Below is a sample of work produced by Dyson between the ages of 5 and 9.
The following is from a 2005 Dyson email; we later had an extended correspondence about whether the gravitational field need be quantized and whether black holes were the most efficient graviton detectors.
...Thank you very much for sending me your four papers. I read three of them and will soon read the fourth. All interesting. But to me the most interesting is the discrete Hilbert Space paper, especially your reference  proving that lengths cannot be measured with error smaller than the Planck length. I was unaware of this reference but I had reached the same conclusion independently.
From the Times profile:
NYTimes: ...During World War II, Dyson worked for the Royal Air Force at Bomber Command, calculating the most effective ways to deploy pilots, some of whom he knew would die. Dyson says he was “sickened” and “depressed” that many more planes were going down than needed to because military leadership relied on misguided institutional mythologies rather than statistical studies. Even more upsetting, Dyson writes in “Weapons and Hope,” he became an expert on “how to murder most economically another hundred thousand people.” This work, Dyson told the writer Kenneth Brower, created an “emptiness of the soul.”
Then came two blinding flashes of light. Dyson’s reaction to Hiroshima and Nagasaki was complicated. Like many physicists, Dyson has always loved explosions, and, of course, uncovering the secrets of nature is the first motivation of science. When he was interviewed for the 1980 documentary “The Day After Trinity,” Dyson addressed the seduction: “I felt it myself, the glitter of nuclear weapons. It is irresistible if you come to them as a scientist. To feel it’s there in your hands. To release the energy that fuels the stars. To let it do your bidding. And to perform these miracles, to lift a million tons of rock into the sky, it is something that gives people an illusion of illimitable power, and it is in some ways responsible for all our troubles, I would say, this what you might call ‘technical arrogance’ that overcomes people when they see what they can do with their minds.”
Eventually, Dyson would be sure nuclear weapons were the worst evil. But in 1945, drawn to these irreducible components of life, Dyson left mathematics and took up physics. Still, he did not want to be another dusty Englishman toiling alone in a dim Cambridge laboratory. Since childhood, some part of him had always known that the “Americans held the future in their hands and that the smart thing for me to do would be to join them.” That the United States was now the country of Einstein and Oppenheimer was reason enough to go, but Dyson’s sister Alice says that “he escaped to America so he could make his own life,” removed from the shadow of his now famous musical father. “I know how he felt,” says Oliver Sacks, who came to New York not long after medical school. “I was the fifth Dr. Sacks in my family. I felt it was time to get out and find a place of my own.”
In 1947, Dyson enrolled as a doctoral candidate at Cornell, studying with Hans Bethe, who had the reputation of being the greatest problem-solver in physics. Alice Dyson says that once in Ithaca, her brother “became so much more human,” and Dyson does not disagree. “I really felt it was quite amazing how accepted I was,” he says. “In 1963, I’d only been a U.S. citizen for about five years, and I was testifying to the Senate, representing the Federation of American Scientists in favor of the nuclear-test-ban treaty.”
After sizing him up over a few meals, Bethe gave Dyson a problem and told him to come back in six months. “You just sit down and do it,” Dyson told me. “It’s probably the hardest work you’ll do in your life. Without having done that, you’ve never understood what science is all about.” This smaller problem was part of a much larger one inherited from Einstein, among others, involving the need for a theory to describe the behavior of atoms and electrons emitting and absorbing light. Put another way, it was the question of how to move physics forward, creating agreement among the disparate laws of atomic structure, radiation, solid-state physics, plasma physics, maser and laser technology, optical and microwave spectroscopy, electronics and chemistry. Many were working on achieving this broad rapport, including Julian Schwinger at Harvard University; a Japanese physicist named Shinichiro Tomonaga, whose calculations arrived in America from war-depleted Kyoto on cheap brown paper; and Feynman, also at Cornell, a man so brilliant he did complex calculations in his head. Initially, Bethe asked Dyson to make some difficult measurements [calculations?] involving electrons. But soon enough Dyson went further.
The breakthrough came on summer trips Dyson made in 1948, traveling around America by Greyhound bus and also, for four days, in a car with Feynman. Feynman was driving to Albuquerque, and Dyson joined him just for the pleasure of riding alongside “a unique person who had such an amazing combination of gifts.” The irrepressible Feynman and the “quiet and dignified English fellow,” as Feynman described Dyson, picked up gypsy hitchhikers; took shelter from an Oklahoma flood in the only available hotel they could find, a brothel, where Feynman pretended to sleep and heard Dyson relieve himself in their room sink rather than risk the common bathroom in the hall; spoke of Feynman’s realization that he had enjoyed military work on the Manhattan Project too much and therefore could do it no more; and talked about Feynman’s ideas in a way that made Dyson forever understand what the nature of true genius is. Dyson wanted to unify one big theory; Feynman was out to unify all of physics. Inspired by this and by a mesmerizing sermon on nonviolence that Dyson happened to hear a traveling divinity student deliver in Berkeley, Dyson sat aboard his final Greyhound of the summer, heading East. He had no pencil or paper. He was thinking very hard. On a bumpy stretch of highway, long after dark, somewhere out in the middle of Nebraska, Dyson says, “Suddenly the physics problem became clear.” What Feynman, Schwinger and Tomonaga were doing was stylistically different, but it was all “fundamentally the same.”
Dyson is always effacing when discussing his work — he has variously called himself a tinkerer, a clean-up man and a bridge builder who merely supplied the cantilevers linking other men’s ideas. Bethe thought more highly of him. “He is the best I have ever had or observed,” Bethe wrote in a letter to Oppenheimer, who invited Dyson to the institute for an initial fellowship. There, with Einstein indifferent to him and the chain-smoking Oppenheimer openly doubting Dyson’s physics, Dyson wrote his renowned paper “The Radiation Theories of Tomonaga, Schwinger and Feynman.” Oppenheimer sent Dyson a note: “Nolo contendere — R.O.” If you could do that in a year, who needed a Ph.D.? The institute was perfect for him. He could work all morning and, as he wrote to his parents, in the afternoons go for walks in the woods to see “strange new birds, insects and plants.” It was, Dyson says, the happiest sustained moment in his life. It was also the last great discovery he would make in physics.