifolds could be made to take on many different shapes, they nonetheless had a “preferred” geometry, just as a piece of silk draped over a dressmaker’s mannequin takes on the mannequin’s form.
Thurston proposed that every three-dimensional manifold could be broken down into one or more of eight types of component, including a spherical type. Thurston’s theory—which became known as the geometrization conjecture—describes all possible three-dimensional manifolds and is thus a powerful generalization of the Poincaré. If it was confirmed, then Poincaré’s conjecture would be, too. Proving Thurston and Poincaré “definitely swings open doors,” Barry Mazur, a mathematician at Harvard, said. The implications of the conjectures for other disciplines may not be apparent for years, but for mathematicians the problems are fundamental. “This is a kind of twentieth-century Pythagorean theorem,” Mazur added. “It changes the landscape.”
In 1982, Thurston won a Fields Medal for his contributions to topology. That year, Richard Hamilton, a mathematician at Cornell, published a paper on an equation called the Ricci flow, which he suspected could be relevant for solving Thurston’s conjecture and thus the Poincaré. Like a heat equation, which describes how heat distributes itself evenly through a substance—flowing from hotter to cooler parts of a metal sheet, for example—to create a more uniform temperature, the Ricci flow, by smoothing out irregularities, gives manifolds a more uniform geometry.
Hamilton, the son of a Cincinnati doctor, defied the math profession’s nerdy stereotype. Brash and irreverent, he rode horses, windsurfed, and had a succession of girlfriends. He treated math as merely one of life’s pleasures. At forty-nine, he was considered a brilliant lecturer, but he had published relatively little beyond a series of seminal articles on the Ricci flow, and he had few graduate students. Perelman had read Hamilton’s papers and went to hear him give a talk at the Institute for Advanced Study. Afterward, Perelman shyly spoke to him.
“I really wanted to ask him something,” Perelman recalled. “He was smiling, and he was quite patient. He actually told me a couple of things that he published a few years later. He did not hesitate to tell me. Hamilton’s openness and generosity—it really attracted me. I can’t say that most mathematicians act like that.
“I was working on different things, though occasionally I would think about the Ricci flow,” Perelman added. “You didn’t have to be a great mathematician to see that this would be useful for geometrization. I felt I didn’t know very much. I kept asking questions.”
Shing-Tung Yau was also asking Hamilton questions about the Ricci flow. Yau and Hamilton had met in the seventies, and had becom close, despite considerable differences in temperament and background. A mathematician at the University of California at San Diego wh knows both men called them “the mathematical loves of each other’s lives.
Yau’s family moved to Hong Kong from mainland China in 1949, when he was five months old, along with hundreds of thousands of other refugees fleeing Mao’s armies. The previous year, his father, a relief worker for the United Nations, had lost most of the family’s savings in a series of failed ventures. In Hong Kong, to support his wife and eight children, he tutored college students in classical Chinese literature and philosophy.
When Yau was fourteen, his father died of kidney cancer, leaving his mother dependent on handouts from Christian missionaries and whatever small sums she earned from selling handicrafts. Until then, Yau had been an indifferent student. But he began to devote himself to schoolwork, tutoring other students in math to make money. “Part of the thing that drives Yau is that he sees his own life as being his father’s revenge,” said Dan Stroock, the M.I.T. mathematician, who has known Yau for twenty years. “Yau’s father was like the Talmudist whose children are starving.”
Yau studied math at the Chinese University of Hong Kong, where he attracted the attention of Shiing-Shen Chern, the pre?minent Chinese mathematician, who helped him win a scholarship to the University of California at Berkeley. Chern was the author of a famous theorem combining topology and geometry. He spent most of his career in the United States, at Berkeley. He made frequent visits to Hong Kong, Taiwan, and, later, China, where he was a revered symbol of Chinese intellectual achievement, to promote the study of math and science.
In 1969, Yau started graduate school at Berkeley, enrolling in seven graduate courses each term and auditing several others. He sent half of his scholarship money back to his mother in China and impressed his professors with his tenacity. He was obliged to share credit for his first major result when he learned that two other mathematicians were working on the same problem. In 1976, he proved a twenty-year-old conjecture pertaining to a type of manifold that is now crucial to string theory. A French mathematician had formulated a proof of the problem, which is known as Calabi’s conjecture, but Yau’s, because it was more general, was more powerful. (Physicists now refer to Calabi-Yau manifolds.) “He was not so much thinking up some original way of looking at a subject but solving extremely hard technical problems that at the time only he could solve, by sheer intellect and force of will,” Phillip Griffiths, a geometer and a former director of the Institute for Advanced Study, said.
In 1980, when Yau was thirty, he became one of the youngest mathematicians ever to be appointed to the permanent faculty of the Institute for Advanced Study, and he began to attract talented students. He won a Fields Medal two years later, the first Chinese ever to do so. By this time, Chern was seventy years old and on the verge of retirement. According to a relative of Chern’s, “Yau decided that he was going to be the next famous Chinese mathematician and that it was time for Chern to step down.”
Harvard had been trying to recruit Yau, and when, in 1983, it was about to make him a second offer Phillip Griffiths told the dean of faculty a version of a story from “The Romance of the Three Kingdoms,” a Chinese classic. In the third century A.D., a Chinese warlord dreamed of creating an empire, but the most brilliant general in China was working for a rival. Three times, the warlord went to his enemy’s kingdom to seek out the general. Impressed, the general agreed to join him, and together they succeeded in founding a dynasty. Taking the hint, the dean flew to Philadelphia, where Yau lived at the time, to make him an offer. Even so, Yau turned down the job. Finally, in 1987, he agreed to go to Harvard.
Yau’s entrepreneurial drive extended to collaborations with colleagues and students, and, in addition to conducting his own research, he began organizing seminars. He frequently allied himself with brilliantly inventive mathematicians, including Richard Schoen and William Meeks. But Yau was especially impressed by Hamilton, as much for his swagger as for his imagination. “I can have fun with Hamilton,” Yau told us during the string-theory conference in Beijing. “I can go swimming with him. I go out with him and his girlfriends and all that.” Yau was convinced that Hamilton could use the Ricci-flow equation to solve the Poincaré and Thurston conjectures, and he urged him to focus on the problems. “Meeting Yau changed his mathematical life,” a friend of both mathematicians said of Hamilton. “This was the first time he had been on to something extremely big. Talking to Yau gave him courage and direction.”
Yau believed that if he could help solve the Poincaré it would be a victory not just for him but also for China. In the mid-nineties, Yau and several other Chinese scholars began meeting with President Jiang Zemin to discuss how to rebuild the country’s scientific institutions, which had been largely destroyed during the Cultural Revolution. Chinese universities were in dire condition. According to Steve Smale, who won a Fields for proving the Poincaré in higher dimensions, and who, after retiring from Berkeley, taught in Hong Kong, Peking University had “halls filled with the smell of urine, one common room, one office for all the assistant professors,” and paid its faculty wretchedly low salaries. Yau persuaded a Hong Kong real-estate mogul to help finance a mathematics institute at the Chinese Academy of Sciences, in Beijing, and to endow a Fields-style medal for Chinese mathematicians under the age of forty-five. On his trips to China, Yau touted Hamilton and their joint work on the Ricci flow and the Poincaré as a model for young Chinese mathematicians. As he put it in Beijing, “They always say that the whole country should learn from Mao or some big heroes. So I made a joke to them, but I was half serious. I said the whole country should learn from Hamilton.”
Grigory Perelman was learning from Hamilton already. In 1993, he began a two-year fellowship at Berkeley. While he was there, Hamilto gave several talks on campus, and in one he mentioned that he was working on the Poincaré. Hamilton’s Ricci-flow strategy was extremel technical and tricky to execute. After one of his talks at Berkeley, he told Perelman about his biggest obstacle. As a space is smoothed unde the Ricci flow, some regions deform into what mathematicians refer to as “singularities.” Some regions, called “necks,” become attenuate areas of infinite density. More troubling to Hamilton was a kind of singularity he called the “cigar.” If cigars formed, Hamilton worried, i might be impossible to achieve uniform geometry. Perelman realized that a paper he had written on Alexandrov spaces might help Hamilto prove Thurston’s conjecture—and the Poincaré—once Hamilton solved the cigar problem. “At some point, I asked Hamilton if he knew certain collapsing result that I had proved but not published—which turned out to be very useful,” Perelman said. “Later, I realized that h didn’t understand what I was talking about.” Dan Stroock, of M.I.T., said, “Perelman may have learned stuff from Yau and Hamilton, but, a the time, they were not learning from him.
By the end of his first year at Berkeley, Perelman had written several strikingly original papers. He was asked to give a lecture at the 1994 I.M.U. congress, in Zurich, and invited to apply for jobs at Stanford, Princeton, the Institute for Advanced Study, and the University of Tel Aviv. Like Yau, Perelman was a formidable problem solver. Instead of spending years constructing an intricate theoretical framework, or defining new areas of research, he focussed on obtaining particular results. According to Mikhail Gromov, a renowned Russian geometer who has collaborated with Perelman, he had been trying to overcome a technical difficulty relating to Alexandrov spaces and had apparently been stumped. “He couldn’t do it,” Gromov said. “It was hopeless.”
Perelman told us that he liked to work on several problems at once. At Berkeley, however, he found himself returning again and again to Hamilton’s Ricci-flow equation and the problem that Hamilton thought he could solve with it. Some of Perelman’s friends noticed that he was becoming more and more ascetic. Visitors from St. Petersburg who stayed in his apartment were struck by how sparsely furnished it was. Others worried that he seemed to want to reduce life to a set of rigid axioms. When a member of a hiring committee at Stanford asked him for a C.V. to include with requests for letters of recommendation, Perelman balked. “If they know my work, they don’t need my C.V.,” he said. “If they need my C.V., they don’t know my work.”
Ultimately, he received several job offers. But he declined them all, and in the summer of 1995 returned to St. Petersburg, to his old job at the Steklov Institute, where he was paid less than a hundred dollars a month. (He told a friend that he had saved enough money in the United States to live on for the rest of his life.) His father had moved to Israel two years earlier, and his younger sister was planning to join him there after she finished college. His mother, however, had decided to remain in St. Petersburg, and Perelman moved in with her. “I realize that in Russia I work better,” he told colleagues at the Steklov.
At twenty-nine, Perelman was firmly established as a mathematician and yet largely unburdened by professional responsibilities. He was free to pursue whatever problems he wanted to, and he knew that his work, should he choose to publish it, would be shown serious consideration. Yakov Eliashberg, a mathematician at Stanford who knew Perelman at Berkeley, thinks that Perelman returned to Russia in order to work on the Poincaré. “Why not?” Perelman said when we asked whether Eliashberg’s hunch was correct.
The Internet made it possible for Perelman to work alone while continuing to tap a common pool of knowledge. Perelman searched Hamilton’s papers for clues to his thinking and gave several seminars on his work. “He didn’t need any help,” Gromov said. “He likes to be alone. He reminds me of Newton—this obsession with an idea, working by yourself, the disregard for other people’s opinion. Newton was more obnoxious. Perelman is nicer, but very obsessed.”
In 1995, Hamilton published a paper in which he discussed a few of his ideas for completing a proof of the Poincaré. Reading the paper, Perelman realized that Hamilton had made no progress on overcoming his obstacles—the necks and the cigars. “I hadn’t seen any evidence of progress after early 1992,” Perelman told us. “Maybe he got stuck even earlier.” However, Perelman thought he saw a way around the impasse. In 1996, he wrote Hamilton a long letter outlining his notion, in the hope of collaborating. “He did not answer,” Perelman said. “So I decided to work alone.” |
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发表于 2006-8-27 09:03:20
发表于 2006-8-27 10:05:32
发表于 2006-8-27 12:39:08
