Scheffé was born in New York City on April 11, 1907, the child of German immigrants.

He graduated in 1924, took night classes at Cooper Union, and a year later entered the Polytechnic Institute of Brooklyn.

[2] Staying at Wisconsin, he married his wife Miriam in 1934 and finished his PhD in 1935, on the subject of differential equations, under the supervision of Rudolf Ernest Langer.

At Princeton, he began working in statistics instead of in pure mathematics, and assisted the U.S. war effort as a consultant with the Office of Scientific Research and Development.

He settled at the University of California, Berkeley from 1953 until he retired in 1974; he took a turn as department chair there as well, from 1965 to 1968.