The Einstein of maths
Sam Leith on Alexandre Grothendieck,
the revolutionary number-cruncher who was last heard of in the Pyrenees
raging about the Devil
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 mindboggled for a week after he explained the concept of the
‘cardinality of infinities’ (some infinities are bigger than others,
it turns out).
Mystery man: Grothendieck
before he disappeared
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 There was one blurred and out-of-date photograph,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
www.grothendieck-circle.org — describes him simply as ‘the Einstein
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. He used,
indeed, to sleep on the floor instead of a bed, but is said to have
mellowed to the extent that he now owns a bed and tends a garden with
enthusiasm. A vegetarian, he presses on his rare visitors armfuls
of apples and figs.
His later work survives in mimeographs and photocopies; his lettres
fleuves — correspondence in French or English, often running to hundreds
of pages, mixing philosophical invective, attacks on rival mathematicians
and, seeded like nuggets in the texts, insights into maths on a very,
very high level.
One of the last members of the mathematical establishment to come
into contact with him was Leila Schneps. Through a series of coincidences,
she and her future husband, Pierre Lochak, learned from a market trader
in the town he left in 1991 that ‘the crazy mathematician’ had turned
up in another town in the Pyrenees. Schneps and Lochak in due course
staked out the marketplace of the town, carrying an out-of-date photograph
of Grothendieck, and waited for the greatest mathematician of the
20th century to show up in search of beansprouts.
‘We spent all morning there in the market. And then there he was.’
Were they not worried he’d run away? ‘We were scared. We didn’t know
what would happen. But he was really, really nice. He said he didn’t
want to be found, but he was friendly. We told him that one of his
conjectures had been proved. He had no idea. He’d stopped being interested
in maths at that stage. He thought his unpublished work would all
have been long forgotten.’
Grothendieck’s first disappearance, in a sense, came in 1970, when
at the very height of his powers he abandoned a post that had been
created for him at the Institute of High Scientific Studies (and which
remains probably the most prestigious tenure in his field of mathematics)
on the grounds that it was partly funded by the military industrial
complex. In 1988, he was awarded the Crafoord Prize. He refused to
Grothendieck’s father was an anarchist who died in Auschwitz; Alexandre,
along with his German mother Hanka, was interned in France during
the war as an ‘undesirable’. These days, what we know of Grothendieck’s
thinking suggests his guiding preoccupation is the problem of evil.
He lives alone and works, for 12 hours a day, on a 50-volume manuscript
which addresses, among other things, the physics of free will.
One story has it that Grothendieck is now convinced that the Devil
is working to falsify the speed of light. Schneps ascribes his concerns
with the speed of light to his anxiety about the methodological compromises
physicists make. He talks constantly, however, about the Devil, semi-metaphorically,
sitting behind good people and nudging them in the direction of compromise,
of the fudge, of the move towards corruption. ‘Uncompromising’ is
the expression Schneps favours.
In his correspondence with Leila Schneps, he told her he would be
willing to share his research into physics with her if she could answer
one question: ‘What is a metre?’
She and Lochak, baffled, took a month to write back — and did so at
length. But before this letter arrived, Grothendieck dispatched three
letters in quick succession. His first letter appeared to threaten
suicide. His second was ‘the warmest, warmest thing ... saying it’s
just amazing anyone cares....’ The third addressed ‘Leila Schneps’
in bitterly sarcastic inverted commas. They found their subsequent
letters returned unopened. ‘We went to see him and he slammed the
door in our faces....’
Has Grothendieck — runs the obvious question — gone mad? Well, possibly.
It all depends on what you mean by ‘mad’.
‘He lives alone and he writes on really deep ideas,’ says Schneps.
‘In the past, what about saints or prophets? Did people think they
had gone mad? He cannot bear to live in the world we’re in.... He’s
certainly abnormal. I could not possibly call him mad. People say
there’s normal and there’s insane. These are not the only two categories....’
‘I never once doubted,’ Grothendieck writes in an early chapter of
Récoltes et Semailles, his philosophical autobiography, ‘that I would
eventually succeed in getting to the bottom of things.’
A more important mathematician than John Nash, a more extraordinary
and horrific back story, and a beautiful, beautiful mind. If anyone
can figure out what a metre is, who is to say that we will not one
day have it back?
© 2004 The Spectator.co.uk