1 THE TWO PATHS OF THE MATHEMATIZATION OF THE THE TWO PATHS OF THE MATHEMATIZATION OF THE SOCIAL AND ECONOMIC SCIENCES SOCIAL AND ECONOMIC SCIENCES GIORGIO ISRAEL Dipartimento di Matematica Università degli Studi di Roma "La Sapienza" P.le A. Moro, 2 00185 — ROMA (Italy) «We seek no lessons from the history of nations or of mankind's blunderings, which represent for us only an abyss of disorder.» (François Quesnay) «History depicts human heart: it is in history that we must look for the advantages and the drawbacks of the different legislations.» (Napoléon Bonaparte) SUMMARY — The aim of this paper is to show that two ways were open for the mathematization of social and economic sciences at the end of the Eighteenth Century. The first way was to follow the tradition of the arithmétique politique which was conveyed by Condorcet in the programme of the mathématique sociale: in this approach the calculus of probability had a central role. The other way was to imitate more strictly the analytical-deterministic approach and the mathematical methods of mathematical physics and mechanics. We emphasize here the strong paradigmatic aspects which led to the final success of the second approach and we provide the historical elements explaining this development. We describe also the decline of the tradition of the arithmétique politique and the causes of this decline. A special attention is devoted to the work of the last arithméticien politicien, E.-E. Duvillard de Durand. The Appendix provides a detailed biography of Duvillard and other unpublished materials. 1. INTRODUCTION In a paper of some years ago, Claude Ménard put forward the following question: “Why was there no probabilistic revolution in economic thought?”. 1 His thesis was roughly that there was no probabilistic revolution in economic thought because those which began to mathematize economics (from Cournot onwards) referred principally to the model of classical mathematical-physics and in particular 1 C. MÉNARD C., "Why Was There no Probabilistic Revolution in Economic Thought?", in Probability since 1800, Interdisciplinary Studies of Scientific Development, Workshop at the Centre for Interdisciplinary Research of the University of Bielefeld, Sept. 16-20, 1982, ed. by M. Heidelberger, L. Krüger, 1983, p. 203-212.