Grigori Perelman
Grigori Yakovlevich Perelman , born 13 June 1966 in
Leningrad,
USSR , sometimes known as Grisha Perelman, is a
Russian
mathematician who has made landmark contributions to Riemannian geometry and geometric topology. In particular, it appears that he has proven Thurston's geometrization conjecture. If so, this solves in the affirmative the famous Poincar conjecture, posed in 1904 and regarded as one of the most important and difficult open problems in mathematics.
In August 2006, Perelman was awarded the Fields Medal, which is widely considered to be the top honor a mathematician can receive.
Encyclopedia
Grigori Yakovlevich Perelman , born 13 June 1966 in
Leningrad,
USSR , sometimes known as
Grisha Perelman, is a
Russian
mathematician who has made landmark contributions to Riemannian geometry and geometric topology. In particular, it appears that he has proven Thurston's geometrization conjecture. If so, this solves in the affirmative the famous Poincaré conjecture, posed in 1904 and regarded as one of the most important and difficult open problems in mathematics.
In August 2006, Perelman was awarded the Fields Medal, which is widely considered to be the top honor a mathematician can receive. However, he declined to accept the award or appear at the congress.
Early life and education
Grigori Perelman was born in Leningrad to a Jewish family on June 13, 1966. His early mathematical education occurred at the world-famous
Leningrad Secondary School #239, a specialized school with advanced mathematics and
physics programs. In 1982, as a member of the
USSR team competing in the International Mathematical Olympiad, an international competition for high school students, he won a gold medal, achieving a perfect score. In the late 1980s, Perelman went on to earn a Candidate of Science degree at the Mathematics and Mechanics Faculty of the
Leningrad State University, one of the leading universities in the former Soviet Union. His dissertation was entitled
"Saddle surfaces in Euclidean spaces" .
He was also a talented violinist and played table tennis. According to the Fields medalist
Shing-Tung Yau this paper was aimed at "putting the finishing touches to the complete proof of the Poincaré Conjecture".
The true extent of the contribution of Zhu and Cao, as well as the ethics of Yau's involvement, has been controversial. Yau is both an editor-in-chief of the
Asian Journal of Mathematics as well as Cao's doctoral advisor. Sylvia Nasar and David Gruber, writing for
The New Yorker is an American [i] magazine [i] that publishes reportage, criticism, es ...
, has suggested that Yau was intent on being associated, directly or indirectly, with the proof of the conjecture and pressured the journal's editors to accept Zhu and Cao's paper on unusually short notice. Cao has stated, "Hamilton and Perelman have done the most important fundamental works. They are the giants and our heroes. In my mind there is no question at all that Perelman deserves the Fields Medal. We just follow the footsteps of Hamilton and Perelman and explain the details. I hope everyone who read our paper would agree that we have given a rather fair account." Cao also defended Yau by saying that Yau had remarked Perelman was deserving of the Fields Medal, including to reporters from
The New Yorker.
In July 2006, John Morgan of Columbia University and Gang Tian of the Massachusetts Institute of Technology posted a paper on the arXiv titled, "Ricci Flow and the Poincaré Conjecture." In this paper, they claim to provide a "detailed proof of the Poincaré Conjecture". On 24 Aug 2006, Morgan delivered a lecture at the ICM in Madrid on the Poincaré conjecture.
The above work seems to demonstrate that Perelman's outline can indeed be expanded into a complete proof of the geometrization conjecture:
Dennis Overbye of the
New York Times has said that "there is a growing feeling, a cautious optimism that [mathematicians] have finally achieved a landmark not just of mathematics, but of human thought." Nigel Hitchin, professor of mathematics at Oxford University, has said that "I think for many months or even years now people have been saying they were convinced by the argument. I think it's a done deal."
The Fields Medal and Millennium Prize
In May 2006, a committee of nine mathematicians voted to award Perelman a Fields Medal for his work on the Poincaré conjecture.hn M. Ball|Sir John Ball]], president of the International Mathematical Union, approached Perelman in
St. Petersburg in June 2006 to persuade him to accept the prize. After 10 hours of persuading over two days, he gave up. Two weeks later, Perelman summed up the conversation as: "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." He went on to say that the prize "was completely irrelevant for me. Everybody understood that if the proof is correct then no other recognition is needed."
He had previously turned down a prestigious prize from the European Mathematical Society,lman is also due to receive a share of a Millennium Prize . While he has not pursued formal publication in a
peer-reviewed mathematics journal of his proof, as the rules for this prize require, many mathematicians feel that the scrutiny to which his eprints outlining his alleged proof have been subjected exceeds the "proof-checking" implicit in a normal peer review. The Clay Mathematics Institute has explicitly stated that the governing board which awards the prizes may change the formal requirements, in which case Perelman would become eligible to receive a share of the prize. Perelman has stated that "I’m not going to decide whether to accept the prize until it is offered."thdrawal from mathematics
According to various sources, in the spring of 2003, Perelman suffered a bitter personal blow when the faculty of the Steklov Institute allegedly declined to re-elect him as a member, According to a recent interview, Perelman is currently jobless, living with his mother in St Petersburg, and subsisting on her modest pension.as stated that he is disappointed with mathematics' ethical standards, in particular of Yau's effort to downplay his role in the proof and play up the work of Cao and Zhu. He has said that "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.", combined with the possibility of being awarded a Fields medal, led him to quit professional mathematics. He has said that "As long as I was not conspicuous, I had a choice. Either to make some ugly thing" "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.”essor Marcus du Sautoy of Oxford University has said that "He has sort of alienated himself from the math community. He has become disillusioned with mathematics, which is quite sad. He's not interested in money. The big prize for him is proving his theorem."ibliography
Perelman's proof of the geometrization conjecture:*
Notes
References
See also
- Clay Mathematics Institute
- Fields Medal
- Geometrization conjecture
- Homology sphere
- Manifold Destiny
- Poincaré conjecture
- Ricci curvature
- Ricci flow
- Soul theorem
- Uniformization theorem
External links
- at Petersburg Department of Steklov Institute of Mathematics
