Behrend studied number theory for his doctorate at the University of Berlin with Erhard Schmidt as his advisor. He was awarded his doctorate in 1933 for his dissertation Über numeri abundantes Ⓣ. Even before the award of his doctorate he had published three papers on number theory, the first two being Über einen Satz von Herrn Jarnik Ⓣ (1932) and Über numeri abundantes Ⓣ (1932). Of course 1933, the year that Behrend was awarded his doctorate, was also the year that Hitler came to power in Germany. We have not mentioned earlier that the Behrend family were Jewish since it had not seemed particularly significant prior to 1933. However on 7 April 1933 the Nazis passed a law which, under clause three, ordered the retirement of civil servants who were not of Aryan descent, with exemptions for participants in World War I and pre-war officials. This did not affect Behrend directly since he was not in employment at this time, but it quickly affected the family. Behrend's father was, by this time, headmaster of a leading Berlin school and he was first demoted and later dismissed from his post.
After the award of his doctorate Behrend decided to leave Germany and continue his studies away from Nazi influence. He went first to England, where he studied at Cambridge, then moved to Zürich and finally to Prague. In Prague he worked as an actuary in a life insurance company but also undertook research in pure mathematics at the Charles University and was awarded a D.Sc. for his significant contributions in 1938. At this time he published Über Systeme reeller algebraischer Gleichungen Ⓣ which appeared in Compositio Mathematica in 1939. The Nazi threat which had made him leave Germany in 1933 was by this time making him feel unsafe in Prague. He left Prague in 1939, returning first to Zürich, and then to London in England shortly before the outbreak of World War II.
Like many Germans who fled from the Nazi threat, he found himself in England which was at war with his native Germany. He continued his work on number theory and published On obtaining an estimate of the frequency of the primes by means of the elementary properties of the integers in the Journal of the London Mathematical Society in 1940. The fact that he was passionately anti-Nazi did nothing to help save him from being interned as an enemy alien in 1940 and he was put on the ship the Dunera bound for Australia. He served periods of internment at Hay, Orange and Tatura in Australia. His experiences in Camp 7 at Hay during 1940-41 are related in . One should not think that internment meant an end to mathematics, for he gave lecture courses at the Camp and prepared some of his younger fellow internees for mathematics examinations at the University of Melbourne.
After his release in 1942, Behrend was appointed as a tutor at the University of Melbourne. He continued his research in number theory and published On the frequency of the primes in the Journal of the Royal Society of New South Wales in 1942. This paper was a continuation of the one he had published in London two years earlier. In the following year he published a paper on a totally different topic. This was A polyhedral model of the projective plane which also appeared in the Journal of the Royal Society of New South Wales. Donald Coxeter reviewed the paper, writing:-
The author improves upon the work of Merz and Humbert (1942) by constructing a simpler model of the projective plane in the form of a polyhedron in ordinary space without any singular vertices. There are 6 vertices of degree 3, 6 of degree 4, 21 edges, 9 quadrangular faces and one hexagonal face. Six of the quadrangular faces penetrate one another along "false edges." Adequate instructions are given for carrying out the construction in paper or thin cardboard.Behrend was promoted to lecturer in the Mathematics Department of the University of Melbourne in 1943, then to senior lecturer in 1948, and finally to associate professor 1954-62. He maintained his interest in number theory, writing On sets of integers which contain no three terms in arithmetical progression in 1946. Two years later he again published on a new topic with his paper The uniform convergence of sequences of monotonic functions. In the same year of 1948 he also published Generalization of an inequality of Heilbronn and Rohrbach and Some remarks on the distribution of sequences of real numbers, with Some remarks on the construction of continuous non-differentiable functions being published in the Proceedings of the London Mathematical Society in the following year.
In A contribution to the theory of magnitudes and the foundations of analysis (1956) Behrend characterised the additive semigroup of positive real numbers, the "magnitudes" of the title. In the same year in Note on the compactification of separated uniform spaces he gave a simple method of obtaining, for any uniform space S, a uniform structure which is totally bounded and compatible with the topology of S. He gave criteria for the uniformizability of a topological space in Uniformizability and compactifiability of topological spaces (1957). His main interest had by now firmly moved from number theory to topology and he is particularly remembered for introducing modern general topology to the University of Melbourne.
Behrend is commemorated by the 'Behrend memorial lecture in mathematics', established at the University of Melbourne in 1963 with funds provided by his widow.
For more information about Behrend's life and details of his outstanding contributions to teaching see his obotuary at THIS LINK.
Article by: J J O'Connor and E F Robertson