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Harold Davenport attended Accrington Grammar School. His main interests were mathematics and chemistry, and in 1924 he obtained a scholarship to attend Manchester University. He studied mathematics at Manchester being taught complex analysis by Mordell and applied mathematics by Milne. He graduated in 1927.
After Manchester he went to Trinity College, Cambridge to take another 'first degree' which was a common thing to do at that time. Coxeter was among the friends he made at Cambridge. Coxeter wrote:
When Davenport was working for the Tripos he seemed wonderfully relaxed. He would give me a cheerful welcome whenever I dropped in to see him under the Clock in Trinity Great Court. I would find him listening to Scheherazade on the phonograph or reading Gibbon's 'Decline and Fall' for the third time.Davenport was most attracted by Littlewood's lectures on the theory of primes and Besicovitch on almost periodic functions. Davenport wrote a Ph.D. thesis at Cambridge under Littlewood's supervision. He was awarded a Trinity fellowship in 1932 and soon after taking up the fellowship he visited Hasse in Marburg and wrote an important joint work with him.
Davenport met Heilbronn while in Germany and they worked together for many years. After returning to Cambridge his research struck an incredibly rich vein and he published a great number of papers. At this time life in Cambridge was enriched by a large number of visiting mathematicians who were escaping from the Nazi threat on the continent. Those who interacted with Davenport included Richard Rado, Hirsch, Courant, Taussky (later TausskyTodd), Kober and Mahler.
He left Cambridge in 1937, accepting an offer from Mordell of an assistant lectureship at the University of Manchester. At Manchester he was influenced by Mordell to become interested in the geometry of numbers and Diophantine approximation. While at Manchester he had Mahler, Erdös and Beniamino Segre as colleagues.
In 1941 Davenport was appointed to the chair of mathematics at the University College of North Wales at Bangor. Then London in 1945 he succeeded Jeffrey as Astor professor of mathematics in London. In 1958 he returned to Cambridge as Rouse Ball professor.
Davenport worked on number theory, in particular the geometry of numbers, Diophantine approximation and the analytic theory of numbers. He wrote a number of important textbooks and monographs. The higher arithmetic (1952) was a book written at a low level in an attempt to bring results in number theory before as wide an audience as possible.
He wrote a monograph Analytic methods for Diophantine equation and Diophantine inequalities (1962) which includes many of his contributions extending the HardyLittlewood method. He also wrote an important monograph on the analytic approach to the theory of the distribution of primes Multiplicative number theory (1967).
Davenport was elected a Fellow of the Royal Society in 1940 while still an assistant lecturer, receiving its Sylvester Medal in 1967:
... in recognition of his many distinguished contributions to the theory of numbers.He was President of the London Mathematical Society during 195759, and was awarded the Berwick Prize of the Society in 1954.
Davenport described his philosophy of mathematics in the following way:
Mathematicians are extremely lucky, they are paid for doing what they would by nature have to do anyway. One should not have a nonteaching fellowship too long, there comes a time when one must make a contribution to society. Great mathematics is achieved by solving difficult problems not by fabricating elaborate theories in search of a problem.Always a heavy smoker (he tried to give up the habit several times but always failed), Davenport succumbed to lung cancer at a young age. His influence on those around him is summed up in [6] as follows:
... the extent which he helped others can only be guessed, he was probably responsible for encouraging work at least as extensive as his own. ... He made his collaborators and colleagues his friends, and gave them generously of his humour and wisdom. He made a practice of writing helpful letters to all who approached him on mathematical matters whether they were professionals, students, amateurs or even cranks. By correspondence and by direct contact he stimulated and encouraged many mathematicians to do much of their best mathematics.References (7 books/articles)
References elsewhere in this archive:
Harold Davenport was elected to the Royal Society of London in 1940. You can see a history of the Royal Society and a list of the members among the mathematicians in our archive.
He was awarded the Sylvester Medal of the Royal Society in 1967. You can see a history of the Sylvester Medal and a list of the winners.
H Davenport was the London Mathematical Society President in 1957  1959. You can see a history of the LMS and a list of the presidents.