Shulman graduated from Columbia University in 1943, and joined the United States Navy Reserve. He achieved his PhD at Columbia in 1949, and became a fellow at California Institute of Technology. From 1953 to 1979, he worked at Bell Labs, eventually becoming head of the Biophysical Research staff.
Shulman joined the faculty at Yale in 1979. He was a Guggenheim Fellow in 1962. He is a member of the National Academy of Sciences.