The 1954 textbook Real Functions established Georg Aumann as a significant voice in real analysis, providing a structured resource that Paul Halmos deemed a necessary addition for modern analysts. Beyond this pedagogical contribution, Aumann navigated a complex career in Germany, bridging theoretical mathematics and cryptology while serving multiple major academic institutions across Munich, Würzburg, and Frankfurt.
Academic Formation and Early Career
Born in Munich in 1906, Aumann pursued mathematics and physics at the Ludwig-Maximilians-Universität München beginning in 1925. He studied under professors including Constantin Carathéodory and Heinrich Tietze. In 1931, he earned his Doctor of Philosophy with a thesis concerning the theory of decomposition spaces. By 1933, he achieved habilitation at both the Technical University of Munich and the Ludwig-Maximilians-Universität München. His early career included an appointment at the Institute for Advanced Study in Princeton and an extraordinary professorship at Goethe University Frankfurt in 1936.
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During World War II, Aumann was conscripted for military service. He operated as part of a specialized group recruited by Wilhelm Fenner, which included Alexander Aigner, Wolfgang Franz, Oswald Teichmueller, Ernst Witt, and Johann Friedrich Schultze. This collective formed the core of Section IVc within the Cipher Department of the High Command of the Wehrmacht, known as OKW/Chi. Aumann conducted research on cryptography theory and participated in the breaking of complex ciphers.
Post-war Research and Professional Standing
Following the war, Aumann returned to university teaching, holding a full professorship at the University of Würzburg in 1949 before moving to the Ludwig-Maximilians-Universität München in 1950 and eventually the Technical University of Munich in 1960. He became a full member of the Bavarian Academy of Sciences in 1958. His academic recognition included an Honorary Doctor of Science degree from the University of Erlangen in 1977. His output was extensive, spanning three-dimensional analysis, complex polynomials, and cluster theory.
Contributions to Set and Relation Theory
In 1970, Aumann expanded the theory of binary relations by generalizing the set membership relation. He defined a contact relation using the calculus of relations, specifically applying compositions involving the converse of set membership and complementary relations. By 1977, he further demonstrated how a neighborhood system within the power set could be identified through specific binary relations on maps, a framework later advanced by Gunther Schmidt and Michael Winter.
Fast facts
- Born: 1906, Munich
- Died: 1980, Munich
- Education: Ludwig-Maximilians-Universität München
- Academic Membership: Bavarian Academy of Sciences and Humanities
- Key Textbook: Real Functions (1954)
- Wartime Role: Cryptanalyst at OKW/Chi
Questions readers ask
What subjects did Aumann study as an undergraduate?
He studied mathematics and physics at the Ludwig-Maximilians-Universität München.
Which major academic institutions employed Aumann?
He held positions at Goethe University Frankfurt, the University of Würzburg, the Ludwig-Maximilians-Universität München, and the Technical University of Munich.
Achievements
- Held posts at Technical University of Munich
- Fields: mathematics, function and cluster analysis
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