the long term, short term considerations may be of the essence. The German military adaptation of the Enigma might have made it unbreakable; the British version of the Enigma, which has attracted far less attention, had more rotors and a non-reciprocal plugboard, and was apparently invulnerable to German attack. The successful continuation of the Polish work may very well have depended critically on Turing as an individual. It was not that Turing merely played the expert part expected of him. Rather, it was at a time when a distinctly pessimistic attitude prevailed, that Turing took on the Naval Enigma problem precisely because no-one else thought it tractable, and so he could have it to himself. This individualistic approach was also necessary in developing from scratch a suitable statistical theory. Thus, it can well be maintained that the Anglo-American command of the Atlantic battle, crucial in the central strategy of the Western war, was owed to Alan Turing's work. Turing did not create great new fundamental mathematics in this work, but he brought to bear the insights of a deep thinker. The Bletchley Park analysts compared their work with chess problems, and G. H. Hardy had famously called chess problems the hymn tunes of mathematics, as distinct from serious, interesting problems (Hardy 1940). Yet unusually these military hymns had some beauty. In a remarkable comment on an episode in mathematics and war, the contemporary chronicler of the Naval Enigma section ended (Mahon 1945) In finishing this account of Hut 8's activities