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Jean le Rond d'Alembert

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Jean le Rond d'Alembert
Pastel portrait of d'Alembert by Maurice Quentin de La Tour, 1753
Jean-Baptiste le Rond d'Alembert

(1717-11-16)16 November 1717
Paris, France
Died29 October 1783(1783-10-29) (aged 65)
Paris, France
Alma materUniversity of Paris
Known forD'Alembert criterion
D'Alembert force
D'Alembert operator
D'Alembert reduction
D'Alembert system
D'Alembert's form of the principle of virtual work
D'Alembert's formula
D'Alembert's equation
D'Alembert's functional equation
D'Alembert's paradox
D'Alembert's principle
D'Alembert's theorem
D'Alembert–Euler condition
Tree of Diderot and d'Alembert
Cauchy–Riemann equations
Fluid mechanics
Three-body problem
AwardsForMemRS (1748)
Scientific career
Notable studentsPierre-Simon Laplace

Jean-Baptiste le Rond d'Alembert[1] (/dæləmˈbɛər/ dal-əm-BAIR;[2] French: [ʒɑ̃ batist ʁɔ̃ dalɑ̃bɛːʁ]; 16 November 1717 – 29 October 1783) was a French mathematician, mechanician, physicist, philosopher, and music theorist. Until 1759 he was, together with Denis Diderot, a co-editor of the Encyclopédie.[3] D'Alembert's formula for obtaining solutions to the wave equation is named after him.[4][5][6] The wave equation is sometimes referred to as d'Alembert's equation, and the fundamental theorem of algebra is named after d'Alembert in French.

Early years


Born in Paris, d'Alembert was the natural son of the writer Claudine Guérin de Tencin and the chevalier Louis-Camus Destouches, an artillery officer. Destouches was abroad at the time of d'Alembert's birth. Days after birth his mother left him on the steps of the Saint-Jean-le-Rond de Paris [fr] church. According to custom, he was named after the patron saint of the church. D'Alembert was placed in an orphanage for foundling children, but his father found him and placed him with the wife of a glazier, Madame Rousseau, with whom he lived for nearly 50 years.[7] She gave him little encouragement. When he told her of some discovery he had made or something he had written she generally replied,

You will never be anything but a philosopher—and what is that but an ass who plagues himself all his life, that he may be talked about after he is dead.[8]

Destouches secretly paid for the education of Jean le Rond, but did not want his paternity officially recognised.

Studies and adult life


D'Alembert first attended a private school. The chevalier Destouches left d'Alembert an annuity of 1,200 livres on his death in 1726. Under the influence of the Destouches family, at the age of 12 d'Alembert entered the Jansenist Collège des Quatre-Nations (the institution was also known under the name "Collège Mazarin"). Here he studied philosophy, law, and the arts, graduating as baccalauréat en arts in 1735.

In his later life, d'Alembert scorned the Cartesian principles he had been taught by the Jansenists: "physical promotion, innate ideas and the vortices". The Jansenists steered d'Alembert toward an ecclesiastical career, attempting to deter him from pursuits such as poetry and mathematics. Theology was, however, "rather unsubstantial fodder" for d'Alembert. He entered law school for two years, and was nominated avocat in 1738.

He was also interested in medicine and mathematics. Jean enrolled first as Jean-Baptiste Daremberg and subsequently changed his name, perhaps for reasons of euphony, to d’Alembert.[9]

Later, in recognition of d'Alembert's achievements, Frederick the Great of Prussia proposed the name "d'Alembert" for a suspected (but non-existent) moon of Venus, however d'Alembert refused the honor.[10]


Nouvelles expériences sur la résistance des fluides
Front page of a 1758 copy of Traité de dynamique

In July 1739 he made his first contribution to the field of mathematics, pointing out the errors he had detected in Analyse démontrée (published 1708 by Charles-René Reynaud) in a communication addressed to the Académie des Sciences. At the time L'analyse démontrée was a standard work, which d'Alembert himself had used to study the foundations of mathematics. D'Alembert was also a Latin scholar of some note and worked in the latter part of his life on a translation of Tacitus, for which he received wide praise including that of Denis Diderot.

In 1740, he submitted his second scientific work from the field of fluid mechanics Mémoire sur la réfraction des corps solides, which was recognised by Clairaut. In this work d'Alembert theoretically explained refraction.

In 1741, after several failed attempts, d'Alembert was elected into the Académie des Sciences. He was later elected to the Berlin Academy in 1746[11] and a Fellow of the Royal Society in 1748.[12]

In 1743, he published his most famous work, Traité de dynamique, in which he developed his own laws of motion.[13]

When the Encyclopédie was organised in the late 1740s, d'Alembert was engaged as co-editor (for mathematics and science) with Diderot, and served until a series of crises temporarily interrupted the publication in 1757. He authored over a thousand articles for it, including the famous Preliminary Discourse. D'Alembert "abandoned the foundation of Materialism"[14] when he "doubted whether there exists outside us anything corresponding to what we suppose we see."[14] In this way, d'Alembert agreed with the Idealist Berkeley and anticipated the transcendental idealism of Kant.[citation needed]

In 1752, he wrote about what is now called D'Alembert's paradox: that the drag on a body immersed in an inviscid, incompressible fluid is zero.

In 1754, d'Alembert was elected a member of the Académie des sciences, of which he became Permanent Secretary on 9 April 1772.[15]

In 1757, an article by d'Alembert in the seventh volume of the Encyclopedia suggested that the Geneva clergymen had moved from Calvinism to pure Socinianism, basing this on information provided by Voltaire. The Pastors of Geneva were indignant, and appointed a committee to answer these charges. Under pressure from Jacob Vernes, Jean-Jacques Rousseau and others, d'Alembert eventually made the excuse that he considered anyone who did not accept the Church of Rome to be a Socinianist, and that was all he meant, and he abstained from further work on the encyclopaedia following his response to the critique.[16]

He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1781.[17]

Music theories


D'Alembert's first exposure to music theory was in 1749 when he was called upon to review a Mémoire submitted to the Académie by Jean-Philippe Rameau. This article, written in conjunction with Diderot, would later form the basis of Rameau's 1750 treatise Démonstration du principe de l'harmonie. D'Alembert wrote a glowing review praising the author's deductive character as an ideal scientific model. He saw in Rameau's music theories support for his own scientific ideas, a fully systematic method with a strongly deductive synthetic structure.

Two years later, in 1752, d'Alembert attempted a fully comprehensive survey of Rameau's works in his Eléments de musique théorique et pratique suivant les principes de M. Rameau.[18] Emphasizing Rameau's main claim that music was a mathematical science that had a single principle from which could be deduced all the elements and rules of musical practice as well as the explicit Cartesian methodology employed, d'Alembert helped to popularise the work of the composer and advertise his own theories.[18] He claims to have "clarified, developed, and simplified" the principles of Rameau, arguing that the single idea of the corps sonore [fr] was not sufficient to derive the entirety of music.[19] D'Alembert instead claimed that three principles would be necessary to generate the major musical mode, the minor mode, and the identity of octaves. Because he was not a musician, however, d'Alembert misconstrued the finer points of Rameau's thinking, changing and removing concepts that would not fit neatly into his understanding of music.

Although initially grateful, Rameau eventually turned on d'Alembert while voicing his increasing dissatisfaction with J. J. Rousseau's Encyclopédie articles on music.[20] This led to a series of bitter exchanges between the men and contributed to the end of d'Alembert and Rameau's friendship. A long preliminary discourse d'Alembert wrote for the 1762 edition of his Elémens attempted to summarise the dispute and act as a final rebuttal.

D'Alembert also discussed various aspects of the state of music in his celebrated Discours préliminaire of Diderot's Encyclopédie. D'Alembert claims that, compared to the other arts, music, "which speaks simultaneously to the imagination and the senses," has not been able to represent or imitate as much of reality because of the "lack of sufficient inventiveness and resourcefulness of those who cultivate it."[21] He wanted musical expression to deal with all physical sensations rather than merely the passions alone. D'Alembert believed that modern (Baroque) music had only achieved perfection in his age, as there existed no classical Greek models to study and imitate. He claimed that "time destroyed all models which the ancients may have left us in this genre."[22] He praises Rameau as "that manly, courageous, and fruitful genius" who picked up the slack left by Jean-Baptiste Lully in the French musical arts.[23]

Portrait of Jean Le Rond d'Alembert, 1777, by Catherine Lusurier.

Personal life


D'Alembert was a participant in several Parisian salons, particularly those of Marie Thérèse Rodet Geoffrin, of the marquise du Deffand and of Julie de Lespinasse. D'Alembert became infatuated with Julie de Lespinasse, and eventually took up residence with her.



He suffered bad health for many years and his death was as the result of a urinary bladder illness. As a known unbeliever,[24][25][26] D'Alembert was buried in a common unmarked grave.



In France, the fundamental theorem of algebra is known as the d'Alembert/Gauss theorem, as an error in d'Alembert's proof was caught by Gauss.

He also created his ratio test, a test to determine if a series converges.

The D'Alembert operator, which first arose in D'Alembert's analysis of vibrating strings, plays an important role in modern theoretical physics.

While he made great strides in mathematics and physics, d'Alembert is also famously known for incorrectly arguing in Croix ou Pile that the probability of a coin landing heads increased for every time that it came up tails. In gambling, the strategy of decreasing one's bet the more one wins and increasing one's bet the more one loses is therefore called the D'Alembert system, a type of martingale.

In South Australia, a small inshore island in south-western Spencer Gulf was named Ile d'Alembert by the French explorer, Nicolas Baudin during his expedition to New Holland. The island is better known by the alternative English name of Lipson Island. The island is a conservation park and seabird rookery.

Fictional portrayal


Diderot portrayed d'Alembert in Le rêve de D'Alembert (D'Alembert's Dream), written after the two men had become estranged. It depicts d'Alembert ill in bed, conducting a debate on materialist philosophy in his sleep.

D'Alembert's Principle, a 1996 novel by Andrew Crumey, takes its title from D'Alembert's principle in physics. Its first part describes d'Alembert's life and his infatuation with Julie de Lespinasse.

List of works

  • D'Alembert, Jean Le Rond (1743). Traité de dynamique (2nd ed.). Gabay (1990 reprint).
  • D'Alembert, Jean Le Rond (1747a). "Recherches sur la courbe que forme une corde tenduë mise en vibration (Researches on the curve that a tense cord forms [when] set into vibration)". Histoire de l'académie royale des sciences et belles lettres de Berlin. Vol. 3. pp. 214–219.
  • D'Alembert, Jean Le Rond (1747b). "Suite des recherches sur la courbe que forme une corde tenduë mise en vibration (Further researches on the curve that a tense cord forms [when] set into vibration)". Histoire de l'académie royale des sciences et belles lettres de Berlin. Vol. 3. pp. 220–249.
  • D'Alembert, Jean Le Rond (1750). "Addition au mémoire sur la courbe que forme une corde tenduë mise en vibration". Histoire de l'académie royale des sciences et belles lettres de Berlin. Vol. 6. pp. 355–60.
  • Recherches sur differens points importans du systeme du monde (in French). Vol. 1. Paris: Michel Antoine David. 1754.
  • D'Alembert, Jean Le Rond (1995). Preliminary Discourse to the Encyclopedia of Diderot. Translated by Schwab, Richard N.; Rex, Walter E. University of Chicago Press.

See also



  1. ^ His last name is also written as D'Alembert in English.
  2. ^ "Alembert, d'". Random House Webster's Unabridged Dictionary.
  3. ^ "Jean Le Rond d'Alembert | French mathematician and philosopher". Encyclopedia Britannica. Retrieved 26 June 2021.
  4. ^ D'Alembert 1747a.
  5. ^ D'Alembert 1747b.
  6. ^ D'Alembert 1750.
  7. ^ Hall 1906, p. 5.
  8. ^ The National Cyclopaedia of Useful Knowledge, Vol I, London, Charles Knight, 1847, p.417.
  9. ^ "Jean Le Rond d'Alembert | French mathematician and philosopher". Encyclopedia Britannica. Retrieved 10 April 2023.
  10. ^ Ley, Willy. 1952. Article "Moon of Venus" in Galaxy Science Fiction July 1952. MDP Publishing Galaxy Science Fiction Digital Series, 2016. Retrieved from Google Books.
  11. ^ Hankins 1990, p. 26.
  12. ^ "Library and Archive Catalogue". Royal Society. Archived from the original on 10 April 2020. Retrieved 3 December 2010.
  13. ^ D'Alembert 1743.
  14. ^ a b Friedrich Albert Lange, History of Materialism and Critique of its Present Importance, "Kant and Materialism"
  15. ^ Jean LE ROND, dit d’ ALEMBERT (1717-1783) Secrétaire perpétuel www.academie-francaise.fr/immortels Archived 31 May 2012 at the Wayback Machine
  16. ^ Smith Richardson 1858, pp. 8–9.
  17. ^ "Book of Members, 1780–2010: Chapter A" (PDF). American Academy of Arts and Sciences. Retrieved 14 April 2011.
  18. ^ a b Christensen 1989, p. 415.
  19. ^ Bernard 1980.
  20. ^ The New Grove Dictionary of Music and Musicians, 2nd ed., s.v. "Alembert, Jean le Rond d'"
  21. ^ D'Alembert 1995, p. 38.
  22. ^ D'Alembert 1995, p. 69.
  23. ^ D'Alembert 1995, p. 100.
  24. ^ Israel 2011, p. 115: "D'Alembert, though privately an atheist and materialist, presented the respectable public face of 'la philosophie' in the French capital while remaining henceforth uninterruptedly aligned with Voltaire."
  25. ^ Force & Popkin 1990, p. 167: "Unlike the French and English deists, and unlike the scientific atheists such as Diderot, d'Alembert, and d'Holbach, such English scientists as David Hartley and Joseph Priestley presented their scientific theories as evidence for their scriptural views."
  26. ^ Horowitz 1999, pp. 52–53: "In positive theory there was a wide divergence between Voltaire's panpsychic deism and Diderot's physiological materialism, or d'Alembert's agnostic positivism and Helvetius' sociological materialism."