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By Root 2247 0

As a high-school student he had worked on the problem of pure number theory known as partitions—a number’s partitions being the ways it can be subdivided into sums of whole numbers: the partitions of 4 are 1 + 1 + 1 + 1, 1 + 1 + 2, 1 + 3, 2 + 2, and 4. The number of partitions rises fairly rapidly—14 has 135 partitions—and the question of just how rapidly has all the hallmarks of classic number theory. It is easy to state. A child can work out the first few cases. And from its contemplation arises a glorious world with the intricacy and beauty of origami. Dyson followed a path trod earlier by the Indian prodigy Srinivasa Ramanujan at the beginning of the century. By his sophomore year at Cambridge he arrived at a set of conjectures about partitions that he could not prove. Instead of setting them aside, he made a virtue of his failure. He published them as only his second paper. “Professor Littlewood,” he wrote of one of his famous professors, “when he makes use of an algebraic identity, always saves himself the trouble of proving it; he maintains that an identity, if true, can be verified in a few lines by anybody obtuse enough to feel the need of verification. My object … is to confute this assertion… .” Dyson promised to state a series of interesting identities that he could not prove. He would also, he boasted, “indulge in some even vaguer guesses concerning the existence of identities which I am not only unable to prove but unable to state… . Needless to say, I strongly recommend my readers to supply the missing proofs, or, even better, the missing identities.” Routine mathematical discourse was not for him.

One day an assistant of Dirac’s told Dyson, “I am leaving physics for mathematics; I find physics messy, unrigorous, elusive.” Dyson replied, “I am leaving mathematics for physics for exactly the same reasons.” He felt that mathematics was an interesting game but not so interesting as the real world. The United States seemed the only possible place to pursue physics now. He had never heard of Cornell, but he was advised that Bethe would be the best person in the world to work with, and Bethe was at Cornell.

He went with the attitude of an explorer to a strange land, eager to expose himself to the flora and fauna and the possibly dangerous inhabitants. He played his first game of poker. He experienced the American form of “picnic,” which surprisingly involved the frying of steak on an open-air grill. He ventured forth on automobile excursions. “We go through some wild country,” he wrote his parents shortly after his arrival—the wild country in this case being the stretch of exurban New York lying between Ithaca and Rochester. He traveled with a theoretician called Richard Feynman: “the first example I have met of that rare species, the native American scientist.”

He has developed a private version of the quantum theory … ; in general he is always sizzling with new ideas, most of which are more spectacular than helpful, and hardly any of which get very far before some newer inspiration eclipses them… . when he bursts into the room with his latest brain-wave and proceeds to expound it with the most lavish sound effects and waving about of the arms, life at least is not dull.

Although Dyson was nominally a mere graduate student, for his first assignment Bethe had handed him a live problem: a version of the Lamb shift, fresh from Shelter Island. Bethe himself had already made the first fast break in the theoretical problem posed by Lamb’s experiment. On the train ride home, using a scrap of paper, he made a fast, intuitive calculation that soon made a dozen of his colleagues say, if only I had … He telephoned Feynman when the train reached Schenectady, and he made sure his preliminary draft was in the hands of Oppenheimer and the other Shelter Island alumni within a week. It was a blunt Los Alamos–style estimate, ignoring the effects of relativity and evading the infinities by arbitrarily cutting them off. Bethe’s breakthrough was sure to be superseded by a more rigorous treatment of the kind Schwinger was known