You are the world's cleverest man. You have solved one of maths' most intractable problems. Do you a) accept a $1m reward, or b) reject the money, barricade yourself inside your flat and refuse to answer the door? The answer, if you are the reclusive Russian genius Grigory Perelman, is b).

The Clay Mathematics Institute in Cambridge, Massachusetts, last week honoured Perelman for his solution to a problem posed almost a century ago by French mathematician Henri Poincaré. The theorem – known as Poincaré's conjecture – involves the deep structure of three-dimensional shapes. It is one of seven elusive challenges set by the institute, each carrying a $1m reward. It took the world's leading mathematicians several years to verify that Perelman had definitively solved the problem in a paper published in 2002.

Perelman, however, doesn't want the cash. This latest snub follows his refusal in 2006 to collect the maths equivalent of an Oscar, the Fields Medal. Perelman is currently jobless and lives with his mother and sister in a small flat in St Petersburg. (He has his own spartan one-bedroom flat, allegedly full of cockroaches, but rarely uses it.)

Perelman refuses to talk to the journalists camped outside his home. One who managed to reach him on his mobile was told: "You are disturbing me. I am picking mushrooms." The handful of neighbours who have seen him paint a picture of a scruffily dressed, unworldly eccentric. "He always wears the same tatty coat and trousers. He never cuts his nails or beard. When he walks he simply stares at the ground, rather than looking from side to side," one told a Moscow newspaper.

"He has rather strange moral principles. He feels tiny improper things very strongly," says Sergei Kisliakov, director of St Petersburg's Steklov Mathematics Institute, where the maths prodigy once worked as a researcher.

According to Kisliakov, Perelman quit the world of mathematics in disgust four years ago. His decision to spurn the Fields Medal may have been driven by a sense that his fellow mathematicians were not worthy to award it. "He severed all contact with the community, and wanted to find a job unrelated to maths," Kisliakov says. "I don't know whether he succeeded in that."