While crossing Nebraska on a Greyhound bus, Dr. Dyson was struck by an epiphany: The theories were mathematically equivalent — different ways of saying the same thing. The result was QED. Feynman called it “the jewel of physics — our proudest possession.”

By the time Dr. Dyson published the details in 1949, a doctorate must have seemed superfluous. He was appointed professor of physics at Cornell in 1951. Teaching, he soon realized, was not for him. In 1953, he became a scholar at the Institute for Advanced Study, where he spent the rest of his career.

Dr. Dyson did not begrudge Feynman, Schwinger and Tomonaga the Nobel they received in 1965. “I think it’s almost true without exception if you want to win a Nobel Prize, you should have a long attention span, get hold of some deep and important problem and stay with it for 10 years,” he told The Times Magazine in 2009. “That wasn’t my style.”

He preferred to move from problem to problem, both theoretical and practical. In the late 1950s, consulting for General Atomics in San Diego, he helped design the Triga reactor, which is used for scientific research and nuclear medicine, and worked on Project Orion, which aimed to explore the solar system with an enormous spaceship powered by exploding nuclear bombs.

With the signing of the Limited Nuclear Test Ban Treaty of 1963, Dr. Dyson’s dreams of reaching Saturn by 1970 were put to rest. Despite his disappointment, he came to support the treaty and, sometimes as a member of Jason, an elite group of scientific advisers, consulted with the government on disarmament and defense.

But his interests were not moored to the earth’s surface. Any advanced civilization, he observed in a paper published in 1960, would ultimately expand to the point where it needed all the energy its solar system could provide. The ultimate solution would be to build a shell around the sun — a Dyson sphere — to capture its output. Earthlings, he speculated in a thought experiment, might conceivably do this by dismantling Jupiter and reassembling the pieces.