PBK, 1971 Sheldon Traveling Scholarship, 1971-72 Marshall Scholarship, 1972-74 Sloan Fellowship, 1980-83 MacArthur Fellowship, 1986-1991 Cole Prize in Number Theory, AMS, 1987 Fellow of American Academy of Arts and Sciences, 1992 Member of National Academy of Sciences, 2004 Member of American Philosophical Society, 2017