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He was elected to Fellowship of the Royal Society in July 1951, for the work done fifteen years before, but equal originality was on the way: his first successful work on was submitted as a paper that November. Long overlooked, it was a founding paper of modern non-linear dynamical theory.

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At the same time, in 1950, there emerged a clear direction for new thought. Rather than return to classical mathematics, the novel potential of the computer still held his attention, and he became a pioneer of its personal use. For, as he settled in Manchester, buying his own first house at outlying Wilmslow, he had an entirely fresh field in view. It was what he described as the mathematical theory of morphogenesis: the theory of growth and form in biology.

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Upon British declaration of war on 3 September, Turing took up full-time work at the wartime cryptanalytic headquarters, Bletchley Park. The Polish work was limited as it depended upon the very particular way the Germans had been using the Enigma. One of their ideas was embodied in a machine called a Bomba. The way forward lay in Turing's generalisation of the Polish Bombe into a far more powerful device, capable of breaking any Enigma message where a small portion of plaintext could be guessed correctly. Another Cambridge mathematican, W. G. Welchman, made an important contribution, but the critical factor was Turing's brilliant mechanisation of subtle logical deductions.

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Alan Turing — a short biography

Publicly, he sponsored the entry into Britain of a young German Jewish refugee. Secretly, he worked part-time for the British cryptanalytic department, the so-called Government Code and Cypher School. His appointment marked the first scientific input into a hitherto arts-based department. That revolution was caused by the failure of pre-scientific methods to penetrate the mechanical Enigma cipher used by Germany. No significant progress was made, however, until the gift of vital ideas and information in July 1939 from Poland, where mathematicians had been employed on the problem much earlier.

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Besides illustrating the always razor-edge state of the war of wits, this crisis brought about a new ingredient in Alan Turing's experience: electronic technology made its first appearance at Bletchley Park as telephone engineers were pressed into an effort to gain ever higher speeds of mechanical working. As it turned out, however, the electronic engineers found themselves called upon to mechanize the breaking of the 'Fish' material: messages enciphered on the quite different system used for Hitler's strategic communications. Here again Turing's statistical ideas underlay the methods employed, though it was M. H. A. Newman who played the organising role. The conjunction of Turing's thoughts with the practicality of large-scale electronic machinery, arising from this technical U-boat Enigma change, came to have momentous consequences.

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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.

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By 1942 Alan Turing was the genius loci at Bletchley Park, famous as 'Prof', shabby, nail-bitten, tie-less, sometimes halting in speech and awkward of manner, the source of many hilarious anecdotes about bicycles, gas masks, and the Home Guard; the foe of charlatans and status-seekers, relentless in long shift work with his colleagues, mostly of student age. To one of these, Joan Clarke, he proposed marriage, and was gladly accepted. But then he retracted, telling her of his homosexuality.