DeWitt was born on 28 December 1933 in San Jose, California, son of Carl Bryce Seligman, a country doctor, and Honor Pettit Seligman, a teacher of mathematics and Latin. His surname at birth was Seligman but at his father's urging he and his brothers changed their name to DeWitt in the 1950s, a name from their mother's side of the family, as they had encountered mistaken preconceptions while attending High Schools in the eastern United States. His brothers were the theoretical physicist Bryce Seligman DeWitt, Lloyd Lewis DeWitt (1926-1988), who joined the United States Foreign Service and Hiram Pettit DeWitt (b.1936), a teacher. He grew up largely in California, leaving to attend high school at the Putney School in Vermont. He returned to California to enrol at Stanford University, gaining his bachelor's degree in 1955, masters in 1960 and doctorate in 1966, the doctoral thesis being on the cod icefishes of the genus Notothenia. He was one of the last graduate students to be supervised by George Sprague Myers.
