He is a member of the Norwegian Academy of Science and Letters and the National Academy of Sciences, USA. He won a Lester R. Ford Award in 1966 and again in 1973. He was awarded the National Medal of Science in 1986, the Wolf Prize in 1987, the Abel Prize in 2005 and the Lomonosov Gold Medal in 2013. The American Mathematical Society selected him as its Gibbs Lecturer for 2007. In 2012 he became a fellow of the American Mathematical Society.