Jean Le Rond d’Alembert

Jean Le Rond d’Alembert (born November 17, 1717, Paris, France—died October 29, 1783, Paris) was a French mathematician, philosopher, and writer, who achieved fame as a mathematician and scientist before acquiring a considerable reputation as a contributor to and editor of the famous Encyclopédie.

Early life

The illegitimate son of a famous hostess, Mme de Tencin, and one of her lovers, the chevalier Destouches-Canon, d’Alembert was abandoned on the steps of the Parisian church of Saint-Jean-le-Rond, from which he derived his Christian name. Although Mme de Tencin never recognized her son, Destouches eventually sought out the child and entrusted him to a glazier’s wife, whom d’Alembert always treated as his mother. Through his father’s influence, he was admitted to a prestigious Jansenist school, enrolling first as Jean-Baptiste Daremberg and subsequently changing his name, perhaps for reasons of euphony, to d’Alembert. Although Destouches never disclosed his identity as father of the child, he left his son an annuity of 1,200 livres. D’Alembert’s teachers at first hoped to train him for theology, being perhaps encouraged by a commentary he wrote on St. Paul’s Letter to the Romans, but they inspired in him only a lifelong aversion to the subject. He spent two years studying law and became an advocate in 1738, although he never practiced. After taking up medicine for a year, he finally devoted himself to mathematics—“the only occupation,” he said later, “which really interested me.” Apart from some private lessons, d’Alembert was almost entirely self-taught.

Mathematics

In 1739 he read his first paper to the Academy of Sciences, of which he became a member in 1741. In 1743, at the age of 26, he published his important Traité de dynamique, a fundamental treatise on dynamics containing the famous “d’Alembert’s principle,” which states that Newton’s third law of motion (for every action there is an equal and opposite reaction) is true for bodies that are free to move as well as for bodies rigidly fixed. Other mathematical works followed very rapidly; in 1744 he applied his principle to the theory of equilibrium and motion of fluids, in his Traité de l’équilibre et du mouvement des fluides. This discovery was followed by the development of partial differential equations, a branch of the theory of calculus, the first papers on which were published in his Réflexions sur la cause générale des vents (1747). It won him a prize at the Berlin Academy, to which he was elected the same year. In 1747 he applied his new calculus to the problem of vibrating strings, in his Recherches sur les cordes vibrantes; in 1749 he furnished a method of applying his principles to the motion of any body of a given shape; and in 1749 he found an explanation of the precession of the equinoxes (a gradual change in the position of the Earth’s orbit), determined its characteristics, and explained the phenomenon of the nutation (nodding) of the Earth’s axis, in Recherches sur la précession des équinoxes et sur la nutation de l’axe de la terre. In 1752 he published Essai d’une nouvelle théorie de la résistance des fluides, an essay containing various original ideas and new observations. In it he considered air as an incompressible elastic fluid composed of small particles and, carrying over from the principles of solid body mechanics the view that resistance is related to loss of momentum on impact of moving bodies, he produced the surprising result that the resistance of the particles was zero. D’Alembert was himself dissatisfied with the result; the conclusion is known as “d’Alembert’s paradox” and is not accepted by modern physicists. In the Memoirs of the Berlin Academy he published findings of his research on integral calculus—which devises relationships of variables by means of rates of change of their numerical value—a branch of mathematical science that is greatly indebted to him. In his Recherches sur différents points importants du système du monde (1754–56) he perfected the solution of the problem of the perturbations (variations of orbit) of the planets that he had presented to the academy some years before. From 1761 to 1780 he published eight volumes of his Opuscules mathématiques.

The Encyclopédie

Meanwhile, d’Alembert began an active social life and frequented well-known salons, where he acquired a considerable reputation as a witty conversationalist and mimic. Like his fellow Philosophes—those thinkers, writers, and scientists who believed in the sovereignty of reason and nature (as opposed to authority and revelation) and rebelled against old dogmas and institutions—he turned to the improvement of society. A rationalist thinker in the free-thinking tradition, he opposed religion and stood for tolerance and free discussion; in politics the Philosophes sought a liberal monarchy with an “enlightened” king who would supplant the old aristocracy with a new, intellectual aristocracy. Believing in man’s need to rely on his own powers, they promulgated a new social morality to replace Christian ethics. Science, the only real source of knowledge, had to be popularized for the benefit of the people, and it was in this tradition that he became associated with the Encyclopédie about 1746. When the original idea of a translation into French of Ephraim Chambers’ English Cyclopædia was replaced by that of a new work under the general editorship of the Philosophe Denis Diderot, d’Alembert was made editor of the mathematical and scientific articles. In fact, he not only helped with the general editorship and contributed articles on other subjects but also tried to secure support for the enterprise in influential circles. He wrote the Discours préliminaire that introduced the first volume of the work in 1751. This was a remarkable attempt to present a unified view of contemporary knowledge, tracing the development and interrelationship of its various branches and showing how they formed coherent parts of a single structure; the second section of the Discours was devoted to the intellectual history of Europe from the time of the Renaissance. In 1752 d’Alembert wrote a preface to Volume III, which was a vigorous rejoinder to the Encyclopédie’s critics, while an Éloge de Montesquieu, which served as the preface to Volume V (1755), skillfully but somewhat disingenuously presented Montesquieu as one of the Encyclopédie’s supporters. Montesquieu had, in fact, refused an invitation to write the articles “Democracy” and “Despotism,” and the promised article on “Taste” remained unfinished at his death in 1755.

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Numbers and Mathematics

In 1756 d’Alembert went to stay with Voltaire at Geneva, where he also collected information for an Encyclopédie article, “Genève,” which praised the doctrines and practices of the Genevan pastors. When it appeared in 1757, it aroused angry protests in Geneva because it affirmed that many of the ministers no longer believed in Christ’s divinity and also advocated (probably at Voltaire’s instigation) the establishment of a theatre. This article prompted Rousseau, who had contributed the articles on music to the Encyclopédie, to argue in his Lettre à d’Alembert sur les spectacles (1758) that the theatre is invariably a corrupting influence. D’Alembert himself replied with an incisive but not unfriendly Lettre à J.-J. Rousseau, citoyen de Genève. Gradually discouraged by the growing difficulties of the enterprise, d’Alembert gave up his share of the editorship at the beginning of 1758, thereafter limiting his commitment to the production of mathematical and scientific articles.