awarded the Fields Medal in 1962 for work in differential topology: he had shown that there are different smooth structures on the 7-dimensional sphere and had also disproved that two triangulations of a space can be made isomorphic by subdivision. He was also the winner of the Wolf Prize in 1989. He won the 2011 Abel Prize ‘for pioneering discoveries in topology, geometry, and algebra’. More recently his interests have been in dynamical systems.