He was one of the founders of K-theory, a branch of topology. He has collaborated with many other mathematicians, for example with Raoul Bott and Isadore Singer on the developments leading to the Atiyah-Singer index theorem. He later turned to an interest in gauge field theories, paving the way for the work of others such as Witten.

In 1966, when he was 37 years old, he won the Fields Medal.

He has been president of the Royal Society, and master of Trinity College at the University of Cambridge.

He is the president of the Pugwash Conferences on Science and World Affairs.