Karl Menger

Last updated
Karl Menger
Karl Menger 1970 Shimer College Wiki.jpg
Born(1902-01-13)January 13, 1902
DiedOctober 5, 1985(1985-10-05) (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 Austrian-American 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

Computer illustration of the "Menger sponge". Menger sponge (IFS).jpg
Computer illustration of the "Menger sponge".

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.

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 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.

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]

Notes

  1. "Biography of Karl Menger". Illinois Institute of Technology . Retrieved 2010-12-22.
  2. Menger, Karl (1934-08-01). "Das Unsicherheitsmoment in der Wertlehre". Zeitschrift für Nationalökonomie (in German). 5 (4): 459–485. doi:10.1007/BF01311578. ISSN   1617-7134.
  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

Related Research Articles

Carl Menger Founder of the Austrian School of economics

Carl Menger was an Austrian economist and the founder of the Austrian School of economics. Menger contributed to the development of the theory of marginalism, which rejected the cost-of-production theories of value, such as were developed by the classical economists such as Adam Smith and David Ricardo. As a departure from such, he would go on to call his resultant perspective, the "Subjective Theory of Value".

Sierpiński carpet Plane fractal built from squares

The Sierpiński carpet is a plane fractal first described by Wacław Sierpiński in 1916. The carpet is one generalization of the Cantor set to two dimensions; another is the Cantor dust.

Wacław Sierpiński

Wacław Franciszek Sierpiński was a Polish mathematician. He was known for contributions to set theory, number theory, theory of functions and topology. He published over 700 papers and 50 books.

Alfred Tarski American mathematician

Alfred Tarski, born Alfred Teitelbaum, was a Polish-American logician and mathematician. A prolific author best known for his work on model theory, metamathematics, and algebraic logic, he also contributed to abstract algebra, topology, geometry, measure theory, mathematical logic, set theory, and analytic philosophy.

Menger sponge

In mathematics, the Menger sponge is a fractal curve. It is a three-dimensional generalization of the one-dimensional Cantor set and two-dimensional Sierpinski carpet. It was first described by Karl Menger in 1926, in his studies of the concept of topological dimension.

Arthur Cayley

Arthur Cayley was a prolific British mathematician who worked mostly on algebra. He helped found the modern British school of pure mathematics.

Distance geometry is the characterization and study of sets of points based only on given values of the distances between member pairs. More abstractly, it is the study of semimetric spaces and the isometric transformations between them. In this view, it can be considered as a subject within general topology.

Nigel Hitchin British mathematician

Nigel James Hitchin FRS is a British mathematician working in the fields of differential geometry, gauge theory, algebraic geometry, and mathematical physics. He is a Professor Emeritus of Mathematics at the University of Oxford.

Chennai Mathematical Institute

Chennai Mathematical Institute (CMI) is a premier research and education institute in Chennai, India. It was founded by the SPIC Science Foundation in 1989, and offers undergraduate as well as postgraduate programmes in physics, mathematics and computer science, besides its key strength in the form of high-end research in Mathematics. CMI is noted for its research in the field of algebraic geometry, in particular in the area of moduli of bundles.

Franz Leopold Alt was an Austrian-born American mathematician who made major contributions to computer science in its early days. He was best known as one of the founders of the Association for Computing Machinery, and served as its president from 1950 to 1952.

David Eisenbud American mathematician

David Eisenbud is an American mathematician. He is a professor of mathematics at the University of California, Berkeley and was Director of the Mathematical Sciences Research Institute (MSRI) from 1997 to 2007. He was reappointed to this office in 2013, and his term has been extended until July 31, 2022.

Margaret Wertheim

Margaret Wertheim is an Australian-born science writer, curator, and artist based in the United States. She is the author of books on the cultural history of physics, and has written about science, including for the New York Times, Los Angeles Times, Guardian, Aeon and Cabinet. Wertheim and her twin sister, Christine Wertheim, are co-founders of the Institute For Figuring (IFF), a Los Angeles-based non-profit organization though which they create projects at the intersection of art, science and mathematics. Their IFF projects include their Crochet Coral Reef, which has been shown at the 2019 Venice Biennale, Hayward Gallery (London), Museum of Arts and Design (NYC), and the Smithsonian's National Museum of Natural History. For her work with public science engagement, Wertheim won the 2016 Klopsteg Memorial Award from the American Association of Physics Teachers and Australia's Scientia Medal (2017).

Johannes de Groot

Johannes de Groot was a Dutch mathematician, the leading Dutch topologist for more than two decades following World War II.

Karl Sigmund

Karl Sigmund is a Professor of Mathematics at the University of Vienna and one of the pioneers of evolutionary game theory.

Georg Nöbeling German mathematician

Georg August Nöbeling was a German mathematician.

Geometry Branch of mathematics

Geometry is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space that are related with distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a geometer.

Claudio Procesi is an Italian mathematician, known for works in algebra and representation theory.

Trivandrum Ramakrishnan "T. R." Ramadas is an Indian mathematician who specializes in algebraic and differential geometry, and mathematical physics. He was awarded the Shanti Swarup Bhatnagar Prize for Science and Technology in 1998, the highest science award in India, in the mathematical sciences category.

Harald Niederreiter

Harald G. Niederreiter is an Austrian mathematician known for his work in discrepancy theory, algebraic geometry, quasi-Monte Carlo methods, and cryptography.

Yuri Tschinkel is a Russian-German-American mathematician, specializing in algebraic geometry, automorphic forms and number theory.