TURING, A. 4 ITEMS

i. "Some calculations of the Riemann zeta-function" [in:] Proceedings of the London Mathematical Society, series 3, vol. 3, no. 9, March 1953, pp.99-117. Oxford: Clarendon Press, 1953, original green printed wrappers, (bought from Yelm Books, Whitestone, 1999), [T&W T64; Origins of Cyberspace 938]ii. "The word problem in semi-groups with cancellation" [in:] Annals of Mathematics, second series, vol. 52., no. 2, September 1950, pp.491-505. Princeton: Princeton University Press, 1950, original wrappers, (ownership stamp of M.G.L. Meyer, University of Chicago; bought from Yelm Books, Whitestone, NY, 1999), [T&W T66], slightly brownediii. "A method for the calculation of the zeta-function" [from:] Proceedings of the London Mathematical Society, series 2, vol. 48, 1943, pp.180-197. Oxford: Clarendon Press, 1943, plain green wrappers, (bought from Dailey Rare Books, Los Angeles, 2006), [not in T&W]iv. "Solvable and unsolvable problems" [in:] Haslett, A.W., editor, Science News, vol. 31. London: Penguin Books, 1954, pp.7-23, original paper covers, preserved in cloth folding box, [T&W T63; Origins of Cyberspace 939]8vo

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The first and third papers document Turing's efforts to solve the celebrated mathematical problem known as the "Riemann Hypothesis", a long-standing conjecture originally postulated by Bernard Riemann (1826-1866) in 1859 that that the zeros of the zeta function lie on a certain straight line. Turing realised that a machine could be used to attack the problem. When at Princeton before the war he made unofficial use of the machine shop in the physics department to construct an electric multiplier, a precursor to his later combination of theoretical mathematics and hands-on electronics he would employ at Bletchley Park. In 1939 he tried a new approach having inspected the analogue Liverpool tide prediction machine. He later used the Manchester computer to attempt to solve the same problem. The hypothesis remains unproven. The second paper uses the Turing machine concept to prove that a previously difficult problem in group theory could be reduced to one that the American mathematician Emil Post (1897-1954) had already shown to be unsolvable.

The fourth paper summarises his most theoretical work in computer science to date (a year before his death).