Karl Menger
Karl Menger



Born  (19020113)January 13, 1902 
Died  October 5, 1985(19851005) (aged 83)
Highland Park, Illinois, USA

Nationality  Austrian 
Alma mater  University of Vienna 
Known for  Menger sponge Menger's theorem Distance geometry 
Scientific career  
Fields  Mathematics 
Institutions  Illinois Institute of Technology University of Notre Dame University of Vienna 
Thesis  Über die Dimensionalität von Punktmengen (1924) 
Doctoral advisor  Hans Hahn 
Doctoral students  Abraham Wald Witold Hurewicz 
Karl Menger (January 13, 1902 – October 5, 1985) was an AustrianAmerican mathematician. He was the son of the economist Carl Menger. He is credited with Menger's theorem. He worked on mathematics of algebras, algebra of geometries, curve and dimension theory, etc. Moreover, he contributed to game theory and social sciences.
Biography
Karl Menger was a student of Hans Hahn and received his PhD from the University of Vienna in 1924. L. E. J. Brouwer invited Menger in 1925 to teach at the University of Amsterdam. In 1927, he returned to Vienna to accept a professorship there. In 1930 and 1931 he was visiting lecturer at Harvard University and The Rice Institute. From 1937 to 1946 he was a professor at the University of Notre Dame. From 1946 to 1971, he was a professor at Illinois Institute of Technology in Chicago. In 1983, IIT awarded Menger a Doctor of Humane Letters and Sciences degree.^{[1]}
Contributions to mathematics
His most famous popular contribution was the Menger sponge (mistakenly known as Sierpinski's sponge), a threedimensional version of Sierpinski's carpet. It is also related to the Cantor set.
With Arthur Cayley, Menger is considered one of the founders of distance geometry; especially by having formalized definitions to the notions of angle and of curvature in terms of directly measurable physical quantities, namely ratios of distance values. The characteristic mathematical expressions appearing in those definitions are Cayley–Menger determinants.
He was an active participant of the Vienna Circle which had discussions in the 1920s on social science and philosophy. During that time, he published an influential result^{[2]} on the St. Petersburg paradox with applications to the utility theory in economics; this result has since been criticised as fundamentally misleading.^{[3]} Later he contributed to the development of game theory with Oskar Morgenstern.
Legacy
Menger's longest and last academic post was at the Illinois Institute of Technology, which hosts an annual IIT Karl Menger Lecture and offers the IIT Karl Menger Student Award to an exceptional student for scholarship each year.^{[4]}
See also
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Copyright
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