Jean le Rond d'Alembert was a mathematician and physicist who applied his considerable genius to solving problems in mechanics. This is the branch of physics that deals with the effect of forces on matter, either at rest or in motion. His most important contribution was d'Alembert's principle, which states that the forces in an object that resist acceleration must be equal and opposite to the forces that produce the acceleration. D'Alembert was a pioneer in the development of calculus. He also served as science editor of Denis Diderot's Encyclopédie.
D'Alembert was born in Paris on November 17, 1717. He was the illegitimate son of Claudine-Alexandrine Guérin, Marquise de Tencin, an intelligent and unprincipled woman who broke her vows as a nun and became the mistress of many powerful men. D'Alembert's father was the Chevalier Louis-Camus Destouches, a military officer. D'Alembert's mother apparently regarded her pregnancy as an unwelcome accident and later abandoned her infant son on the steps of the church of Saint-Jean-le-Rond. The foundling was baptized with the name of the church, then sent to a foster home in Picardy.
After Destouches returned from military service, he brought his son back to Paris and arranged for him to be raised by one Madame Rousseau, the wife of a glazier. D'Alembert always regarded this woman as his real mother, and he continued to live in her home until he was 47 years old. Destouches provided for his son and paid for his education. When Destouches died in 1726, he left the boy a legacy that gave d'Alembert a modest lifetime income of 1,200 livres a year. D'Alembert always cherished the independence this income provided.
D'Alembert attended the Collège des Quatre-Nations (also called Mazarin College), a school run by Jansenists, members of a religious sect. While at college, he adopted the name Jean-Baptiste Daremberg, later shortened to d'Alembert. Despite the urging of teachers, however, d'Alembert rejected the religious life. After receiving a bachelor's degree in 1735, he went on to study law, receiving a license to practice in 1738. He also studied medicine for a year. Neither the law nor medicine held much lasting appeal for d'Alembert. He finally settled upon a career in mathematics, a vocation for which he had much natural talent.
In 1739, d'Alembert submitted his first paper to the French Académie Royale des Sciences, a critique of a mathematics book written by Father Charles Reyneau. Over the next two years, d'Alembert sent the Académie additional papers on such topics as fluid mechanics and the integration of differential equations. After several failed attempts to join the Académie, he was finally admitted in May 1741.
During the 1740s, d'Alembert became a fixture in French intellectual and social salons, where he was known for his gaiety and wit. He took his place among leading philosophes, thinkers of the Enlightenment, a philosophical movement marked by an emphasis on human reason and a rejection of traditional religious and political ideas. Although d'Alembert never married, he shared a close relationship for many years with Julie de Lespinasse, a popular salon hostess.
From 1741 through 1743, d'Alembert studied various problems in dynamics, the branch of mechanics that deals with the effect of forces on the motion of bodies. His writings were hastily collected into a book, Traité de dynamique (1743), that became his most important scientific work. This book introduced the famous principle that bears d'Alembert's name. The principle was actually an extension of Isaac Newton's third law of motion, which states that for every force exerted on a static body, there is an equal and opposite force from that body. D'Alembert maintained that the law applied not only to bodies at rest, but to bodies in motion as well. This was the dawn of a new era in the science of mechanics. The next year, d'Alembert published Traité de l'équilibre et du mouvement des fluides (1744), in which he applied his principle to the motion of fluids.
D'Alembert published Réflexions sur la cause générale des ventsin 1747, a treatise on winds that won a prize from the Prussian Academy. This paper marked the first general use of partial differential equations in mathematical physics. That same year, d'Alembert published an article on the motion of vibrating strings. This paper is notable for the first use of a wave equation in physics. While d'Alembert pioneered both partial differential equations and wave equations, it was left to his Swiss contemporary Leonhard Euler to develop these concepts more fully.
Next, d'Alembert turned his attention to astronomy, applying calculus to celestial mechanics. In 1749 he issued Recherches sur la précession des équinoxes et sur la nutation de la terre. This book dealt with the precession of the equinoxes; that is, the slow, gradual westward motion of the equinoxes due to the movement of the Earth's axis. D'Alembert's research on astronomy continued in Recherches sur différens points importants du systeme du monde. This three-volume work, published in 1754-1756, dealt mainly with the motion of the moon.
D'Alembert issued one more scientific publication in the 1750s, returning to the subject of fluid mechanics in Essai d'une nouvelle théorie de la résistance des fluides(1752). In this essay, he introduced such important concepts as the components of fluid velocity and acceleration . With Élémens de musique théorique et pratique suivant les principes de M. Rameau (1752), however, d'Alembert departed from science to indulge an interest in music. In this work, he described the new theory of musical structure advanced by French composer Jean-Philippe Rameau.
Much of the 1750s was devoted to work on Diderot's Encyclopédie. This monumental work was conceived by Diderot as a synthesis of all human knowledge, with an emphasis on new ideas and scientific discoveries. D'Alembert's first task was writing the Discours préliminaire(1751), an introduction that sought to show the links between disciplines and to trace the progress of thought, culminating in the philosophy of the Enlightenment. The discourse was widely praised. Its publication led to d'Alembert's acceptance into the French Académie in 1754. He later became very active in that organization, eventually being elected its permanent secretary.
D'Alembert wrote 1,500 articles for the Encyclopédie. While many of these articles discussed mathematics and science, others addressed philosophy and the arts. In fact, d'Alembert was increasingly drawn to nonscientific topics. Between 1753 and 1767, he published five volumes of Mélanges de littérature et de philosophie. This collection contained essays on music, law, and religion; a treatise on philosophy; translations of Tacitus; and a hodgepodge of other material.
In 1757, d'Alembert visited the French writer Voltaire, his closest friend among the philosophes. One result of the visit was an article on Geneva, Switzerland, which appeared in the seventh volume of the Encyclopédie. This article caused a furor with its depiction of Protestant ministers, managing to offend Roman Catholics and Calvinists alike. The uproar caused d'Alembert to resign as an editor of the project.
During the following decades, d'Alembert resumed scientific publication. From 1761 to 1780, he issued eight volumes of Opuscules mathématiques, which included essays on hydrodynamics, astronomy, and lenses. At this time, d'Alembert was almost alone in regarding the differential as the limit of a function, a key concept in modern calculus. However, he could never rise above the traditional focus on geometry, which prevented him from ever putting the idea of the limit into a purely algorithmic form.
In 1764, d'Alembert spent three months in the court of Frederick the Great. Although he was offered the presidency of the Prussian Academy, d'Alembert declined. He also turned down an offer from Russian Empress Catherine the Great to tutor her son for 100,000 livres a year. Above all, d'Alembert prized his financial independence and the intellectual freedom it afforded. D'Alembert published a work on religion the following year, in which he called for the suppression of both the Jesuits and their rivals, the Jansenists. This book, not one of d'Alembert's better efforts, was written at Voltaire's behest. It was issued anonymously, but the author's identity was known.
D'Alembert's final years were not easy. He became seriously ill in 1765 and moved into the home of Julie de Lespinasse, who nursed him back to health. He continued to live with Lespinasse until her death in 1776. After she died, d'Alembert discovered evidence of love affairs with other men among Lespinasse's effects, which made her loss doubly painful. He withdrew into a lonely, bitter retirement, living in a small apartment provided by the French Académie. D'Alembert died in Paris on October 29, 1783. He had outlived many of his fellow philosophes, but the scientific and philosophical legacy of this remarkable group of thinkers survives.
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