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The Pure and the Applied: Bourbakism Comes to Mathematical Economics

Published online by Cambridge University Press:  26 September 2008

E. Roy Weintraub
Affiliation:
Department of EconomicsDuke University
Philip Mirowski
Affiliation:
Department of EconomicsUniversity of Notre Dame

Abstract

In the minds of many, the Bourbakist trend in mathematics was characterized by pursuit of rigor to the detriment of concern for applications or didactic concessions to the nonmathematician, which would seem to render the concept of a Bourbakist incursion into a field of applied mathematices an oxymoron. We argue that such a conjuncture did in fact happen in postwar mathematical economics, and describe the career of Gérard Debreu to illustrate how it happened. Using the work of Leo Corry on the fate of the Bourbakist program in mathematics, we demonstrate that many of the same problems of the search for a formal structure with which to ground mathematical practice also happened in the case of Debreu. We view this case study as an alternative exemplar to conventional discussions concerning the “unreasonable effectiveness” of mathematics in science.

Type
Article
Copyright
Copyright © Cambridge University Press 1994

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References

Andler, Martin. 1988. “Entretien avec trois membres de Nicolas Bourbaki.” Gazette des Mathématiciens 35: 4349.Google Scholar
Artin, E. 1953. “Review of Bourbaki [Elements, Book II, Chapters 1–7 (1942–52)].” Bulletin of the American Mathematical Society 59: 474–79.CrossRefGoogle Scholar
Beed, Clive, and Kane, Owen. 1992. “What Is the Critique of the Mathematization of Economics?Kyklos 44: 581611.CrossRefGoogle Scholar
Borges, Jorge Luis. 1964. Labyrinths. New York: New Directions.Google Scholar
Bourbaki, Nicolas. 1949. “The Foundations of Mathematics for the Working Mathematician.” Journal of symbolic Logic 14(1): 18.CrossRefGoogle Scholar
Bourbaki, Nicolas. [1948] 1950. “The Architecture of Mathematics.” Americam Mathematical Monthly 57: 221–32.CrossRefGoogle Scholar
Browder, Felix. 1989. “The Stone Age of Mathematics on the Midway,” in Duren 1989.CrossRefGoogle Scholar
Campbell, Douglas M., and Higgens, John C., eds 1984. Mathematics: People, problems, Results, vol 1. Belmont, Calif.: Wadswroth.Google Scholar
Cartan, Henri. 1943. “Sur le fondement logique des mathématiques.” La Revue Scientifique: Revue rose illustrée 81(1): 311.Google Scholar
Cartan, Henri. [1958] 1980. “Nicolas Bourbaki and Contemporary Mathematics.” The Mathematical Intelligencer 2(4): 175–80. Additionally published as “Nicolas Bourbaki und die heutige Mathematik,” Arbeitsgemeinschaft für Forschung des Landes Nord. Westf., vol. 76, 1979.CrossRefGoogle Scholar
Caws, Peter. 1988. Structuralism: The Art of the Intelligible. London: Humanities Press.Google Scholar
Chihara, Charles. 1990. Constructability and Mathematical Existence. Oxford: Clarendon Press.Google Scholar
Christ, Carl. 1952. “History of the Cowles Commission, 1932–1952.” In Economic Theory and Measurement. Chicago: Cowles Commission.Google Scholar
Christ, Carl. 1994. “The Cowles Commission's Contributions to Econometrics at Chicago, 1939–1955.” Journal of Economic Literature 32: 3059.Google Scholar
Corry, Leo. 1989. “Linearity and Reflexivity in the Growth of Mathematical Knowledge.” science in Context 3(2): 409–40.CrossRefGoogle Scholar
Corry, Leo. 1992a. “Nicolas Bourbaki and the Concept of Mathematical Structure.” Syntheses 22: 315–48.CrossRefGoogle Scholar
Corry, Leo. 1992b. “Nicolas Bourbaki and the Structuralist Program.” Unpublished.Google Scholar
Debreu, Gérard. 1959. The Theory of value. New Haven: Yale University Press.Google Scholar
Debreu, Gérad. 1983. Mathematical Economics: Twenty Collected Papers of Gérard Debreu. New York: Cambridge University Press.CrossRefGoogle Scholar
Debreu, Gérard. [1983] 1984.“Economic Theory in the Mathematical Mode.” American Economic Review 74(3): 267–78. This is a reprint of Debreu's Nobel prize lecture, which originally appeared in Les Prix Nobel, 1983, Stockholm, The Nobel Foundation.Google Scholar
Debreu, Gérard. 1986. “Theoretical Models: Mathematical Form and Economic Content.” Econometrica 54(6): 1259–70.CrossRefGoogle Scholar
Debreu, Gérard. 1991. “The Mathematization of Economic Theory.” American Economic Review 81(1): 17.Google Scholar
Debreu, Gérard. 1992a. “Random Walk and Life Philosophy.” In Eminent Economists: Their Life Philosophies, edited by Szenberg, Michael, 107–14. New York: Cambridge University Press.Google Scholar
Debreu, Gérard. 1992b. Interview with Roy Weintraub, Berkeley, 45 May.Google Scholar
Dieudonné, Jean. 1939. “Les méthodes axiomatiques modernes et les fondements des mathématiques.” La Revue Scientifique: Revue rose illustrée 77(3): 224–32.Google Scholar
Dieudonné, Jean. 1970. “The Work of Nicolas Bourbaki.” American Mathematical Monthly 77: 134–45.CrossRefGoogle Scholar
Dieudonné, Jean. 1982a. A Panorama of Pure Mathematics (as seen by Nicolas Bourbaki), translated by Macdonald, I. G.. New York: Academic Press.Google Scholar
Dieudonné, Jean. 1982b. “The Work of Bourbaki in the Last Thirty Years.” Notices of the American Mathematical Society 29: 618–23.Google Scholar
Dieudonné, Jean. 1992. Mathematics — The Music of Reason. Berlin: Springer Verlag.CrossRefGoogle Scholar
Douglas, Mary. 1989. Purity and Danger. London: Ark.Google Scholar
Dreze, Jacques H. 1964. “Some Postwar Contributions of French Economists to Theory and Public Policy, with Special Emphasis on Problems of Resource Allocation.” American Economic Review 54(4, part 2, Supplement): 164.Google Scholar
Duren, Peter, ed. 1989. A Century of Mathematics in America, Part II. Providence, R.I.: American Mathematical Society.Google Scholar
Epstein, Roy. 1987. A History of Econometrics. Amsterdam: North Holland.Google Scholar
Ewing, John. 1992. “Review of The History of Modern Mathematics.” Historia Mathematica 19(1): 9398.CrossRefGoogle Scholar
Feiwel, George. 1987. “Oral History II: An Interview with Gérard Debrey.” In Arrow and the Ascent of Modern Economic Theory, 243–57, edited by Feiwel, George. London: Macmillan.CrossRefGoogle Scholar
Frink, O. 1950. “Review of Bourbaki 1949.” Mathematical Reviews 11: 73.Google Scholar
Gandy, R. O. 1959. “Review of Bourbaki.” Journal of Symbolic Logic 24: 7173.CrossRefGoogle Scholar
Gell-Mann, Murray. 1992. “Nature Conformable to Herself.” Bulletin of the Santa Fe Institute 7(1): 710.Google Scholar
Gilles, Donald, ed 1992. Revolutions in Mathematics. Oxford: Clarendon press.CrossRefGoogle Scholar
Grandmont, Jean-Michael. 1984. “Gérard Debrey, Prix Nobel d'Economie 1983.” Société d'études et de documentation économiques, industrielles et sociales 38 (Mars): 12.Google Scholar
Guedj, Denis. 1985. “Nicholas Bourbaki, Collective Mathematician: An Interview with Claude Chevalley,” translated by Grey, Jeremy. Mathematical Intelligencer 7(2): 1822.CrossRefGoogle Scholar
Gutting, Gary. 1989. Michel Foucalut's Archaeology of Scientific Reason. New York: Cambridge University Press.CrossRefGoogle Scholar
Hildenbrand, Werner. 1983a. ”An Axiomatic Analysis of the Economic Equilibrium: On the Award of the Nobel Prize to Gérard Debreu.” Neue Zurcher Zeitung. November 4.Google Scholar
Hildenbrand, Werner. 1983b. “Introduction.” In Debreu 1983, 129.Google Scholar
Hildenbrand, Werner. 1994. Market Demand, Princeton, N.J.: Princeton University Press.CrossRefGoogle Scholar
Ingrao, Bruna, and Israel, Giorgio. 1990. The Invisible Hand: Economic Equilibrium in the History of Science. Cambridge, Mass.: MIT Press.Google Scholar
Israel, Giorgio. 1981. “Rigor and Axiomatics in Modern Mathematis.” Fundamenta Scientiae 2: 205–19.Google Scholar
Klamer, Arjo, and Colander, David. 1990. The Making of an Economist. Boulder, Colo.: Westview Press.Google Scholar
Kline, Morris. 1972. Mathematical Thought from Ancient to Modern Times. New York:: Oxford.Google Scholar
Kurz, Heinz D., and Salvadori, Neri. 1992. “Von Neumann's Growth Model and the ‘Classical’ Tradition.” University of Graz. Unpublished.Google Scholar
Lax, Peter D. 1989. ”The Flowering of Applied Mathematics in America.” In A Century of Mathematics in America, Part II, edited by Duran, et al. Providence, R.I.: American Mathematical Society.Google Scholar
Mandelbrot, Benoit. 1989. “Chaos, Bourbaki, and Poincaré.” Mathematical Intelligencer 11(3): 1012.Google Scholar
Mantel, Rolf. 1974. “On the Characterization of Aggregate Excess Demand.” Journal of Economic Theory 7: 348–53.CrossRefGoogle Scholar
Mathias, A. 1992. “The Ignorance of Bourbaki.” Mathematical Intelligencer 14(3): 413.CrossRefGoogle Scholar
Mirowski, Philip. 1989. More Heat Than Light. New York: Cambridge University Press.CrossRefGoogle Scholar
Mirowski, Philip. 1991. “The How, the When and the Why of Mathematical Expression in the History of Economics.” Journal of Economic Perspectives 5: 148–58.CrossRefGoogle Scholar
Mirowski, Philip. 1993. “What Could Mathematical Rigor Mean?History of Economics Review 20: 4160.CrossRefGoogle Scholar
Mirowski, Philip. ed. 1994. Natural Images in Economics: Markets Read in Tooth and Claw. New York: Cambridge University Press.Google Scholar
Morgan, Mary S. 1990. History of Econometrics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Mumford, David. 1991. “A Foreword for Non-Mathematicians.” In The Unreal Life of Oscar Zariski, edited by Parikh, Carol, xv–xxvii San Diego: Academic Press.Google Scholar
Punzo, L. 1991. “The School of Mathematical Formalism and the Viennese Circle of Mathematical Economists.” Journal of the History of Economic Thought 13(1): 118.CrossRefGoogle Scholar
Reingold, Nathan. 1991. “The Peculiarities of the Americans, Or Are There National Styles in the Sciences?Science in Context 4(2): 347–66.CrossRefGoogle ScholarPubMed
Samuelson, Paul A. 1947. Foundations of Economic Analysis. Cambridge, Mass.: Harvard University Press.Google Scholar
Samuelson, paul A. 1983. “The 1983 Nobel Prize in Economics.” Science 222: 987–89.CrossRefGoogle ScholarPubMed
Schumpeter, Joseph. 1954. A History of Economic Analysis. New York: Oxford University Press.Google Scholar
Sonnenschein, Hugo. 1972. “Market Excess Demand Functions.” Econometrica 40: 549–63.CrossRefGoogle Scholar
Stone, Marshall. 1946. “Lectures on Convexity.” Mimeo transcript prepared by Harley Flanders.Google Scholar
Stone, Marshall. 1989. “Reminiscences of Mathematics at Chicago.” In Duren 1989.CrossRefGoogle Scholar
Tapon, Francis. 1973. “A Contemporary Example of the Transition to Maturity in the Social Sciences: The Peculiar State of Economics in France.” Duke University. Unpublished.Google Scholar
Varian, Hal. 1984. “Gérard Debreu's Contribution to Economics.” Scandinavian Journal of Economics 86(1): 414.CrossRefGoogle Scholar
von Neumann, John, and Morgenstern, Oskar. 1944. The Theory of Games and Economic Behavior. Princeton, N.J.: Princeton University Press.Google Scholar
Walton, Karen. 1990. “Is Nicolas Bourbaki Alive?” The Mathematics Teacher, November: 666–68.Google Scholar
Weintraub, E. R. 1985. General Equilibrium Analysis: Studies in Appraisal. New York: Cambridge University Press.Google Scholar
Weintraub, E. R. 1991. Stabilizing Dynamics: Constructing Economic Knowledge. New York: Cambridge University Press.CrossRefGoogle Scholar
Weintraub, E. R. ed. 1992. Towards a History of Game Theory. Durham, N.C.: Duke University Press.Google Scholar
Weyl, Hermann. 1970. “David Hilbert and his Mathematical Work.” In Hilbert, edited by Reid, Constance, 245–83. New York: Springer Verlag. This piece is a slight modification of the paper of the same title that originally appeared in 1944 in the Bulletin of the American Mathematical Society 50: 612–54.CrossRefGoogle Scholar