**Gustav Doetsch**attended the Wöhler Realgymnasium in Frankfurt am Main from 1904. He graduated from the school in 1911 and for the next three years studied mathematics, physics and philosophy in Göttingen, Munich and Berlin. It was common practice among German students at this time to study at a number of different universities during their undergraduate years and Doetsch was typical in this respect. He had been intending to continue with his education but the outbreak of World War I in 1914 meant that he was forced to interrupt his studies.

He served as an artillery observer for the first part of the war and then, from 1916, he flew on aircraft as an observer. He was decorated for his services before the end of the war, and in December 1918 he ended active service as a highly decorated flying officer. After the war ended he was able to continue with his academic studies, first in Frankfurt and then in Göttingen where his doctoral dissertation *Eine neue Verallgemeinerung der Borelschen Summabilitätstheorie der divergenten Reihen* Ⓣ was supervised by Edmund Landau. Doetsch was awarded his doctorate in 1920, and in the following year he submitted his habilitation thesis to the Technical University of Hanover and received the right to lecture. He taught at the University of Halle from 1922 to 1924 before being appointed as Ordinary Professor of Descriptive Geometry at the Technical University of Stuttgart. In 1922 he published a famous work on the applications of mathematics which asked fundamental questions about the character of the mathematical sciences. He writes in the article that it is strange that deep mathematics, understood by only a very few specialists, provides such a powerful tool in directing the natural sciences. Doetsch says that the natural scientist turns to mathematics to provide an explanation for experimental facts. However, in his eyes, the use of mathematics in the natural sciences gives at best an "approximate image of reality". Also in the 1920s Doetsch collaborated with Felix Bernstein on what is considered today to be the modern version of the Laplace transform. This remained one of the main research topics of his whole career.

During his years in Stuttgart, Doetsch became an active member of the peace movement. While at Stuttgart he was approached a number of times with offers of chairs in other universities. For example he was offered the chair of mathematics at the University of Greifswald in 1927 and three years later at the University of Giessen. It was in the spring of 1930 that he received the offer from Giessen and his letter of rejection is dated 2 March. However, when he was offered the chair at the University of Freiburg he accepted, taking up the post in the summer of 1931.

Doetsch had collaborated with a number of Jewish mathematicians; his doctoral supervisor was Edmund Landau and his collaborator on the Laplace transform was Felix Bernstein, both Jewish mathematicians. Doetsch, however, seems to have given wholehearted support to the ideas of National Socialism as put forward by the Nazis in the 1930s. On 30 January 1933 the National Socialist party led by Hitler came to power in Germany and Nazi policies began to have a major impact on the German Mathematical Society and on its members. Both Edmund Landau and Felix Bernstein were dismissed from their posts, actions which were approved of by Doetsch, who gave his full support to Bieberbach in his attempt to become chairman of the German Mathematical Society in 1934. Doetsch argued that Perron, who had been appointed as chairman of the German Mathematical Society in September 1933, could no longer be tolerated and he argued strongly for the idea that Bieberbach should be made chairman for life.

Despite his support for the Third Reich, Doetsch was investigated by them, particularly over his earlier involvement with the peace movement. However his position as an Air Force reserve seems to have been sufficient to ensure further investigations were dropped. From around 1936 Doetsch seems to have been less energetic in his support for National Socialism. However, he does not seem to have made friends in Freiburg, on the contrary he fell out with many of his colleagues despite being held in high regard as an applied mathematician. His most important mathematical contribution during this time was his major text on the Laplace transform and its applications to engineering published in 1937, the first such text to be written.

When World War II started Doetsch was already taking part in an exercise as a Captain in the Air Force reserve. He was kept in the Air Force despite his attempts to return to the University of Freiburg. He contacted Wilhelm Süss, at this time rector of the University of Freiburg, asking him to help argue for his return but to no avail. Doetsch was given a role with the Reichsluftfahrtministerium (Reich Air Force Ministry) in Berlin coordinating the mathematical contributions relevant to the war effort by the Air Force. However because of his difficult personality he was not trusted by the majority of the mathematicians who felt that they were better served by cooperating with the German Mathematical Society than with the Reich Air Force Ministry. In this respect Doetsch and Süss, who was chairman of the German Mathematical Society, were in direct competition and relations between the two men became very poor. Doetsch made major efforts in the Reich Air Force Ministry to coordinate mathematicians and mathematical knowledge for the purposes of the war. In particular he put a large effort into developing a programme to collect mathematical formulae and mathematical tables which were needed for aviation research. From 1942 Doetsch became increasingly isolated in the Reich Air Force Ministry and consequently in 1944 he was transferred to the Institute for Theoretical Ballistics at the Aviation Research Institute Hermann Göring at Braunschweig. At the end of war Doetsch returned to the University of Freiburg but in the autumn 1945 he was suspended from his duties as professor.

In June 1946 he made a request to retire from lecturing in order to be able to dedicate himself entirely to research. The request was rejected. He was reinstated to his chair at Freiburg in 1951 but was now completely isolated within the university. He served for a further ten years before he retired in 1961, but during that time he had no contact with other mathematicians at the Mathematics Institute. Walter Felscher writes:-

Doetsch remained active mathematically despite his isolation in Freiburg. He gave a number of lectures at other institutions, for example in Santa Fé in Argentina in 1950, in Madrid in 1952, and in Rome in 1953.... between1958and1969I held positions at Freiburg, and during the earlier of these years I still saw the announcements posted of Doetsch's lectures. However, Doetsch never came to the mathematics department and did not hold his lectures in the building where all other mathematicians taught(instead, he used classrooms in the university's main building, normally used by philologists). He did not visit faculty meetings, did not use the secretarial staff, and did not take part in social gatherings of the faculty's members. I never noticed him taking part in examination boards, nor did he then seem to have doctoral students or assistants.

**Article by:** *J J O'Connor* and *E F Robertson*

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