IT WAS inevitable that this week’s award of the Fields medals, mathematics’ highest honour, would be dominated by Grigori Perelman’s refusal to accept his. Perelman’s work on the Poincaré conjecture is of such stature that he would have dominated the headlines whether he had turned up or not. Even so, Perelman’s no-show is small beer compared with other upheavals taking place in mathematics today.
For one thing, mathematicians are struggling to stomach the implications of computer-assisted proofs. For millennia, mathematics has held a unique position: once the truth of a proposition is established, it exists unassailable forever. No other science…
