The Mathematician Who Turned Down a Million Dollars

The Poincaré conjecture, proposed by Henri Poincaré in 1904, asks whether every closed three-dimensional space without holes is topologically a sphere. By the late twentieth century it was the most stubborn open problem in topology. The Clay Mathematics Institute named it one of seven Millennium Prize Problems in 2000 and attached $1 million to a verified solution.

In November 2002, a quiet Russian mathematician named Grigori Perelman, working out of the Steklov Institute in Saint Petersburg, posted three papers to arXiv. They built on Richard Hamilton's research program on Ricci flow — a way of smoothing the geometry of a manifold over time — and used it to prove not only the Poincaré conjecture but the broader geometrization conjecture of which it is a special case.

Three independent groups spent the next four years checking the proof line by line. They confirmed it. By 2006 the conjecture was a theorem.

Perelman did not show up for the rewards. In August 2006 the International Mathematical Union awarded him the Fields Medal — the field's highest honour, never previously declined — and he refused, telling IMU president John Ball that the prize was "completely irrelevant for me." In March 2010 the Clay Institute awarded him the $1 million Millennium Prize. He turned it down, saying it was unjust because Hamilton was not being similarly honoured. He also said, more bluntly, that he disagreed with the organised mathematical community.

He quit his job at the Steklov in December 2005 and has lived since with his mother in Saint Petersburg, declining interviews. The most quoted line he has given a journalist who tried to call: "You are disturbing me. I am picking mushrooms."