- Karl Menger
:"This article is about the mathematician (who also contributed to economics), not about his father, the economist
Carl Menger ."Karl Menger (
Vienna ,Austria ,January 13 1902 –Highland Park, Illinois , U.S.,October 5 1985 ) was amathematician of great scope and depth.He was the son of the famous economist
Carl Menger .He worked in mathematics on algebras, curve and dimension theory, and geometries. Moreover, he contributed to game theory and social sciences. He was a student of
Hans Hahn and received his PhD from theUniversity of Vienna in 1924, L. E. J. Brouwer invited Menger to teach at theUniversity of Amsterdam . In 1925, he returned to Vienna and obtained a professorship in 1928. From 1937 to 1946 he was a professor at theUniversity of Notre Dame . From 1946 to 1971, he was professor at theIllinois Institute of Technology inChicago . He also taught for a time atDuke University .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 theCantor set .With
Arthur Cayley , Menger is considered one of the founders ofdistance geometry ; especially by having formalized definitions to the notions of "angle" and of "curvature" in terms of directly measurablephysical quantities , namely ratios of "distance" values.The characteristic mathematical expressions appearing in those definitions are
Cayley-Menger determinant s.He also is credited with
Menger's theorem .He was an active participant of the
Vienna Circle which had discussions in the 1920s on social science and philosophy. During that time, he proved an important result on theSt. Petersburg paradox with interesting applications to theutility theory ineconomics . Later he contributed to the development ofgame theory withOskar Morgenstern .Further reading
*Crilly, Tony, 2005, "Paul Urysohn and Karl Menger: papers on dimension theory" in Grattan-Guiness, I., ed., "Landmark Writings in Western Mathematics". Elsevier: 844-55.
External links
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* [http://www.iit.edu/csl/am/about/menger/about.shtml Karl Menger Biography at the Illinois Institute of Technology]
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