Parelman's Proof

Grigori Yakovlevich Perelman (Russian : Григорий Яковлевич Перельман), born 13 June 1966 in Leningrad, USSR (now St. Petersburg, Russia), sometimes known as Grisha Perelman, is a Russian mathematician who has made landmark contributions to Riemannian geometry and geometric topology. In particular, he proved Thurston's geometrization conjecture. This solves in the affirmative the famous Poincare conjecture, posed in 1904 and regarded as one of the most important and difficult open problems in mathematics until it was solved.

In August 2006, Perelman was awarded the Fields Medal for "his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow". Perelman declined to accept the award or to appear at the congres.

On 22 December 2006, the journal Science recognized Perelman's proof of the Poincaré Conjecture as the scientific "Breakthrough of the Year," the first such recognition in the area of mathematics.

Grigori Perelman was born in Leningrad (now Saint Petersburg) to a Jewish family on 13 June 1966. His early mathematical education occurred at the 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 (the Soviet equivalent to the Ph.D.) 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".

After graduation, Perelman began work at the renowned Leningrad Department of Steklov Institute of Mathematics of the USSR Academy of Sciences, where his advisors were Aleksandr Danilovich Aleksandrov and Yuri Dmitrievich Burago. In the late 80s and early 90s, Perelman held posts at several universities in the United States. In 1992, he was invited to spend a semester each at the Courant Institute in New York University and Stony Brook University. From there, he accepted a two-year Miller Research Fellowship at the University of California, Bekerley in 1993. He was offered jobs at several top universities in the US, including Princeton and Stanford, but he rejected them all and returned to the Steklov Institute in the summer of 1995.

He has a younger sister, Elena, who is also a mathematician. She received a PhD from Weizmann Institute and is a biostatician at Karolinska Institute.

Perelman is a talented violinist and also plays table tennis.

Here his proof about Ricci Flow and Geometrization of Three-Manifolds :

Click to Download