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.

His work for a German subsidiary of the Bell Telephone Company brought him into contact with leading American engineers in the field of filters.

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 became interested in mathematics at the age of thirteen and continued to demonstrate that he was academically inclined as he grew.

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.

His paper, A reactance theorem,[9] is a milestone in filter theory and inspired Cauer to generalise this approach into what has now become the field of network synthesis.

[5] 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.

[10] In 1927 Cauer went to work as a research assistant at Richard Courant's Institute of Mathematics at the University of Göttingen.

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.

[5] Cauer met, and had strong contacts with, many of the key researchers in the field of filter design at Bell Labs.

[11] 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.

By contrast, his correspondence with his American and European acquaintances was warm, technically deep and often included personal family news and greetings.

[12] 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.

[11] After leaving the Technical Institute for Mix & Genest, Cauer sought to become active in the Verband Deutscher Elektrotechniker (VDE, the German Electrical Engineers Society).

[12] 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 anti-Jewish hysteria of the time forced many academics to leave their posts, including the director of the Mathematics Institute, Richard Courant.

[1] Soviet intelligence was actively looking for scientists they could use in their own researches and Cauer was on their list of people to find but it would seem that this was unknown to his executioners.

He is considered the founder of the field and the publication of his principal work in English was enthusiastically greeted, even though this did not happen until seventeen years later (in 1958).

However, it was soon realised that Cauer's Tchebyscheff approximation could just as easily be applied to the rather more useful ladder topology and ideal transformers could be dispensed with.

In his habilitation thesis[c] Cauer begins to extend this work by showing that a global canonical form cannot be found in the general case for three-element kind multiports (that is, networks containing all three R, L and C elements) for the generation of realisation solutions, as it can be for the two-element kind case.