American mathematician awarded, together with the British mathematician Sir Michael Francis Atiyah (Atiyah, Sir Michael Francis), the 2004 Abel Prize by the Norwegian Academy of Sciences and Letters for “their discovery and proof of the index theorem, bringing together topology, geometry and analysis, and their outstanding role in building new bridges between mathematics and theoretical physics.”

After graduating with a degree in mathematics from the University of Michigan (Michigan, University of) at Ann Arbor in 1944, Singer had his further education interrupted by a three-year stint in the U.S. Army. Following his discharge, he attended the University of Chicago (Chicago, University of), where he earned a master's degree (1948) and a doctorate (1950), both in mathematics.

In 1950 Singer began his academic career at the Massachusetts Institute of Technology (MIT) in Cambridge, where he taught for the next two years. Although he accepted short-term appointments at the University of California (California, University of), Los Angeles, Columbia University in New York City, and the Institute for Advanced Study in Princeton, N.J., Singer returned to MIT in 1954 and made it his home until 1977, when he left for the University of California, Berkeley. In 1987 he returned once more to MIT, where he finished his career.

In addition to the Atiyah-Singer Index Theorem, Singer made other major contributions to geometry, analysis, mathematical physics, and pedagogy. His Differential Geometry: Lectures (1962) is considered a classic.

Among his many honours, Singer was awarded the Bôcher Prize (1969) and the Steele Prize for Lifetime Achievement (2000), both given by the American Mathematical Society (AMS). Singer also served as vice president of the AMS (1970–72).