Perfect Rigour

” Kolmogorov believed that a mathematician who aspired to greatness had to be well versed in music, the visual arts, and poetry, and—no less important—he had to be sound of body

Why, I pleaded, was the king of Spain undeserving of the honor of hanging a medal around Perelman’s neck?
“Who the hell are kings?” Gromov was really cranked up now. “Kings are the same kind of crap as communists. Why should a king give a mathematician his prize? Who is he? He is nothing. From a mathematician’s point of view, he is nothing.

So it is perhaps no accident that the founders of the dissident movement in the Soviet Union16 were mathematicians and physicists. The Soviet Union was not a good place for people who took things literally and expected the world to function in predictable, logical, and fair ways.

“He believes he is the one who decides when he should be getting a prize and when he should not be,” Gromov told me quite simply.

The problems were extremely difficult, and the level of difficulty was increased with little regard for the students’ actual abilities and achievements. “The general concept always was that the carrot should be hanging just barely above the level to which the rabbit could jump,” Golovanov explained to me. “But Grisha believes that the rabbit should always be jumping higher and higher.”

Wrote Mikhail Berg: “Many of us would have wanted to take the school with us after graduation, like a turtle’s armor, because we could feel comfortable only within the confines of its precise and logically understandable rules.”

The joy of feeling my brain rev up, rush toward a solution, reach it, and be affirmed for it felt like love, truth, hope, and justice all handed to me at once.

“There are several stages of teaching,” he said. “There are the student, apprenticeship stages, like in the medieval guild. Then there are the craftsman, the master—these are the stages of mastery. Then there is the art stage. But there is a stage beyond the art stage. This is the witchcraft stage. A sort of magic. It’s a question of charisma and all sorts of other things.”