Grigori Perelman

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Grigori Yakovlevich Perelman is a Russian mathematician known for major breakthroughs in geometry and topology. He is most famous for proving the Poincaré conjecture, a long-standing question about the shape of three-dimensional spaces, as part of his work on Ricci flow and Thurston’s geometrization conjecture. He posted his ideas online in the early 2000s, and other mathematicians later filled in the details to complete the proofs.

Perelman was born on June 13, 1966, in Leningrad (now Saint Petersburg). He showed exceptional talent in mathematics from a young age, winning a gold medal with a perfect score at the International Mathematical Olympiad in 1982. He earned his PhD from Leningrad State University in 1990, working under Aleksandr Aleksandrov and Yuri Burago. Early in his career he contributed to the study of Alexandrov spaces, a field he helped lay the foundations for with Burago and the geometer Mikhael Gromov.

During the 1990s Perelman spent time in the United States, including brief periods at the Courant Institute (New York University) and the University of California, Berkeley. In 1994 he proved the soul conjecture in Riemannian geometry, a result about spaces with nonnegative curvature. In the early 2000s he developed new techniques for analyzing Ricci flow, a process that deforms geometric shapes, and used these ideas to prove the Poincaré conjecture and to advance Thurston’s geometrization program. His work introduced important concepts such as the noncollapsing theorem and the canonical neighborhoods theorem, which helped resolve how singularities in Ricci flow behave.

Perelman’s papers were concise and highly technical, but they were quickly recognized as groundbreaking. In 2006 the International Mathematical Union offered him the Fields Medal for his contributions to geometry and his innovative insights into Ricci flow, but he declined the prize, saying money and fame were not his goals. He had previously declined another major prize, the European Mathematical Society prize, in 1996. In 2010 he also declined the Millennium Prize for solving the Poincaré conjecture, stating that he did not agree with the awarding process and did not see his work as more deserving than others who helped along the way. He left the Steklov Institute in 2005 and, by 2006, had largely withdrawn from public life and stopped pursuing mathematical research, living in seclusion in Saint Petersburg and avoiding interviews.

Perelman’s work reshaped the field of geometric analysis and topology, providing a solution to the Poincaré conjecture and offering deep new ideas about how geometric spaces evolve. His quiet life and his refusals of major honors have continued to intrigue scholars and the public alike.