Grigori Yakovlevich Perelman

Background

Ethnicity: Perelman was born into a Jewish family in Leningrad during the Soviet period.

Grigori Yakovlevich Perelman was born on June 13, 1966, in Leningrad, then part of the Soviet Union and now Saint Petersburg, Russia. His father, Yakov Perelman, was an electrical engineer, and his mother, Lyubov Lvovna, was a mathematics teacher at a technical college. Perelman grew up in a Jewish family and had a younger sister, Elena, who also became a mathematician.

His parents encouraged mathematics, logic, chess, and music. He learned to play the violin and joined a mathematics circle directed by Sergei Rukshin, who helped prepare talented students for advanced study. Perelman won a gold medal with a perfect score at the 1982 International Mathematical Olympiad in Budapest, an achievement that enabled his admission to Leningrad State University without the usual entrance examination.

Education

Perelman attended Special Mathematics and Physics School No. 239 in Leningrad from 1980 to 1982. The school was part of the Soviet system of specialized institutions developed to cultivate advanced ability in mathematics and physics.

He studied mathematics at Leningrad State University from 1982 to 1987. The university, founded in the eighteenth century and later named for Andrei Zhdanov during the Soviet period, was one of the Soviet Union's major centers of higher education and scientific research. Perelman's undergraduate work was influenced by mathematicians including Viktor Zalgaller and Aleksandr Danilovich Aleksandrov.

From 1987 to 1990 he pursued graduate work at the Steklov Institute of Mathematics in Leningrad, defending a thesis on saddle surfaces in Euclidean spaces in 1990. The Steklov Institute, established in Moscow in 1934 and later expanded through a Leningrad branch, was a leading Soviet institution for pure mathematics and mathematical physics. Aleksandrov was formally associated with his supervision, while Yuri Burago played a major practical role in his graduate training.

Career

Perelman began his research career at the Leningrad branch of the Steklov Institute of Mathematics. His early work concerned convex geometry, Aleksandrov spaces, and geometric analysis. In 1990 he spent several months at the Institut des Hautes Études Scientifiques near Paris, where he worked with Mikhail Gromov on spaces of curvature bounded below. IHES is an independent research institute known for fundamental work in mathematics and theoretical physics.

During the early 1990s Perelman held research fellowships and visiting positions in the United States. He worked at the Courant Institute of Mathematical Sciences of New York University and at the State University of New York at Stony Brook in 1992–1993, and was a Miller Research Fellow at the University of California, Berkeley, from 1993 to 1995. These institutions were major American centers for mathematical research, particularly in analysis, geometry, and mathematical physics.

Perelman returned to the Steklov Institute in Saint Petersburg in 1995 and became a senior researcher. His work in the 1990s included a proof of the soul conjecture of Cheeger and Gromoll and important research on Alexandrov spaces and manifolds of positive Ricci curvature.

In November 2002 he posted The Entropy Formula for the Ricci Flow and Its Geometric Applications as an electronic preprint. Two further preprints, Ricci Flow with Surgery on Three-Manifolds and Finite Extinction Time for the Solutions to the Ricci Flow on Certain Three-Manifolds, appeared in 2003. Together, the papers supplied the central analytic and geometric steps in the proof of the Poincaré conjecture and also established the Thurston geometrization conjecture for three-manifolds. The work built on Richard Hamilton's Ricci-flow program while introducing new monotonicity and singularity-analysis methods.

Perelman lectured on his work at institutions including the Massachusetts Institute of Technology, the State University of New York at Stony Brook, Columbia University, and Princeton University in 2003. He declined professorships offered by several universities and resigned from the Steklov Institute in December 2005, saying that he was disappointed in mathematics and wanted to try something else. His subsequent professional activities have not been publicly documented in comparable detail.

Achievements

• Perelman proved the Poincaré conjecture by developing decisive parts of the Ricci-flow program for three-manifolds. The conjecture, formulated by Henri Poincaré in 1904, asks whether every simply connected closed three-manifold is topologically equivalent to a three-dimensional sphere.

• Perelman's work also established the Thurston geometrization conjecture for three-manifolds, a broader framework that classifies three-dimensional spaces according to geometric structures.

• His research introduced major advances in the analysis of Ricci flow, including entropy methods and techniques for controlling geometric singularities.

Works

• paper

  • Finite Extinction Time for the Solutions to the Ricci Flow on Certain Three-Manifolds

    (Perelman's third major preprint proved finite-time extinc...)

    2003
  • Proof of the Soul Conjecture of Cheeger and Gromoll

    (Perelman's 1994 work proved the soul conjecture of Cheege...)

    1994
  • The Entropy Formula for the Ricci Flow and Its Geometric Applications

    (Perelman's first 2002 Ricci-flow preprint introduced a mo...)

    2002
  • Perelman's Solution of Poincare Conjecture | Clay Mathematics Institute

    (The Clay Mathematics Institute's account of Perelman's so...)

    2002
  • Ricci Flow with Surgery on Three-Manifolds

    (Perelman's second major Ricci-flow preprint constructed R...)

    2003
  • A D Aleksandrov spaces with curvatures bounded below

    (A joint paper by Perelman, Yuri Burago, and Mikhail Gromo...)

    1992

Religion

Perelman was born into a Jewish family and is identified with Judaism. His childhood and early mathematical education unfolded in the Soviet Union, where Jewish identity existed within a formally secular state and could affect access to some institutions and opportunities.

His parents supported his education, while his mother worked as a mathematics teacher and his father encouraged mathematical and logical problem-solving. Public accounts do not establish a detailed account of Perelman's religious practice or theology.

Views

Perelman's documented professional conduct reflects a strong preference for mathematical work over public recognition, institutional status, and financial reward. He declined the Fields Medal and the Clay Millennium Prize, and his explanations emphasized concerns about the distribution of credit and his dissatisfaction with aspects of the mathematical community.

His research philosophy was closely connected with geometric analysis: he used analytic evolution equations, especially Ricci flow, to study the global structure of three-dimensional spaces. This approach linked differential geometry, topology, and partial differential equations.

Personality

Accounts by colleagues and biographers describe Perelman as highly private, austere, intellectually demanding, and resistant to conventional academic status. His resignation from the Steklov Institute and refusal of major honors demonstrated a sustained detachment from publicity, wealth, and professional recognition.

Interests

• Chess, violin, and classical music.

• Music & Bands

  Classical music and opera were part of his family environment; his mother took him to the opera, and he learned to play the violin.

Connections

Perelman's parents were Yakov Perelman, an electrical engineer, and Lyubov Lvovna, a mathematics teacher. His younger sister, Elena Perelman, also became a mathematician.

Richard Hamilton's Ricci-flow research provided the framework that Perelman developed in his work on the Poincaré and geometrization conjectures. Perelman attended Hamilton's lectures during his time in the United States and later acknowledged Hamilton's contribution to the broader breakthrough.

Father:

Yakov Perelman

Electrical engineer and Perelman's father.

Mother:

Lyubov Lvovna

Mathematics teacher at a technical college and Perelman's mother.

Sister:

Elena Perelman

Mathematician and Perelman's younger sister.

colleague:

Richard Hamilton

Hamilton's Ricci-flow program provided an important foundation for Perelman's work on the Poincaré and geometrization conjectures.

References

• Grigori Yakovlevich Perelman (1966 - ) - Biography - MacTutor History of Mathematics Biographical account covering Perelman's family, education, research career, work on Alexandrov spaces, proof of the Poincaré conjecture, and declined honors.
• Poincaré Conjecture - Clay Mathematics Institute Institutional account of the Poincaré conjecture, Perelman's 2002 and 2003 preprints, and the relationship between the Poincaré and Thurston geometrization conjectures.
• Fields Medal - International Mathematical Union International Mathematical Union record identifying Perelman as a 2006 Fields Medal recipient and noting that he declined the award.
• Press Release of March 10, 2010 Clay Mathematics Institute press release announcing the Millennium Prize for Perelman's resolution of the Poincaré conjecture.
  2010
• The Puzzling Case of Grigory Perelman Feature article discussing Perelman's mathematical achievement, withdrawal from public academic life, and refusal of major honors.
• Perelman biography Earlier University of St Andrews biographical page documenting Perelman's education, research appointments, publications, and mathematical achievements.
• Grigory Perelman Biography Biographical reference account describing Perelman's early life, education, career, and work on the Poincaré conjecture.
• Grigori Perelman - Mathematician Biography, Facts and Pictures Biographical reference account describing Perelman's life and mathematical work, including his 1966 birth in Leningrad.