by P. M. Cohn

© Oxford University Press 2004 All rights reserved

**Heilbronn, Hans Arnold** (1908-1975), mathematician, was born on 8 October 1908 in Berlin, the son of Alfred Heilbronn, timber merchant, and his wife, Gertrud. No details of his ancestry are known, but the name (after a town in Baden-Württemberg) was not infrequent among Jews and suggests that the family was resident in Germany for a number of generations.

From 1914 to 1926 he attended the Heinrich von Kleist Realgymnasium, Berlin, and then entered university, reading first medicine, then mathematics and natural science in Berlin, Freiburg, and Göttingen. Mathematics soon became his main interest and in 1930 he became assistant to E. Landau at Göttingen. In 1931 he gained his DPhil for a thesis using function theory to improve prime number estimates. With his first few papers on prime numbers and analysis (some written jointly with Landau) he had begun to make a name for himself when Hitler's rise to power in 1933 effectively barred academic careers for Jews in Germany.

Landau, a man of high standards, had formed a good opinion of Heilbronn, and Harold Davenport, who had met Heilbronn in Germany, described him as 'one of the most promising German mathematicians' (Cassels and Fröhlich, 120). In November 1933 Heilbronn moved to Britain, supporting himself at first until, with the help of the Academic Assistance Council, he obtained a one-year position at Bristol University. At this time there was much interest in a conjecture made by Gauss in the early 1800s on the class number of definite binary quadratic forms, which was closely related to a problem on quadratic number fields. Some progress towards its proof had been made; building on this work, Heilbronn was able to prove Gauss's conjecture. His work represented important steps in an area of research that has remained active. In 1935 he was awarded a Bevan fellowship at Trinity College, Cambridge, and he spent the next five years there, during which time he wrote a dozen papers, some with Davenport, mainly on 'Waring's problem'. At this time he was able to help his parents and sister leave Germany and they made their home in Cambridge. When his fellowship expired in 1940, Trinity College council resolved to continue his position and salary, but, like many other refugees, he was interned. On his release he joined the Pioneer Corps and later the intelligence corps.

In 1946 Heilbronn returned to Bristol as reader; from 1949 he was professor and head of department. His research, interrupted by the war, resumed, as witness his elegant and decisive contributions on Euclid's algorithm, Zeta-functions, and the geometry of numbers. As a bachelor Heilbronn lived at Hawthorn's Hotel, across the road from the mathematics department, going to his family in Cambridge during vacations. Tall and athletic in appearance, he was keen on sports, especially rowing and tennis. His somewhat formal manner and the duelling scars he carried from his student days could be overpowering at first, but his friendly attitude, lacking all pomposity or aggressiveness, won him many friends. He was an excellent lecturer, always accessible to his students and taking an interest in their work, though his intellectual honesty did not allow him to pass over in politeness whatever he considered below standard. In all he exerted a major influence on mathematicians of the younger generation going well beyond what was recorded in print.

Towards the end of the 1950s, feeling concerned that government plans for university expansion would lead to a drop in standards, Heilbronn tried to convince policy makers of the dangers that lay ahead. This remained without effect so with characteristic directness he resigned his chair at Bristol and left the university in 1964. On 19 March of the same year he married Mrs Dorothy Greaves (1899/1900-1990), daughter of Philip Henry Shaw, a widow who lived in Cambridge and with whom he shared a keen interest in bridge. He also took up an invitation to spend some time in Caltech, and later that year he and his wife settled in Toronto, where he had accepted a chair at the university. Here he built up an active research school. Heilbronn was elected fellow of the Royal Society in 1951 and of the Royal Society of Canada in 1967. He was also a member (and during 1959-61 president) of the London Mathematical Society, the American Mathematical Society, and the Canadian Mathematical Congress. He was involved in planning the International Congress of Mathematicians in Vancouver in 1974, but at this time his previously robust health began to fail. He died on 28 April 1975 during an operation to implant a pacemaker. His widow on her death (13 September 1990) left a substantial sum to Trinity College, Cambridge, reportedly to fund scholarships for mathematics students from Europe.

P. M. COHN

**Sources **

J. W. S. Cassels and A. Fröhlich, *Memoirs FRS,* 22 (1976), 119-35

E. J. Kani and R. A. Smith, *The collected papers of Hans Arnold Heilbronn* (1988)

Mrs Linfoot, *Mathematical Intelligencer,* 15 (1993), 39-43n

private information (2004)

m. cert.

**Archives **

Bodl. Oxf., Society for Protection of Science and Learning MSS and home office files

Trinity Cam., corresp. with Harold Davenport

**Likenesses **

photograph, repro. in Cassels and Fröhlich, *Memoirs FRS,* facing p. 119

photograph, repro. in Kani and Smith, *Collected papers,* 1

photograph, repro. in Linfoot, *Mathematical Intelligencer,* 39

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