Turing, who had met and impressed von Neumann when he studied in the United States during the mid-1930s, was involved in similar research in Britain. Having spent the war at the Bletchley Park code-breaking center, he worked on the development of a stored-program machine at the National Physical Laboratory in Teddington, before joining the University of Manchester in 1948 and contributing to similar projects there. Brilliant though he was as a theorist, Turing lacked the pragmatism and political guile that proved indispensable to von Neumann.

Critical to von Neumann’s success was his decision to assemble a team with more mathematicians than engineers, thereby reversing the conventional ratio in the hope of creating a culture that would foster bold and original thinking. He was fortunate in being able to choose his colleagues from the gifted émigrés who had fled to the United States from wartorn Europe. Mr. Dyson describes how one couple, the Ulans, ate in cheap cafeterias when they first arrived, being “too impoverished” to afford American restaurants, but having been “too wealthy in Poland to have learned to cook.”

Another coup was to speed up the development process by using existing components, including mass-manufactured vacuum tubes, rather than developing them from scratch as rival teams were doing. I.B.M. adopted a similar approach in 1980 when it completed the design of its best-selling 5150 Personal Computer within a year by building it from parts made by other companies.

Worldly though von Neumann was, his passion was research, not commerce, and the computer’s development was conducted accordingly. His team’s work was fully documented and published immediately, to share the results with fellow mathematicians, scientists and engineers, just as “open source” design projects do today. He and his colleagues also decided against patenting the machine, to ensure that their ideas would be applied as widely as possible.

Good call. When von Neumann left Princeton in 1954 to join the Atomic Energy Commission, his critics ganged up against the computer project, which foundered. By then, numerous copies and adaptations of the original machine were being built, including I.B.M.’s first electronic computer, the 701. And it is through those machines that we continue to benefit from Turing’s visionary thinking and the ingenuity of von Neumann’s team.