zoom_in Click to enlarge

Grigori Perelman

▲ ▼

description Grigori Perelman Overview

Grigori Perelman was a Russian mathematician whose independent work significantly advanced theoretical topology. He is most notably recognized for proving the Poincaré conjecture, a longstanding problem considered one of the greatest mathematical achievements of the 20th century. Perelman's solution utilized complex and innovative techniques, particularly recursion, and remains influential within the field. His dedication to pure mathematics, combined with his refusal of substantial awards, establishes him as a unique figure for mathematicians and those interested in intellectual rigor and self-directed research.

help Grigori Perelman FAQ

What is the Poincaré conjecture that Grigori Perelman proved?

Henri Poincaré's 1904 conjecture states that every simply connected, closed three-dimensional manifold is homeomorphic to the three-dimensional sphere—meaning any three-dimensional shape without holes can be continuously deformed into a sphere. Perelman proved this using a technique called Ricci flow with surgery, building on earlier work by Richard Hamilton.

Did Grigori Perelman refuse the Fields Medal and the Millennium Prize?

Yes, Perelman declined the Fields Medal in 2006, considered mathematics' highest honor, and also refused the Clay Mathematics Institute's one-million-dollar Millennium Prize in 2010. He is the only person to have turned down both awards, reportedly citing his disagreement with the mathematical community's ethical standards.

How did Perelman publish his proof of the Poincaré conjecture?

Rather than submitting to a traditional peer-reviewed journal, Perelman posted three preprints on the arXiv online repository between November 2002 and July 2003. The mathematical community then spent several years of intense verification, with groups led by Bruce Kleiner, John Lott, John Morgan, and Gang Tian confirming the proof's completeness.

Where was Grigori Perelman working when he proved the Poincaré conjecture?

Perelman was at the Steklov Institute of Mathematics in St. Petersburg, Russia, when he completed and posted his proof. He had previously spent time at American universities including UC Berkeley in the 1990s before returning to Russia and eventually withdrawing from academic life entirely.