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The papers consist of correspondence, school notebooks, research notes and drafts, diaries, photographs, and publications documenting most aspects of Davenport's life and work. His contributions to his subject as student, teacher, writer and researcher, are well documented and the collection as a whole is of pedagogical interest. Less fully represented are his extensive travels for visits and conferences (which can sometimes only be deduced from a jotted heading on a lecture script) and his work for the London Mathematical Society.

The 60 boxes of material are organised into seven series: Biographical and personal papers, School and university notebooks and lecture notes, Lectures and addresses, Publications, Research notes and drafts, Faculty of Mathematics, Cambridge and Correspondence.

Series A, Biographical and personal papers, includes Davenport's unpublished reminiscences and reflections on his life's work, written shortly before his death with the assistance of his wife and his colleague D. J. Lewis (A.8-10). Other documentation on his career includes, unusually, his examination scripts and marks awarded at Manchester University in 1927 preserved by his principal tutor, L. J. Mordell (A.30-31).

Series B, School and university notebooks and lecture notes, is a record of mathematical teaching at Manchester 1924-1927 (B.23-54) and Cambridge 1927-1932 (B.55-92), by means of Davenport's notes, carefully taken and preserved, of lecture courses, class work and exercises.

Series C, Lectures and addresses, is a substantial section representing Davenport's own contribution to the teaching of mathematics from the 1930s as a Research Fellow in Cambridge through his various university appointments and lectures abroad, including the lectures at Michigan, later published in book form (C.115-124). Several of these contain sets of problems and solutions, and some examination material. On a less technical note is the address given in 1947 at Accrington Grammar School, Davenport's old school (C.131). A new generation in the filiation of mathematics is represented by the notes on Davenport's lectures at London in 1946 made by C. A. Rogers, his research student, collaborator and eventual successor as Astor Professor (C.167).

Series D, Publications, includes drafts, sometimes accompanied by correspondence with collaborators (see especially D.110-120) or publishers, for Davenport's many papers. These have been linked wherever possible to the numbered list in the Bibliography appended to the Royal Society Memoir by C. A. Rogers and others (Biographical Memoirs of Fellows of the Royal Society, 17, 1971). In addition, there is considerable material relating to work not listed in the official bibliography: this includes Davenport's books, The higher arithmetic (D.89-92) and Multiplicative number theory (D.170-182), book reviews (D.208), unpublished work (D.201-203) and a posthumous publication (D.207).

Series E, Research notes and drafts, contains a variety of material: paginated narrative sequences perhaps intended for lectures or papers, notes and calculations often on problems arising from work by others, and miscellaneous shorter unidentified notes. There is in consequence some potential overlap with other series, notably C and D. Of interest is the collaborative work with Helmut Hasse arising from Davenport's period in Marburg (E.1-15). Davenport's notes of lectures and talks by others (E.103-126) include mathematicians of an older generation (K. Mahler, L. J. Mordell, C. L. Siegel), friends and contemporaries (P. Erdös, H. A. Heilbronn), and pupils and successors (B. J. Birch, J. W. S. Cassels, C. A. Rogers, K. F. Roth). Another link in the pedagogic chain is J. E. Littlewood's extended list of 'Research Problems' and Davenport's 'Comments' (E.131)

Series F, Faculty of Mathematics, Cambridge, is small but includes a little material on research, examinations and the newly-created Department of Applied Mathematics and Theoretical Physics.

In Series G, Correspondence, Davenport's links as student, teacher and collaborator with several generations can be traced. Early correspondence with E. A. Milne (G.206) and L. J. Mordell (G.208) feature their recognition and fostering of Davenport's talent, and that with E. Bombieri (G.28-39), D. J. Lewis (G.175-184) and C. A. Rogers (G.268-278), among many others, indicate his continuing contributions. Special mention must be made of Davenport's close connection with German mathematicians, several of whom he met during his early visits to Marburg and elsewhere and whom he helped and encouraged when they were forced to emigrate: see his correspondence with H. A. Heilbronn (G.123-142), H. Kober (G.165), K. Mahler (G.194-201), and R. Rado (G.257). There is also correspondence with H. Hasse (G.116-122), who remained in Germany. Davenport's command of the language is evident both in the correspondence and in the drafts for lectures and papers elsewhere in the collection.

The material is presented alphabetically, with dates and a brief indication of any information of particular interest.

Taylor's undimmed scientific reputation, the high respect he enjoyed, and the eagerness with which younger scientists continued to seek and accept his advice, emerge with remarkable clarity from the letters, most of which date from the later period of his life.

As with the personal correspondence in Section A, only incoming letters usually survive. Professor G.K. Batchelor was, however, able to obtain originals or photocopies of Taylor's letters from some of his correspondents, and thus reconstruct a relatively complete sequence. Examples of this can be found at D.7, D.13, D.29, D.43-D.46, D.52, D.60, D.64, D.65, D.71, D.87.

Apart from these more substantial exchanges, some ms. drafts or copies of Taylor's replies to individual correspondents also survive. They are noted in the relevant entries. A full list is appended below for ease of reference.

D.6, D.7, D.9

D.10, D.12, D.13, D.14

D.21, D.24, D.29

D.30, D.35

D.41, D.44

D.50, D.52, D.53

D.60, D.64, D.65

D.71, D.72, D.74, D.76

D.87

D.91

Batchelor was instrumental in the move to establish departments within the mathematics faculty. In 1959 DAMTP was founded with him as first head of department – a role he was not to relinquish until 1983. As such he was able to shape the department, supervising its move into its first consolidated home in former premises of CUP on the Mill Lane site and introducing a fluid dynamics laboratory in the face of opposition from the Department of Physics. He continued as its head of Department until his early retirement in 1983

The material is not extensive, and is arranged as follows:

D/1-D/12: General correspondence and papers: including papers relating to Synge's appointment; his plan of research; and material relating to Lord Rothschild's 1971 Green Paper 'A Framework for Government Research and Development' (D/5-D/7),

D/13-D/17: Chemistry Division: administrative papers

D/18-D/19: Project reports on Synge's research

Manuscript and typescript drafts, proofs, and research (including photocopies of photographs and correspondence) for J.J. Thomson and the Cavendish Laboratory in his Day, an account of Thomson and his work by G.P. Thomson published in 1964 by Nelson as part of the 'British Men of Science' series. Also correspondence with publishers, and other pieces by G.P. Thomson about his father, several commissioned for the centenary of J.J. Thomson's birth in 1956; the material was often drawn upon for later accounts and there is considerable overlap in the content.

Includes a hardback notebook (D/17), originally used by G.P. Thomson for mathematical notes on Gamma Functions (c. 1910-12) and continuing with drafts for the biography of his father.

Photographs for an exhibition 'Figures' by Gaskell and David Inshaw held in Trinity College Library in one box accompanied by a folder of similar materials: photographs, a newscutting, and exhibition poster from the exhibition. Accompanied by a box of photographs by Gaskell which include those used in the exhibition amongst many others.