D’Alembert: Mathematics and the Enlightenment

The mathematician and philosopher Jean le Rond d’Alembert (1717–1783), coeditor of the Encyclopédie, is a central figure of the Enlightenment. As a scientist, he worked in various fields of “pure” or “mixed” mathematics. We will present a few of his research topics in the realm of pure mathematics: the integral calculus (integration of algebraic functions, of linear differential systems; beginning of the theory of partial differential equations); the operations on imaginary quantities and the proof of the fundamental theorem of algebra; the foundation of infinitesimal analysis with the concept of limit. Whereas some of these works are to be situated directly in a framework of pure mathematics, other originated in the search for solutions to mechanical problems. However, in these latter cases, d’Alembert, at a certain moment, develops a study of pure analysis for itself. From there, we examine d’Alembert’s general conception of mathematics, which is far from the utilitarian view often attributed to him by the historiography. Moreover, for him, as he argued in the Encyclopédie, mathematics could play an important role in the promotion of the Enlightenment and the emancipation of society.