Alan Mathison Turing was born on 23 June 1912, the second and last child (after his brother John) of Julius Mathison and Ethel Sara Turing. The unusual name of Turing placed him in a distinctive family tree of English gentry, far from rich but determinedly upper-middle-class in the peculiar sense of the English class system.

His father Julius had entered the Indian Civil Service, serving in the Madras Presidency, and had their met and married Ethel Sara Stoney. She was the daughter of the chief engineer of the Madras railways, who came from an Anglo-Irish family of somewhat similar social status.

The name of Turing was best known for the work of Julius’ brother H. D. Turing on fly fishing, and had no connection with the scientific or academic worlds. The name of Stoney however was notable for a remote relative, the Irish physicist George Johnstone Stoney (1826-1911), today best known for his identification of the natural units of physical quantities.

Possibly the engineering base of his mother’s family, with its respect for applied science, had some influence, but if so it was subordinated to the demands of class, church and Empire. Certainly the elder brother John F. Turing, who became a London solicitor, showed no sign of it.

By 1933 Turing had already introduced himself to Russell and Whitehead’s Principia Mathematica and so to the then arcane area of mathematical logic. Bertrand Russell had thought of logic as a solid foundation for mathematical truth, but many questions had since been raised about how truth could be captured by any formalism.

In particular, in 1931 Gödel had shattered Russell’s picture by showing the incompleteness of mathematics: the existence of true statements about numbers which could not be proved by the formal application of set rules of deduction.

In 1935, Turing learnt from the lecture course of the Cambridge topologist M. H. A. Newman that a further question, posed by Hilbert, still lay open. It was the question of Decidability, the Entscheidungs problem.

In 1938 Turing was offered a temporary post at Princeton by von Neumann but instead returned to Cambridge. He had no University lectureship; in the year 1938-9 he lived on his King’s College fellowship, as logician and number theorist.

Unusually for a mathematician, he joined in Wittgenstein’s classes on the philosophy of mathematics; unusually again, he engineered gear-wheel parts for a special machine to calculate the Riemann Zeta-function.

On September 1, 1939, Nazi troops invaded Poland. Three days later, Turing reported to Bletchley Park, a Victorian Tudor-Gothic estate northwest of London where the British cipher service had secretly relocated.

He and the other code-breakers arrived at Bletchley under the guise of “Captain Ridley’s Shooting Party” (which had some locals grumbling about able-bodied men not doing their bit in the war). The task they faced was daunting.

Since the use of radio communications in the First World War, effective cryptography—insuring that private messages could be sent via a public medium—had been critical to the military. The Nazis were convinced that their encryption system-based on a machine that looked like a souped-up typewriter, called the Enigma—would play a vital role in their expected victory.