جائزة نوبل و علاقة بروفيسر مايكل عطية بالسودان

'I'm a bit of a jack of all trades'

There's no Nobel prize for maths, but Sir Michael Atiyah has won the next best thing. James Meek finds out what goes on inside the mind of a brilliant mathematician

Wednesday April 21, 2004
The Guardian


Sir Michael Atiya

It doesn't matter how brilliant you are as a mathematician: you will never win the Nobel prize for maths, because there isn't one. There is, however, an N Abel prize, and Sir Michael Atiyah, who is a brilliant British mathematician, has won it. Sitting on a sofa in his big apartment, on a high floor of a modern block in the professorial quarter of south Edinburgh, Atiyah underplays the Nobel-sized bounty that comes with the prize: £480,000, which he will share with his fellow winner, Isadore Singer of the US. "If they'd given me this prize when I was younger, it would have been very useful," he says. "At my stage of life I don't know what I'm going to do with it. I'll probably use it for good causes. I'll probably give a little party."
Atiyah, who will be 75 tomorrow, won the most prestigious prize in maths, the Fields Medal, in 1966. "But it doesn't carry much money, and these days if a prize doesn't carry much money it doesn't get noticed," he says. Now he has the prestige prize and the money prize. Strictly speaking, it is called the Abel prize, after the 19th-century Norwegian mathematician Niels Abel. Since his first initial was "N", though, it seems reasonable to call it the N Abel prize.

The prize was awarded for the Atiyah-Singer Index Theorem, which the two men arrived at 40 years ago, and have worked on ever since. The citation said that the theorem is "one of the great landmarks of 20th-century mathematics, influencing profoundly many of the most important later developments in topology, differential geometry and quantum field theory." But what is it?

A bridge, says Atiyah, bringing together all the separate fields of maths - algebra, geometry, calculus, trigonometry, together with their myriad applications in economics, engineering and physics. "I'm a bit of a jack of all trades, I suppose. I don't specialise in any one. I pick up a bit here, a bit there, and if I find a connection between them, I get excited."

In 1990, Atiyah published a book called The Geometry and Physics of Knots, just as physicists were, with the help of his theorem, unravelling the mysteries of string theory, which promises to explain how the universe is made. Atiyah's knots were the kind you might tie with everyday string. String theory deals with invisible, conceptual, cross-dimensional items which physicists now believe underlie all matter. But the charm of maths, and Atiyah's bridge, is that his findings about ordinary knots could be used to illuminate the physicists' findings about cosmic "strings".

Atiyah's mother was Scottish. His father's family were Arabs, Anglophile Lebanese Christians who left the Ottoman empire for the British empire in the 19th century. His grandfather came to Khartoum in Sudan with General Kitchener. The young Atiyah grew up in imperial Khartoum in the 1930s and 1940s, where his father, Edward, worked as a liaison official between the Sudanese and the colonial authorities.

"My father's main dream was to go to Oxford. He wanted to convert himself into an Englishman," says Atiyah. "It didn't quite work out. When he came back to Sudan, he found he wasn't part of the English class structure, he was regarded as one of the lower classes, although he was Oxford-educated and regarded himself as culturally English. That turned him over a bit. He became an Arab nationalist to some extent. All his life was divided between wanting passionately to be English and yet sympathising with the Arab political position within the British empire."

Atiyah felt the same sense of divided loyalty. After a few years at the tiny Diocesan school in Khartoum he went to boarding school in Cairo. To the dismay of fellow pupils he was always trying to, "identify myself with the English ... I was wanting to pull myself away from the Arab background." Even though he spoke Arabic fluently, written Arabic was the only school subject he ever failed in.

At the end of the war, the family moved to England. After two years at Manchester Grammar School and two years' national service in the army, Atiyah went to Cambridge. Although his father used to joke that as a child Atiyah had an uncanny facility for making a profit when converting his pocket money from one currency to another, Atiyah does not remember any mathematical epiphany in his teens. He has a poor memory, he says, which is one of the reasons why he picked maths.

"Medicine, you've got to learn all this anatomy; law, you've got to learn all these legal cases; history, you have to read vast numbers of books. Mathematics - very few facts. That's why people with mathematical talent can do something very young, very early, they can soar off, they don't need to be burdened with vast amounts of facts. A few key things and off you go."

Atiyah uses images from the language of travellers to explain to lay people what it is like inside the mind of a brilliant mathematician. He talks about the journey to his greatest work in terms of a mountaineer. By exploring the whole country of maths, he says, "you get to the top of Mount Everest and look round. It's a long route, and when you get to the top, it's a big scene you can see."

Most of his work, he says, is pure thought. "I'm not the sort of person who does my mathematics writing on paper. I do that at the last stage of the game. I do my mathematics in my head. I sit down for a hard day's work and I write nothing all day. I just think. And I walk up and down because that helps keep me awake, it keeps the blood circulating, and I think and think.

"The main thrust of your thinking can only take place in big chunks of time, not only for hours but for days, weeks, you carry these ideas with you. You go out for a walk and you take your ideas with you. You go on a bus, you take a train, even when you go to sleep you wake up in the morning and you've got this enormously complicated set of ideas with you for long periods, maybe even for a year or two."

Vision is the key. Atiyah points out that, in the apparent banality of looking round a living room and identifying things, the brain is doing something extraordinary. "I look at this room, I see bookshelves, a piano, carpets. It's the same with mathematics. I look at a lot of mathematical things, I see how they are all related. You don't just see them - you've got to know what they mean, you've got to give significance to them. The brain has a really fantastic ability to do that.

"Vision is an enormously complicated process involving at least a dozen parts of the brain, each of which recognises something; one recognises a horizontal line, one recognises perspective, one recognises colour, one recognises motion. Somehow they're all integrated together ... You can't really visualise four dimensions or five dimensions but you get a rough idea of what it's like by comparison with three."

In 1955, Atiyah joined Princeton's Institute for Advanced Study, the gathering point for the most brilliant mathematical minds in the US. It was Albert Einstein's final academic home; he died a few months before Atiyah arrived. The institute's head was Robert Oppenheimer, the father of the atom bomb, who had been victimised by the McCarthy anti-communist witch hunt the previous year. Atiyah says these cold-war shadows, and scientists' responsibility for creating nuclear weapons, did not touch him then. "Ours was the first generation to have the mushroom cloud over our lives, so it was a very unsettled period internationally. But Princeton was a very ivory-tower place, a small intellectual retreat, very Europeanised. It wasn't like New York or Washington, it wasn't in the midst of the maelstrom ... we didn't discuss politics, although we were all concerned."

Decades later, after a stellar career of work, teaching, awards and professorships at Oxford, Princeton and Edinburgh, Atiyah returned to the issue of nuclear weapons. As president of the Royal Society in 1995, he made an unusually harsh attack on Britain's ownership of a nuclear arsenal. As a result, he was asked by Joseph Rotblat to become president of the Pugwash disarmament conferences. His views on Britain's nuclear weapons remain strong. "It was a crazy, misguided, post-imperial attempt to maintain British status. It wasted an awful lot of resources in terms of scientific manpower. Instead of doing what the Germans and Japanese did and turn out motor cars and become wealthy, we poured it down the drain."

His convictions culminated last year in Atiyah taking part in a political demonstration for the first time in his life. He marched in Edinburgh with thousands of other protesters against the invasion of Iraq.

The "war on terror", as presently run, is a self-perpetuating engine, he argues, turning out as many or more terrorists than it destroys or arrests. "I think Tony Blair really is in a terrible, terrible dilemma. So, of course, is George Bush, but George Bush you can make allowances for: he's just stupid. And Tony Blair is smart, and it's much more difficult to understand why he's driven himself into this position.

"The real fundamental cause of these things arises out of the Israeli-Palestinian problem. Much more generally, it's the influence of the west on its former colonies. The impact of the west is very complicated, some plus, some minus, but what's being implemented now is the negative part, imposing western power for economic, political, strategic reasons, which I think more and more leads to hostility, and the Israeli-Palestinian thing is at the core of that. As long as that's not stopped in a satisfactory way, the problem will continue. It is the terrible irony of the world that the Jews suffered terribly during the war in the Holocaust, and now are in some senses the cause of the next Holocaust."




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