Heins received his bachelor's degree in 1937, his master's degree in 1939, and his Ph.D. in 1940, under Joseph L. Walsh, from Harvard University with thesis Extremal Problems for Functions Analytic and Single-Valued in a Doubly-Connected Region.
[3] He then worked on topological methods from 1940 to 1942 as Marston Morse's assistant at the Institute for Advanced Study in Princeton.
Heins was from 1942 to 1944 an assistant professor at the Illinois Institute of Technology and in 1944–1945 an applied mathematician at the Chief Ordnance Office of the U.S. Army.
[4] His doctoral students include Bernard Epstein and Jang-Mei Wu.
[5] In the academic year 1952–1953 Heins was a Fulbright Fellow at the Sorbonne and in 1979 a visiting professor at the University of Paris VI.