Needed to be longer, the story behind how he solved the problem and his troubles with Yau (the reason he's retired from mathematics and wont accept the prizes it seems) is very interesting indeed, here's an article covering both if you want more info on Perelman and the Poincare conjecture.

http://www.newyorker.com/archive/2006/08/28/060828fa_fact2

Why fail? She got the answer right.

Some people get too worried about how they're perceived if they make a mistake with simple math, so, in her case, I guess the anxiety froze her brain.

Poincaré, a famous french mathematician, once admitted to being terrible at making even the simplest arithmetic operations.