Wilhelm Cauer (24 June 1900 – 22 April 1945) was a German mathematician and scientist. He is most noted for his work on the analysis and synthesis of electrical filters and his work marked the beginning of the field of network synthesis. Prior to his work, electronic filter design used techniques which accurately predicted filter behaviour only under unrealistic conditions. This required a certain amount of experience on the part of the designer to choose suitable sections to include in the design. Cauer placed the field on a firm mathematical footing, providing tools that could produce exact solutions to a given specification for the design of an electronic filter.
Cauer initially specialised in general relativity but soon switched to electrical engineering. His work for a German subsidiary of the Bell Telephone Company brought him into contact with leading American engineers in the field of filters. This proved useful when Cauer was unable to feed his children during the German economic crisis of the 1920s and he moved to the US. He studied early computer techniques in the US prior to returning to Germany. According to Wilhelm Cauer's son Emil the rise of Nazism in Germany stifled Cauer's career because he had a remote Jewish ancestor. Cauer was murdered during the fall of Berlin by Soviet soldiers.
The manuscripts for some of Cauer's most important unpublished works were destroyed during the war. However, his family succeeded in reconstructing much of this from his notes and volume II of Theorie der linearen Wechselstromschaltungen was published after his death. Cauer's legacy continues today, with network synthesis being the method of choice for network design.
Wilhelm Adolf Eduard Cauer was born in Berlin, Germany, on 24 June 1900. He came from a long line of academics. His early grammar school (gymnasium) was the Kaiserin Augusta Gymnasium, an institution founded by his great-grandfather, Ludwig Cauer. This school was located on Cauerstrasse, named after Ludwig, in the Charlottenburg district of Berlin. The building still exists, but is now a primary school, the Ludwig Cauer Grundschule. He later attended the Mommsen Gymnasium, Berlin. His father, also Wilhelm Cauer, was a Privy Councillor and a professor of railway engineering at the Technische Hochschule in Charlottenburg (now Technische Universität Berlin). Cauer became interested in mathematics at the age of thirteen and continued to demonstrate that he was academically inclined as he grew.
Briefly, Cauer served in the German army in the final stages of World War I. He married Karoline Cauer (a relation) in 1925 and eventually fathered six children.
Cauer started off in a field completely unrelated to filters; from 1922 he worked with Max von Laue on general relativity, and his first publication (1923) was in this field. For reasons that are not clear, he changed his field after this to electrical engineering. He graduated in applied physics in 1924 from the Technische Hochschule in Charlottenburg (now Technische Universität Berlin).
He then spent a period working for Mix & Genest, a branch of the Bell Telephone Company, applying probability theory to telephone switching. He also worked on timer relays. He had two telecommunications-related publications during this period on "Telephone switching systems" and "Losses of real inductors".
The relationship of Mix & Genest with Bell gave Cauer an easy path to collaboration with AT&T's engineers at Bell Labs in the US which must have been of enormous help when Cauer embarked on a study of filter design. Bell were at the forefront of filter design at this time with the likes of George Campbell in Boston and Otto Zobel in New York making major contributions. However, it was with Ronald M. Foster that Cauer had much correspondence and it was his work that Cauer recognised as being of such importance. His paper, A reactance theorem, is a milestone in filter theory and inspired Cauer to generalise this approach into what has now become the field of network synthesis.
In June 1926 Cauer presented his thesis paper, The realisation of impedances of specified frequency dependence[a], at the Institute of Applied Mathematics and Mechanics of the Technische Hochschule Charlottenburg. This paper is the beginning of modern network synthesis.
In 1927 Cauer went to work as a research assistant at Richard Courant's Institute of Mathematics at the University of Göttingen. In 1928 he obtained his habilitation and became an external university lecturer.
Cauer found that he could not support his family during the economic crisis of the 1920s and in 1930 took his family to the USA where he had obtained a scholarship (a Rockefeller fellowship) to study at MIT and Harvard University. He worked with Vannevar Bush who was building machines for the solution of mathematical problems. Essentially, these were what we would now call analogue computers: Cauer was interested in using them to solve linear systems to aid in filter designs. His work on Filter circuits[b] was completed in 1931 while still in the US.
Cauer met, and had strong contacts with, many of the key researchers in the field of filter design at Bell Labs. These included Hendrik Bode, George Campbell, Sidney Darlington, Foster and Otto Zobel.
For a short while, Cauer worked for the Wired Radio Company in Newark, New Jersey but then returned to Göttingen with the intention of building a fast analogue computer there. However, he was unable to obtain funding due to the depression.
Cauer seems to have got on very poorly with his German colleagues. According to Rainer Pauli, his correspondence with them was usually brief and business-like, rarely, if ever, discussing issues in depth. By contrast, his correspondence with his American and European acquaintances was warm, technically deep and often included personal family news and greetings. This correspondence went beyond his American contacts and included A.C. Bartlett of the General Electric Company in Wembley, Roger Julia of Lignes Télégraphiques et Téléphoniques in Paris, mathematicians Gustav Herglotz, Georg Pick and Hungarian graph theorist Dénes Kőnig.
After leaving the Technical Institute for Mix & Genest, Cauer sought to become active in the Verband Deutscher Elektrotechniker (VDE, the German Electrical Engineers Society). He left the VDE, however, in 1942 after a serious falling out with Wagner, previously his PhD supervisor and ally.
In November 1933 Cauer signed the Vow of allegiance of the Professors of the German Universities and High-Schools to Adolf Hitler and the National Socialistic State.
The rising force of Nazism became a major obstacle to Cauer's work from 1933 onwards. The anti-Jewish hysteria of the time forced many academics to leave their posts, including the director of the Mathematics Institute, Richard Courant. Although Cauer was not Jewish, it became known that he had a Jewish ancestor, Daniel Itzig, who had been a banker to Frederick II of Prussia. While this revelation was not sufficient to have Cauer removed under the race laws, it stifled his future career. Thus he gained the title of professor but was never given a chair.
By 1935 Cauer had three children whom he was finding increasingly difficult to support, which prompted him to return to industry. In 1936 he temporarily worked for the aircraft manufacturer Fieseler at their Fi 156 Storch works in Kassel and then became director of the laboratory of Mix & Genest in Berlin. Nevertheless, he did continue to lecture at the Technische Hochschule Berlin from 1939.