Karl Menger (January 13, 1902 – October 5, 1985) was an Austrian–American mathematician, the son of the economist Carl Menger. In mathematics, Menger studied the theory of algebras and the dimension theory of low-regularity ("rough") curves and regions; in graph theory, he is credited with Menger's theorem. Outside of mathematics, Menger has substantial contributions to game theory and social sciences.
With Arthur Cayley, Menger is considered one of the founders of distance geometry; especially by having formalized definitions of 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.
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]
Crilly, Tony, 2005, "Paul Urysohn and Karl Menger: papers on dimension theory" in Grattan-Guinness, I., ed., Landmark Writings in Western Mathematics. Elsevier: 844–55.
Golland, Louise and Sigmund, Karl "Exact Thought in a Demented Time: Karl Menger and his Viennese Mathematical Colloquium" The Mathematical Intelligencer 2000, Vol 22,1, 34-45
.jpg)
