French mathematician, encyclopedist, and theoretical physicist. In association with Denis Diderot, he helped plan the great Encyclopédie, for which he also wrote the ‘Discours préliminaire’ (1751). He framed several theorems and principles – notably d'Alembert's principle – in dynamics and celestial mechanics, and devised the theory of partial differential equations.
The principle that now bears his name was first published in his Traité de dynamique (1743), and was an extension of the third of Isaac Newton's laws of motion. D'Alembert maintained that the law was valid not merely for a static body, but also for mobile bodies. Within a year he had found a means of applying the principle to the theory of equilibrium and the motion of fluids. Using also the theory of partial differential equations, he studied the properties of sound, and air compression, and also managed to relate his principle to an investigation of the motion of any body in a given figure.
A Paris foundling, d'Alembert had his education financed by a sponsor. First he studied law, then medicine, before deciding to devote his life to mathematics.
D'Alembert's first published mathematical work was a paper on integral calculus in 1739. This and later papers were fundamental to the development of calculus. His mathematical treatises were collected in ‘Opuscules mathématiques’ (1761–80).
From the early 1750s, together with other mathematicians such as Joseph Lagrange and Pierre Laplace, he applied calculus to celestial mechanics. In particular, d'Alembert worked out in 1754 the theory needed to set Newton's discovery of the precession of the equinoxes on a sound mathematical basis, and explained the phenomenon of the oscillation of the Earth's axis. He also gave accurate calculations of the perturbations in the orbits of the known planets.
For the Encyclopédie d'Alembert wrote on scientific topics, linking, especially, various branches of science. But when the Catholic Church in France denounced the project, he resigned his editorship.