After being awarded his Ph.D. by MIT, he spent one year as a postdoctoral researcher at the University of California, Berkeley, and then accepted a position at Bell Labs in New Providence, New Jersey. It was there he developed Shor's algorithm, for which he was awarded the Nevanlinna Prize at the 23rd International Congress of Mathematicians in 1998 and the Gödel Prize in 1999. In 1999 he was awarded a MacArthur Fellowship. In 2017 he received the Dirac Medal of the ICTP and for 2019 the BBVA Foundation Frontiers of Knowledge Award in Basic Sciences.