George Bergman · CC BY-SA 4.0

Proved the Poincaré conjecture in 2002–2003, resolving a problem that had stood unsolved for nearly a century, by developing new techniques in the analysis of Ricci flow; he had earlier proved the long-open soul conjecture in Riemannian geometry in 1994. In 2006 he declined the Fields Medal, and later turned down the $1 million Millennium Prize awarded for the same proof, saying he wasn't interested in money or fame and didn't want to be "on display like an animal in a zoo."