Abstract
This column is a forum for discussion of mathematical communities throughout the world, and through all time. Our definition of “mathematical community” is the broadest. We include “schools” of mathematics, circles of correspondence, mathematical societies, student organizations, and informal communities of cardinality greater than one. What we say about the communities is just as unrestricted. We welcome contributions from mathematicians of all kinds and in all places, and also from scientists, historians, anthropologists, and others.
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References
An excellent biographical introduction is Seymour Kass (1996), Karl Menger,Notices of the AMS 43, 558–561.
For further material, see K. Menger,Reminiscences of the Vienna Circle and the Mathematical Colloquium, Vienna Circle Collection vol. 20, Kluwer, Dordrecht (1994); K. Menger,Selected Papers in Logic and Foundations, Didactics, Economics, Vienna Circle Collection vol. 13, Kluwer, Dordrecht (1979); and the recent reprinting of theErgebnisse eines mathematischen Kolloquiums (eds. E. Dierker and K. Sigmund, Springer, Wien 1998), with contributions from G. Debreu, K. Sigmund, W. Hildebrand, R. Engelking, J.W. Dawson, Jr., and F. Alt.
For more on the Vienna Circle, see K. Sigmund: A philosopher’s mathematician—Hans Hahn and the Vienna Circle,Mathematical Intelligencer M (4), 16–29 (1995). The authoritative biography on Gödel is by J.W. Dawson, Jr.Logical Dilemmas: the life and work of Kurt Gödel, Peters, Mass. (1997).
There is an enormous literature on the economics aspect. For a start see E. Craven, The emigration of Austrian economists,Hist, of Political Economics 18 (1989), 1–32, as well as M. Dore, P. Chakravarty, and R. Goodwin (eds),John von Neumann and Modern Economics, Oxford UP (1989); and in particular the articles by K.J. Arrow, Von Neumann and the Existence Theorem for General Equilibrium (pp. 15–28); P.A. Samuelson, A Revisionist View of von Neumann’s Growth Model (pp. 100–124); and LF. Punzo, Von Neumann and Karl Menger’s Mathematical Colloquium, (pp. 29–68). Karl Menger’s contribution to game theory is highlighted in R.J. Leonard’s essays: From Parlor Games to Social Science,J. of Economic Literature 23, 730–761, and: Ethics and the Excluded Middle: Karl Menger and Social Science in Interwar Vienna,Isis 89 (1998), 1–26.
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Senechal, M., Golland, L. & Sigmund, K. Exact thought in a demented time: Karl menger and his viennese mathematical colloquium. The Mathematical Intelligencer 22, 34–45 (2000). https://doi.org/10.1007/BF03024445
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DOI: https://doi.org/10.1007/BF03024445