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# AMT/C

Unpublished manuscripts and drafts- AMT/C/1
'The difference Ψ (x) - x', CTS with AMS mathematical calculations and corrections in red ink. [c. 1937].

Paper, 7 sh. in envelope.

- AMT/C/2
Blueprint, 'Zeta function machine', signed D.C.M. and dated 17 July 1939. Probably prepared in connection with AMT's article 'A method for the calculation of the zeta function', published 1943 but received 1939 (see bibliography in Royal Society memoir, A/36).

Paper, 1 item.

- AMT/C/3
TS, 'Some theorems about Church's system'*, with AMS annotations. n.d. Includes MS note by R.O. Gandy on un-numbered front page, 'numbers inserted by ROG', and note by Gandy on last page, 'Some Theorems about Church's system (including fallacious consistency proof)'. Also includes one further page on same subject but not part of this paper. n.d.

Paper, 21 sh. in envelope.

* AMT worked with Alonzo Church at Princeton, 1936-8, and published 2 articles on the subject in 1942

- AMT/C/4
Untitled TS with AMS annotations. n.d. Probably continuation of 'Some theorems about Church's system'. Pages numbered 37-43, beginning '§5. Consequences of the Peano axioms'.

Paper, 7 sh. in envelope.

- AMT/C/5
Untitled TS with AMS annotations. n.d. Probably continuation of 'Some theorems about Church's system'. Pages numbered 60-73, beginning '9. Finite models of Church's and Zermelo's systems'. Last page has MS note by R.O. Gandy, 'Continuation of a paper about virtual types in Church's system? Consistency and completeness for the system with axioms of finitude in place of inf. are sketched'.

Paper, 14 sh. in envelope.

- AMT/C/6
TS, 'A practical form of type theory II' with AMS annotations. c. 1948. This was intended as a continuation of B/3, the contents being summarised on page 1 by AMT, 'In this paper theorems A and B enunciated in Part 1 are proved'. Page 1 also bears MS note by R.O. Gandy, 'Pages no

^{d}by ROG as they lay (manuscript pages given letter, e.g., 50A, 50B, etc)'. Includes many AMS additional papers, numbered 1-81, followed by a sequence of manuscript pages as follows: 1, 'note to p.7', 2-16, 18, 19, 22.Paper, 125 items in envelope.

- AMT/C/7
CTS, 'A diffusion reaction theory of morphogenesis in plants', with MS corrections. Title page reads: 'The mathematical author (A.T.) is the originator of the theory (which will appear shortly in the Proceedings of the Royal Society) and is responsible for the exactitude with which his ideas and the relevant physical and mathematical concepts are represented, while the botanical author (C.W.W.*) has tried to give the theory an appropriate botanical setting'. [Jan. x May 1952]

Paper, 20 sh. in envelope.

* Claude Wilson Wardlaw

- AMT/C/8
TS, 'Morphogen theory of phyllotaxis. Part I. Geometrical and descriptive phyllotaxis.' TS made by N.E. Hoskin and B. Richards, based largely on AMT's TS in C/25. Includes MS corrections by N.E. Hoskin after AMT's death. Accompanying MS note by R.O. Gandy reads 'Draft of paper intended for Transactions of Royal Society written by N. E. Hoskin and B. Richards from manuscripts of A.M. T. and notes of lectures given in Manchester'. [After Dec. 1954].

Paper, 42 sh. in envelope.

- AMT/C/9
TS continuation of 'Morphogen theory of phyllotaxis', 'Part II. Chemical theory of morphogenesis'. With MS corrections. [After 1954].

Paper, 13 sh. in envelope.

- AMT/C/10
TS continuation of 'Morphogen theory of phyllotaxis', 'Part III. A solution of the morphogenetical equations for the case of spherical symmetry', (by B. Richards). [After 1954].

Paper, 16 sh. in envelope.

- AMT/C/11
TS, 'Intelligent machinery', with AMS corrections and additions. Pages numbered 1-37, with 2 un-numbered pages of references and notes. Page 1 has MS note by R.O. Gandy, 'Turing's typed draft'. n.d.

Paper, 40 sh. in envelope.

- AMT/C/12
TS, 'The reform of mathematical notation and phraseology', with AMS corrections. Includes MS annotations by R.O. Gandy. Pages numbered 1-8, 13-18, and one un-numbered last page. Page 13 has a note by R.O. Gandy, 'No sign of pages 9-12'. n.d.

Paper, 15 sh. in envelope.

- AMT/C/13
AMS, 'General tensors in a group'. Pages not numbered. n.d.

Paper, 21 sh. in envelope.

- AMT/C/14
TS, 'Minimum cost sequential analysis', with AMS annotations. Includes some pages of AMS notes and calculations. n.d.

Paper, 17 sh. in envelope.

- AMT/C/15
TS and AMS, 'A note on normal numbers.' AMS written on back of TS draft of another paper. n.d.

Paper, 11 sh. in envelope.

- AMT/C/16
TS, 'The word problem in compact groups', with AMS annotations. Includes 1 AMS page entitled, 'The word problem is solvable in simple groups'. Page 1 has AMS note, 'Please let me have this back soon'. n.d.

Paper, 4 sh. in envelope.

- AMT/C/17
TS, untitled, with AMS annotations. First page(s) missing, but last page has MS title by R.O. Gandy, 'On Permutation Groups'. (Probably related to work at the Cypher School, Bletchley). n.d.

Paper, 32 sh. in envelope.

- AMT/C/18
AMS, 'The game of poker'. Unfinished draft (pp. 1-13 only numbered), with extensive notes and calculations, many on reverse of mathematical exercises by other individuals. The scanned images represent the physical documents. Some of the images appear upside down because a single sheet of paper has writing in one direction on the front and in the other direction on the back. n.d.

Paper, 33 sh. in envelope.

- AMT/C/19
AMS, 'The game of "Psychology"'. Pages un-numbered, most written on reverse of mathematical exercises by other individuals. The scanned images represent the physical documents. Some of the images appear upside down because a single sheet of paper has writing in one direction on the front and in the other direction on the back. n.d.

Paper, 8 sh. in envelope.

- AMT/C/20
AMS, 'The elliptic integrals K, E.' Includes MS note on back by Mrs Turing, 'Problem on Elliptic Functions worked out by A.M. Turing for the amusement of Malcolm MacPhail, Humble Oil and Refining Company, Houston, Texas, U.S.A.' n.d.

Paper, 1 sh. in envelope.

- AMT/C/21
Photostat copy of K/2, 'Précis of Relativity Theory'.

Paper, 1 item in envelope. Incomplete.

See also K/2

- AMT/C/22
AMS, 'The rules of GO' (a game for 2 players with counters). Written on King's College, Cambridge, writing paper. n.d.

Paper, 1 sh. in envelope.

- AMT/C/23
Xerox AMS notes and calculations by AMT, 'Two contour-integral proofs', 'Ingham's proof', and 'Another proof'. Pages numbered 3 and 4. Page 3 has MS note by Good, 'A note by Turing for I.J. Good, c. 1943'. Page 4 is addressed, 'Dr I.J. Good, Hut 11' [at Bletchley Park]. Copies made available by I.J. Good from his own archives.

Paper, 2 sh. in envelope.

- AMT/C/24-27
Work on morphogenesis. Folders of notes, calculations and diagrams, received from N.E. Hoskin in 1978, and additional to the material on the subject listed as C/7-10. The papers are part of the extensive notes and drafts left at AMT's death which some of his colleagues (R.O. Gandy, N.E. Hoskin, and B. Richards) intended to prepare for publication. The material is mainly AMT's AMS and TS, with many additions and corrections. It includes diagrams, tables, calculations, and computer routines. Sometimes both sides of the paper are used; many pages have other work on the back. Some of the material constitutes relatively substantial paginated sequences, whilst some consists of random pages which have not been assigned a definite place or description. All titles and descriptions in inverted commas are those which appear on the AMS. Later notes or comments in the hands of Hoskin and Gandy are identified and indicated wherever possible. See also Dr. J. Swinton's web pages http://www.swintons.net/jonathan/turing.htm for a detailed analysis of page sequences and contents.

Paper, 4 envelopes.

- AMT/C/28
TS copy of Fellowship Dissertation, 'On the Gaussian Error Function', 1935.

Paper, 1 item in envelope.

- AMT/C/29
Xerox AMS, 'Nature of Spirit'. Essay written during a visit to Clock House, Bromsgrove (home of his friend Christopher Morcom). [Apr. 1932]. Xerox supplied by Andrew Hodges, original with Morcom family.

Paper, 6 sh. in envelope.

- AMT/C/30
Xerox TS, 'Treatise on the Enigma'. c. 1939-42. Part of the records of the National Security Agency transferred to US National Archives and Records Administration in Apr. 1995.

Paper, 61 sh. in envelope.

- AMT/C/31
Xerox TS report on AMT's visit to the Naval Computing Machine Laboratory at Dayton, Ohio. Dec. 1942. Part of the records of the US National Archives and Records Administration 'Crane Collection'.

Paper, 9 sh. in envelope.

- AMT/C/32
Xerox TS, 'Proposed electronic calculator' (ACE). A report on the detailed design of an electronic computer and account of its operation, written as an employee of the National Physical Laboratory. 1946. Part of the records of the Public Record Office, Kew (ref.: DSIR 10/385).

Paper, 48 sh. in envelope.

- AMT/C/33
TS with AMS annotations, 'Minimum weight structures'. 1953. Includes TS, 'Minimum weight design: Memories of Alan Turing', by Dr R.K. Livesley describing his work with AMT and computing at Manchester University in the early 1950s.

Paper, 2 items in envelope.