THERE can’t be many people that would turn down a Nobel prize. So after the International Mathematical Union announced this week that it was awarding what some consider the mathematical equivalent, the prestigious Fields medal, to the Russian mathematician Grigori Perelman, it may seem surprising that Perelman has decided to refuse it. He was supposed to have received the award this week from King Juan Carlos of Spain at the International Congress of Mathematicians in Madrid, but as 91av went to press, he looked set to turn it down.
Perelman was to have been awarded the Fields medal for work made public four years ago that proves a century-old idea about the nature of four-dimensional geometry, the Poincaré conjecture. There is more at stake in Perelman’s snub than wounded pride. In a confusing twist, two Chinese mathematicians, Huai-Dong Cao of Lehigh University in Pennsylvania and Xi-Ping Zhu of Harvard University, published “a first written account of a complete proof” of the Poincaré conjecture in June, according to The Asian Journal of Mathematics, where it appeared. The underlying issue that emerges when you add together Perelman’s work and attitude, the Chinese claims, and the problems of attributing proper credit, is that mathematicians are finding it increasingly difficult to decide whether or not something has been proved.
Proof is supposed to be what sets mathematics apart from the other sciences. Traditionally, the subject has not been an evolutionary one in which the fittest theory survives. New insights don’t suddenly overturn the theorems of the previous generation. The subject is like a huge pyramid, with each generation building on the secure foundations…
