Magazine article The Spectator

The Einstein of Maths

Magazine article The Spectator

The Einstein of Maths

Article excerpt

The odds are that the name Alexandre Grothendieck will mean little or nothing to most Spectator readers. It's a name I heard for the first time in high summer two years or so ago, not long, as I remember it, after the film A Beautiful Mind had come out. I was in the garden of my friend Umar's house in Cambridge, and we were waiting for his ancient cast-iron barbecue, Camp Freddie, to cook some sausages.

Umar is a mathematician of considerable braininess, and when we are together we often end up talking maths. That is, I tend to ask him to explain what he does, and he tends to try, and I tend not to understand. But sometimes we strike gold. An entire afternoon was once passed happily playing logic games involving prisoners with different-coloured hats. I have giggled ignorantly at maths jokes ('What's purple and commutes?' 'An Abelian grape'), hummed and hawed over the question of whether maths is discovered or invented, and been mind-boggled for a week after he explained the concept of the 'cardinality of infinities' (some infinities are bigger than others, it turns out).

By Grothendieck I was riveted. The story, in short, is of a mathematician of staggering accomplishment (in one of the hens'-teeth-rare public references to him he is described as 'the mathematician whose work was to lead to a unification of geometry, number theory, topology and complex analysis') who has retreated, like a Salinger or a Pynchon of number theory, into utter isolation. The most recent cutting dismisses him as 'last heard of raging about the Devil somewhere in the Pyrenees'.

It would not be an exaggeration, I think, to describe Grothendieck as a legendary figure in the mathematical world. Yet if you run a search through the cuttings library of the mainstream press, you will find barely a single mention of his name. Until very recently, even the Internet, that repository of all arcane knowledge, contained little verging on nothing. There was one blurred and out-of-date photograph, a couple of fragments. Nothing at all for the lay reader to go on.

There are, I'd say, two good reasons why this would be so. In the first place, the luminous brilliance of Grothendieck's mathematical achievement - his 1966 Fields Medal, the Nobel Prize of maths, is an indicator - is matched only by the near impossibility of explaining it to anyone without a background in pure maths.

His work - especially in the golden period between 1955 and 1970 - is described as being 'maximally deep'; that is, he was interested in stating his solutions to mathematical problems in the most general way possible, and applying congruences across discrete fields. He used, for example, algebraic geometry to crack number theory - and as Umar puts it, 'number theory was the bigger fish to crack'. The mathematician Leila Schneps - custodian of the newly established website - describes him simply as 'the Einstein of mathematics'.

But there is another reason why he has retreated below the radar of the non-mathematical world. Grothendieck doesn't write popularising books like Stephen Hawking; he doesn't tour American universities lecturing undergraduates; and he doesn't, any more, publish his researches and discoveries in mathematical journals. In fact, 13 years ago, Grothendieck more or less disappeared altogether.

In the Pyrenean village in which he had lived since the 1970s, he burned thousands of pages of manuscript in the garden of his then girlfriend, left on her kitchen table an enormous manuscript copy of a memoir by his mother, and vanished.

The biographical section of the Grothendieck Circle ends in 1991: 'In August, Grothendieck leaves his home suddenly, without warning anyone, for an unknown location. He spends his time writing an enormous work on physics and philosophical meditations on themes such as free choice, determinism and the existence of evil. He refuses practically every human contact.'

Among the few images of him with which we are left, the most recent show a shaven-headed, bespectacled man - in looks not a million miles from Foucault - with the austere grace of a Buddhist monk. …

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