See the Alan Turing Home Page
for a guide to this website.

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

Introduction and overview.

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

Mechanical Intelligence (including all electronic computing)

This page is Pure Mathematics

Morphogenesis

Mathematical Logic, plus cryptology.

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.

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

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.

The same level of scholarship is extended to Turing's unpublished pure mathematical papers, where the editor's difficulties are magnified by the illegibility and incompleteness of the manuscripts.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.

The Word Problem in Compact Groups

On Permutation Groups

The difference ψ(x) - x

(with S. Skewes) On a Theorem of Littlewood

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.