Gödel's classic paper of 1931 did not settle Hilbert's Entscheidungsproblem. The young logician Alan Turing took up the problem and, in the course of his attack, conceived the basic principle of the modern computer – the idea of controlling the machine's operations by means of a program of coded instructions stored in the computer's memory. The transition from mathematical logic to electronic hardware took twelve years (1936–1948), and Turing played a central role in this transformation.

In a reference to Turing's famous paper of 1936, “On Computable Numbers, with an Application to the Entscheidungsproblem,” one of the pioneers of the electronic computer, John Womersley, aptly described the new machines as “Turing in hardware” (Womersley, 2005 [1946], 39). With Gödel's (1931) introduction of the idea of representing logical and arithmetical statements as numbers, together with his foundational contributions to recursion theory, the new machines might also be described, in a more distant sense, as “Gödel in hardware.” Gödel himself, however, took little interest in the development of the electronic computer (Wang, 1987, 171).

By what steps did the logicomathematical results of the 1930s lead to the modern stored-program digital computer? The answer offered by computing folklore runs “von Neumann … ENIAC … EDVAC.… Princeton”; the true story is rather different, however. This chapter charts the development of the electronic stored-program digital computer, from the extraordinary Colossus computers built for code breaking during World War II to the first successful run of a stored program in 1948.