Grigori Perelman: Ricci Flow Surgery, Poincaré, and a Refused Fields Medal

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Grigori Perelman was born in Leningrad in 1966 to Lyubov, who gave up graduate study in mathematics to raise him and enrolled him at 10 in Sergei Rukshin's after-school math program. At 16 he won gold with a perfect score at the 1982 International Mathematical Olympiad in Budapest. He earned his PhD at Leningrad State University in 1990, held fellowships at NYU's Courant Institute and UC Berkeley, and in 1994 proved the soul conjecture in Riemannian geometry. He turned down offers from Stanford and Princeton and returned to St. Petersburg in 1995 to the Steklov Institute, where he spent about seven years on the Poincaré conjecture, posed by Henri Poincaré in 1904 and tied to William Thurston's geometrization conjecture.

Building on Richard Hamilton's Ricci flow, which stalled at singularities, Perelman showed that singularities take predictable shapes and could be cut out by surgery before the flow continued. He posted the work on the arXiv in November 2002 and March 2003 and lectured at MIT, Princeton and NYU. Three teams spent years checking it, and a 2006 paper claiming the first complete written proof angered many. He resigned from Steklov by the end of 2005, refused the Fields Medal in August 2006, and in 2010 refused the Clay Institute's $1 million Millennium Prize, saying his contribution was no greater than Hamilton's. He withdrew to St. Petersburg and cared for his mother.

• He showed that singularities in the Ricci flow always form either a collapsing cylinder or a collapsing sphere.
• He skipped the journals entirely, writing terse papers aimed at the few experts able to follow them.
• The president of the International Mathematical Union spent 10 hours over two days in St. Petersburg trying to persuade him to take the Fields Medal.
• He said he would not be exhibited like an animal in a zoo, and that conformist mathematicians tolerate the dishonest ones.
• When reporters called about the prize money, he told them he was busy gathering mushrooms.