Grigory Perelman, a reclusive mathematician, solved the long-standing Poincaré conjecture.
This beautiful New Yorker article gives a layman's perspective on it all as well as a fascinating insight into the psychology and politics at the highest echelons of mathematics.
Anyway, it is so famous and difficult that the problem was one of the seven selected for a $1m Millenium prize.
However, Professor Perelman has, according to this article, turned down the prize money, despite living unemployed in a cockroach infested 1 bedroom flat, saying "I have all I want."