Four Are Given Highest Honor in Mathematics

By KENNETH CHANG
Published: August 22, 2006

Grigory Perelman, a reclusive Russian mathematician who solved a key piece in a century-old puzzle known as the Poincaré conjecture, was one of four mathematicians awarded the Fields Medal today.

The Fields Medal, often described as mathematics? equivalent to the Nobel Prize, is given every four years. The other Fields medalists, announced at the International Congress for Mathematicians in Madrid, are Andrei Okounkov, a professor of mathematics at Princeton; Terence Tao, 31, a professor of mathematics at the University of California, Los Angeles; and Wendelin Werner, a professor of mathematics at the University of Paris-Sud in Orsay.

Dr. Perelman, 40, is known not only for his work on the Poincaré conjecture, among the most heralded unsolved math problems, but also because he has declined previous mathematical prizes and has turned down job offers from Princeton, Stanford and other universities. He has said he wants no part of $1 million that the Clay Mathematics Institute in Cambridge, Mass. has offered for the first published proof of the conjecture.

According to an article in the Aug. 28 issue of The New Yorker, Sir John M. Ball, president of the International Mathematical Union, the organization that chooses the Fields medalists, visited Dr. Perelman in St. Petersburg, where he lives with his mother, to persuade him to accept a Fields Honor, but Dr. Perelman said, "I refuse."

The union decided to bestow a medal on Dr. Perelman anyway.

Beginning in 2002, Dr. Perelman, who was then at the Steklov Institute of Mathematics of the Russian Academy of Sciences in St. Petersburg, published a series of papers on the Internet and gave lectures at several American universities describing how he had overcome a roadblock in the proof of the Poincaré conjecture.

The conjecture, devised by Henri Poincaré in 1904, essentially says that the only shape that does not have any holes and fits within a finite space is a sphere. That is certainly true looking at two-dimensional surfaces in the everyday three-dimensional world, but the conjecture says the same is true for three-dimensional surfaces embedded in four dimensions.

Dr. Perelman solved a difficult problem that other mathematicians had encountered when trying to prove the conjecture using a technique called Ricci flow that smoothes out bumps in a surface and transforms the surfaces into simpler forms.

Dr. Okounkov, born in 1969 in Moscow, was recognized for work that tied together different fields of mathematics that had seemed unrelated. "This is the striking feature of Okounkov's work, finding unexpected links," said Enrico Arbarello, a professor of geometry at the University of Rome in Italy.

Dr. Okounkov's work has found use in describing the changing surfaces of melting crystals. The boundary between melted and non-melted is created randomly, but the random process inevitably produces a border in the shape of a heart.

Dr. Tao, a native of Australia and one of the youngest Fields Medal winners ever at age 31, has worked in several different fields, producing significant advances in the understanding of prime numbers, techniques that might lead to simplifying the equations of Einstein's theory of general relativity and the equations of quantum mechanics that describe how light bounces around in a fiber optic cable.

Dr. Werner, born in Germany in 1968, has also worked at the intersection of mathematics and physics, describing phenomena like percolation and shapes produced by the random paths of Brownian motion.

The medal was conceived by John Charles Fields, a Canadian mathematician, "in recognition of work already done and as an encouragement for further achievements on the part of the recipient."

Since 1936, when the medal was first awarded, judges have interpreted the terms of Dr. Fields' trust fund to mean that the award should usually be limited to mathematicians 40 years old or younger.

【按】我已经通过向朋友借阅杂志的方式读到了这篇刚发表于《纽约客》的精彩无比的报道，可惜没有电子版可以分享。这篇文章爆料之多令人惊讶，可以毫不夸张地说，我认为Sylvia Nasar将有可能因此最终拿下Pulitzer Prize （1998年时她差一点靠著名的"A Beautiful Mind"一书获得这一新闻界的最高荣誉）。这篇文章一下子把在此之前的Wall Street Journal, Nature, Notices of the AMS, New York Times等所有报道全部比下去，估计那些记者们读完此文后也会心悦诚服、甘拜下风！

＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝
Another interesting article after “A beautiful Mind”

送交者: Yamaguchi 2006年8月22日09:36:32 于 [教育与学术]

Sylvia Nasar, the author of "A beautiful Mind", has written a very interesting article "Manifold Destiny －－－Who really solved the Poincaré conjecture?" to be published in "The New Yorker" Magazine in the issue of August 28, 2006.

She co-authored with David Gruber, see

http://www.newyorker.com/main/magazine/

Nasar and Gruber interviewed both Professor Yau at Beijing. They also had a rare interview of G. Perelman at St. Peterburg in June 2006.

Nasar and Gruber also interviewed many mathematicians, including John Ball, the president of ICM, M. Gromov and Perelman’s teacher, just to name a few.

The article has a short but widely known story about Kefeng Liu.

If you have a friend who wants to take a risk to make quick money, it might be a good idea to translate this article into Chinese and sell in China over the weekend. It might be a best-seller story.

However, please contact with authors above for copyright.

If I were a math teacher in China, I would recommend my students to read the article privately.

好东西藏在主贴后面，狡猾也:）

News from Russia. Perelman is Jewish.

The New Yorker is Jewish-leaning . xixixi. With hold my judgement until I get my issue.
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http://www.kommersant.com/page.asp?idr=530&id=699531

Award Loses a Hero
// Russian Mathematician Grigory Perelman Refuses Fields Prize
Yesterday the names were announced of the four laureates of the highest prize in the field of mathematics, the Fields Prize. Among the winners were two Russian scholars, Andrey Okunkov and Grigory Perelman. Perelman refused the prize and an additional $1 million award for reasons that were not entirely clear. His colleagues offered several explanations, ranging from the laureate's "eccentric individualism" to his possible exit from the field of mathematics.
The names of the nominees for the Fields Prize (the equivalent of the Nobel Prize for mathematics) were announced August 22 during the ceremony opening the International Congress of Mathematicians in Madrid. This year's winners were Australia's Terence Tao, France's Wendelin Werner, and Russia's Andrey Okunkov and Grigory Perelman.

The Fields Medal (carrying an award of $9,500) is awarded by the International Mathematics Congress every four years. The award was founded by Canadian scholar John Charles Fields and was first awarded in 1936. Since 1950 the Fields Medal has been regularly awarded personally by the King of Spain for contributions to the development of the science of mathematics as a whole. The prize can be awarded to up to four scholars under the age of 40. To date, 44 mathematicians have received the award, including eight Russians.

Grigory Perelman received the prize for his proof of Poincare's conjecture for three-dimensional surfaces. This part of Poincare's conjecture was one of the "millennium prize problems" for which the American Clay Mathematics Institute promised a purse of $1 million to anyone who came up with a solution. However, Perelman refused the award without explaining his reasons. Similarly, according to American mathematician John Boll, Perelman did not want to come to Madrid, since he does not consider himself a part of the "international mathematics community." "He has no hostility towards mathematicians, and it is inconceivable that he would," said Anatoly Vershik, the president of the St. Petersburg Mathematics Society and the head of the laboratory at the St. Petersburg branch of the Steklov Mathematics Institute, where Perelman worked until recently. "Certain norms of life and the situation of the sciences simply do not suit him, just like anyone else."

It is also said that Perelman simply has no love for prizes and publicity. Ten years ago, he turned down a prestigious prize from the European Mathematical Society, claiming that he had not completed his work within the framework of the requirements for the prize. Vershik commented that the discovery itself was the real prize for the mathematician, one that "does not require material affirmation."

Nonetheless Perelman, who left the Steklov Institute six months ago, could have done with the money. "He was an undoubted favorite at the institute," Vershik told Kommersant. "It is possible that he left in order to pursue mathematics far from prying eyes. It is possible that his move was a show of individualism of the highest kind." Rumors are already flying within the mathematics society that Perelman not only left the institute but also decided to abandon his mathematics career and science in general.

On the other hand, it is possible that Perelman was reacting to attempts to discredit his discoveries: a source in the Steklov Institute told Kommersant that a group of Chinese-American academics headed by a mathematician named Yau has launched an "anti-Perelman" campaign, alleging that the Russian academic's work is incomplete and claiming that only the Chinese know the whole story of three-dimensional surfaces. Perelman has not commented on the allegations: once it was announced that he had been awarded the Fields Medal, he completely stopped communicating with his colleagues. "I tried to track him down," mathematician Valery Kozlov, the vice president of the Russian Academy of Sciences, told Kommersant. "But my attempts were unsuccessful."

Since Perelman no longer works for the Russian Academy of Sciences, according to Kozlov, the Academy cannot award him the prize in Russia (a celebration in Perelman's honor, according to information obtained by Kommersant, is being planned only by the Steklov Institute). However, the presidium of the Academy is confident that the scientific discoveries made by the retired mathematician will nevertheless serve as proof that "it is pointless to attack Russian science." Celebrating the Russian achievement, Kozlov said, "the science we do, especially mathematics, is of the very highest level and demonstrates good prospects."

The New Yoker 的文章，我看完了，蛮长的，大概14页，还有一个 Perelman 和 Yau 的漫画。

8月28号才能正式出版。

看完了，就一个观点，做人还是诚实点好。
这数学界的八卦，是是非非还是少掺和，做好自己的事情就好。

猛料在哪里

数学不需要猛料，数学需要猛人。

不过可以引用这篇文章的Perelman的话，
Perelman said about his meeting with Sir John Ball in June 2006,
'He proposed to me three alternatives: accept and come; accept and don't come, they send the medal later; third, I don't accept the prize. From the very beginning, I have chozen the third one.'
'Everybody understood that if the proof is correct then no other recoginition is needed.'

文章简介了三位数学家： Perelman, Yau and Hamilton. 和 Perelman 对Cao-Zhu 文章的看法。
还有一些数学家的一些评价，包括 Phillip Griffiths, Barray Mazur, Dan Stroock, Mikhail Gromov， Alexander Givental， John Morgan 等。

个人最喜欢的还是这句话:"what's in the name" by Poincar\'e
还有这句：'If they know my work, they don't need my C.V.; If they need my C.V., they don't kow my work" by Perelman.

请问C.V.是什么意思？

事实上Perelman这么一做，反而知道他的人更多了。