Grigori Perelman
Who was Grigori Perelman?
Russian mathematician who proved the Poincaré conjecture in 2003 but famously declined the Fields Medal and the $1 million Millennium Prize.
Biographical data adapted from Wikipedia’s article on Grigori Perelman (CC BY-SA 4.0).
Biography
Grigori Yakovlevich Perelman was born on June 13, 1966, in Saint Petersburg, Russia (then Leningrad, Soviet Union). He is an exceptionally talented mathematician and geometer who made significant contributions to geometric analysis, Riemannian geometry, and geometric topology, changing key areas of modern mathematics. He attended Saint Petersburg Lyceum 239, a school focused on mathematics and physics, before studying at the Mathematics and Mechanics Faculty of Saint Petersburg State University, where his outstanding talent was noticed by both teachers and classmates.
Perelman gained international recognition in the 1990s for his work on Alexandrov spaces, which he did in part with Yuri Burago, Mikhael Gromov, and Anton Petrunin. In 1994, he solved the soul conjecture in Riemannian geometry, a problem that had remained unresolved for 20 years. This accomplishment earned him the European Mathematical Society Prize in 1996 and established him as a leading figure in geometric analysis. He held a research position at the Steklov Institute of Mathematics in Saint Petersburg during much of this time.
Perelman's most significant achievement came in 2002 and 2003 when he published papers on the arXiv preprint server introducing new techniques for analyzing Ricci flow. These papers provided a proof of the Poincaré conjecture, one of the most famous unsolved problems in mathematics, which questions whether every simply connected, closed three-dimensional manifold is topologically equivalent to a three-sphere. His work also proved Thurston's geometrization conjecture, a broader result that classifies the geometry of three-dimensional manifolds. Verifying and elaborating on his arguments took years for teams of mathematicians, and in December 2006, the journal Science named the proof its Breakthrough of the Year, marking the first time a mathematical result received that honor.
Despite his major achievements, Perelman declined both major prizes offered to him. In August 2006, he refused the Fields Medal, mathematics' highest honor, saying he was not interested in money or fame and did not want to be treated like an animal in a zoo. On March 18, 2010, the Clay Mathematics Institute announced that he had met the criteria for the Millennium Prize of one million dollars for solving the Poincaré conjecture. He also turned down this prize on July 1, 2010. He had already left the Steklov Institute in 2005 and by 2006 announced that he had quit professional mathematics, citing disappointment with the integrity he saw in the mathematical community.
Since 2006, Perelman has lived privately in Saint Petersburg and has refused all requests for interviews. His retreat from public and professional life has made him a mysterious figure in contemporary science. Even though he is not actively researching, the methods he introduced for controlling Ricci flow with surgery continue to impact geometric analysis, and his proof of the geometrization conjecture remains a key result in modern topology.
Before Fame
Grigori Perelman grew up in Leningrad during the later years of the Soviet Union, a time when math education was highly valued, and special schools produced many top mathematicians. He went to Saint Petersburg Lyceum 239, known for its challenging math and science subjects, and represented the Soviet Union at the 1982 International Mathematical Olympiad, where he got a perfect score and won a gold medal. This achievement showed his exceptional math skills.
He studied at Saint Petersburg State University for both his undergraduate and graduate degrees and later worked at the Steklov Institute of Mathematics. During visits to the U.S. in the early 1990s, he held positions at places like the University of California, Berkeley, and gained attention from leading mathematicians for his unique approach to geometry. During this time and after he returned to Russia, he focused on the problem of Ricci flow, eventually making the breakthrough that would make him famous.
Key Achievements
- Proved the Poincaré conjecture in 2002–2003, resolving a century-old open problem in topology.
- Proved Thurston's geometrization conjecture, providing a complete classification framework for the geometry of three-dimensional manifolds.
- Proved the soul conjecture in Riemannian geometry in 1994, solving a 20-year-old open problem.
- Developed new techniques in Ricci flow with surgery that fundamentally advanced geometric analysis.
- Was awarded the Fields Medal (2006) and the Clay Millennium Prize (2010), both of which he declined.
Did You Know?
- 01.Perelman achieved a perfect score of 42 out of 42 at the 1982 International Mathematical Olympiad, winning a gold medal while representing the Soviet Union.
- 02.He turned down a prestigious faculty position at several leading American universities in the 1990s, choosing instead to return to the Steklov Institute in Saint Petersburg.
- 03.When declining the Fields Medal in 2006, Perelman specifically compared the prospect of public recognition to being put on display like an animal in a zoo.
- 04.The Clay Mathematics Institute had to change its rules regarding the Millennium Prize because Perelman's proof was published on a preprint server rather than in a peer-reviewed journal as originally required.
- 05.Science magazine's designation of Perelman's proof as the 2006 Breakthrough of the Year marked the first time in the award's history that a mathematical result had been selected.
Family & Personal Life
Awards & Honors
| Award | Year | Details |
|---|---|---|
| Fields medal | 2006 | — |
| EMS Prize | 1996 | — |
| Millennium Problems | 2010 | — |