FACES OF MATHEMATICS

Michael
Atiyah

Professor Sir Michael Atiyah

University of Edinburgh

Michael Atiyah has made fundamental contributions to many areas of mathematics, but especially to topology, geometry and analysis. From his first major contribution -- topological K-theory - to his more recent work on quantum field theory, Atiyah has been influential in the development of new theoretical tools and has supplied far-reaching insights. He is a notable collaborator, with his name linked with other oustanding mathematcians through their joint research. He was awarded a Fields Medal in 1966, has been President of the Royal Society and Master of Trinity College, Cambridge. Atiyah has been the recipient of many honours and awards, including a a knighthood in 1983 and the Order of Merit in 1992.

"I think it is true that most people know that there is research in physics and chemistry -- there are new thing to be discovered -- but that they view mathematics as a working language that has been worked out once and for all by the Ancient Greeks, with a few bits by Sir Isaac Newton, and that what they learnt at school was mathematics. So how can you go on doing mathematics? People ask me ``What do you do? How can you discover theorems?'' It is a very difficult concept that it is still developing. People think of it as a language that has all been written down.

"I was always very attracted to geometry: I liked geometry because of its concrete nature, but I realised that you had to apply a variety of tools in order to make progress. That became the guiding thread through most of my subsequent life. I'm still doing geometry in the broad sense, but I discovered that to do geometry you had to do almost everything else as well: you get involved with topology, differential geometry, algebra, mathematical physics, you name it: but in some sense I still regard myself as a geometer.

"Most of my mathematics takes place in my head: I don't write much on paper, not until it is all finished, and then as you're trying to go through it all and organise it, you explain it to somebody else, and that naturally evolves into a discussion, and then you focus on particular problems, and so on. Mathematics is normally a solitary exercise. You sit and you think hard for an hour. It gets a bit boring, so a bit of social interaction adds a whole new dimension and makes life so much more interesting and attractive. Some people don't collaborate and work by themselves, but I find interaction one of the satisfying parts."

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