Grigori Perelman
Grigori Yakovlevich Perelman (Russian Григорий Яковлевич Перельман, scientific transliteration Grigorii Jakovlevic Perel'man; born June 13, 1966 in Leningrad ) is a Russian mathematician and expert in the mathematical branches of topology and differential geometry, in particular in the field of Ricci flow.
In 2002 he published his proof of the Poincaré conjecture. This is one of the established in the year 2000 Millennium problems the seven greatest unsolved problems in mathematics, of which so far only the Poincaré conjecture was solved.
Life
Perelman is the son of Jewish parents, his father was an electrical engineer, his mother a math teacher. His mathematical education began in the fall of 1976 on the math club in Leningrad Pioneer Palace. At 14, he attended the Mathematical technical school number 239 in Leningrad. In 1982, he won a gold medal as a student at the International Mathematical Olympiad ( with perfect score ) and was therefore admitted without entrance exam to study. So he was not affected by the deprivation of Jewish study candidates in the examination of the entrance test that there was also the end of the Brezhnev era and during the Andropov era. After graduation, he worked at the Steklov Institute of Mathematics in Leningrad at Yuri Dmitrievich Burago. Perelman received his doctorate in 1990 at the Faculty of Mathematics and Mechanics at the University of St. Petersburg on saddle surfaces in Euclidean spaces, that is, he obtained according to Russian names candidate status ( C.Sc. ), which corresponds to a Western European promotion. His doctoral supervisor was Burago, but since this foresaw difficulties due to the Jewish origins of Perelman - in the 1970s and 1980s consisted in the admission to doctoral studies in particular on the Steklov Institute in this regard, nor limitations - they pushed the academician Alexander Danilovich Aleksandrov as official maintainer before.
As a post-doctoral researcher Perelman was supported by Mikhail Gromov from the Institut des Hautes Études Scientifiques and invited there. In 1992 he was in the U.S. at the State University of New York at Stony Brook and at the Courant Institute of Mathematical Sciences of New York University with Jeff Cheeger. 1993/94 he was a Miller Research Fellow at the University of California, Berkeley and then went despite offers from Princeton University and Stanford University in 1995 to the Steklov Institute in St. Petersburg back. After Ludwig Faddejew you let him, because you knew his abilities, working largely undisturbed there, even though he ( called in Russia Doctor ) hardly published and refused to defend his habilitation. He had the only leading scientist at the Institute "only" candidate status. By the fall of 2002, Perelman was best known for his work in differential geometry. However, he had fallen out with his former boss Burago and the Department of Olga Ladyschenskaja and its successor Seregin connected. 2005 there was a conflict with the administration of the Steklov Institute, the relaxed about the fact that unspent research grants to employees were paid, which Perelman did not agree. In December 2005 he left the Steklov Institute, where he told the director Kisljakow that he was disappointed with the math and wanted to try something different.
The EMS price of the European Mathematical Society, which he was awarded in 1996, he refused. The Fields Medal from the International Mathematical Union, which he was awarded in 2006, he refused. Even the prize money of one million dollars the Clay Mathematics Institute, which he was awarded in 2010, he refused.
After he studied for a time in the dacha of a friend completely isolated, he now lives again on the outskirts of St. Petersburg with his mother. Since he quit his position at the Steklov Institute in 2005, Perelman is without permanent employment. In 2011 he was proposed by Faddejew with the support of the Steklov Institute for inclusion in the Russian Academy of Sciences.
Perelman plays the violin and is also an avid table tennis player. His younger sister Elena is also a mathematician. She received her Ph.D. at the Weizmann Institute and works at the Karolinska Institute in Stockholm as Biostatistikerin.
Work
Perelman drew attention to himself before his work on the Poincaré conjecture by working in differential geometry. This work earned him the prize for young mathematicians of the European Mathematical Society ( EMS price ) 1996.
Perelman developed the theory of Alexandrov spaces ( limited downward curvature ) including a structure theory and a stability theorem. Alexandrov spaces are named after his teacher AD Alexandrov and are more flexible than Riemannian manifolds. With his teacher Burago Mikhail Leonidovich Gromov and he also published a review article on these spaces.
In 1994, he gave a new short and elegant proof of the theorem Soul ( Soul theorem), which was first proved by Jeff Cheeger and Detlef Gromoll 1972.
In 1994 he was a speaker at the ICM in Zurich ( spaces with curvature bounded below ).
The Poincaré conjecture and the Fields Medal
In November 2002, he published on the document server preprint arXiv the first article in a series that the intention was to prove the geometrization of William Thurston. In this proof of the Poincaré conjecture as a special case. Perelman also sent the proof in emails to known mathematician. He had in his time experienced in the U.S. by the opportunity to prove the geometrization and the Poincaré conjecture about the theory of Ricci flows of Richard Hamilton from the early 1980s. Hamilton himself was working on it and had in the U.S. contact to Perelman. Perelman worked after his return to Russia seven years in relative isolation at the evidence and offered his own words, during this period, once Hamilton cooperation at what but did not reply. In April 2003, Perelman held in Princeton, Stony Brook and Columbia University ( where Hamilton was in the audience ) talks about his work. Then he left it to others to verify the accuracy of, and did not participate further in it.
The work of Perelman was checked for a long time (2003-2006) of the mathematical art. Meanwhile, three teams of experts have examined the evidence (, Huai -Dong Cao and Xi - Ping Zhu, Bruce Kleiner and John Lott TianGang and John Morgan ) and expressed after intensive work with a positive proof for its correctness. Richard Hamilton also checked the correctness independently with Tom Ilmanen and Gerhard Huisken. Although the proof of Perelman contained a few inaccuracies and small errors, but could be resolved in the context of reviewing the evidence, which showed no significant problems.
Perelman was awarded the Fields Medal in 2006, the evidence, which is generally true much more than "just" the official recognition of the proof: The medal comes in mathematics in rating a Nobel Prize the same. Nevertheless, he refused, as the EMS price. He was the first prize winner of the highest math award, who refused to receive. Like it so far occurred only with Alexander Grothendieck, the Fields Medal was awarded in 1966. Unlike Perelman Grothendieck accepted the award, although he refused for political reasons to travel to the official ceremony in Moscow. Before the ceremony had in the summer of 2006, even the president of the International Mathematical Union ( IMU), the Briton John M. Ball, tried unsuccessfully in St. Petersburg to persuade Perelman to accept the prize.
Soon after his rejection of the Fields Medal he gave in June 2006, the first time an interview in which he at length entered on the history and complained about other mathematicians would falsely claim shares in the proof of the Poincare conjecture for itself. He was referring to the first complete publication of the proof by Cao and Zhu, two protégés Shing -Tung Yau, who also lectured on the string theory conference in Beijing in June 2006 and a matter of long-standing, the preparatory work of Richard Hamilton, with the Yau on Ricci rivers worked, and stressed the incompleteness of Perelman's publications. The publication of Cao and Zhu also raised in its title a similar impression. The interview with Perelman was part of an article by Sylvia Nasar ( best-selling author of a book about John Forbes Nash ) and David Gruber Manifold Destiny in The New Yorker on 28 August 2006. Therein Perelman announced simultaneously to its withdrawal from mathematics. Yau found himself later in the article represented unfair and denied Perelman to have priority in doubt, where he was supported by Hamilton.
Already in 2000, the Clay Mathematics Institute had counted the Poincaré conjecture among the seven most important unsolved mathematical problems and for solving an annual award of one million dollars ( under the condition of its publication in a professional journal ). Perelman, who published his work on the internet, so far neither showed interest to publish his proof in a professional journal, still working on it to claim the prize for themselves. The Clay Institute in Cambridge, Massachusetts, USA, which also financed the verification of the proof by Tiang and Morgan, as well as another team, Perelman said, still following thorough testing on March 18, 2010, the prize money for the first solution of one of the seven Millennium Problems about. However, this declined again from the award. He justified this decision by saying that Richard Hamilton had made an equal contribution to the solution of the problem.