Grigory Perelman left his job as a researcher at the Steklov Institute of Mathematics, in St. Petersburg, last December; he has few friends; and he lives with his mother in an apartment on the outskirts of the city. Although he had never granted an interview before, he was cordial and frank when we visited him, in late June, taking us on a long walking tour of the city. “I’m looking for some friends, and they don’t have to be mathematicians,” he said.