The most mathematical mind

kw: book reviews, nonfiction, biographies, mathematicians

For one to live mathematics, there are certain consequences. Human life is, as Spock frequently said, "Quite Illogical". If ever there was a true Vulcan among us, his name was Grigory Perelman. Further, he is one of the luckiest persons ever; without a series of powerful protectors, he'd never have attained a situation in which he could hear about the Poincaré Conjecture, let alone become the one to prove it.

In the declining days of the U.S.S.R., mathematics became a favored enclave for some very eccentric Russians. Favored because the Party powers could not understand it, and its practitioners were clearly apolitical. Even so, some celebrated mathematicians were disgraced when any whiff of political interest was imputed to them. But many were protected by their very inscrutability, and by the sudden realization, over sixty years ago, that their labors were crucial to the arms race with the West.

The peculiar development of mathematics in Russia is outlined in loving detail by one if its beneficiaries, Masha Gessen, in her biography of another, Grigory (Grisha) Perelman, Perfect Rigor: A Genius + The Mathematical Breakthrough of the Century. This is not just an unauthorized biography; it is one that its subject would almost certainly object to. Perelman lives in his head so deeply that, if something doesn't interest him (and there is very little that does interest him), then it ought not be done, not by him, not by anybody. He has so far lived apart from the world, and now lives in opposition to it. Everything the author learned about him she learned from his acquaintances.

Perelman won several awards and prizes for his breakthroughs in mathematics. The first, many years ago, he declined to receive because he hadn't completed a solution, merely showed how a solution could be achieved. This was a portent. There was one which he did receive, and which led to extended visits to the West, primarily France and America. It was to be the last.

On 12 November 2002, Perelman posted a paper on arXiv and sent a covering email message to a handful of mathematicians whom he deemed competent to judge his work. This paper, accompanied at intervals by two others, completed the proof of the Poincaré Conjecture, a problam posed a century earlier, about whether a sphere of any dimensionality is truly the simplest topological object. He had spent about eight years producing his proof. It took his colleagues a further four to completely confirm it.

In the end, he was offered the Fields Medal and the $1Million Clay Millennium Prize, both of which he turned down. First, considering them politically tainted (he hated politics with the visceral disgust most people reserve for vipers), he refused them with strained politeness. Then, as various persons, including his closest colleagues (it is hard to say if he considered any to be friends) implored him, and tried to arrange a compromise, he reacted with increasing stridency, and finally aggressive vulgarity, and cut himself off from all former associations. His rigid rules include that nobody ought to force friendship, or favor, on another. He is now 44. One wonders what will become of him.

Considering the unique status of mathematics in mid-cold-war Russia, it is likely that, had his talents lain elsewhere—physics or music or writing, for example—he'd have gone nowhere and probably ended up dying in a Gulag. Only someone deeply hidden in the protective bubble of Russian mathematics could survive while at the same time living by rigid internal rules than none other could comprehend. He was more stiffly logical than any Pharisee (as Pharisees are portrayed in the Christian Gospels). Having the added handicap of being a Jew in officially anti-Semitic Russia, it is amazing how favored a life he lived, prior to recent days at least.

In a late chapter, Ms Gessen explores the notion that Perelman may be Aspergian, one "afflicted" with Asperger's Syndrome, also called "high-functioning Autism". He certainly fits the description, to which I can only say, it is unlikely that anyone could have solved the Conjecture who is not Aspergian. One Aspergian, John E. Robison, offers a clue: Learning about and conforming to social niceties takes a certain amount of brain power, probably quite a lot. If one never bothers to do so, whatever the reason, there is more brain power available for intellectual work. This squares with the experience of Aspergians I know. The high incidence of Aspergian tendencies among the most celebrated mathematicians attests to the same notion.

However Perelman came by his formidable mathematical intelligence, his last communication indicates he has decided to develop a different skill set. He simply said he was pursuing new interests. If he can hold out for a few years, and most people forget what he looks like so he doesn't get accosted in the street, he may again emerge, but in what form, only he knows. I wish him well.