Karl Menger

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Karl Menger (1970)
The sponge named after Karl Menger.

Karl Menger (born January 13, 1902 in Vienna , Austria-Hungary ; died October 5, 1985 in Chicago ) was an Austrian mathematician . He was the son of the economist Carl Menger .

Life

Menger worked in the field of algebra , topology , curve and dimension theory and dealt with the general theory of space and spatial structures. He also worked on ethical issues and formal studies of human relationships. The so-called Menger sponge , which was named after him, has become particularly well known . Menger learned from Hans Hahn and received his doctorate in 1924 from the University of Vienna . There he was a member of the Vienna Circle .

Among other things, he dealt with distance geometry, i.e. properties of sets of points that only use the values ​​of their mutual distances. Here he used the first of Arthur Cayley introduced Cayley-Menger determinant .

In 1927 Menger was able to prove a statement from the field of graph theory about the connection between disjoint paths and separating vertex sets in a graph , which became known as Menger's theorem. Furthermore, Menger-Nöbeling's theorem about the embedding of finite-dimensional, compact, metric spaces in suitable Euclidean spaces is associated with his name.

From 1928 to 1936 Menger worked as a university professor for geometry in Vienna and was a member of the Vienna Circle . Between 1937 and 1946 he was professor of mathematics at the University of Notre Dame in Indiana (USA), from 1946 professor at the Illinois Institute of Technology in Chicago .

Another area of research Menger were fuzzy sets ( fuzzy set theory ).

In 1932 he gave a plenary lecture at the International Congress of Mathematicians in Zurich (Newer Methods and Problems of Geometry).

In 1928 he received the Richard Lieben Prize .

See also

Fonts

  • Selecta mathematica. Vol. 1. Edited by Bert Schweizer, Abe Sklar, Karl Sigmund, Peter Gruber, Edmund Hlawka, Ludwig Reich and Leopold Butterer. Springer-Verlag, Vienna, 2002. x + 606 pp. ISBN 3-211-83734-5
  • Selecta mathematica. Vol. 2. Edited by Bert Schweizer, Abe Sklar, Karl Sigmund, Peter Gruber, Edmund Hlawka, Ludwig Reich and Leopold Blätter. Springer-Verlag, Vienna, 2003. x + 674 pp. ISBN 3-211-83834-1
  • Reminiscences of the Vienna Circle and the Mathematical Colloquium, Kluwer 1994 (Ed. Louise Golland)
  • Selected papers in logic and foundations, didactics, economics, Dordrecht: Reidel 1979
  • Calculus: a modern approach, Boston: Ginn 1955
  • Géométrie générale, Gauthier-Villars 1954
  • Curve theory, Teubner 1932
  • Dimension theory, Teubner 1928

literature

Web links

Commons : Karl Menger  - Collection of images, videos and audio files