Alan Turing's Scientific Papers

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.

• On the Gaussian Error Function, King's College Fellowship dissertation (1935).

  This was never published. Only the Preface is reproduced in the Collected Works.

  Scan of complete original dissertation in the Turing Digital Archive.

  The Preface is given in printed form in the Impact volume, together with a substantial review of the thesis by Sandy L. Zabell.

• Equivalence of Left and Right Almost Periodicity, J. London Math. Soc. 10, pp 284-285 (1935)

  Scan of an offprint in the Turing Digital Archive.

• Finite Approximations to Lie Groups, Ann. of Math. 39 (1), pp 105-111 (1938)

  Scan of an offprint in the Turing Digital Archive.

• The Extensions of a Group, Compositio Math. 5, pp 357-367 (1938)


• A Method for the Calculation of the Zeta-Function, Proc. London Math. Soc. (2) pp 180-197 (1943, submitted 1939)

  Scan of an offprint in the Turing Digital Archive.
  Scan of Turing's blueprint for his zeta-function calculating machine, 1939, in the Turing Digital Archive.

• Rounding-off Errors in Matrix Processes, Quart. J. Mech. Appl. Math. 1, pp 287-308 (1948)

  Scan of an offprint in the Turing Digital Archive.

  Typographically reset in the Impact volume, with substantial review by Lenore Blum.

• The Word problem in Semi-Groups with Cancellation, Ann. of Math. 52 (2), pp 491-505 (1950)

  Scan of an offprint in the Turing Digital Archive.

  Typographically reset in the Impact volume, with substantial review.

• Some Calculations of the Riemann Zeta-function, Proc. London Math. Soc. (3) pp 99-117 (1953)

  Typographically reset in the Impact volume, with substantial review and annotation by Dennis Hejhal and Andrew Odlyzko.

• Solvable and Unsolvable Problems, Science News 31, pp 7-23 (1954) is included in this volume of the Collected Works as well as in the Mechanical Intelligence volume. See the previous page for details.

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

• A Note on Normal Numbers. Here J. L. Britton has treated only Turing's typescript. A manuscript version also survives in the 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 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.

• 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)

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.