# Heinrich Behnke

### Quick Info

Born
9 October 1898
Hamburg, Germany
Died
10 October 1979
Münster, Germany

Summary
Heinrich Behnke was a German mathematician who worked on complex analysis and wrote many articles on mathematicians.

### Biography

Heinrich Behnke was born in Horn, a suburb of Hamburg, into a Lutheran family. He entered Göttingen University in the autumn of 1918 where he attended lectures by Hilbert, Landau and Hecke. In [4] Behnke gives some details of Göttingen University at the time he studied there. Behnke began to work under Hecke, so when Hecke decided to accept the offer of a chair of mathematics at the newly founded university in Hamburg, Behnke was left with a difficult decision. On the one hand he wanted to continue to work with Hecke, but he had no wish to return to his home town. Behnke describes making the decision in [1] which saw him return to his home town to continue working for his doctorate. He submitted his doctoral thesis Über analytische Funktionen und algebraische Zahlen to Hamburg which he received in May 1922.

After receiving his doctorate he went to Heidelberg to study during the summer semester. There he met his future wife Aenne Albersheim who was the daughter of a Frankfurt-am-Main Jewish family. Returning to Hamburg in August he was appointed as an assistant and submitted his habilitation thesis to Hamburg in the summer of 1924 and, now with his lecturing qualification, he began lecturing in Hamburg. Behnke now considered himself to be sufficiently secure financially to marry Aenne Albersheim in the summer of 1925. Sadly Aenne died in childbirth in 1927 and Behnke found himself a widower with a child to support, though he still did not have the professorship he needed for permanent employment. At this time the Albersheim family rallied round and looked after Behnke's young son.

It was later in 1927 that Behnke received an offer of an ordinary professorship at the Westfälische Wilhelms University of Münster. Again Behnke faced a dilemma. On the one hand it was a great achievement to be offered a full professorship while still a Privatdozent, but on the other hand Münster was in a Roman Catholic region of Germany (and Behnke was a Lutheran) and it was the smallest Prussian university. Behnke consulted friends and colleagues before making his decision, and finally, when told that 'Münster is better than its reputation', he decided to accept. He still felt nervous as he travelled there to take up his appointment, and this was not helped by his mother-in-law and brother-in-law who travelled with him as far as Kassel but refused to continue the journey to Münster.

In Münster, Behnke met Barbara Marshall, a former mathematics student from Münster who came from a Roman Catholic family of intellectuals. They married in 1932 and soon after this Behnke's son, who up until then had been looked after by his first wife's family, was brought to Münster to be brought up by his father and stepmother. On 30 January 1933 the National Socialist party led by Hitler came to power in Germany. Behnke was an Aryan so was certainly not affected by the Civil Service Law, passed on 7 April 1933, which provided the means of removing Jewish teachers from the universities. However, Behnke's first wife had been Jewish, so his son was half Jewish. This became a constant source of worry to Behnke, who tried to keep this fact secret and, as a consequence, tried his best not to become involved in any political discussions. Of course anti-Semitism was rife in Germany long before the national Socialists came to power, but up to 1933 Münster, probably because of its Catholic tradition, had been little affected.

Henri Cartan spoke of his friendship with Behnke who soon built up a vigorous research group in Münster:-
... Behnke was a friend of mine. My first invitation to go to Germany occurred in May 1931. Behnke was teaching in Münster-in-Westfalen, and he had a lot of students, about 40. I was invited because I had published a note in the Comptes Rendus de l'Académie des Sciences about circled domains, where I had proved quite easily a theorem which had been proved earlier by Behnke, but under certain conditions, in a particular case. So I was invited to give several lectures in Münster.
Peter Tullen was an assistant of Behnke in Münster. Henri Cartan said:-
Behnke's assistant in 1931, namely Peter Thullen, was to become one of my best friends. We collaborated and wrote a paper together for the Mathematische Annalen. I always had a good relationship with Thullen.
Behnke and Thullen wrote the classic text Theorie der Funktionen mehrerer komplexer Veränderlichen (1934) which was the first systematic survey of the theory of domains in $\mathbb{C}^{n}$ or spread over $\mathbb{C}^{n}$, including basic properties of holomorphic and meromorphic functions, continuation problems, the Levi problem, meromorphic functions with prescribed zeros and poles (Cousin problems), domains of holomorphy, Runge approximation, holomorphic mappings and transformation groups.

Thullen was a Roman Catholic who took a major role in Catholic youth organisations until they were disbanded by the Nazis. He left for Rome in October 1933 telling Behnke that he could never return to Germany while Hitler was in power. Indeed he went to Ecuador and did not return to Europe until several years after the end of World War II. Behnke however took a different course of action. As he wrote in [1]:-
Had I known in 1933 all that was before us, I would not have had the courage to avoid escaping abroad. Also in the following Nazi years I frequently played with the idea of leaving, until Jewish friends made it clear to me that positions abroad must be kept open for them.
Mathematical life in Münster changed greatly over the years after the National Socialists came to power. When Henri Cartan visited Münster in 1931 there were about 200 students in the elementary mathematics classes. By 1933 there were 50 such students, and in the following two years there were 5 and 2 respectively. However the number of advanced students held up and, not having students studying elementary mathematics meant that research flourished. Behnke wrote [1]:-
The scientific work of the seminar ran better from 1935 to 1939 than at any other time. Here the trust between professors and students was not troubled in the slightest.
During this time three students of Behnke were awarded their doctorates. Friedrich Sommer received his doctorate in 1936 and, in 1937 Karl Stein and Wolfgang Rothstein received doctorates for their theses Zur Theorie der Funktionen mehrerer komplexer Veränderlichen; Die Regularitätshüllen niederdimensionaler Mannigfaltigkeiten and Zur Theorie der analytischen Abbildungen im Raume zweier komplexer Veränderlichen ; Das Verhalten der Abbildungen auf glatten analytischen Randhyperflächen respectively. Behnke wrote quite a number of joint papers with Stein during the years following World War II. For example they wrote Entwicklung analytischer Funktionen auf Riemannschen Flächen (1949), Konvergente Folgen nichtschlichter Regularitätsbereiche (1949), Elementarfunktionen auf Riemannschen Flächen als Hilfsmittel für die Funktionentheorie mehrerer Veränderlichen (1950), Die Singularitäten der analytischen Funktionen mehrerer Veränderlichen (1951), and Der Severische Satz über analytische Fortsetzung von Funktionen mehrerer Veränderlichen und der Kontinuitätssatz (1954).

Behnke became an editor of Mathematische Annalen in 1938. In 1939 he became worried about his responsibilities, particularly in regard to Blumenthal who was also an editor and had been supported in this role by Hilbert despite pressure for his dismissal exerted by the National Socialists since Blumenthal was Jewish. Behnke wrote to Hecke on 27 January 1939 (see [2]):-
The statement ... at the end of every volume that I am responsible for the text, today means something quite different from earlier years. ... Today it is a political obligation ... Neither the publisher, nor the other editors can protect me from the fact that I am the first who could be made liable for Blumenthal working with us.
Behnke continued as an editor of Mathematische Annalen until the end of 1972 except, of course, for the years between 1945 and 1947 when the journal ceased publication.

Travelling was one of Behnke's favourite pastimes and in particular he loved visiting Switzerland. Every year he took his summer holidays there and he was in Chexbres when it became clear that World War II was about the begin. He returned through Germany with difficulty due to mobilisation and by the time he reached Münster the university was closed. This did not stop students working for their doctorates, and in fact this gave professors more time to devote to such matters. After a semester the university reopened but now it was militarised. During the war, however, Behnke's worries about his son increased. He wrote to Hecke on 19 August 1942 [2]:-
You have certainly already heard of the new measures against half-Jews. According to them my son must now leave school. Süss wishes to enquire at the ministry whether I will be allowed to send my son to Switzerland. That is thoroughly uncertain and experienced colleagues have warned me. An accusation could still be brought against me on account of paragraph 71 of the civil service law if I tried to send him abroad. That could also be seen as an action inimical to the state. Sometimes one must simply doubt the sense of this world. Are we all only here in order to reciprocally torment one another?
He continued to teach at Münster and by the time the city was damaged in the first daylight bombing raid by the allies on 10 October 1943, Behnke was the only professor of mathematics left there. Parts of the university were damaged and the mathematics building became unusable. After Germany was defeated Behnke was appointed as Dean at Münster, holding this position until 1949.

We have mentioned above Behnke's classic text written with his assistant Thullen. He also published Klassische Funktionentheorie in two volumes, the first appearing in 1947, the second in the following year. He wrote another book with his former doctoral student Friedrich Sommer. This was Theorie der analytischen Funktionen einer komplexen Veränderlichen which was first published in 1955 with a second edition appearing in 1962. The book was based on lectures given by Behnke and Sommer at Münster:-
It pursues two objectives. The first is to give a rigorous detailed account of the classical theory of functions of a complex variable for beginning students who have had prior training in classical real analysis. The second is to give an account of the theory of Riemann surfaces and analytic functions on Riemann surfaces.
In 1956 Behnke published Vorlesungen über allgemeine Zahlentheorie which treated elementary number theory from an algebraic point of view. With Hans Grauert, Behnke wrote the paper Analysis in non-compact complex spaces (1960) which was based on a lecture Behnke gave at a conference on analytic functions at Princeton in 1957. It is a continuation of the report by Behnke given at the International Congress of Mathematicians in Amsterdam in 1954.

In addition to his work on complex analysis, Behnke wrote many articles on mathematicians. For example he published works on Weierstrass, Toeplitz, Reidemeister, Hopf, Aleksandrov, Klein, Blumenthal, von Neumann, and Lorey. He also was a leading expert on mathematical education publishing articles such as Freiheit und Autorität im mathematischen Leben (1972) which considers the professor-student relationship and the way in which a framework, like the Erlanger program, may be immensely stimulating and yet end by being stifling and having to be discarded. Also Die Autonomie der Geometrie (1971) which considers the way that geometry is taught in schools.

### References (show)

1. H Behnke, Semesterberichte (Göttingen, 1978).
2. S L Segal, Mathematicians under the Nazis (Princeton, NJ, 2003).
3. H Behnke, Die goldenen ersten Jahre des Mathematischen Seminars der Universität Hamburg, Mitt. Math. Gesellsch. Hamburg 10 (4) (1976), 225-240.
4. H Behnke, Die hohe Zeit Göttingens. Zu einer Biographie über Hilbert, Math.-Phys. Semesterber. 18 (1971), 1-6.
5. H Griesel, Zur Vollendung des 80. Lebensjahres von Prof. Dr. Dr. h.c. Dr. h.c. Heinrich Behnke (Münster) am 9. Oktober 1978, Praxis Math. 20 (1) (1978), 305-306.
6. H Grauert and R Remmert, In memoriam Heinrich Behnke (German), Math. Ann. 255 (1) (1981), 1-4.
7. O Krafft, Heinrich Behnke - 50 Jahre Doktor der Mathematik, Math.-Phys. Semesterber. 21 (1974), 1-4.
8. V R Remmert, Ungleiche Partner in der Mathematik im 'Dritten Reich' : Heinrich Behnke und Wilhelm Süss, Math. Semesterber. 49 (1) (2002), 11-27.
9. H Tietz, Heinrich Behnke (German), Math.-Phys. Semesterber. 27 (1) (1980), 1-3.
10. H Tietz, Im Herbst des Lebens. Heinrich Behnke zum 80. Geburtstag, Math.-Phys. Semesterber. 25 (2) (1978), 165-171.
11. H Tietz, Menschen - Mein Studium, meine Lehrer, Mitt. Dtsch. Math.-Ver. (4) (1999), 43-52.