Karl Menger
Karl Menger  

Born 

January 13, 1902
Died  October 5, 1985
Highland Park, Illinois, USA

(aged 83)
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 
Doctoral advisor  Hans Hahn 
Doctoral students  Abraham Wald 
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.
Contents
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 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.
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.^{[2]}
Notes
 ^ "Biography of Karl Menger". Illinois Institute of Technology. Retrieved 20101222.
 ^ "Remembering Karl Menger". Illinois Institute of Technology. Retrieved 20090326.
Further reading
 Crilly, Tony, 2005, "Paul Urysohn and Karl Menger: papers on dimension theory" in GrattanGuinness, I., ed., Landmark Writings in Western Mathematics. Elsevier: 844–55.
 Golland, Louise and Karl Sigmund "Exact Thought in a Demented Time: Karl Menger and his Viennese Mathematical Colloquium" The Mathematical Intelligencer 2000, Vol 22,1, 3445
External links
 O'Connor, John J.; Robertson, Edmund F., "Karl Menger", MacTutor History of Mathematics archive, University of St Andrews.
 Karl Menger at the Mathematics Genealogy Project
 1902 births
 1985 deaths
 20thcentury American mathematicians
 Austrian mathematicians
 Vienna Circle
 Harvard University staff
 Rice University staff
 Duke University faculty
 University of Notre Dame faculty
 Illinois Institute of Technology faculty
 American people of Austrian descent
 University of Vienna alumni
 Scientists from Vienna
 AustroHungarian mathematicians