He was born in Detroit, and received his undergraduate degree from the University of Michigan in 1944. After obtaining his Ph.D. from the University of Chicago in 1950, he went to MIT, where he has spent nearly all his career.
Singer is a member of the National Academy of Sciences and the American Academy of Arts and Sciences. Among the awards he has received are the Bocher Prize (1969) and the Steele Prize for Lifetime Achievement (2000), both from the American Mathematical Society, the Eugene Wigner Medal (1988), and the National Medal of Science (1983).