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... 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. Newman that a further question, posed by Hilbert. It was the question of Decidability, the Entscheidungsproblem. Could there exist, at least in principle, a definite method or process by which it could be decided whether any given mathematical assertion was provable? To answer such a question needed a definition of 'method', which would be precise. Turing supplied this. He analysed what could be achieved by a person performing a methodical process, and seizing on the idea of something done 'mechanically', expressed the analysis in terms of a theoretical machine able to perform certain precisely defined elementary operations on symbols on paper tape. His work introduced a concept of practical significance, the idea of the Universal Turing Machine. ...