During World War II, he worked as part of a group of five mathematicians, recruited by Wilhelm Fenner, and which included Ernst Witt, Alexander Aigner, Oswald Teichmueller and Johann Friedrich Schultze, and led by Wolfgang Franz, to form the backbone of the new mathematical research department in the late 1930s, which would eventually be called: Section IVc of Cipher Department of the High Command of the Wehrmacht (abbr.

Born in Munich, George Aumann initially considered a career as a civil servant.

He was promoted in 1931 to Doctor of Philosophy with a thesis titled: contributions to the theory of decomposition spaces (German:Beiträge zur Theorie der Zerlegungsräume)[5] In 1933 he habilitated twice, at the Technical University of Munich, and at the University of Munich (with different degrees of postdoctoral dissertation).

At the beginning of the war, he was conscripted for military service[4] Appeals to a full professorship failed several times because he was regarded as politically unreliable among the Nazis Ministry of Education.

In a review, Paul Halmos said "The quality, quantity, organization, and exposition of its contents, together with the fact that much of the material in it has not been available hitherto in book form, serve to make it a recommended part of the library of every modern analyst.

[citation needed] In 1958 Aumann became a full member of the Bavarian Academy of Sciences[8] In 1977 the University of Erlangen awarded Aumann an Honorary Doctor of Science degree, Doctor rerum naturalium honoris causa.

The elements of a universe U form the domain of this relation while the range is the power set on U, denoted P(U).

[11] Aumann showed in 1977 how a neighborhood system r in the power set on A can be identified from a corresponding binary relation