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He also studied in Strasbourg, Munich and Göttingen. He was appointed to the teaching staff in Vienna in 1905 and he became professor of mathematics there in 1921. In session 1905-06 Hahn substituted for Otto Stolz at Innsbruck.
Hahn was a pioneer in set theory and functional analysis and is best remembered for the Hahn-Banach theorem. He also made important contributions to the calculus of variations, developing ideas of Weierstrass.
During the 1920s Hahn, together with Frank and von Mises, was a member of the Vienna Circle of Logical Positivists, a discussion group of gifted scientists and philosophers who met regularly in Vienna.
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