Pure Mathematics, Volume 2

Published Papers. Equivalence of Left and Right Almost Periodicity. Finite Approximations to Lie Groups. The Extensions of a Group. A Method for the Calculation of the Zeta-Function. Rounding-Off Errors in Matrix Processes. The Word Problem in Semi-Groups with Cancellation. Some Calculations 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 Unpublished Papers.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's Statistical 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 written for this Volume by I.J. Good). Notes and Summaries. Bibliography. Index.

The collected works of Turing, including a substantial amount of unpublished material, will comprise four volumes: Mechanical Intelligence, Pure Mathematics, Morphogenesis and Mathematical Logic. 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. What is maybe surprising about these papers is that although they were written decades ago, they address major issues which concern researchers today.