Russian mathematician born in 1966, famous for proving the Poincaré conjecture in 2003, one of the seven Millennium Prize Problems. He refused the Fields Medal (2006) and the Clay Prize of one million dollars (2010).
Grigori Perelman(1966 — ?)
Grigori Perelman
Russie, Union soviétique
7 min read
Frequently asked questions
Key Facts
- Born on June 13, 1966 in Leningrad (USSR)
- Proves the Poincaré conjecture between 2002 and 2003 through work on Ricci flow
- Refuses the Fields Medal in 2006, the first time in the history of this award
- Refuses the Clay Prize of one million dollars in 2010
- Withdraws from public life and the mathematical community in the 2000s
Works & Achievements
Perelman elegantly solved in a few pages an open problem in Riemannian geometry that the leading specialists had been unable to crack for twenty years, earning him international recognition.
The first of three foundational papers, it introduces the notion of monotone entropy for the Ricci flow — a key mathematical tool for controlling the evolution of geometric singularities.
The second paper, it describes the topological "surgery" procedure that allows the Ricci flow to continue beyond singularities and decompose the manifold into geometrically simple pieces.
The third and final paper, it completes the proof by showing that the Ricci flow becomes extinct in finite time for simply connected manifolds, which directly implies the Poincaré conjecture.
By proving the Poincaré conjecture, Perelman in fact established a far more general result: Thurston's geometrization conjecture, which classifies all possible three-dimensional manifolds.
Anecdotes
In 2006, the president of the International Mathematical Union, Sir John Ball, traveled personally to Saint Petersburg to persuade Perelman to accept the Fields Medal. Perelman flatly refused, stating that he did not feel he belonged in the mathematical community and that the award meant nothing to him. It was the first time in history that this supreme distinction in mathematics had ever been declined.
Perelman published his proof of the Poincaré conjecture not in a traditional scientific journal, but in three papers posted freely on arXiv, an online preprint platform, between November 2002 and July 2003. This approach, highly unusual for a discovery of such magnitude, reflected his radical independence from academic institutions.
In 2010, the Clay Mathematics Institute awarded him a one-million-dollar prize for solving one of the Millennium Prize Problems. Perelman refused this enormous sum as well, arguing that Richard Hamilton's contribution — whose work on Ricci flow he had built upon — was just as important as his own and deserved equal recognition.
After withdrawing from the mathematical world around 2005–2006, Perelman led an extremely reclusive life in a modest apartment in Saint Petersburg with his mother. The few journalists who managed to reach him described someone living in near-total austerity, refusing all interviews and any contact with the academic world.
Perelman was recognized as a prodigy early on: at 16, he won a gold medal at the 1982 International Mathematical Olympiad in Budapest with a perfect score. This feat earned him direct admission to Leningrad University, bypassing the standard entrance examinations.
Primary Sources
In this paper we present a monotonicity formula for the Ricci flow [...] We also verify several assertions related to Richard Hamilton's program for geometrization of three-dimensional manifolds.
This is a technical paper, which is a continuation of [I]. Here we verify most of the assertions, made in [I, §13]; the exceptions are (1) and (2) of [I, §13.2], which turned out to be unjustified, and which will not be used elsewhere.
In this note we prove that the solution to the Ricci flow [...] becomes extinct in finite time [...] This confirms the heuristics in [I,§13].
I know how to control the universe. Why should I run after a million dollars?
Key Places
Perelman's birthplace and the setting of his entire life. After his stays abroad, he returned permanently and lives there in seclusion with his mother in an apartment in the Kupchino district.
Perelman worked here as a researcher for most of his career. He resigned from the position around 2005, shortly after posting his papers on the Poincaré conjecture.
In 2003, Perelman delivered a memorable series of lectures at Berkeley, publicly outlining his proof for the first time before the international mathematics community.
Perelman made research visits to Princeton in the early 1990s, coming into contact with leading geometers from around the world — most notably Richard Hamilton, whose work he would go on to extend.
At the 2006 International Congress of Mathematicians held in Madrid, the Fields Medal was awarded to Perelman in his absence — an unprecedented event in the history of the prize.
Typical Objects
Perelman filled dense notebooks with calculations and topological diagrams, often working alone for years before publishing anything.
Rather than going through traditional academic journals, Perelman chose to share his proof as three freely downloadable PDF files on the arXiv server, opening access to his discovery to everyone.
The mathematician's traditional tool, the blackboard was the medium on which Perelman presented his ideas during the rare seminars he gave at Berkeley and MIT in 2003.
Perelman used a simple computer for his numerical computations and for writing his papers in LaTeX, the standard typesetting language in mathematics.
William Thurston's work on the geometrization of 3-dimensional manifolds, published in the 1980s, formed the theoretical foundation on which Perelman built his proof.
Richard Hamilton had developed in the 1980s a mathematical tool — the Ricci flow — which Perelman took up, refined, and decisively extended to arrive at his proof.
School Curriculum
Vocabulary & Tags
Key Vocabulary
Daily Life
Morning
Perelman had no fixed schedule when he woke up, a hallmark of his withdrawn life in Saint Petersburg. His mornings were devoted to pure mathematical reflection, often in bed or in an armchair, with a simple notebook within reach. Former colleagues describe him as someone capable of concentrating for hours without interruption.
Afternoon
Perelman's afternoons were often spent on long solitary walks in the parks and forests around Saint Petersburg, a practice he considered inseparable from his thinking. He loved mushrooms and would pick them on these outings. During his years of active research, he would spend entire afternoons working on calculations at his blackboard or computer.
Evening
In the evenings, Perelman enjoyed classical music, particularly opera and the works of Russian composers. His social life was virtually nonexistent after his withdrawal from the academic world. He lived in a modest apartment with his mother, sharing simple meals and avoiding all contact with the media.
Food
Perelman followed an extremely frugal, almost ascetic diet. He was particularly fond of mushrooms he foraged himself, Russian black bread, traditional soups (borscht, solyanka), and simple dairy products. He paid no attention whatsoever to questions of social prestige surrounding food.
Clothing
Perelman was famous for his complete indifference to his appearance. He wore ordinary, worn-out clothes and simple shoes, and let his nails and beard grow to unusual lengths. On the rare occasions he gave talks abroad, his disheveled look stood in stark contrast to the prestige of his discoveries.
Housing
Perelman lives in a standard Soviet-era apartment (of the “Khrushchyovka” type) in the working-class Kupchino district of Saint Petersburg, with his mother. This modest home, devoid of any luxury, stands in radical contrast to what American universities — eager to recruit him at any price — could have offered him.
Historical Timeline
Period Vocabulary
Liens externes & ressources
Références
Œuvres
Preuve de la conjecture de l'âme (soul conjecture)
1994
The entropy formula for the Ricci flow and its geometric applications (arXiv)
2002
Ricci flow with surgery on three-manifolds (arXiv)
2003
Finite extinction time for the solutions to the Ricci flow on certain three-manifolds (arXiv)
2003
Démonstration complète de la conjecture de géométrisation de Thurston
2003
