From the American Philosophical Society:
One of the world's greatest living mathematicians, Sir 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, Sir Michael 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 outstanding mathematicians through their joint research … A superb lecturer, he possesses the ability to explain sophisticated mathematics in a simple geometric way ... In 1993 he was awarded the American Philosophical Society's Benjamin Franklin Medal for Distinguished Achievement in the Sciences. The citation read "in recognition of significant contributions to a remarkable range of mathematical topics, which established links between differential geometry, topology, and analysis; and creating useful mathematical tools for physicists."
Fields Medalist, 1966
Abel Prize Laureate, 2004