“The work of Perelman on the famous Poincare conjecture is widely admired”
“Mathematics is normally a solitary exercise. You sit and you think hard for an hour”. One might think, wrongly, that these words belong to someone who dislikes mathematics. They were said by Sir Michael Atiyah (born 22 April 1929, London), one of the greatest mathematicians of all time. Atiyah has made fundamental contributions to many areas of mathematics, especially to topology, geometry and analysis. Already his early achievements – the topological ‘K-theory’ and the ‘index theorem’— led to him being awarded a Fields Medal in 1966. Those ideas would later prove essential for some areas of physics, such as elementary particles and cosmology. Atiyah has been the recipient of many honours and awards, including a knighthood in 1983 and the Order of Merit in 1992.

You have said "People think of mathematics as a language that has all been written down". How would you explain to a non-mathematician that mathematics are constantly evolving? What is a 'discovery' in mathematics?

There are good reasons why the general public think that mathematical development stopped several centuries ago, at the level they encountered in high school.
First, mathematics is a very old subject and correct mathematics does not change with time. Euclid's geometry is still right, as is the calculus of Newton and Leibniz, whereas the physics of Aristotle is now only of interest to historians and philosophers. This means that at school students still have to work their way through (parts of) Euclid and Newton, but do not learn the physics of Aristotle. Unless they go on to higher studies in mathematical sciences, they do not encounter more recent work.
But mathematics continues to evolve, often in response to the needs of other disciplines. For example Einstein's modification of Newtonian gravity needed the development of new forms of geometry, going beyond Euclid.
New developments in mathematics, the creation of the successors of Euclid and Newton, gradually filter down and will affect the school curriculum of your children and grandchildren.

Your work has been very important for some areas of physics, such as string theory. Are you interested in the less mathematical (more physical) aspects of this theory? Do you think it is useful as a 'theory of everything'?
I am interested both in the mathematical content of string theory and in its physical interpretation. But it is not yet clear how much of the theory will ultimately explain the real world and how much will be absorbed into mathematics.

Why are mathematicians so comfortable with the notion of the infinite while physicists --if I understand correctly-- tend to think that a theory is not working well when its mathematics has a lot of infinites?
The notion of "the infinite" is one of the oldest and hardest questions in mathematics. Understanding how to interpret and use this notion has been one of the major successes in the history of mathematics. Calculus depends on understanding the infinitely small. At a more elementary level, counting, 1,2,3... can go on for ever (or until you get tired!). This involves an infinite process.
Both mathematicians and physicists use infinity in various ways. The only difference is that we are more careful - they are more courageous (or foolhardy!).

After Perelman’s work, can the Poincare conjecture be considered proven?
The work of Perelman on the famous Poincare conjecture is widely admired. But in mathematical questions of this complexity final judgement is suspended until the complete proof has been written down, scrutinized by the mathematical community and accepted. That stage has not yet come.

When you meet other important mathematicians, do you talk mathematics? Do you often exchange views with other 'maestros' on how mathematics have evolved in recent decades?
Mathematicians always talk among themselves. Sometimes on major issues, sometimes on small technical problems, and sometimes on the World Cup or on gardening - we are human too!

Biography of Sir Michael Atiyah
-------------------------------------------------------
http://www.icm2006.org/press/bulletins/bulletin08