|Died||October 5, 1985 83) (aged|
|Alma mater||University of Vienna|
|Known for|| Menger sponge |
|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 |
Karl Menger (January 13, 1902 – October 5, 1985) was an Austrian-American 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.
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.
His most famous popular contribution was the Menger sponge (mistakenly known as Sierpinski's sponge), a three-dimensional 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 resulton the St. Petersburg paradox with applications to the utility theory in economics; this result has since been criticised as fundamentally misleading. Later he contributed to the development of game theory with Oskar Morgenstern.
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.
Carl Menger von Wolfensgrün was an Austrian economist and the founder of the Austrian School of economics. Menger contributed to the development of the theories of marginalism and marginal utility, which rejected cost-of-production theory of value, such as developed by the classical economists such as Adam Smith and David Ricardo. As a departure from such, he would go on to call his resultant perspective, the subjective theory of value.
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In mathematics, the Menger sponge is a fractal curve. It is a three-dimensional generalization of the one-dimensional Cantor set and two-dimensional Sierpinski carpet. It was first described by Karl Menger in 1926, in his studies of the concept of topological dimension.
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