Fieldsmedaljen (
1990)
The MacArthur Fellows Program (
1982)
Isaac Newton Medal (
2010)
[14]Lorentz-medaljen (
2010)
[15]Harveyprisen (
2005) (statsborgerskap:
USA)
[16]Oskar Klein-medaljen (
1998)
[17]Henri Poincaré Prize (
2006) (sammen med: Ljudvig Faddejev, David Ruelle)
[18]Fundamental Physics-prisen (
2012)
[19]National Medal of Science (
2002)
[20]Josiah Willard Gibbs Lectureship (
1998)
[21]Albert Einstein World Award of Science (
2016)
[22]Alan T. Waterman Award (
1986)
[23]Kyotoprisen for naturvitenskapelig grunnforskning (
2014)
[24]Fellow of the American Physical Society
Albert Einstein-medaljen (
1985)
Dannie Heinemanprisen for matematisk fysikk (
1998)
[25]Diracmedaljen (
1985) (sammen med: Jakov Zeldovitsj)
[26]Crafoord Prize in Mathematics (
2008) (arbeidsområde:
matematikk, statsborgerskap:
USA)
[27]Nemmers Prize in Mathematics (
2000)
Medlem av American Academy of Arts and Sciences Fellow
Honorary doctor of the Chinese Academy of Sciences (
2016)
[28]Utenlandsk medlem av Royal Society (
1999)
[29][30]Æresdoktor ved Harvard University (
2005)
[31]Clay Research Award (
2001) (sammen med: Stanislav Smirnov)
Golden Plate Award (
1997)
[32][33]APS Medal for Exceptional Achievement in Research (
2016)
[34]CrafoordprisenFellow of the AAAS (
2019)
[35]Fellow of the American Mathematical Society (
2013)
[12][13]Clarivate Citation Laureates (
2002) (arbeidsområde:
fysikk)
[36]James Madison-medalje (
1993)
[6]