Puzzles
A century-old shape puzzle was solved by a mathematician who then refused every prize
In 1904, Henri Poincaré asked whether any three-dimensional space with no holes in it (in a precise topological sense) can always be stretched and deformed into a perfect sphere, the way this is known to be true in two dimensions. It became one of the most famous open problems in mathematics.
Reveal the answer
Yes, it's always possible; Grigori Perelman proved it in 2002-2003 using techniques from geometric analysis. He posted his proof online rather than in a journal, declined the $1 million Millennium Prize awarded for solving it in 2010, and turned down mathematics' highest honor, the Fields Medal, calling the recognition irrelevant to the work itself.
— Grigori Perelman, Poincaré Conjecture — arXiv preprints, 2002-2003