Turing Sources

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The Alan Turing Bibliography

compiled by Andrew Hodges
author of Alan Turing: the Enigma

Part 4: Mathematical Logic plus cryptology




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.

Mathematical Logic

This volume of the Collected Works includes introductory material and commentary by the editors C. E. M. Yates and R. O. Gandy, and also by Solomon Feferman.

  • On Computable Numbers, with an application to the Entscheidungsproblem, Proc. Lond. Math. Soc. (2) 42 pp 230-265 (1936); correction ibid. 43, pp 544-546 (1937).

    Available directly from the London Mathematical Society as a facsimile pdf. Note that it falls within a volume dated 1937, but this volume was published in parts. This meant that the first half of Turing's paper appeared on 23 November 1936 and the second half just scraped into 1936 on December 23.

    Typographically reset in the Impact volume, with many accompanying commentaries.

    Typographically reset in The Essential Turing.
    Original typography reproduced in The Undecidable.
    Typographically reset again in Stephen Hawking's mathematical sourcebook God created the Integers, with an introduction by Hawking.

    There is no complete manuscript or typescript of this work. However, six pages of the typescript survive because Turing used the reverse sides for manuscript notes on Normal Numbers. See them in the Turing Digital Archive here. The typing is not Turing's but the inserted mathematical expressions are in his handwriting.

    The paper is also available as a PDF file from ComLab, Oxford University.

  • Computability and λ-definability, J. Symbolic Logic 2 pp 153-163 (1937)

    Typographically reset in the Impact volume, with commentary.

  • Scan of an offprint in the Turing Digital Archive

  • The p-function in λ-K conversion, J. Symbolic Logic 2 p 164 (1937)

    Typographically reset in the Impact volume, with commentary.

  • Systems of logic based on ordinals, Proc. Lond. Math. Soc (2) 45 pp 161-228 (1939).

    This was also Turing's Princeton Ph.D. thesis (1938), and a typescript is in Princeton University library. The thesis was published in book form by Princeton University Press as Alan Turing's Systems of Logic: The Princeton Thesis in 2012.

    Typographically reset in the Impact volume, with commentaries.

    Typographically reset in The Essential Turing.
    Original typography reproduced in The Undecidable.

    Online pdf version available from Prof. Armando Matos.

    Scan of an offprint in the Turing Digital Archive

  • (with M. H. A. Newman) A formal theorem in Church's theory of types, J. Symbolic Logic 7 pp 28-33 (1942)

  • The use of dots as brackets in Church's system, J. Symbolic Logic 7, pp 146-156 (1942)
  • Scan of an offprint in the Turing Digital Archive

    Typographically reset in the Impact volume, with commentary.

  • Practical forms of type-theory, J. Symbolic Logic 13, pp 80-94 (1948)

    Scan of Turing's draft typescript and offprint of the published paper in Turing Digital Archive

    Typographically reset in the Impact volume, with commentary.

Turing's unpublished manuscripts on mathematical logic have been edited for inclusion in this Collected Works volume:

  • Some theorems about Church's system (three MSS, 1941)

  • Practical forms of type theory II (1943-4)

  • The reform of mathematical notation (1944-5)

    This text is also given in a printed form in the Impact volume, with commentary.

Scans of these manuscripts are in the Turing Digital Archive, in sections C3, C4, C5, C6 and C12.




Cryptology

  • In April 1996 the National Security Agency (USA) declassified thousands of documents from the Second World War, including what was listed as:

    NR 964 CBCB55 9024A 19390000 TURING'S TREATISE ON THE ENIGMA

    This is the 1940 text by Turing on Enigma decipherment which was known as the 'Prof's Book' at Bletchley Park.

    Part III of the volume of the Collected Works includes a selection of pages from this text, together with a brief preface by myself. This preface is also available on this site.

    These pages are reproduced as typescript in the Impact volume, together with new commentary on Turing's Enigma work.

    Another section of the text is included in The Essential Turing.

    A better version of the text was subsequently released by the British government and is in the (British) National Archives, HW25/3. This revealed another title: Mathematical theory of ENIGMA machine. In September 2001 the National Archives put a few of the early pages on-line, as the Enigma was 'in the news'; see the feature here.

    The Turing Digital Archive has a scan of the entire American copy.


  • Cryptographic History of Work on the German Naval Enigma (c. 1945) by C. H. O'D. Alexander. This very valuable history of work on the Naval Enigma problem is the closest to giving Turing's account of the early story. It is in the National Archives, at HW/25/1.

    The transcribed text is available on-line here.

  • History of Hut 8 (c.1945) by A. P. Mahon. Also in the National Archives, at HW 25/2.

    An excerpt is typographically reset in The Essential Turing.

    There is a copy in the Turing Archive (item B.27b), but it is not yet scanned.

    The transcribed text is available on-line here.

  • Report by Turing on U. S. Navy cryptanalytic work and their machinery, November 1942. National Archives, HW 57/10 (released October 2004). Transcript of the opening part of the report on this site.

  • Report written by Turing in December 1942 after his visit to the NCR factory at Dayton. Ohio, where the American Bombes were being built. This report has also been released and may be read in its entirety on this website.

    This report has also been published with an introduction and annotation by Lee A. Gladwin of the US National Archives. See:

    • Visit to National Cash Register Corporation of Dayton, Ohio, and the following article Alan Turing's visit to Dayton, Lee A. Gladwin, Cryptologia XXV, pp. 1-17 (2001).

  • Speech System 'Delilah' — report on progress, 6 June 1944. Three-page typescript report in the National Archives, HW 62/6.

    Transcript of the Delilah report on this site

    Printed in the Impact volume, with commentary by Craig Bauer and John Harper.


  • Report on speech secrecy system DELILAH, a technical description compiled by A. M. Turing and Lieutenant D. Bayley. 80-page typescript report in the National Archives, HW 25/36.

    This report is published as a full transcript in Cryptologia, 36:4 295-340 (2012).


  • The applications of probability to cryptography by A. M. Turing, undated, document in National Archives HW 25/37
    and
    Paper on statistics of repetitions by A. M. Turing, undated, document in National Archives HW 25/38.

    These two important papers give the Bayesian theory lying behind the Banburismus scoring method. They can be obtained directly from the National Archives for a small online payment. They were only released by GCHQ in April 2012. See this news item.


  • There are further important memoranda by Turing on Enigma methods, not yet listed here.

  • It is likely that there is further major writing by Turing yet to be released from government secrecy. One might conjecture about the following items: reports on the security of Allied cryptosystems; a 1945 report on his visit to Germany; a 1946 report for GCHQ on the potential of the digital computer he was designing at the NPL; a 1948/9 report for GCHQ commenting on Shannon's theory of communication and cryptography; a 1948/9 report for GCHQ on the potential of the Manchester computer; reports on the work he did for GCHQ between 1948 and 1952.



The Alan Turing Bibliography:

Overview | Mechanical Intelligence | Pure Mathematics

Morphogenesis | Mathematical Logic plus cryptology




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