- Otto Hahn Medal, Max-Planck-Gesellschaft, 1992
- Prix de la Mairie de Paris, Premier Congrès Européen de Mathématiques, 1992
- Henri Poincaré Prize, 1997
- Prize of the International Congress of Mathematical Physics, Brisbane, 1997
- Fields Medal, IMU, ICM Berlin, 1998
- Crafoord Prize, 2008
- Shaw Prize in Mathematical Sciences, 2012
- Fundamental Physics Prize, 2012
- Breakthrough Prize in Mathematics, 2014