In his axiomatization of set theory, “one can divine the germ of von Neumann’s future interest in computing machines,” says Ulam, speaking with hindsight from 1958. “The economy of the treatment seems to indicate a more fundamental interest in brevity than in virtuosity for its own sake. It thereby helped prepare the grounds for an investigation of the limits of finite formalism by means of the concept of ‘machine.’ ”33 Von Neumann’s style was now set. He would approach a subject, identify the axioms that made it tick, and then, using those axioms, extend the subject beyond where it was when
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