**Jean d'Alembert** was a a French mathematician who was a pioneer in the study of differential equations and their use of in physics. He studied the equilibrium and motion of fluids.

- He was baptised Jean Le Rond, named after the church on whose steps he had been found.
- He enrolled in the name of Jean-Baptiste Daremberg but soon changed his name to Jean d'Alembert.
- The Collège des Quatre Nations was an excellent place for d'Alembert to study mathematics even though the course was elementary.
- The mathematics course, given by Professor Carron, was based on Varignon's lectures and d'Alembert was able to make use of the excellent mathematics library at the Collège.
- However, d'Alembert was turned off the study of theology at the Collège.
- In 1738 d'Alembert qualified as an advocate but he seems to have decided that this was not the career for him.
- The following year d'Alembert studied medicine but this was a topic that he found even worse than theology.
- In July 1739 d'Alembert read his first paper to the Paris Academy of Science on some errors he had found in Reyneau's standard text Analyse démontrée Ⓣ(Analysis demonstrated) which were not of great significance but marked the start of his mathematical career.
- In May 1741 d'Alembert was admitted to the Paris Academy of Science, on the strength of these and papers on the integral calculus.
- Before discussing d'Alembert's contributions it is useful to discuss his personality, which was to have a major effect on the way his scientific work was to develop.
- In one sense d'Alembert's life was uneventful.
- D'Alembert helped to resolve the controversy in mathematical physics over the conservation of kinetic energy by improving Newton's definition of force in his Traité de dynamique Ⓣ(Treatise on dynamics) which he published in 1743.
- This also contains d'Alembert's principle of mechanics.
- This is an important work and the preface contains a clear statement by d'Alembert of an attempt to lay a firm foundation for mechanics.
- D'Alembert was a mathematician, not a physicist, and he believed mechanics was just as much a part of mathematics as geometry or algebra.
- D'Alembert thought mechanics should be made into a completely rationalistic mathematical system.
- D'Alembert had begun to read parts of his Traité de dynamique to the Academy in late 1742 but soon afterwards Clairaut began to read his own work on dynamics to the Academy.
- Clearly a rivalry quickly sprung up and d'Alembert stopped reading the work to the Academy and rushed into print with the treatise.
- D'Alembert stated his position clearly that he believed mechanics to be based on metaphysical principles and not on experimental evidence.
- For d'Alembert these laws of motion were logical necessities.
- In 1744 d'Alembert applied his results to the equilibrium and motion of fluids and published Traité de l'équilibre et du mouvement des fluides Ⓣ(Treatise on the equilibrium and motion of fluids).
- D'Alembert thought it a better approach, of course, as one might expect, Daniel Bernoulli did not share this view.
- D'Alembert became unhappy at the Paris Academy, almost certainly because of his rivalry with Clairaut and disagreements with others.
- In around 1746 d'Alembert's life took a rather sudden change.
- In 1746 he was introduced to Mme Geoffrin, the rich, imperious, unintellectual but generous founder of a salon to which d'Alembert was suddenly invited.
- Around the same time d'Alembert began to become involved in a major project, namely editing the Encyclopédie with Diderot.
- 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 Encyclopédie for many years.
- Euler, however, saw the power of the methods introduced by d'Alembert and soon developed these far further than had d'Alembert.
- This work by d'Alembert on the winds suffers from a defect which was typical of all of his work, namely it was mathematically very sound but was based on rather poor physical evidence.
- A heated argument between d'Alembert and Clairaut resulted in the two fine mathematicians trading insults in the scientific journals of the day.
- The year 1747 was an important one for d'Alembert in that a second important work of his appeared in that year, namely his article on vibrating strings.
- Euler had learnt of d'Alembert's work in around 1743 through letters from Daniel Bernoulli.
- However, Daniel Bernoulli became highly critical of d'Alembert after reading his Traité de l'équilibre et du mouvement des fluides Ⓣ(Treatise on the equilibrium and motion of fluids) for reasons we noted above.
- When d'Alembert won the prize of the Prussian Academy of Sciences with his essay on winds he produced a work which Euler considered superior to that of Daniel Bernoulli.
- Certainly at this time Euler and d'Alembert were on very good terms with Euler having high respect for d'Alembert's work and the two corresponded on many topics of mutual interest.
- However relations between Euler and d'Alembert soon took a turn for the worse after the dispute in the Berlin Academy involving Samuel König which began in 1751.
- The situation became more relevant to d'Alembert in 1752 when he was invited to became President of the Berlin Academy.
- Another reason for d'Alembert to feel angry with Euler was that he felt that Euler was stealing his ideas and not giving him due credit.
- In one sense d'Alembert was justified but on the other hand his work was usually so muddled that Euler could not follow it and resorted to starting from scratch to clarify the problem being solved.
- The Paris Academy had not been a place for d'Alembert to publish after he fell out with colleagues there and he was sending his mathematical papers to the Berlin Academy during the 1750s.
- However Euler was unhappy to publish these works and d'Alembert stopped publishing his mathematical articles, collecting them together and publishing them as Opuscules mathématiques Ⓣ(Booklets on mathematics) which appeared in eight volumes between 1761 and 1780.
- This was not the only offer d'Alembert turned down.
- D'Alembert made other important contributions to mathematics which we have not yet mentioned.
- His ideas on limits led him to the test for convergence, known today as d'Alembert's ratio test, which appears in Volume 5 of Opuscules mathématiques Ⓣ(Booklets on mathematics).
- In the latter part of his life d'Alembert turned more towards literature and philosophy.
- D'Alembert's philosophical works appear mainly in the five volume work Mélanges de littérature et de philosophie Ⓣ(Mixtures of literature and philosophy) which appeared between 1753 and 1767.
- D'Alembert was elected to the French Academy on 28 November 1754.
- D'Alembert complained from 1765, after a bout of illness, that his mind was no longer able to concentrate on mathematics.
- As a known unbeliever, d'Alembert was buried in a common unmarked grave.

Born 17 November 1717, Paris, France. Died 29 October 1783, Paris, France.

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