Karl Menger

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This article is about the mathematician. For his father, the economist, see Carl Menger.
Karl Menger
PhD, 1924)
Known forMenger characterization theorem
Menger curvature
Menger space
Menger sponge
Menger's theorem
Menger–Nöbeling theorem
Cayley–Menger determinant
Scientific career
FieldsMathematics
InstitutionsIllinois Institute of Technology
University of Notre Dame
University of Vienna
Thesis Über die Dimensionalität von Punktmengen  (1924)
Doctoral advisorHans Hahn
Doctoral studentsAbraham Wald
Witold Hurewicz
Georg Nöbeling

Karl Menger (January 13, 1902 – October 5, 1985) was an Austrian–American

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.

Biography

Karl Menger was a student of

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 (IIT) in Chicago. In 1983, IIT awarded Menger a Doctor of Humane Letters and Sciences degree.[1]

Contributions to mathematics

Computer illustration of the "Menger sponge".

His most famous popular contribution was the

Sierpiński carpet. It is also related to the Cantor set
.

With

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

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 was a founding member of the Econometric Society.

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.[4]

See also

Notes

  1. ^ "Biography of Karl Menger". Illinois Institute of Technology. Retrieved 2010-12-22.
  2. S2CID 151290589
    .
  3. ^ Peters, O. and Gell-Mann, M., 2016. Evaluating gambles using dynamics. Chaos: An Interdisciplinary Journal of Nonlinear Science, 26(2), p.023103
  4. ^ "Remembering Karl Menger". Illinois Institute of Technology. Archived from the original on 2009-04-02. Retrieved 2009-03-26.

Further reading

  • 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

External links

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