The rarefied world of early 20th-century mathematics seems light years away from today’s PCs and virtual-reality video games. Yet it was a 1936 paper by Cambridge University mathematician Alan M. Turing that laid the foundation for the electronic wonders now crowding into every corner of modern life.

A shy, awkward man born into the British upper middle class in 1912, Turing played a seminal role in the creation of computers. To be sure, many other people contributed, from mathematicians Charles Babbage and Ada Lovelace in the 1830s to Herman Hollerith — whose tabulating company became IBM (IBM ) — at the turn of the century. But it was Turing who made the critical conceptual breakthrough, almost as an aside in a paper he wrote while in his 20s. Attempting to resolve a long-standing debate over whether any one method could prove or disprove all mathematical statements, Turing invoked the notion of a “universal machine” that could be given instructions to perform a variety of tasks. Turing spoke of a “machine” only abstractly, as a sequence of steps to be executed. But his realization that the data fed into a system also could function as its directions opened the door to the invention of software. “He is the one who found the underlying reason why an automatic calculating device can do so many things,” says Martin Davis, professor emeritus of computer science at New York University and a visiting scholar at the University of California at Berkeley.

As basic as Turing’s notion seems today, it was radical in the mid-1930s. But before the first programmable computers were built, Turing got diverted into the war effort. He worked for five years at Bletchley Park, north of London, with dozens of Britain’s brightest minds. Through endless hours and logical deduction, they unraveled the Enigma code used by the Germans to send messages to field commanders and U-boats.

Turing was himself an enigma. He adored maps and chess as a child and survived the brutal boarding school system by withdrawing into eccentricity.

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