Mr. Backus was a bit of a maverick even as a teenager. He grew up in an affluent family in Wilmington, Del., the son of a stockbroker. He had a complicated, difficult relationship with his family, and he was a wayward student.

In a series of interviews in 2000 and 2001 in San Francisco, where he lived at the time, Mr. Backus recalled that his family had sent him to an exclusive private high school, the Hill School in Pennsylvania.

“The delight of that place was all the rules you could break,” he recalled.

After flunking out of the University of Virginia, Mr. Backus was drafted in 1943. But his scores on Army aptitude tests were so high that he was dispatched on government-financed programs to three universities, with his studies ranging from engineering to medicine.

After the war, Mr. Backus found his footing as a student at Columbia University and pursued an interest in mathematics, receiving his master’s degree in 1950. Shortly before he graduated, Mr. Backus wandered by the I.B.M. headquarters on Madison Avenue in New York, where one of its room-size electronic calculators was on display.

When a tour guide inquired, Mr. Backus mentioned that he was a graduate student in math; he was whisked upstairs and asked a series of questions Mr. Backus described as math “brain teasers.” It was an informal oral exam, with no recorded score.

He was hired on the spot. As what? “As a programmer,” Mr. Backus replied, shrugging. “That was the way it was done in those days.”

Back then, there was no field of computer science, no courses or schools. The first written reference to “software” as a computer term, as something distinct from hardware, did not come until 1958.