Jean le Rond d'Alembert

French mathematician and philosopher

• Born: November 17, 1717
• Birthplace: Paris, France
• Died: October 29, 1783
• Place of death: Paris, France

A pioneer in the use of differential calculus, d’Alembert applied his mathematical genius to solving problems in mechanics. He provided valuable assistance with Denis Diderot’s Encyclopedia and wrote a number of treatises on musical theory.

Early Life

On the night of November 17, 1717, Mme Claudine-Alexandrine Guérin, marquise de Tencin, gave birth to a son whom she promptly abandoned on the steps of the Church of Saint-Jean-Le-Rond. There, he was baptized with the name of the church, Jean le Rond d’Alembert (zhah luh-roh dah-lahm-behr); he was then sent to the Maison de la Coucher, from which he went to a foster home in Picardy. When his father, Louis-Camus Destouches, a military officer, returned to Paris, he sought his son and arranged for the child to be cared for by Mme Rousseau, the wife of a glazier. D’Alembert would always regard Mme Rousseau as his real mother and would continue to live with her until 1765, when illness compelled him to seek new quarters in the home of Julie de Lespinasse.

Destouches continued to watch over his illegitimate child, sending him to private schools; when Destouches died in 1726, he left the boy a legacy of twelve hundred livres a year. The sum, though not luxurious, guaranteed him an independence he cherished throughout his life. Through the interest of the Destouches family, the young man entered the Jansenist Collège des Quatre-Nations, where he took the name Jean-Baptiste Daremberg, later changing it, perhaps for euphony, to d’Alembert. Although he, like many other Enlightenment figures, abandoned the religious training he received there, he never shed the Cartesian influence that dominated the school.

After receiving his baccalauréat in 1735, he spent two years studying law, receiving a license to practice in 1738. Neither jurisprudence nor medicine, to which he devoted a year, held his interest. He turned to mathematics, for which he had a natural talent. At the age of twenty-two, he submitted his first paper to the Academy of Sciences. In that piece, he corrected a number of errors in Father Charles Reyneau’s Analyse demontrée (1714). A second paper, on refraction and fluid mechanics, followed the next year, and in May, 1741, he was made an adjunct member of the Academy of Sciences.

Life’s Work

Two years later, d’Alembert published a major contribution to mechanics, Traité de dynamique (1743), which includes his famous principle stating that the force that acts on a body in a system is the sum of the forces within the system restraining it and the external forces acting on that system. Although Sir Isaac Newton and Johann Bernoulli had already offered similar observations, neither had expressed the matter so simply. The effect of d’Alembert’s principle was to convert a problem of dynamics to one of statics, making it easier to solve. The treatise is characteristic of d’Alembert’s work in several ways: It illustrates his exceptional facility with mathematics, it reveals a desire to find universal laws in a discipline, and it indicates his ability to reduce complex matters to simple components. Over the next several years, he wrote a number of other innovative works in both mathematics and fluid mechanics.

At the same time that d’Alembert was establishing himself as one of Europe’s leading mathematicians—in 1752, Frederick the Great offered him the presidency of the Berlin Academy—he emerged as a leading figure of the Parisian salons. In 1743, he was introduced to the influential Mme du Deffand, who would secure his election to the French Academy in 1754. He remained a fixture of her assemblies until Julie de Lespinasse, whom he met there, established her own salon following a quarrel with the older woman. Later in the 1740’s, he also joined the gatherings at the homes of Mme Marie-Thérèse Rodet Geoffrin and Anne-Louise Bénédicte de Bourbon, duchesse du Maine. Not striking in appearance—he was short and, according to a contemporary, “of rather undistinguished features, with a fresh complexion that tends to ruddiness,” his eyes small and his mouth large—he compensated for his looks with his excellent ability with mimicry and his lively conversation.

While enjoying the female-dominated world of the salons, d’Alembert was also meeting a number of important male intellectuals, with whom he dined weekly at the Hôtel du Panier Fleuri—Denis Diderot, Jean-Jacques Rousseau (no relation to his stepmother), and Étienne Bonnot de Condillac. He probably also knew Gua de Malves, a fellow mathematician and member of the Academy of Sciences, who was chosen as the first editor of the Encyclopédie: Ou, Dictionnaire raisonné des sciences, des arts, et des métiers (1751-1772; Encyclopedia, 1965), and Malves may have been the one who introduced d’Alembert to the project; after Malves resigned, d’Alembert was named coeditor with Diderot.

D’Alembert did not plan to assume as much responsibility for the work as his coeditor. He wrote to Samuel Formey in September, 1749:

I never intended to have a hand in [the Encyclopedia] except for what has to do with mathematics and physical astronomy. I am in a position to do only that, and besides, I do not intend to condemn myself for ten years to the tedium of seven or eight folios.

It was Diderot who conceived of the work as a summation of human knowledge, but d’Alembert’s involvement extended well beyond the mathematical articles that the title page credits to him.

His contributions took many forms. He used his scientific contacts to solicit articles, and his connection with the world of the salons, which Diderot did not frequent, permitted him to enlist support among the aristocracy and upper middle class. Not only was such backing politically important, given the controversial nature of the enterprise, but also the financial assistance d’Alembert secured may well have prevented its collapse. Mme Geoffrin alone is reported to have donated more than 100,000 livres.

Also significant are the fifteen hundred articles that d’Alembert wrote, including the important Discours préliminaire (1751; Preliminary Discourse to the Encyclopedia of Diderot, 1963). Praised by all the great French intellectuals as well as Frederick the Great, it seeks to explain the purpose and plan of the Encyclopedia by showing the links between disciplines and tracing the progress of knowledge from the Renaissance to 1750. In its view of the Enlightenment as the culmination of progress in thought, it reflects the philosophes’ optimistic, humanistic attitude. D’Alembert’s own understanding of the role of the philosopher and the nature of learning also emerges clearly in this essay. For him, “The universe is but a vast ocean, on the surface of which we perceive certain islands more or less large, whose link with the continent is hidden from us.” The goal of the scientist is to discover, not invent, these concealed links, and mathematics would provide the means for establishing these connections. Just as physicists of the twenty-first century seek the one force that impels all nature, so d’Alembert sought the single principle that underlies all knowledge.

In 1756, d’Alembert went to Geneva to visit Voltaire, his closest friend among the philosophes, and to gather information for an article on this center of Calvinism. In an earlier work, d’Alembert had antagonized the Church by criticizing ecclesiastical control of education. “Genève,” with its intended praise of Protestant ministers, provoked sharp protests from the Catholic establishment in France, and Calvinists were upset as well by d’Alembert’s portrait of them as virtual agnostics.

Opposition to the Encyclopedia was growing in court circles; in March, 1759, permission to publish would be withdrawn. Never as daring as Voltaire or Diderot, d’Alembert resigned as coeditor in 1758, despite protests from his friends and associates. He did, however, continue to write articles on mathematics and science.

While the controversy surrounding the enterprise, especially “Genève,” was the primary reason for d’Alembert’s distancing himself from the Encyclopedia, another important factor was his growing disagreement with Diderot over the direction the work had been taking. By 1758, Diderot, who had published a treatise on mathematics, Mémoires sur différens sujets de mathématiques (1748), had come to believe that no further progress was possible in that field, so he rejected his coeditor’s emphasis on mathematics as the key to knowledge, stating that “the reign of mathematics is over.” D’Alembert’s Cartesian theories also troubled Diderot. Like René Descartes, d’Alembert believed that matter is inert; Diderot disagreed. While d’Alembert maintained that the most precise sciences were those such as geometry that relied on abstract principles derived from reason, Diderot regarded experimentation and observation—empiricism—as the best guarantees of reliability. For d’Alembert, the more abstruse the science the better, for he sought to solve problems. Diderot preferred knowledge that directly affected life. In later years, Diderot continued to praise d’Alembert’s mathematical abilities, and d’Alembert unsuccessfully tried to secure Diderot’s election to the French Academy, but the two remained only distant friends.

Withdrawing from the Encyclopedia did not signal d’Alembert’s rejection of the Enlightenment. Instead, he sought to use the French Academy as a forum to promulgate the views of the philosophes. His first speech before the French Academy urged toleration and freedom of expression, and in 1769 he nearly succeeded in having the body offer a prize for the best poem on the subject of “The Progress of Reason Under Louis X,” the notion of such progress being a fundamental tenet of the Enlightenment. In 1768, when the king of Denmark, Christian VII, visited the French Academy, and again in March, 1771, when Gustavus III of Sweden attended a session, d’Alembert spoke of the benefits of enlightened policies. Through his influence in the salons, he arranged for the election of nine philosophes to the French Academy between 1760 and 1770, and a number of others sympathetic to their cause also entered because of d’Alembert. Elected permanent secretary of the body in 1772, he threafter used his official eulogies to attack the enemies of the Enlightenment and to encourage advanced ideas.

D’Alembert also continued to publish. The first three volumes of Opuscules mathématiques (1761-1780) contain much original work on hydrodynamics, lenses, and astronomy. His anonymous Sur la destruction des Jésuites en France (1765; An Account of the Destruction of the Jesuits in France, 1766), occasioned by the suppression of the order, discusses the danger of linking civil and ecclesiastical power because theological disputes then disturb domestic peace. In addition to attacking the Jesuits, d’Alembert urged the suppression of their rivals, the Jansenists.

Active as he was in the French Academy, d’Alembert’s last years were marked by physical and emotional pain. Devoted to Julie de Lespinasse, he was doubly distressed by her death in 1776 and the discovery of love letters to her from the comte de Guibert and the marquis de Mora. As permanent secretary of the French Academy, d’Alembert was entitled to a small apartment in the Louvre, and there he spent the final seven years of his life, which ended on October 29, 1783. Although he produced little original work of his own during this period, he remained an important correspondent of Voltaire and Frederick the Great, urging the monarch to grant asylum to those persecuted for their views. He also encouraged young mathematicians such as Joseph-Louis Lagrange, Pierre-Simon Laplace, and the marquis de Condorcet.

Significance

Voltaire sometimes doubted Jean le Rond d’Alembert’s zeal for the cause of Enlightenment, and d’Alembert’s distancing himself from the encyclopédistes reveals that he was not one to take great risks. He observed that “honest men can no longer fight except by hiding behind the hedges, but from that position they can fire some good shots at the wild beasts infesting the country.” From his post in the salons and the French Academy, he worked, as he told Voltaire, “to gain esteem for the little flock” of philosophes.

If Voltaire could accuse d’Alembert of excessive caution, d’Alembert could in turn charge Voltaire with toadying to the powerful. In his 1753 Essai sur les gens de lettres, d’Alembert urged writers to rely solely on their talents, and he reminded the nobility that intellectuals were their equals. “I am determined never to put myself in the service of anyone and to die as free as I have lived,” he wrote Voltaire. Neither Frederick the Great’s repeated invitations to assume the presidency of the Berlin Academy nor Catherine the Great’s offer of 100,000 livres a year to tutor her son Grand Duke Paul could lure him away from France and independence.

In both his life and thought he was loyal to the ideals of the philosophes, so it is fitting that early twentieth century scholar Ernst Cassirer should choose him as the representative of the Enlightenment and call him “one of the most important scholars of the age and one of its intellectual spokesmen.” His belief in the ability of reason to solve any problem epitomizes the view of eighteenth century intellectuals, but he also recognized the role of experimentation and imagination. In his Eléméns de musique théorique et practique suivant les principes de M. Rameau (1752), d’Alembert dissented from Jean-Philippe Rameau’s view that one can devise mathematical rules for composition. As in his article on elocution in the Encyclopedia, he argued that rules are necessary, but only genius can elevate a work beyond mediocrity. Excellent scientist though he was, he ranked the artist above the philosopher.

Bibliography

Cassirer, Ernst. The Philosophy of the Enlightenment. Translated by Fritz A. C. Koelln and James P. Pettegrove. Princeton, N.J.: Princeton University Press, 1951. Explores how Enlightenment thinkers looked at nature, psychology, religion, history, society, and aesthetics. Includes a great deal of information about d’Alembert.

Essar, Dennis F. The Language Theory, Epistemology, and Aesthetics of Jean Lerond d’Alembert. Oxford, England: Voltaire Foundation at the Taylor Institution, 1976. A study of d’Alembert’s philosophy. Argues that d’Alembert’s “position in the Enlightenment remains of central, pivotal importance.” Also treats d’Alembert’s mathematical and scientific contributions.

Grimsley, Ronald. Jean d’Alembert, 1717-83. Oxford, England: Clarendon Press, 1963. A topical study of d’Alembert’s contributions to the Encyclopedia, his relations with other philosophers, and his own views. Largely ignores the scientific and mathematical aspects of d’Alembert’s career.

Hankins, Thomas L. Jean d’Alembert: Science and the Enlightenment. Oxford, England: Clarendon Press, 1970. An ideal complement to Grimsley’s book, for it concentrates on d’Alembert’s contributions to science and mathematics. Relates d’Alembert’s achievements to those of other scientists and the role of science to that of philosophy in the eighteenth century.

James, Ioan. Remarkable Mathematicians: From Euler to von Neumann. Washington, D.C.: Mathematical Association of America, 2002. Includes a chapter on d’Alembert’s contributions to mathematics.

Kafker, Frank A. The Encyclopedists as a Group: A Collective Biography of the Authors of the “Encyclopédie.” Oxford, England: Voltaire Foundation, 1996. Examines the life and thought of d’Alembert and the other authors who created the Encyclopedia.

Pappas, John Nicholas. Voltaire and d’Alembert. Bloomington: Indiana University Press, 1962. Drawing heavily on the correspondence between the two, this study seeks to rectify the view, fostered in large part by Voltaire, that d’Alembert was a hesitant follower of the older intellectual. Notes that the influence was mutual and shows where the two differed.

Van Treese, Glen Joseph. D’Alembert and Frederick the Great: A Study of Their Relationship. New York: Learned Publications, 1974. Treats the origin, nature, and consequences of the friendship between d’Alembert and the Prussian ruler. Offers a portrait of the two men and their age.