Intuition and space maps

Yesterday, the Russian mathematician Gregori Perelman declined to appear to receive math's highest honor, perhaps, if you believe this account, because he is "disillusioned" with the discipline.

Perelman has offered a proof of the Poincaré conjecture of French mathematician Henri Poincaré. The conjecture is one of seven famous math problems for which the Clay Mathematics Institute is offering $1million - each - to solve. So far Perelman's proof has withstood the scrutiny of his contemporaries.

Henri Poincaré, who was a prodigious talent and who, according to this, worked from first principles rather than building on the work of others, is said to have remarked that "it is by logic we prove and by intuition we invent." Poincaré suggested a truism about three dimensional manifolds, a subject in topology, that Perelman may have been able to plumb with a hunch of his own.

Orbifolds, which are a kind of manifold, are used by mathematical theorists to suggest the surface of time and dimension as well as the contours of music.

But who knows how he arrived at his conclusions? Perelman is apparently not talking and the reason for his absence from the award ceremony is, like intuition, a mystery.