The physicist Freeman Dyson, who has died aged 96, became famous within science for mathematical solutions so advanced that they could only be applied to complex problems of atomic theory and popular with the public for ideas so far-fetched they seemed beyond lunacy. As a young postgraduate student, Dyson devised – while taking a Greyhound bus ride in America – the answer to a conundrum in quantum electrodynamics that had stumped giants of physics such as Richard Feynman and Hans Bethe. As an author, guru and apostle for science, Dyson also cheerfully proposed that humans might genetically engineer trees that could grow on comets, to provide new habitats for genetically altered humans.

He had already proposed the ultimate solution to the energy crisis: a sufficiently advanced civilisation would, he argued, crunch up all the unused planets and asteroids to form a giant shell around its parent star, to reflect and exploit its radiation. Science fiction writers were delighted. The first suggestion became known as the Dyson tree. The second is called the Dyson sphere.

He was born in Crowthorne, Berkshire. His father, George Dyson, was a musician and composer, and his mother, Mildred Atkey, a lawyer. The young Dyson reported that his happiest ever school holiday – from Winchester college – was spent working his way, from 6am to 10pm, through 700 problems in Piaggio’s Differential Equations. “I intended to speak the language of Einstein,” he said in his 1979 memoir Disturbing the Universe. “I was in love with mathematics and nothing else mattered.”

He graduated from Cambridge and in 1943 became a civilian scientist with RAF Bomber Command, which experienced hideous losses with each raid over Germany. Dyson and his colleagues suggested that the Lancaster bomber’s gun turrets slowed the plane, increased its burden and made it more vulnerable to German fighters: without the turrets, it might gain an extra 50mph and be much more manoeuvrable.

Bomber Command, he was later to write, “might have been invented by a mad scientist as an example to exhibit as clearly as possible the evil aspects of science and technology: the Lancaster, in itself a magnificent flying machine, made into a death trap for the boys who flew it. A huge organisation dedicated to the purpose of burning cities and killing people, and doing it badly.”

The young Dyson was already convinced of some moral purpose to the universe and remained a non-denominational Christian all his life.

After the second world war he went to Cornell University in New York state to begin research in physics under Bethe, one of the team at Los Alamos that fashioned the atomic bomb.

By 1947, the challenge was one of pure science: to forge an accurate theory that described how atoms and electrons behaved when they absorbed or emitted light. The broad basis of what was called quantum electrodynamics had been proposed by the British scientist Paul Dirac and other giants of physics. The next step was to calculate the precise behaviour inside an atom. Using different aproaches, both Julian Schwinger and Feynman delivered convincing solutions, but their answers did not quite square with each other.

It was while crossing Nebraska by bus, reading James Joyce and the biography of Pandit Nehru, that the young Dyson saw how to resolve the work of the two men and help win them the 1965 Nobel prize: “It came bursting into my consciousness, like an explosion,” Dyson wrote. “I had no pencil and paper, but everything was so clear I did not need to write it down.”

A few days later he moved – for almost all of the rest of his life – to the Institute of Advanced Study at Princeton, home of Albert Einstein and Robert Oppenheimer, the father of the atomic bomb. “It was exactly a year since I had left England to learn physics from the Americans. And now here I was a year later, walking down the road to the institute on a fine September morning, to teach the great Oppenheimer how to do physics. The whole situation seemed too absurd to be credible,” Dyson wrote later.

He went on to deliver a series of papers that resolved the problems of quantum electrodynamics. He did not share in Feynman’s and Schwinger’s Nobel prize. He did not complain. “I was not inventing new physics,” he said. “I merely clarified what was already there so that others could see the larger picture.”