Complex solutions from a strikingly simple genius

Long before John Forbes Nash, the schizophrenic Nobel laureate fictionalised onscreen in A Beautiful Mind, mathematics has been infused with the legend of the mad genius cut off from the physical world and dwelling in a separate realm of numbers. In ancient times, there was Pythagoras, guru of a cult of geometers, and Archimedes, so distracted by an equation he was scratching in the sand that he was slain by a Roman soldier. Pascal and Newton in the 17th century, Gouml;del in the 20th, each reinforced the image of the mathematician as ascetic, forgoing a regular life to pursue truths too rarefied for the rest of us to understand.

Last week, a reclusive Russian topologist named Grigory Perelman seemed to be playing to type, when he refused to accept the highest honour in mathematics, the Fields Medal, for work pointing toward the solution of Poincareacute;8217;s conjecture, a longstanding hypothesis involving the deep structure of three-dimensional objects. He left open the possibility that he would also spurn a 1 million prize from the Clay Mathematics Institute in Cambridge, Massachussetts.

It wasn8217;t so much a medal he was rejecting but the idea that in the search for nature8217;s secrets the discoverer is more important than the discovery.

Mathematics is supposed to be a Wikipedia-like undertaking, with thousands of self-effacing scriveners quietly labouring over a great self-correcting text. Dr Perelman8217;s papers are almost as studded with names as with numbers. 8220;The Hamilton-Tian conjecture,8221; 8220;Kauml;hler manifolds,8221; 8220;the Bishop-Gromov relative volume comparison theorem,8221; 8220;the Gaussian logarithmic Sobolev inequality, due to L. Gross8221;8212;all have left their fingerprints on The Book.

A purist would say that no one person deserves to stake a claim on a theorem. That seemed to be what Dr Perelman, who has said he disapproves of politics in mathematics, was implying. 8220;If anybody is interested in my way of solving the problem, it8217;s all there. Let them go and read about it,8221; he told The Telegraph. 8220;I have published all my calculations. This is what I can offer the public.8221;