The first school that d'Alembert attended was a private school. He was an illegitamate child, and his mother left him at the steps of a church. His father raised him, but died when d'Alembert was only 9, He left him just enough money to give him security. He entered the Jansenist Collège des Quatre Nations. This was an excellent place for d'Alembert to study mathematics even though the course was elementary. As well as the mathematical training, he learnt about Descartes' physical ideas, but when he formed his own ideas later in his life he would have little respect for the views of Descartes.

The main aim of the Collège was to produce scholars who could become experts in theology and argue the Jansenist case against the Jesuits. However, d'Alembert was turned off the study of theology. After graduating in 1735, he decided that he would make a career in law, but his real passion was for mathematics and he continued to work in his spare time on that subject. In 1739, d'Alembert studied medicine but this was a topic that he found even worse than theology, so he turned to mathematics.

Later that same year, d'Alembert read his first paper on some errors he had found in Reyneau's standard text. In 1740, he submitted a second work on the mechanics of fluids which was praised by Clairaut. In 1741, d'Alembert was admitted to the Paris Academy of Science, on the strength of these and papers on the integral calculus. It took some determination on his part, submitting three unsuccessful applications in quick succession, before his appointment.

In one sense d'Alembert's life was uneventful. He travelled little and worked at the Paris Academy of Science and the French Academy all his life. On another level his life was one of great drama as he argued with almost everyone around him. Despite this tendency, his contributions were truly outstanding. D'Alembert helped to resolve the controversy in mathematical physics over the conservation of kinetic energy by improving Newton's definition of force. He read many papers on physics, but when Clairaut began to read his own works on dynamics, a rivalry between the two began. In 1744, d'Alembert applied his results to the equilibrium and motion of fluids, and published a work which gave an alternative treatment of fluids to the one published by Daniel Bernoulli.

Around the same time d'Alembert was contracted as an editor to cover mathematics and physical astronomy for an encyclopedia, but his work covered a wider field. When the first volume appeared in 1751, it contained a preface written by d'Alembert which was widely acclaimed as a work of great genius. D'Alembert worked on the encyclopedia for many years. In fact he wrote most of the mathematical articles in this 28 volume work.

However, he continued his other mathematical work. He was a pioneer in the study of partial differential equations and he pioneered their use in physics. Euler, however, saw the power of the methods introduced by d'Alembert and soon developed these far further than had d'Alembert. In 1747, d'Alembert published an article on vibrating strings. The article contains the first appearance of the wave equation in print, but suffers from the defect that he used mathematically pleasing simplifications of certain boundary conditions which led to results which were at odds with observation.

D'Alembert made other important contributions to mathematics. He suggested that the theory of limits be put on a firm foundation. He was one of the first to understand the importance of functions and he defined the derivative of a function as the limit of a quotient of increments. His ideas on limits led him to the test for convergence, known today as d'Alembert's ratio test.

In the latter part of his life, d'Alembert turned more towards literature and philosophy. D'Alembert's philosophical works appear mainly in a 5 volume work which appeared between 1753 and 1767. In this work he sets out his skepticism concerning metaphysical problems.

D'Alembert was elected to the French Academy in 1754. In 1772, he was elected perpetual secretary of the French Academy and spent much time writing obituaries for the academy. He became the academy's most influential member, but, in spite of his efforts, that body failed to produce anything noteworthy in the way of literature during his pre-eminence.