Awards
- Breakthrough Award Composite Prize, 2014
- Knighted in the New Year's Honours List, 2012
- Shaw Prize, 2009
- Nemmers Prize, , 2008
- King Faisal Prize, , 2006
- Polya Prize, London Mathematical Society, 1999
- Crafoord Prize, Swedish Royal Academy of Science, 1994
- Royal Medal, Royal Society, 1990
- Fellow, Royal Society, 1986
- Fields Medal, 1986
- Junior Whitehead Prize, London Mathematical Society, 1984
Editorial Boards
- Duke Mathematical Journal, Member of editorial board