Turing Sources

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The Alan Turing Bibliography

compiled by Andrew Hodges
author of Alan Turing: the Enigma

Part 2: Pure mathematics

A full listing of Turing's papers

The detailed listing is split between four webpages, corresponding to the four volumes of the Turing Collected Works.

Pure Mathematics

Each of the published papers is reproduced in the original form in this volume of the Collected Works, together with an introduction, summary, notes, and detailed checking by the editor J. L. Britton.

In editing the unpublished work, J. L. Britton's difficulties were magnified by the illegibility and incompleteness of the manuscripts. The originals (with one exception, a photocopy) are in the Turing Archive.

See this index page of the Turing Digital Archive for the scans of these manuscripts

  • A Note on Normal Numbers. Here J. L. Britton has treated only Turing's typescript. A manuscript version also survives in the Turing Digital Archive, and is slightly different. Of particular interest is that it is written on the reverse side of pages of the typescript of his major paper 'On computable numbers...' (1936). Both manuscript and typescript are in the Turing Digital Archive.

    Printed afresh in the Impact volume, with an important new review by Veronica Becher showing that Turing's work was almost correct.

  • The Word Problem in Compact Groups

  • On Permutation Groups

    Also included in the Impact volume.

  • The difference ψ(x) - x

  • (with S. Skewes) On a Theorem of Littlewood

    Typographically reset in the Impact volume, with substantial review and annotation.

Two further published papers by other authors, substantially the result of completing Turing's work, are included in this volume of the Collected Works:
  • An Analysis of Turing's "The Word problem in Semi-groups with Cancellation", W. W. Boone, Ann. of Math. 67 (1) pp. 195-202 (1958)

  • On the Difference π(x) - li(x), A. M. Cohen and M. J. E. Mayhew, Proc. Lond. Math. Soc. (3) 18, pp 691-713 (1968)
There are further notes by Turing on game theory in the Turing Archive, and also some on tensors and spinors, but these are not included in this volume.

Neither is the item headed Minimum cost sequential analysis, which carries some of the content of the statistical theory Turing developed for cryptanalysis. However the editor has included:

  • Studies in the History of Probability and Statistics, XXXVII A. M. Turing's statistical work in World War II, I. J. Good, Biometrika 66 (2) pp 393-396 (1979)

  • Introductory remarks for the article in Biometrika 66 (1979), I. J. Good, especially written for this volume.

An excerpt from the paper Minimum cost sequential analysis appears in Part III of the Mathematical Logic volume of the Collected Works, with a new commentary from I. J. Good.

The Alan Turing Bibliography:

Overview | Mechanical Intelligence | Pure Mathematics

Morphogenesis | Mathematical Logic plus cryptology

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Andrew Hodges