Grigori Perelman
Native spelling: Григорий Яковлевич Перельман
fl. 1966, Leningrad, Soviet Union (now Saint Petersburg, Russia)
Russian mathematician who proved the Poincaré and geometrization conjectures in 2002–2003 using Ricci flow with surgery, then declined both the Fields Medal (2006) and the Clay Millennium Prize (2010).
Grigori Perelman was born in Leningrad and won a perfect score gold medal at the 1982 International Mathematical Olympiad. He studied at Leningrad State University and worked at the Steklov Institute of Mathematics, also holding research positions in the United States in the early 1990s before returning to Steklov.
Between November 2002 and July 2003, Perelman posted three papers to arXiv presenting a proof of Thurston's geometrization conjecture, which classifies all closed 3-manifolds and implies the Poincaré conjecture (that every simply connected closed 3-manifold is homeomorphic to the 3-sphere) as a special case. Building on Richard Hamilton's programme of Ricci flow, Perelman introduced an entropy functional, a no-local-collapsing theorem, and a surgery procedure to handle singularities, allowing the flow to be continued until the manifold's structure could be classified. After several years of verification by other mathematicians confirmed the proof was correct, this resolved a problem open since 1904 and one of the seven Clay Millennium Prize Problems.
In August 2006 Perelman was awarded the Fields Medal, becoming the first person to decline it. In 2010 the Clay Mathematics Institute awarded him the one-million-dollar Millennium Prize; Perelman declined this too, saying the decision was unfair to Hamilton's foundational contribution and criticising the standards of the mathematical community. He left the Steklov Institute in 2005 and withdrew from mathematics and public life, living privately in Saint Petersburg.
Workplaces: Steklov Institute of Mathematics, Saint Petersburg
Russia