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Papers of Harold Davenport
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Correspondence

The correspondence includes several substantial exchanges of letters, however, many of them are incoming only, sometimes with a brief ms. note by Davenport of his reply on which ensuing correspondence may be based. Mrs. Davenport's notes identifying correspondents and their connections with Davenport often accompany the letters and were drawn upon in compiling the entries.

The content is essentially mathematical though some personal news from Davenport's long-term friends, colleagues and pupils may be included. Davenport's long association with German mathematicians, many of whom became refugees in British universities including Cambridge, is well documented; these are wholly or partly in German. Of special interest are the extensive exchanges with E. Bombieri, G. H. Hardy, H. A. Heilbronn, K. Mahler and L. J. Mordell.

Mordell, a distinguished mathematician of American origin, with a special interest in number theory, was Fielden Professor of Mathematics at Manchester when Davenport took his first degree there. The Manchester School of Mathematics was particularly strong in the 1930s, and included several refugee mathematicians; Davenport also joined it as Assistant Lecturer in 1937. Mordell succeeded Hardy in the Sadleirian Chair at Cambridge 1945-1953 and remained in contact with Cambridge mathematics until his death in 1972. Davenport was among his closest friends. Mordell recognized his quality from a very early stage (see G.208), helped him to share his own special interest in the geometry of numbers, and, according to J. W. S. Cassels, looked on Davenport as ‘his spiritual heir’ (Biographical Memoirs of Fellows of the Royal Society, 19, 1973, pp. 493-520).

Faculty of Mathematics, Cambridge

This series consists of committee notices and reports, with some correspondence and examination papers as well. The papers are arranged into six subgroups: General committees (F.1-6), Needs of faculty and sub-departments (F.7-9), Appointments (F.10-12), Requests for post-graduate places (F.13), Examination papers (F.14-16), and Miscellaneous (F.17). The Needs of faculty and sub-departments papers largely consist of Statements of Needs of various departments, in various areas, such as teaching staff, new equipment, etc. The Appointments material relates to the Appointments Committee of the Faculty of Mathematics. There is also a little correspondence re vacant posts, applications, requests for curricula vitae, etc.

Research notes and drafts

This series has been organized into five subgroups: Collaboration with Helmut Hasse (E.1-15), Titled and untitled drafts (E.16-83), Miscellaneous notes and calculations (E.84-102), Notes on work by others (E.103-126), and Work by others (E.127-135).

Many of the drafts in Titled and untitled drafts were probably intended to form lectures or papers for publication, while others may be no more than extensive notes. A number of these are untitled and very few are dated.

The Notes on work by others falls into two parts: notes made by Davenport at lectures given by others (E.103-E.117) and notes made by him on a particular publication, or line of work, of another (E.118-E.126) Although in many cases Davenport gave the date of publication of the work, few of these notes are themselves dated. Therefore they have been arranged in alphabetical order, with the exception of E.125-126, where the contents of one of Davenport's own folders have been kept together.

Of special interest in the last subgroup Work by others is E.131, a selection and discussion of research problems by J. E. Littlewood, and Davenport's comments on them. This subgroup has been arranged in alphabetical order.

Papers of Harold Davenport

  • DAVT
  • Fonds
  • 1911–1986

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.

Davenport, Harold (1907-1969) mathematician

Publications

Davenport published nearly 200 papers and three books. Most of the material in this series consists of drafts of the published papers, frequently without any other material such as notes or calculations. In some cases, however, these do survive and in others there is more than one draft. Some correspondence is included here, as at D.112-116.

The series incorporates material of other kinds, such as the Adams Prize Essay (D.5-15), the books The higher arithmetic (D.89-92) and Multiplicative number theory (D.170-182), reviews by Davenport (D.208), and some unpublished material, such as 'On writing mathematical papers' (D.201-203).

The Adams Prize Essay materials include material published in various papers, 1938-1946 (including D.2-4), and consists of early drafts of certain chapters (D.5-6), the whole text, probably as submitted to the judges (D.8-14) and a little correspondence.

Material published after Davenport's death can be found at D.204-207, and his 'collected works' are represented at D.210-213.

The material has been arranged in chronological order, and where applicable the Bibliography number of the Royal Society Memoir (Biographical Memoirs of Fellows of the Royal Society, 17, 1971) has been given, as well as the date of publication.

Lectures and addresses

Series C, Lectures and addresses, is arranged into eight subseries. The first five are a chronological run: Cambridge, 1930s (C.1-4), Manchester, 1937-1941 (C.5-12), University College of North Wales, Bangor, 1941-1945 (C.13-16), University College, London, 1945-1957 (C.17-51), and Cambridge, 1958-1969 (C.52-97). The remaining three are Lectures abroad (C.98-129), Societies, conferences, etc. (C.130-158), and Miscellaneous and undated lectures (C.159-193).

The notes at C.13-16, University College of North Wales, Bangor, cannot be dated exactly, but all are from the 1941-1945 period. All are lecture notes, with no other teaching material.

The material at C.17-51, University College, London, 1945-1958, was probably all intended for teaching undergraduates, and many lecture drafts are accompanied by reading lists and in some cases by lists of students' names. There are not only finished drafts, both manuscript, but also notes and calculations. Only C.17-34 can be dated exactly. Items C41-51 were originally kept in an unlabelled binder. The material has been preserved in its original order but has been divided into folders for ease of reference. The numbers in the headings of e.g. C.46, C.47, C.48 probably refer to lectures from extended courses.

All of the material at C.52-97 Cambridge, 1958-69 was used for teaching, probably undergraduates and postgraduates. Several lectures include lists of problems to be attempted by the students (see especially C.62, C.97); it was Davenport's custom to hand these out at the beginning of a lecture course. Some lecture material also includes outlines of the topics to be covered, ms. notes and calculations, and drafts of earlier work, used in the production of the lecture.

Davenport made many visits abroad (see Mrs. Davenport's biographical notes at A.7). The material at C.98-129, Lectures Abroad, is from three universities with which he had particularly close connections: Stanford University, Göttingen and the University of Michigan. Visits to these institutions varied, up to a full academic year, and could involve teaching and examining as well as lecturing. C.98-107 Stanford University, California consists of papers related to Davenport's stay as a visiting professor in 1947-1948, having been invited by Gabor Szegö (see A.60), and his return in 1950. See also Memoir, p.162. Virtually all the material relating to the University Göttingen (C.108-114) is in German. Davenport had a good command of the language, and had made many German friends and colleagues, particularly among the refugees arriving in Cambridge in the 1930s. See Memoir, pp.161, 164. See also G.299-G.303 for material relating to Davenport's appointment and visit to Göttingen in 1966.

The material in the next subseries, Societies, Conferences, etc., C.130-C.158, consists mainly of drafts for lectures given at conferences and to societies, including undergraduate clubs. It does not however present a complete record of Davenport's many visits and conferences. C.152-156 contains material which cannot be accurately dated, and C.157-158 consist of invitations and programmes. Of particular interest is C.131, Davenport's address given at the prize day of his old school.

The papers in the last subseries, Miscellaneous and undated lectures includes collections of lecture material (C.159-C.170 and C.182-C.193) which have been kept together in the order in which they were found. The first of these collections is chiefly material concerning the geometry of numbers, a collection of lecture notes found together in a folder. Most deal with the geometry of numbers and some are dated (1946-1959). They have been kept in their original order. Of particular interest is C.167, C.A. Rogers's notes of a course of lectures given by Davenport, and an account of the seminar and discussion of the lectures. The second collection of papers is far more miscellaneous in character, being mostly notes and calculations. C.171-181 consists of miscellaneous lectures which cannot be dated, although most have titles. The material labelled 'Misc. math.' is described by Professor B.J. Birch (February 1986) as: 'a mixed bag of lecture notes for various courses given mainly at University College. Some of the material was eventually published in Multiplicative Number Theory' (see D.170-D.182).

School and university notebooks and lecture notes

This series consists of notebooks and lecture notes kept at three different institutions: Accrington Grammar School (B.1-22), The Victoria University of Manchester (B.23-54), and Trinity College, Cambridge (B.55-92).

With one exception, the notebooks from Accrington Grammar School (B.1-22) contain Davenport's notes and diagrams on physics, chemistry and mathematics, presumably work for the School Certificate (B.1-2) and the Higher School Certificate (B.3-17), although several are undated. Only B.22 shows Davenport's non-mathematical interests, containing extracts from various writers and drafts of two speeches, possibly delivered to a school debating society.

The notebooks and lecture notes from the Victoria University of Manchester (B.23-54) date from 1924-1927. B.23-30 are hardback notebooks arranged by the covering titles with which Davenport labelled them. Only two, B.24 and B.29, can be dated (1924-1925 and 1925-1926 respectively). None are indexed and only two are paginated (B.29-30). B.31-54 are loose ms. pages of notes on the literature, notes on lecture courses and class work and exercises by Davenport. Many bear an indication of the course number, or of the person giving the lectures and/or supervising the work. The material was kept in bulky wallet folders labelled by Davenport; the contents have been removed and where appropriate preserved in more than one folder for ease of reference. The original folders are at B.54. See B.85-87 for notes originally made at Manchester and subsequently used at Cambridge.

The notebooks and lecture notes from Trinity College, Cambridge (B.55-92) date from 1927-32. B.55-B.64 are hardback notebooks, and excepting B.63-64, all contain lecture notes. Davenport usually labelled the fly-leaves with the name of the lecturer, the subject of the course, and the date. These labels are used as titles here, and his descriptions are preserved in the entries. B.63 and B.64 are exceptions as they are without identification, but it is probable that they come from this period in Davenport's career. B.65-92 are loose ms. pages of notes, chiefly of lectures attended by Davenport. Usually they bear the name of the lecturer and the title of the course, and some are dated. The material was kept in wallet folders labelled by Davenport; the contents have been removed and, where appropriate, preserved in more than one folder for ease of reference. The original folders are at B.89.

Biographical and personal papers

This series consists of drafts, correspondence, diaries, photographs, and documents, and has been arranged into seven subseries: Obituaries and tributes (A.1-7); Autobiographical writings (A.8-14); Career, honours, and awards (A.15-75); Davenport's death (A.75-91); Diaries (A.92-129); Miscellaneous items (A.130-132); and Photographs (A.133-137).

A.1-7, Obituaries and tributes, includes typescript biographical notes made by Mrs. Davenport after her husband's death (A.7). The Autobiographical writings at A.8-14 include reminiscences (A.8-10) made by Davenport with the assistance of his wife and D. J. Lewis in 1969, although very ill. He died in June of that year (see Memoir, p.165). Some, probably earlier, ms. notes on his career survive, as well as notes on his impressions of America and some humorous writings.

The papers at A.15-75 record Davenport's career and honours, and are arranged in chronological order. These records begin with Davenport's school career, 1917-1924 at The Municipal Secondary School, renamed Accrington Grammar School in 1921, and continue with records from The Victoria University of Manchester, 1924-1927. Davenport was an Affiliated Student at Trinity College Cambridge, 1927-29, taking a second first degree, and in 1932 was awarded a research fellowship. 'On the expiry of his Trinity Fellowship in 1937, Davenport was appointed by Mordell to an Assistant Lectureship in Manchester' (Memoir, p.161), where he stayed until 1941. From 1941 to 1945 he was at the University College of North Wales, Bangor, and from 1945-1948 at University College, London. He took up the Rouse Ball Chair of Mathematics at the University of Cambridge from 1958 until his death.

The papers housed as A.76-91 are primarily letters of condolence after Davenport's death. After a period of illness following the removal of a lung, Davenport died on 9 June 1969. (Memoir, p.165)

The diaries at A.92-129 are all small pocket diaries, mainly university diaries covering the academic year, used chiefly to record appointments and addresses. A.130-132 consists of personal miscellaneous items, and the photographs at A.133-137 include group photographs of Davenport and other mathematicians (A.136).

'Products of inhomogeneous linear forms', with H. P. F. Swinnerton-Dyer

(Bibliog. 107).
D.99: 2 letters from H. P. F. Swinnerton-Dyer, 1954, re publication of paper, with 2pp. ms. notes and calculations entitled 'n = 5, r = 1, s = 2', and labelled 'e 107'.
D.100: 33pp. untitled ms. draft (Swinnerton-Dyer's hand), labelled 'first version'.
D.101: 44pp. typescript draft with ms. corrections.

5pp. untitled ms. draft, with 2pp. ms. calculations.

'Group theory (Stanford)'

Lecture and teaching material, from an envelope so inscribed.
C.98: 27pp. ms. draft for course of lectures, variously sub-titled.
C.99: 13pp. ms. draft for course of lectures, variously sub-titled, with 1p. ms. calculations.
Created while at Stanford University, California, 1947-48, 1950.

Lectures and addresses

'Davenport: Theory of Numbers', n.d. Two typescript drafts, 3pp. and 2pp., of list of problems.

'Davenport: Geometry of Numbers', n.d. Two typescript drafts, 3pp. and 2pp., of list of problems.

Created while working at Cambridge University, 1958-1969.

Untitled notes and calculations

Due to the dearth of information on these notes and calculations, no attempt has been made to describe them in detail. Groups of notes have been kept together; E.102 contains miscellaneous single sheets. E.98 consists of 8 folders, and contains material cleared from Davenport's office desk after his death (this information from Professor B. J. Birch, February 1986).

Mathematika, vol. 1, part 1

Davenport was responsible for the founding of this journal (see Memoir, p.164), and remained an editor throughout his life. The first issue contained 2 papers by him (Bibliog. 103 and 104).

Proof copy with Davenport's ms. corrections, including 1p. ms. notes.

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