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 â€"
Highland Park, Illinois,
USA,
October 5 1985) was a
mathematician 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 the
University of Vienna in
1924.
Brouwer invited Menger to teach at the
University of Amsterdam in
1925, afterwards he returned to Vienna and obtained a professorship in
1928. From
1937 to
1946 he was professor for mathematics at the
University of Notre Dame in
Indiana (USA), from 1946 professor on the
Illinois Institute of Technology in
Chicago.
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.
|
Computer illustration of the "Menger sponge". |
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 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 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.
* http://www.iit.edu/~am/Menger/menger.html
