Who is Grigori Perelman? Everything You Need to Know

Quick Facts

Also Known As: Grigori Yakovlevich Perelman

Age: 57 Years, 57 Year Old Males

Family:

father: Yakov Perelman

mother: Lubov Lvovna

siblings: Elena Perelman

Mathematicians Russian Men

More Facts

education: Saint Petersburg State University

awards: Fields Medal

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Childhood & Early Life

Grigori ‘Grisha’ Yakovlevich Perelman was born on June 13, 1966 in Leningrad, Soviet Union (now Saint Petersburg, Russia) to Yakov Perelman and Lubov Lvovna. His father was an electrical engineer and his mother was a teacher of mathematics at a technical college.

He was born to Russian-Jewish parents at a time when Soviet distrust of Jews was strong, and his overtly Jewish surname made him suffer anti-Semitism throughout his life. His father later moved to Israel and his mother left graduate work in mathematics to raise him and his younger sister Elena, who also became a mathematician later.

His father, who was very proud of him, used to encourage him to solve brain teasers and math problems when he was a child, and taught him to play chess. His mother also contributed to his interest in mathematics, and also taught him to play the violin.

By the time he was ten, his talent in mathematics became obvious after he participated in district mathematics competitions. To help develop his talents further, his mother enrolled him into an elite math coaching club run by Sergei Rukshin, a 19-year-old mathematics undergraduate at Leningrad University.

With Rukshin’s help, he also improved his English and entered Leningrad's Special Mathematics and Physics School Number 239 in September 1980. In 1982, he was selected into Soviet Union’s International Mathematical Olympiad team, where he earned a gold medal and secured a direct entry into School of Mathematics and Mechanics at the Leningrad State University.

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Contributions in Mathematics

During his undergraduate year, Grigori Perelman began assisting his former tutor Sergei Rukshin at his summer camps. However, he had to stop eventually as his incredibly high standards were no match for even the best students.

By the time he graduated from university in 1987, he had already published a bunch of papers on various mathematical theories. These included ‘Realization of abstract k-skeletons as k-skeletons of intersections of convex polyhedra in R2k-1’, ‘A remark on Helly's theorem’, a supplement to A D Aleksandrov's ‘On the foundations of geometry’, and ‘On the k-radii of a convex body’.

Despite his remarkable achievements in the undergraduate level, he found it difficult to get into the Leningrad Department of Steklov Institute of Mathematics because the institute did not accept Jews following an old policy. In 1990, a letter from Aleksandr Danilovic Aleksandrov to the director of the institute allowed him to pursue his graduate work there, even though under Yuri Burago instead of Aleksandrov himself.

He had already published the results of his thesis ‘An example of a complete saddle surface in R4 with Gaussian curvature bounded away from zero’ in 1989. The following year, he defended his thesis ‘Saddle Surfaces in Euclidean Spaces’.

With Burago’s efforts, he was invited into the Institut des Hautes Études Scientifiques near Paris by Mikhael Leonidovich Gromov with whom he worked on Aleksandrov's spaces. In 1992, he published his first major paper, ‘A D Aleksandrov spaces with curvatures bounded below’ in collaboration with Burago and Gromov.

He briefly returned to St Petersburg, but on Gromov’s recommendation, he obtained research positions at several universities in the United States. In 1992, he started working on manifolds with lower bounds on Ricci curvature during his stay at the Courant Institute in New York University and Stony Brook University for one semester each.

In 1993, he took two-year-long Miller Research Fellowship at the University of California, Berkeley and published papers like ‘Elements of Morse theory on Aleksandrov spaces’ and ‘Manifolds of positive Ricci curvature with almost maximal volume’. However, his biggest achievement was to answer in his paper ‘Proof of the soul conjecture of Cheeger and Gromoll’ a question asked by the mathematicians twenty years earlier.

In 1994, he was invited to address the International Congress of Mathematicians in Zürich and was offered jobs at top US universities including Princeton and Stanford. However, he returned to the Steklov Institute in Saint Petersburg in 1995 and took up a research-only position.

He initially published his paper ‘The Entropy Formula for the Ricci Flow and Its Geometric Applications’ in November 2002, but did not claim to have solved the Poincaré Conjecture. As experts hailed his paper as a breakthrough on the subject, he published a second paper, ‘Ricci flow with surgery on three-manifolds’, in which he modified Richard S. Hamilton's program to prove the conjecture.

Major Works

Grigori Perelman proved the soul conjecture in 1994 and Thurston's geometrization conjecture in 2003 (confirmed in 2006). He is best known for his work in comparison theorems in Riemannian geometry and for proving the Poincaré conjecture.

Awards & Achievements

In 1982, Grigori Perelman achieved a perfect score and won a gold medal in the International Mathematical Olympiad as part of the Soviet Union team. In 1991, he received the ‘Young Mathematician Prize’ of the Saint Petersburg Mathematical Society for his work on Aleksandrov's spaces of curvature bounded from below.

He turned down an award offered to him by the European Congress of Mathematicians in 1996. Ten years later, in 2006, he also declined the ‘Fields’ Medal, which is equivalent to ‘Noble Prize’ in the field of mathematics, stating that he was “not interested in money or fame”.

For solving of the Poincaré conjecture, he was announced to be the winner of the he first Clay ‘Millennium Prize’ on March 18, 2010. However, this time he turned down the award because he considered the decision unfair as his achievement was no greater than that of Richard S. Hamilton, the mathematician whose model he followed.

Personal Life & Legacy

According to media reports in 2010, Grigori Perelman lives with his elderly mother in a 2-bedroom flat in St. Petersburg despite owning his own studio flat. The family is sustained by his mother’s modest pension and the money sent by his sister who lives in Sweden.

Trivia

Grigori Perelman is believed to have retired from mathematics as his neighbours maintain that he now spends time playing table tennis against the wall, and is only seen while purchasing grocery from the nearby store.

Grigori Perelman Biography