Catalogue of the papers and correspondence of HAROLD DAVENPORT FRS; (1907 - 1969)

OUTLINE OF THE CAREER OF HAROLD DAVENPORT

Davenport was born and educated in Accrington, where his gifts for mathematics and chemistry were early recognised. At the age of sixteen he was awarded scholarships to attend Manchester University (1924 - 27) winning first-class honours and the respect of such tutors as L.J. Mordell and E.A. Milne. The latter encouraged him to enter for a scholarship at Trinity College Cambridge, where he read for the Tripos (1927 - 29), began research with J.E. Littlewood, won a Rayleigh Prize (1931) and a Trinity Fellowship (1932 - 37). Another important event of this period was Davenport's acceptance of an invitation by H. Hasse to stay with him in Marburg, a visit which enabled Davenport to meet several distinguished German mathematicians and to learn the language thoroughly. His first university post was a return to Manchester as Assistant Lecturer (1937 - 41) and in 1941 he was appointed to his first Chair at University College of North Wales, Bangor. In 1945 Davenport, who had married Anne Lofthouse in 1944, moved to University College London as Astor Professor. His first American visit, to Stanford in 1947 - 48, occurred during the London period and was followed by many later transatlantic journeys of varying duration. It was also from the Mathematics Department of University College that Davenport launched the new journal Mathematika (1953). In 1958 he was elected Rouse Ball Professor of Mathematics and Fellow of Trinity College, Cambridge, where he died in 1969.

LIST OF CONTENTS

SECTION A BIOGRAPHICAL AND PERSONAL A.1 - A.137

SECTION B SCHOOL AND UNIVERSITY NOTEBOOKS AND LECTURE NOTES B.1 - B.92

SECTION C LECTURES AND ADDRESSES C.1 - C.193

SECTION D PUBLICATIONS D.1 - D.213

SECTION E RESEARCH NOTES AND DRAFTS E.1 - E.135

SECTION F FACULTY OF MATHEMATICS, CAMBRIDGE F.1 - F.17

SECTION G CORRESPONDENCE G.1 - G.373

The collection, which is substantial, covers most aspects of Davenport's life and work. 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. His contributions to his subject, as student, teacher, writer and researcher, are however very well documented and the collection as a whole is of pedagogical interest.

Section A (Biographical and personal) includes Davenport's own unpublished reminiscences and reflections on his life's work, made shortly before his death with the assistance of his wife and his colleague D.J. Lewis (A.8 - A.10).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, A.31).

Section B (School and university notebooks and lecture notes) is an interesting record of the state of the art in mathematical teaching at Manchester 1924 - 27 (B.23 - B.54) and Cambridge 1927 - 32 (B.55 - B.92), comprising as it does notes, carefully taken and carefully preserved by Davenport, of lecture courses, class work and exercises.

Section 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 invitation lectures abroad, including the lectures at Michigan, later published in book form (C.115 - C.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). Conversely, 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 in 1958 as Astor Professor (C.167).

Section D (Publications) includes drafts, sometimes accompanied by correspondence with collaborators (see especially D.110-D.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); a copy of the Bibliography is reproduced with permission on pp. 125-130.

In addition, there is considerable material relating to work not listed in the official bibliography; this includes Davenport's books on The higher arithmetic (D.89 - D.92) and Multiplicative number theory (D.170 - D.182), book reviews (D.208), unpublished work (D.201 - D.203) and a posthumous publication (D.207).

Section E (Research notes and drafts) is so titled for convenience only. It 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 sections, notably C and D. Of interest is the collaborative work with Helmut Hasse arising from Davenport's period in Marburg (E.1 - E.15). There are also Davenport's notes of lectures and talks by others (E.103 - E.126) which include mathematicians of an older generation (K. Mahler, L.J. Mordell, C.L. Siegel), friends and contemporaries (P. Erdös, H.A. Heilbronn), pupils and successors (B.J. Birch, J.W.S. Cassels, C.A. Rogers, K.F. Roth). Another interesting link in the pedagogic chain is J.E. Littlewood's extended list of `Research Problems' and Davenport's `Comments' (E.131)

Section F (Faculty of Mathematics, Cambridge) is relatively scanty but includes a little material on research, examinations and the newly-created Department of Applied Mathematics and Theoretical Physics.

Section G. (Correspondence) contains several substantial sequences, though the general practice of longhand correspondence often produces tantalising gaps. Once again, 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) show their recognition and fostering of Davenport's talent, and that with E. Bombieri (G.28 - G.39), D.J. Lewis (G.175 - G.184) and C.A. Rogers (G.268 - G.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. Correspondence with H.A. Heilbronn (G.123 - G.142), H. Kober (G.165), K. Mahler (G.194 - G.201), R. Rado (G.257) may be cited as examples. There is also correspondence with H. Hasse (G.116 - G.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 was received from Mrs. Davenport at various dates 1983 - 84. A little additional material was received from Professor B.J. Birch in 1986.

NOT ALL THE MATERIAL IN THE COLLECTION IS YET AVAILABLE FOR CONSULTATION. ENQUIRIES SHOULD BE ADDRESSED IN THE FIRST INSTANCE TO:

THE LIBRARIAN, TRINITY COLLEGE, CAMBRIDGE.