“Hamilton contributed over fifty per cent; the Russian, Perelman, about twenty-five per cent; and the Chinese, Yau, Zhu, and Cao et al., about thirty per cent.”* 50 + 25 + 30 = 100?
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Для всех тех, кто пытались здесь грязью полить Перельмана.
"As long as I was not conspicuous, I had a choice," Perelman explained. "Either to make some ugly thing"--a fuss about the math community's lack of integrity--"or, if I didn't do this kind of thing, to be treated as a pet. Now, when I become a very conspicuous person, I cannot stay a pet and say nothing. That is why I had to quit."
Это слова Перельмана из следующей статьи:
the new yorker articleДостаточно длинная статья описывает как китайский математик Yau (Яу ?) и те кто на Яу работали, занимались тем что 'чинили' оригинальные доказательства других людей и заявляли что это была их личная работа.
Яу попытался сделать это с работой Перельмана, но у него в этот раз снова ничего не получилось.
Так как Яу является уважаемым членом Математического Общества, Перельман не хочет иметь ничего общего с этим обществом.
Слова Яу:
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.”
Кстати Перельман действительно еврей:
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.
Какое то время работал в США и отращивал когти :)
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.
Постепенно Перельман все больше зарывался в математику, уходил в нее полностью с головой:
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.”
Вернулся работать обратно в Россию:
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.
Работал в одиночестве:
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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В это время Яу работал над своим именем тем, что пытался украсть работу Гивенталя о теории струн:
In 1996, a young geometer at Berkeley named Alexander Givental had proved a mathematical conjecture about mirror symmetry, a concept that is fundamental to string theory. Though other mathematicians found Givental’s proof hard to follow, they were optimistic that he had solved the problem. As one geometer put it, “Nobody at the time said it was incomplete and incorrect.”
In the fall of 1997, Kefeng Liu, a former student of Yau’s who taught at Stanford, gave a talk at Harvard on mirror symmetry. According to two geometers in the audience, Liu proceeded to present a proof strikingly similar to Givental’s, describing it as a paper that he had co-authored with Yau and another student of Yau’s. “Liu mentioned Givental but only as one of a long list of people who had contributed to the field,” one of the geometers said. (Liu maintains that his proof was significantly different from Givental’s.)
Around the same time, Givental received an e-mail signed by Yau and his collaborators, explaining that they had found his arguments impossible to follow and his notation baffling, and had come up with a proof of their own. They praised Givental for his “brilliant idea” and wrote, “In the final version of our paper your important contribution will be acknowledged.”
A few weeks later, the paper, “Mirror Principle I,” appeared in the Asian Journal of Mathematics, which is co-edited by Yau. In it, Yau and his coauthors describe their result as “the first complete proof” of the mirror conjecture. They mention Givental’s work only in passing. “Unfortunately,” they write, his proof, “which has been read by many prominent experts, is incomplete.” However, they did not identify a specific mathematical gap.
Givental was taken aback. “I wanted to know what their objection was,” he told us. “Not to expose them or defend myself.” In March, 1998, he published a paper that included a three-page footnote in which he pointed out a number of similarities between Yau’s proof and his own. Several months later, a young mathematician at the University of Chicago who was asked by senior colleagues to investigate the dispute concluded that Givental’s proof was complete. Yau says that he had been working on the proof for years with his students and that they achieved their result independently of Givental. “We had our own ideas, and we wrote them up,” he says.
Яу работал в Гон-Конге, и пытался завлечь следующий математический конгресс в Гон-Конг, но у него не получилось. Конгресс состоялся в Бейджине. Яу пытался спасти ситуацию, добился того, что многие математики/физики включая Стивена Хокина посетили Гон-Конг, где была произвведена большая рекламная компания с участием этих ученых. Плакаты с Яу и другими учеными были расклеены по всему городу.
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Яу в это время не работал над Пойнкаре, но...
Then, on November 12, 2002, Yau received an e-mail message from a Russian mathematician whose name didn’t immediately register. “May I bring to your attention my paper,” the e-mail said.
On November 11th, Perelman had posted a thirty-nine-page paper entitled “The Entropy Formula for the Ricci Flow and Its Geometric Applications,” on arXiv.org, a Web site used by mathematicians to post preprints—articles awaiting publication in refereed journals. He then e-mailed an abstract of his paper to a dozen mathematicians in the United States—including Hamilton, Tian, and Yau—none of whom had heard from him for years. In the abstract, he explained that he had written “a sketch of an eclectic proof” of the geometrization conjecture.
Perelman had not mentioned the proof or shown it to anyone. “I didn’t have any friends with whom I could discuss this,” he said in St. Petersburg. “I didn’t want to discuss my work with someone I didn’t trust.” Andrew Wiles had also kept the fact that he was working on Fermat’s last theorem a secret, but he had had a colleague vet the proof before making it public. Perelman, by casually posting a proof on the Internet of one of the most famous problems in mathematics, was not just flouting academic convention but taking a considerable risk. If the proof was flawed, he would be publicly humiliated, and there would be no way to prevent another mathematician from fixing any errors and claiming victory. But Perelman said he was not particularly concerned. “My reasoning was: if I made an error and someone used my work to construct a correct proof I would be pleased,” he said. “I never set out to be the sole solver of the Poincaré.”
Gang Tian was in his office at M.I.T. when he received Perelman’s e-mail. He and Perelman had been friendly in 1992, when they were both at N.Y.U. and had attended the same weekly math seminar in Princeton. “I immediately realized its importance,” Tian said of Perelman’s paper. Tian began to read the paper and discuss it with colleagues, who were equally enthusiastic.
On November 19th, Vitali Kapovitch, a geometer, sent Perelman an e-mail:
Hi Grisha, Sorry to bother you but a lot of people are asking me about your preprint “The entropy formula for the Ricci . . .” Do I understand it correctly that while you cannot yet do all the steps in the Hamilton program you can do enough so that using some collapsing results you can prove geometrization? Vitali.
Perelman’s response, the next day, was terse: “That’s correct. Grisha.”
In fact, what Perelman had posted on the Internet was only the first installment of his proof. But it was sufficient for mathematicians to see that he had figured out how to solve the Poincaré.
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Яу не понимал доказательство Перельмана:
Hamilton and Yau were stunned by Perelman’s announcement. “We felt that nobody else would be able to discover the solution,” Yau told us in Beijing. “But then, in 2002, Perelman said that he published something. He basically did a shortcut without doing all the detailed estimates that we did.” Moreover, Yau complained, Perelman’s proof “was written in such a messy way that we didn’t understand.”
...
In the April 18, 2003, issue of Science, Yau was featured in an article about Perelman’s proof: “Many experts, although not all, seem convinced that Perelman has stubbed out the cigars and tamed the narrow necks. But they are less confident that he can control the number of surgeries. That could prove a fatal flaw, Yau warns, noting that many other attempted proofs of the Poincaré conjecture have stumbled over similar missing steps.” Proofs should be treated with skepticism until mathematicians have had a chance to review them thoroughly, Yau told us. Until then, he said, “it’s not math—it’s religion.”
By mid-July, Perelman had posted the final two installments of his proof on the Internet, and mathematicians had begun the work of formal explication, painstakingly retracing his steps. In the United States, at least two teams of experts had assigned themselves this task: Gang Tian (Yau’s rival) and John Morgan; and a pair of researchers at the University of Michigan. Both projects were supported by the Clay Institute, which planned to publish Tian and Morgan’s work as a book. The book, in addition to providing other mathematicians with a guide to Perelman’s logic, would allow him to be considered for the Clay Institute’s million-dollar prize for solving the Poincaré. (To be eligible, a proof must be published in a peer-reviewed venue and withstand two years of scrutiny by the mathematical community.)
On September 10, 2004, more than a year after Perelman returned to St. Petersburg, he received a long e-mail from Tian, who said that he had just attended a two-week workshop at Princeton devoted to Perelman’s proof. “I think that we have understood the whole paper,” Tian wrote. “It is all right.”
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Доказательство Поинкаре имеют реальные физические последствия для безопасности работы многих математегов:
In July of that year, the National Science Foundation had given nearly a million dollars in grants to Yau, Hamilton, and several students of Yau’s to study and apply Perelman’s “breakthrough.” An entire branch of mathematics had grown up around efforts to solve the Poincaré, and now that branch appeared at risk of becoming obsolete. Michael Freedman, who won a Fields for proving the Poincaré conjecture for the fourth dimension, told the Times that Perelman’s proof was a “small sorrow for this particular branch of topology.” Yuri Burago said, “It kills the field. After this is done, many mathematicians will move to other branches of mathematics.”
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Яу яростно работал над тем, чтобы получить медаль, от которой Григорий в последствии отказался:
Five months later, Chern died, and Yau’s efforts to insure that he-—not Tian—was recognized as his successor turned vicious. “It’s all about their primacy in China and their leadership among the expatriate Chinese,” Joseph Kohn, a former chairman of the Prince-ton mathematics department, said. “Yau’s not jealous of Tian’s mathematics, but he’s jealous of his power back in China.”
Though Yau had not spent more than a few months at a time on mainland China since he was an infant, he was convinced that his status as the only Chinese Fields Medal winner should make him Chern’s successor. In a speech he gave at Zhejiang University, in Hangzhou, during the summer of 2004, Yau reminded his listeners of his Chinese roots. “When I stepped out from the airplane, I touched the soil of Beijing and felt great joy to be in my mother country,” he said. “I am proud to say that when I was awarded the Fields Medal in mathematics, I held no passport of any country and should certainly be considered Chinese.”
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Яу публикует работу, которую он называет 'Полное Доказательство Поинкаре..."
By the end of the following week, the title of Zhu and Cao’s paper on the A.J.M.’s Web site had changed, to “A Complete Proof of the Poincaré and Geometrization Conjectures: Application of the Hamilton-Perelman Theory of the Ricci Flow.” The abstract had also been revised. A new sentence explained, “This proof should be considered as the crowning achievement of the Hamilton-Perelman theory of Ricci flow.”
Zhu and Cao’s paper was more than three hundred pages long and filled the A.J.M.’s entire June issue. The bulk of the paper is devoted to reconstructing many of Hamilton’s Ricci-flow results—including results that Perelman had made use of in his proof—and much of Perelman’s proof of the Poincaré.
In their introduction, Zhu and Cao credit Perelman with having “brought in fresh new ideas to figure out important steps to overcome the main obstacles that remained in the program of Hamilton.” However, they write, they were obliged to “substitute several key arguments of Perelman by new approaches based on our study, because we were unable to comprehend these original arguments of Perelman which are essential to the completion of the geometrization program.” Mathematicians familiar with Perelman’s proof disputed the idea that Zhu and Cao had contributed significant new approaches to the Poincaré. “Perelman already did it and what he did was complete and correct,” John Morgan said. “I don’t see that they did anything different.”By early June, Yau had begun to promote the proof publicly. On June 3rd, at his mathematics institute in Beijing, he held a press conference. The acting director of the mathematics institute, attempting to explain the relative contributions of the different mathematicians who had worked on the Poincaré, said,
“Hamilton contributed over fifty per cent; the Russian, Perelman, about twenty-five per cent; and the Chinese, Yau, Zhu, and Cao et al., about thirty per cent.” (Evidently, simple addition can sometimes trip up even a mathematician.) Yau added, “Given the significance of the Poincaré, that Chinese mathematicians played a thirty-per-cent role is by no means easy. It is a very important contribution.”
On June 12th, the week before Yau’s conference on string theory opened in Beijing, the South China Morning Post reported, “Mainland mathematicians who helped crack a ‘millennium math problem’ will present the methodology and findings to physicist Stephen Hawking. . . . Yau Shing-Tung, who organized Professor Hawking’s visit and is also Professor Cao’s teacher, said yesterday he would present the findings to Professor Hawking because he believed the knowledge would help his research into the formation of black holes.”
On the morning of his lecture in Beijing, Yau told us,
“We want our contribution understood. And this is also a strategy to encourage Zhu, who is in China and who has done really spectacular work. I mean, important work with a century-long problem, which will probably have another few century-long implications. If you can attach your name in any way, it is a contribution.”---
Perelman repeatedly said that he had retired from the mathematics community and no longer considered himself a professional mathematician. He mentioned a dispute that he had had years earlier with a collaborator over how to credit the author of a particular proof, and said that he was dismayed by the discipline’s lax ethics.
“It is not people who break ethical standards who are regarded as aliens,” he said. “It is people like me who are isolated.” We asked him whether he had read Cao and Zhu’s paper. “It is not clear to me what new contribution did they make,” he said. “Apparently, Zhu did not quite understand the argument and reworked it.” As for Yau, Perelman said, “I can’t say I’m outraged. Other people do worse. Of course, there are many mathematicians who are more or less honest. But almost all of them are conformists. They are more or less honest, but they tolerate those who are not honest.”The prospect of being awarded a Fields Medal had forced him to make a complete break with his profession.
“As long as I was not conspicuous, I had a choice,” Perelman explained. “Either to make some ugly thing”—a fuss about the math community’s lack of integrity—“or, if I didn’t do this kind of thing, to be treated as a pet. Now, when I become a very conspicuous person, I cannot stay a pet and say nothing. That is why I had to quit.” We asked Perelman whether, by refusing the Fields and withdrawing from his profession, he was eliminating any possibility of influencing the discipline.
“I am not a politician!” he replied, angrily. Perelman would not say whether his objection to awards extended to the Clay Institute’s million-dollar prize. “I’m not going to decide whether to accept the prize until it is offered,” he said.
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Mikhail Gromov, the Russian geometer, said that he understood Perelman’s logic: “To do great work, you have to have a pure mind. You can think only about the mathematics. Everything else is human weakness. Accepting prizes is showing weakness.” Others might view Perelman’s refusal to accept a Fields as arrogant, Gromov said, but his principles are admirable. “The ideal scientist does science and cares about nothing else,” he said. “He wants to live this ideal. Now, I don’t think he really lives on this ideal plane. But he wants to.”
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Итак, это конечно очень длинная статья и комментарий получился длинный. Но вот вывод:
Нечего про людей судить без информации.
Перельман не хочет иметь ничего общего с математическим обществом, оно его подвело конкретно, поэтому отказ от медали можно понимать так: Лучше отказаться от медали чем от собственного достоинства.
От миллиона Григорий пока еще не отказался, так как ему его еще не предлагали.
Do not feed the troll.
