Pure Mathematics

Alan Mathison Turing (1912-1954) was a brilliant man who made major contributions in several areas of science. Today his name is mentioned frequently in philosophical discussions about the nature of Artificial Intelligence. Actually, he was a pioneer researcher in computer architecture and software engineering; his work in pure mathematics and mathematical logic extended considerably further and his last work, on morphogenesis in plants, is also acknowledged as being of the greatest originality and of permanent importance. He was one of the leading figures in Twentieth-century science, a fact which would have been known to the general public sooner but for the British Official Secrets Act, which prevented discussion of his wartime work.

Published Papers. Equivalence of Left and Right Almost Periodicity.Finite Approximations to Lie Groups. The Extensions of a Group. A Methodfor the Calculation of the Zeta-Function. Rounding-Off Errors in MatrixProcesses. The Word Problem in Semi-Groups with Cancellation. SomeCalculations of the Riemann Zeta-Function. Solvable and Unsolvable Problems. Unpublished Papers. A Note on Normal Numbers. The Word Problem in Compact Groups. On Permutation Groups. The Difference&PSgr;(x)-x. On a Theorem of Littlewood (with S. Skewes).Related Papers. An Analysis of Turing's "The Word Problem in Semi-Groups with Cancellation" (W.W. Boone). On the Difference&pgr;(x)-li x (A.M. Cohen, M.J.E. Mayhew). Turing'sStatistical Work. Studies in the History of Probability and Statistics XXXVII. A.M. Turing's Statistical Work in World War II (Biometrika 66).Introductory Remarks for the Article in Biometrika 66 (Specially writtenfor this Volume by I.J. Good).
Notes and Summaries.
Bibliography.
Index.