Wilhelm Cauer

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24 June 1900
Berlin, Germany
22 April 1945
Berlin, Germany

Wilhelm Cauer was a German mathematician and physicist who is best known for his work on the analysis and synthesis of electrical filters.


Wilhelm Cauer's mother came from a family with a tradition of being academics or ministers of the church. His father, also named Wilhelm Cauer, was professor of railway engineering at the Technical University of Berlin. Wilhelm, the subject of this biography, was the sixth of his parents' children. Few people can have attended a Gymnasium founded by their great-grandfather situated on a street named after the family - in this case the Cauerstrasse - but this was the start in life that young Wilhelm had. This both encouraged the young lad to study hard but it also made him realise just how much he had to live up to. Emil Cauer, Wilhelm Cauer's son, writes about the family in [1]:-
In general, the family had a high and idealistic belief in the value of education. Even my grandfather's sisters and their stepmother published books while and were active in the women's liberation movement. In a time when some professors still did not tolerate female students, three of my father's sisters completed their doctor's thesis. But at the same time, the males were distanced from the social problems of those times. They were patriotic in an uncomplicated fashion and believed that science and learning were completely independent of politics. They had a high opinion of individual freedom as well as of individual duty to the 'Fatherland'.
It was at the start of his studies at the Mommsen Gymnasium in Berlin that Cauer became fascinated by mathematics and decided that he wanted to make his career in that topic. His mathematics teacher at the Gymnasium was H Beck who was convinced that Cauer should become a university professor. World War I was in progress throughout much of the years he spent in the Gymnasium and when he graduated in June 1917 he was drafted into the army. This was close to the end of the war so Cauer only served for a few months before being able to begin his studies at the Berlin-Charlottenburg Technische Hochschule at Easter 1918. While he was studying here, his former teacher Beck wrote to him in 1920 [1]:-
My dear Mr Cauer: That's a bit too much - to expect you to become a school teacher. You would be eaten alive by the boys. ... I tell you what you should become - a professor, for this profession has the least to do with life. ... I told your father six or seven years ago that you were a born professor.
Beck had progressed from being a Gymnasium teacher to becoming professor of mathematics at Bonn University and, in 1921, Cauer went to Bonn to continue his studies of mathematics and theoretical physics at the university there. Back in Berlin, he began to work for his doctorate under Max von Laue at the University of Berlin on 2 February 1923. He worked on general relativity and published his first paper on that topic in 1923. However, his relationship with von Laue seems to have broken down and Cauer moved to the Berlin-Charlottenburg Technische Hochschule where he was employed as an assistant to Reissner and began to investigate problems in the area of electrical engineering. He was awarded a diploma in "Technical Physics" on 24 March 1924 and later that year, on 1 August, he started working for the Mix & Genest Company, a branch of the Bell Telephone Company working on communication and telephone systems. The important ideas he began to work on at this time were to lead to major developments [4]
... many "ingredients" of a systematic synthesis theory were in the air when Cauer started his scientific career. Especially Foster's reactance theorem was a first conscious step towards a thorough mathematical description of classes of circuits. Cauer immediately recognised the potentialities of Foster's ideas and started a private correspondence with Foster.
In 1925 Cauer married Karoline Cauer, who was related to him; they had six children including the son Emil (mentioned above) who was one of the authors of [1], [2] and [3]. Cauer left the Mix & Genest Company in November 1925 and continued to work at the Berlin-Charlottenburg Technische Hochschule for his doctorate. He was an assistant to Georg Hamel who acted as his thesis advisor. He was awarded a doctorate for his thesis Die Verwirklichung der Wechselstromwiderstände vorgeschriebener Frequenzabhängigkeit on 7 July 1926. This thesis was a significant contribution containing a complete program for network synthesis. Interested in using computers to solve systems of linear equations, he contacted Richard Courant at Göttingen and Vannevar Bush who was developing mechanical computers at the Massachusetts Institute of Technology. Cauer had prepared his habilitation thesis and was ready to submit it by the beginning of 1928. However, there were difficulties regarding him submitting it to the Berlin-Charlottenburg Technische Hochschule so Courant suggested that Cauer transfer to Göttingen. He registered at Göttingen on 1 April 1928 and became a research assistant at Courant's Institute of Mathematics at the University of Göttingen. He submitted his habilitation thesis Untersuchungen über ein Problem, das drei positiv definite quadratische Formen mit Streckenkomplexen in Beziehung setzt to Göttingen in June 1928.

In February 1930 Cauer was awarded a scholarship by the Rockefeller Foundation to allow him to visit the United States. He sailed for the United States with his wife later in that year. In the first half of 1931 he visited Vannevar Bush at the Massachusetts Institute of Technology where he also met Norbert Wiener. An invitation from Oswald Veblen to visit Harvard gave him the chance to meet Eberhard Hopf and David Tamarkin. Before returning to Europe, he worked for the Wired Radio Company in Newark, New Jersey, for three months before sailing back to Germany via Southampton in England. While in the United States he published The Poisson integral for functions with positive real part in the Bulletin of the American Mathematical Society. Back in Göttingen he wanted to build a calculating machine to solve linear equations but, despite having progressed well with the project, this was a time when funding was impossible due to the Depression so it could not proceed. In 1933 the Nazis came to power and, almost immediately, passed their racial laws which saw academics with one Jewish grandparent dismissed from their posts. This had a devastating effect on mathematics at Göttingen but Cauer made efforts to ride out the political storm. Emil Cauer writes [3]:-
But in those days of hysterical investigations it soon became known that one of Cauer's ancestors had been a certain Daniel Itzig (1723-1799), a banker of the Prussian king Frederick II, among whose descendents were a number of well-known bankers, statesmen and composers. Although this did not mean that my father was going to be affected by the Nazi race laws, he was given to understand that there was no future for him at the University of Göttingen.
Cauer also suffered from the problem that his work was not appreciated, really being too innovative to make an immediate impact. His attempts to obtain a professorship at Darmstadt were unsuccessful and by 1934 he was fully aware that he would never obtain a professorship. He made applications to firms such as Philips, Siemens, Telefunken, Deutsche Versuchsanstalt für Luftfahrt, and the aircraft firms Henschel and Junkers but they all rejected his applications for posts in 1934-35. In July 1936 he was employed at Fieseler & Storch aircraft company, then in 1936 he became a director of the laboratory at Mix & Genest. This gave him financial security and, from 1939 onwards, he lectured at the Technical University of Berlin. Cauer published the papers Das Poissonsche Integral und seine Anwendungen auf die Theorie der linearen Wechselstrom-schaltungen (Netzwerke) and Bemerkung über eine Extremalaufgabe von E Zolotareff in 1940. R M Foster, who had corresponded with Cauer for many years, reviewed the first of these papers:-
This is an exposition of the theory of the Poisson integral, especially designed to exhibit those properties which find immediate application in electrical network theory. The importance of the Poisson integral in this field is largely due to the possibility of the representation in this integral form of positive real functions (functions which are regular in the right-hand half-plane, with non-negative real parts in that half-plane, and with real values on the real axis), as previously discussed by the author ...
In 1941 Cauer published the first volume of his classic text Theorie der linearen Wechselstromschaltungen . He had not found it easy to find a publisher for the book which he had largely written during a sabbatical semester during the years 1934-35. He offered his book to the publisher Teubner in December 1935 but they rejected it in 1938. He also offered it to Springer in January 1936 but he was successful when he offered it to Akademische Verlagsgesellschaft in November 1939. R Kahal wrote in his review of the second edition of the book which appeared in 1954:-
The reappearance of this compendium on linear circuit theory will be a welcome event to network enthusiasts. There is no other text in any language quite comparable with this book. The material included contains a considerable amount of Cauer's own researches as well as the work of other European workers which is not generally well-known in this country. ...
An English translation entitled Synthesis of linear communication networks was published in 1958. A second volume of the work was written by Cauer but was destroyed in 1943 in a bombing raid. He did not despair over this but set about rewriting the text from scratch. Having completed the manuscript of the second volume for the second time, he put it into the safe at Mix & Genest but the Russian soldiers destroyed it after the fall of Berlin. Emil Cauer, who was born in 1932, remembers the war years:-
I remember my mother ruling over the family, while my father, home from his office, would withdraw into his study to work on mathematical formulae. He even used to work while we crouched in our air raid shelter during World War II bombing attacks. I would not say he was a workaholic, but that he was dedicated to his work and inclined to be single-minded. He did not like to waste time, and he distinguished the important from the unimportant. This helped him to be broadminded and generous. He was warm and gentle towards me as a child, though sparing of words. He liked to play chess with me, patiently waiting for me to make my helpless moves and briefly explaining where I had gone wrong. I remember with particular affection the evening hours when the family would sit in his study whilst he read out loud in German from foreign books such as 'Robinson Crusoe' by Daniel Defoe.
As the Russian forces approached Berlin, Cauer took his family to stay with relatives in the small town of Witzenhausen in Hesse, about 30 km from Göttingen. He had given some of his unpublished papers to friends in Göttingen as he felt that this would give them a better chance of surviving. Two days before the American army captured Witzenhausen, Cauer left the town and returned to Berlin. It is not quite clear what his reasons were - possibly to support his colleagues in Berlin, perhaps just out of a determination to carry on with his work. Although his name was on a list of scientists that the Russians wanted to capture and use to help with their own scientific advances, this was not known to the soldiers in the Russian army that entered Berlin on 22 April 1945. He was executed by these soldiers in the garden of his home.

Cauer's family assembled the papers he had left with friends in Göttingen and published them after the war ended. Synthesis of Linear Communication Networks was published in New York in 1958 and Theorie der linearen Wechselstromschaltungen, Vol. II was published in Berlin in 1960. Some of the material here would have formed part of the lost second volume, although presumably in a rather different form. Let us end this biography by quoting from Pauli [4]:-
Cauer's program marked a milestone in the development of network synthesis towards a mathematical description of classes of circuits - and hence towards what we nowadays call mathematical systems theory. It is to Cauer's merit that he turned network and system synthesis into a truly systematic business. He provided it with the appropriate mathematical framework just as the discipline was on the rise starting from Foster's reactance theorem. In contrast to the purely utilitarian or engineering approach, Cauer emphasised the scientific aspects and provided the first precise statement of the network synthesis problem, one that has become a valid paradigm for all synthesis problems.

References (show)

  1. E Cauer, W Mathis and R Pauli, Life and Work of Wilhelm Cauer (1900-1945), Proc. Fourteenth International Symposium of Mathematical Theory of Networks and Systems, Perpignan, France, June 19-23, 2000.
  2. E Cauer and W Mathis, Wilhelm Cauer: His Life and the Reception of his Work (University of Hannover, 2002).
  3. E Cauer and W Mathis, Wilhelm Cauer (1900-1945), AEÜ Int. J. Electron. Commun. (1995), 243-251.
  4. R Pauli, The Scientific Work of Wilhelm Cauer and its Key Position at the Transition from Electrical Telegraph Techniques to Linear Systems Theory, Proc. 16th Eur. Meeting on Cybernetics and Systems Research, Vienna, 2-5 April 2002 2 (2002), 934-939.

Additional Resources (show)

Written by J J O'Connor and E F Robertson
Last Update March 2011