BIOGRAPHY

or be distracted. Other than music and table tennis, Perelman’s entire being was dedicated to mathematics. While recounting Perelman’s obsession, Gessen also provides a fascinating account of Soviet mathematics during the twentieth century, a subject that has rarely been covered in popular science writing. For decades, the Soviets worked in complete isolation, without access to journals and unable to attend international conferences. This meant that the same ideas were often developed twice, independently in the East and the West. Hence, several mathematical concepts are now labelled with double-bar relled names, such as the Chaitin–Kolmogorov complexities or the Cook–Levin theorem.

Although mathematics prospered under communism, the great mathematicians who had earned their reputations before the Revolution were often persecuted. Dimitri Egorov, for instance, was arrested in 1930 and died in exile the following year after a hunger strike. The battle between logical maths and illogical idealism continued with Egorov’s first student, Nikolai Luzin, who was denounced after expressing his view on the latest mathematical breakthrough:

was describing his attempt to solve one of the great problems in mathematics, known as the Poincaré Conjecture. Two more papers were promised, and it appeared that the solitary Russian was claiming a solution to this century-old problem.

The Poincaré Conjecture asks questions about the nature of spheres in higher dimensions. I could go on, but Gessen struggles to explain the conjecture in a chapter, so I am going to shy away from trying to explain it in a paragraph.

Perelman: reluctant celebrity

Although the Poincaré Conjecture is a mind-bending problem, it is easy to appreciate its significance in the world of mathematics, because it was included as one of the Millennium Prize Problems. The philanthropist Landon T Clay had decided to offer seven prizes of $1 million each for the solution to seven great problems of mathematics. So it was not long before news began to leak that Perelman might be the first to claim a Clay prize. This is when Perelman’s solitary pilgrimage towards a proof turned him, in his mind, into a freak show.

It seems the set of natural numbers is not an absolutely objective formation. It seems it is a function of the mind of the mathematician who happens to be speaking of a set of natural numbers at the given moment. It seems there are, among the problems of arithmetic, those that absolutely cannot be solved. Such thoughts were at odds with Soviet ideology.

Perelman was more fortunate. Just as he reached mathematical maturity, the Soviet Union began to crumble, censorship fell away and travel opportunities opened up. He spent time in America, attended conferences and had access to all the journals. He could easily have established himself in one of the top-ranking American universities, but in 1995 he returned to Russia and resumed his life as a hermit.

The stor y broke in the New York Times, and the tabloids followed. Disputes about the proof were outlined in a major feature in the New Yorker. Worst of all, lucrative job offers and the spectre of a $1 million prize made Perelman feel like a nerd celebrity rather than a mathematical hero. The St Petersburg city council considered stationing guards outside his apartment block to deter the constant stream of photographers and journalists. Over the course of two years, a cohort of mathematicians checked the proof and gave it their formal blessing. Having officially solved a Clay problem, Perelman was offered the $1 million prize, but he turned it down. He was also offered a Fields Medal, the equivalent of a Nobel Prize in maths, but he turned that down as well. Moreover, since proving the Poincaré Conjecture, Perelman has removed himself from the mathematical community. In fact, it seems

Seven years later, comp l e t e l y out of the blue, Perelman sent out an email to a dozen American mathematicians that pointed to a preliminary paper he had just published online. To the rest of the world, including most of the mathematical community, the paper would have seemed arcane and deeply technical, but the twelve recipients immediately saw that Perelman

MA in biography Consistently rated ‘excellent’ by external examiners and inspectors The course is taught by Jane Ridley and will be based in London from

October 2010. Available full-time (12 months) or part-time,

by research or as a taught MA. Start October or January. For more information visit our site www.buckingham.ac.uk/london/biography or email jane.ridley@buckingham.ac.uk he has turned his back on the rest of the world, which obviously includes journalists.

This f inal f act makes Masha Gessen’s book remarkable, because she has succeeded in recounting Perelman’s story and providing an insight into his character without ever meeting him, speaking to him on the phone or exchanging emails. To order this book for £11.99, see LR bookshop on page 12

LITERARY REVIEW March 2011

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