Karl Menger
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Karl Menger (Vienna, Austria, January 13 1902 – Highland Park, Illinois, U.S., October 5 1985) was a mathematician of great scope and depth. He was the son of the famous economist Carl Menger. He is credited with Menger's theorem.
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 the University of Vienna in 1924, L. E. J. Brouwer invited Menger to teach at the University of Amsterdam. In 1925, he returned to Vienna and obtained a professorship in 1928. From 1937 to 1946 he was a professor at the University of Notre Dame. From 1946 to 1971, he was professor at the Illinois Institute of Technology in Chicago. He also taught for a time at Duke 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 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 proved an important result on the St. Petersburg paradox with interesting applications to the utility theory in economics. Later he contributed to the development of game theory with Oskar 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.