by Heini Halberstam, rev.

© Oxford University Press 2004 All rights reserved

**Davenport, Harold** (1907-1969), mathematician, was born on 30 October 1907 in Huncoat, near Accrington, Lancashire, the elder child and only son of Percy Davenport, a clerk, and, later, the company secretary, at Perseverance Mill, and his wife, Nancy, daughter of John Barnes, the owner of the mill. From Accrington grammar school Davenport won scholarships to Manchester University where, in 1927 at the age of nineteen, he graduated with first-class honours in mathematics. In Manchester he came to the notice of E. A. Milne, who encouraged him to enter for a scholarship at Trinity College, Cambridge. He was successful and in 1929 was classed as wrangler in part two of the mathematical tripos and declared by the examiners to have deserved special credit in the most advanced subjects.

When Davenport first went to Manchester he had an interest in the history of mathematics and thought up the so-called 'birthday paradox' to calculate the number of people needed for a fifty-fifty chance that two share the same birthday. There were no signs of an early commitment to arithmetical questions--he even considered seriously a career in chemistry--but in 1929 all doubts had vanished, and Davenport became Professor J. E. Littlewood's research student, with number theory as his chosen field. Littlewood was then at the height of his fame and Cambridge was soon to become, thanks to his celebrated partnership with G. H. Hardy, a world centre for mathematics. Davenport used his opportunity to the full. His first investigations, into the distribution of quadratic residues, involved pioneering studies of character sums and exponential sums; the skills he acquired then he put to good use in many subsequent researches. Indeed, Davenport assimilated his mathematical experiences so well that they were always readily available for his own and his students' use. By the summer of 1930 his first two papers were in the course of publication, in 1931 he was Rayleigh prizeman, and in 1932 he was elected to a Trinity fellowship.

A long visit to Helmut Hasse in Marburg in 1931 taught Davenport the power of modern algebra in the study of arithmetical questions, as well as giving him a fluent command of German, and their joint work proved to be notably influential. In Germany, Davenport met H. Heilbronn in Göttingen, and, by the time Heilbronn arrived in Cambridge as a refugee in 1933, the two had formed a friendship which led to a successful and lifelong collaboration. Several of their earliest papers were skilful applications of the celebrated circle method of Hardy and Littlewood to novel additive problems, and Davenport himself at this time made several highly original contributions to Waring's problem. He was, for example, the first to prove the best possible result that every sufficiently large integer is representable as the sum of sixteen fourth powers of integers. Years later the mastery he thus gained in all aspects of the circle method was to stand him in good stead in his work on values taken by quadratic and cubic forms in many variables. This work, whether done alone, with collaborators such as B. J. Birch and D. J. Lewis, or by students under his direction, is perhaps the most enduring part of Davenport's mathematical testament.

However, that was still in the future; in 1937, after the expiry of his fellowship, Davenport joined L. J. Mordell as an assistant lecturer in Manchester and set himself to study the geometry of numbers. Although Davenport was by now a scholar of international renown--in 1938 he received the Cambridge ScD, in 1940 he was elected to a fellowship of the Royal Society and won the Adams prize of the University of Cambridge--the Manchester period completed his mathematical education. In 1941 Davenport went to the chair of mathematics at the University College of North Wales in Bangor, where in 1944 he married a colleague from the modern languages department, Annie, daughter of James J. Lofthouse, engineer; there were two sons of the marriage.

In 1945 Davenport became Astor professor of mathematics in University College, London. He drew to him scholars and students from all parts of the world, and when, in 1958, he moved to the Rouse Ball chair of mathematics at Cambridge he recreated there the vitality of his London seminar. Many of his former students demonstrated awe-inspiring qualities; three were winners of Fields medals, 'the Nobel prize of mathematics', and Davenport was proud of them but careful of his many other less able students. He corresponded tirelessly with yet more students (in his beautiful handwriting), giving freely of his enthusiasm, wisdom, and patience.

In 1956 Davenport embarked on his important researches on quadratic forms and his success released a new vitality. From now until his death, and especially after his return to Cambridge, the scale and range of his mathematical activities increased. At the time of his death he was the unquestioned leader of the important British school of number theory.

Davenport was shy and reserved and in later years could put a slight deafness to good use. He was very conservative by temperament, and one of his favourite sayings was that all change was for the worse. He was always accessible, entirely without arrogance, and genuinely modest. While he admired talent enormously, he thought his own achievements more the result of tenacious study and perseverance. He was an outstanding lecturer and exceptionally lucid writer, and his book *The Higher Arithmetic* (1952) is a minor classic.

Davenport was awarded the senior Berwick prize of the London Mathematical Society in 1954, and in 1957-9 he was president of the society. He received the Sylvester medal of the Royal Society in 1967. In 1964 he had been elected an ordinary member of the Royal Society of Science in Uppsala, and in 1968 he received an honorary DSc from the University of Nottingham. He spent the summer term of 1966 at the University of Göttingen, as Gauss professor, the first Englishman to hold this distinguished visiting appointment. He died at Addenbrooke's Hospital, Hills Road, Cambridge, on 9 June 1969. His wife survived him.

HEINI HALBERSTAM, *rev.*

**Sources **

C. A. Rogers, D. A. Burgess, and others, *Memoirs FRS,* 17 (1971), 159-92

personal knowledge (1981)

private information (1981)

d. cert.

**Archives **

Trinity Cam., corresp. and papers

**Likenesses **

W. Stoneman, photograph, 1940, NPG *[see illus.]*

two photographs, RS

**Wealth at death **

£24,739: probate, 17 Nov 1969, *CGPLA Eng. & Wales*

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