Maruhn was awarded his doctorate from the Faculty of Philosophy of the University of Leipzig in 1930 for his thesis Ein Beitrag zur mathematischen Theorie der Gestalt der Himmelsjörper Ⓣ. His thesis advisor was Leon Lichtenstein (1878-1933) and in the years before obtaining his doctorate Maruhn had been Lichtenstein's assistant. The second examiner for his thesis had been Julius Bauschinger (1860-1934) who, along with Gustave Stracke (1887-1943), published Tafeln zur theoretischen Astronomie Ⓣ in 1934. Maruhn's doctoral thesis was published as a 20-page paper in Mathematische Zeitschrift in 1931.
Maruhn sat the State examination to become a Gymnasium teacher in 1931 and he then taught at a number of different schools in Leipzig until 1935. At first he was a trainee teacher, then a Studienassessor, that is a graduate teacher who has recently completed his training. During these years as a school teacher he was very active in research publishing the papers: Über den Laplaceschen Ringkörper Ⓣ (submitted from Leipzig on 26 January 1932), Über den von Laplace postulierten Urkörper Ⓣ (submitted from Leipzig on 6 January 1933), Über einige Gleichgewichtsfiguren rotierender Flüssigkeiten, auf deren Oberflächen singuläre Punkte liegen Ⓣ (submitted from Leipzig on 17 November 1933), Über zwei Gleichgewichtsfiguren rotierender inhomogener Flüssigkeit Ⓣ (submitted from Leipzig on 14 April 1934), and Über die Verzweigung der Lösung einer Integro-Differentialgleichung aus der Theorie der Gleichgewichtsfiguren rotierender Flüssigkeiten Ⓣ (submitted from Leipzig on 30 October 1934). All these papers continue work done by Maruhn's former research advisor Leon Lichtenstein. In 1934 Maruhn married Eva Feldt.
In 1935 Maruhn became a research associate at the German experimental station for flight, the Deutschen Versuchsanstalt der Luftfahrt, which was situated in Berlin-Adlershorst. This German Research Institute for Aviation, founded in 1912, was situated at the former Johannisthal-Adlershof airfield. During most of the time Maruhn worked there the director was Günther Bock. At the Institute Maruhn :-
... occupied himself with rigorous solutions for the flow around ellipsoidal bodies, and thereby obtained both beautiful and numerically valuable results.From Berlin, he submitted the paper Zur Theorie der Gleichgewichtsfiguren rotierender inhomogener Flüssigkeiten Ⓣ which was published in 1936.
In 1937 Maruhn habilitated at the Technische Hochschule in Berlin-Charlottenburg and began lecturing there in the following year. When World War II began in 1939 his work at the Deutschen Versuchsanstalt der Luftfahrt became his contribution to the war effort. However, he also continued to lecture at the Technische Hochschule in Berlin-Charlottenburg. He published Über ein Existenzproblem der Hydrodynamik Ⓣ (submitted from Berlin on 6 October 1938), and Zur eindeutigen Lösbarkeit der potentialtheoretischen Randwertaufgaben bei nichtbeschränkten Randwerten Ⓣ (submitted from Berlin on 13 December 1941). In this last mentioned paper, Maruhn reminds the reader that the solutions of the boundary value problems for Laplace's equation are not unique when the boundary functions are allowed to assume infinite values. He then considers what restrictions must be placed on the boundary functions and the solution functions to insure uniqueness. His next paper Einige Bemerkungen zu den Randwertaufgaben der Potentialtheorie Ⓣ (1942) is in four parts and contains theoretical work on boundary value problems of potential theory which is applied, in the final part, to airfoil theory.
He continued to undertake these two roles in Berlin until 1944 when he was appointed as an Ordinary Professor of Applied Mathematics and head of the Department of Applied Mathematics at the German University of Prague. He worked in Prague, which was under German occupation, until May 1945 when the Czechs rebelled against the occupying Germans. Maruhn was arrested by the Czechs but, after being held for a while, was released. In 1945 he became a lecturer at the University of Jena being promoted to extraordinary professor in 1946 and ordinary professor two years later. He was appointed as Director of the Mathematical Institute in Jena and he taught there until 1949. At Jena, he continued his research on potential theory. He had submitted the paper Über einige Klassen nichtlinearer Randwertaufgaben der Potentialtheorie Ⓣ to Mathematische Zeitschrift on 18 March 1944 but, because of collapse of Germany in 1945, the paper did not appear in print until 1947 by which time he had moved to Jena. He published Potentialtheorie Ⓣ in 1948 which was reviewed by F W Perkins who wrote:-
This summary contains a brief account of papers on (A) special solutions of the potential equation, (B) boundary value problems, (C) connections with boundary value problems for other differential equations, (D) connections with the theory of functions, (E) biharmonic functions.Maruhn published Bemerkungen über das Verhalten von Potentialfunktionen im Unendlichen Ⓣ submitted from Jena on 24 January 1948. He left Jena in 1949 when he was appointed to the Technische Hochschule in Dresden. He was also the Director of the Institute for Pure Mathematics in Dresden. His first publication when in this new position was Über die Potentiale von Belegungen auf unendlichen Flächen Ⓣ, submitted from Dresden on 10 July 1952. J W Green writes in a review:-
The paper is devoted to obtaining bounds for the Newtonian potentials of single and double layers, and their derivatives, when the layers lie on a surface which extends to infinity.In a collaboration with the algebraist Heinrich Grell (1903-1974) and the differential geometer and topologist Willi Ludwig August Rinow (1907-1979), he edited a series of books aimed at teaching mathematics to Gymnasium pupils and college students. These books were entitled Hochschulbücher für Mathematik Ⓣ, the first, Lehrgang der höheren Mathematik Ⓣ, was published in 1953. By the time of Maruhn's death in 1976 around 80 books had appeared in the series and it continued to produce texts until 1990.
In 1958-59 Maruhn spent a year as a Visiting Professor at the Justus-Liebig University of Giessen. He left his position in Dresden in 1959 when he was appointed as an ordinary professor at the University of Giessen. The chair had become vacant due to the death of Egon Ullrich in 1957. He continued to work at Giessen for the rest of his career, retiring in 1973. During the 24 years he taught at Giesson, he was the doctoral advisor of more than a dozen students. He did take study leave during these years, spending 1966-67 as a visiting professor at the University of Waterloo in Canada. He published only a few papers during his time at Giessen the last, Bemerkungen über singuläre Gleichgewichtsfiguren rotierender Flüssigkeiten Ⓣ, being published in 1971. In 1973 Maruhn was made professor emeritus by Giessen.
Article by: J J O'Connor and E F Robertson