I was vaguely aware of the story at the heart of this book, so it was interesting to read a full account of it here. In 2002, the Russian mathematician Gregory Perelman solved one of the biggest problems in mathematics. By proving the Poincaré conjecture, he did what numerous top mathematicians had tried and failed to do since 1904. He was awarded the Fields medal (the mathematics equivalent of the Nobel Prize) for the breakthrough; was offered $1 million by the Clay Mathematics Institute, which in 2000 had offered the sum to anyone who could prove the conjecture; and was offered numerous top academic positions. Perelman didn’t react to this in the way most of us would have, however. He turned all of this down, withdrew completely from the mathematics community, and cut contact with long standing friends, now appearing to live a reclusive existence in St Petersburg. In Perfect Rigour, Masha Gessen aims to make sense of this.
For the book, Gessen interviewed many of Perelman’s (previously) close friends, teachers, and colleagues to get an insight into the man. We never hear from Perelman directly (he certainly doesn’t speak to journalists anymore), but from these interviews Gessen is able to build up a picture of the reasons for his retreat into his own world, and his shunning of the mathematics community, and she probably gets close to the truth of the matter.
One aspect of all this is Perelman’s apparent dislike of honours (like Feynman’s, although clearly to a much greater extent). For Perelman, it’s not the money or accolades that matter – he believes in doing maths for its own sake. It’s about the joy of the discovery, of contributing to our knowledge of the world. It shouldn’t be about prizes and there should not be financial incentives, and, because of this deep conviction, Perelman appears not to have taken kindly to the idea that work should be rewarded with material items.
But there are many other factors involved. The accolades that came Perelman’s way appear to have brought to a head a variety of deep-seated dissatisfactions he has had with the way academic mathematics is practised, and, ultimately, with the way the world works. Gessen looks at how Perelman came to have these dissatisfactions, looking in particular at the influence his schooling and upbringing had on him. Gessen is well placed to understand the impact of his early years, as she was also a young maths prodigy in Russia and of the same generation as Perelman.
As an aside, whilst Gessen doesn’t make these comparisons herself, it was interesting throughout the book to note a few similarities between Perelman and others who have made significant breakthroughs. As well as the Feynman comparison above, there’s speculation that Perelman is autistic (with this being suggested as a big factor in why he has acted as he has) and an account of how once, when asked to clarify something he had told an audience during a lecture, he repeated, word for word, what he had said in the first place – Paul Dirac used to do this. There’s also the bemusement Perelman seems to have felt about people praising him whilst not understanding the work he had done. This is reminiscent of how Einstein used to feel about some of the attention he received.
The book’s discussion of the mathematics itself is fairly limited – we get a short explanation of the Poincaré conjecture and a sketch of Perelman’s proof – and unless you have some kind of background in maths (which I don’t), these sections will probably not be hugely illuminating. I’m not sure whether anyone else could have done a better job, though – it’s an abstract problem in topology which does not lend itself to easy explanation.
In any case, you shouldn’t be put off by the difficulty of the maths, which is not the focus of the book. As an exploration of Perelman’s genius and an insight into this remarkable character, this is worth the read.