# Jean le Rond d'Alembert

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Jean le Rond d'Alembert
Jean-Baptiste le Rond d'Alembert, pastel by Maurice Quentin de La Tour
Born Jean-Baptiste le Rond d'Alembert
16 November 1717
Paris, France
Died 29 October 1783 (aged 65)
Paris, France
Nationality French
Alma mater University of Paris
Known for D'Alembert criterion
D'Alembert force
D'Alembert's form of the principle of virtual work
D'Alembert's formula
D'Alembert equation
D'Alembert's equation
D'Alembert operator
D'Alembert's principle
D'Alembert system
D'Alembert–Euler condition
Tree of Diderot and d'Alembert
Cauchy–Riemann equations
Fluid mechanics
Encyclopédie
Three-body problem
Awards Fellow of the Royal Society
Follow of the Institut de France
Scientific career
Fields Mathematics
Mechanics
Physics
Philosophy
Notable students Pierre-Simon Laplace

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

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

D'Alembert first attended a private school. The chevalier Destouches left d'Alembert an annuity of 1200 livres on his death in 1726. Under the influence of the Destouches family, at the age of twelve 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 was first registered under the name Daremberg, but later changed it to d'Alembert. The name "d'Alembert" was proposed by Frederick the Great of Prussia for a suspected (but non-existent) moon of Venus.[6]

## Career

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 superb 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[7] and a Fellow of the Royal Society in 1748.[8]

In 1743, he published his most famous work, Traité de dynamique, in which he developed his own laws of motion.[9]

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"[10] when he "doubted whether there exists outside us anything corresponding to what we suppose we see."[10] In this way, D'Alembert agreed with the Idealist Berkeley and anticipated the Transcendental idealism of Kant.

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.[11]

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.[12]

He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1781.[13]

## 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.[14] 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.[14] 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.[15] 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.[16] This led to a series of bitter exchanges between the men and contributed to the end of d'Alembert and Rousseau'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."[17] 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."[18] 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.[19]

## 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 Mlle de Lespinasse, and eventually took up residence with her.

## Death

He suffered bad health for many years and his death was as the result of a urinary bladder illness. As a known unbeliever,[20][21][22] D'Alembert was buried in a common unmarked grave.

## Legacy

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 see 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 novel by Andrew Crumey (1996), 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.

## Notes

1. ^
2. ^
3. ^
4. ^
5. ^ Hall 1906, p. 5.
6. ^ 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.
7. ^ Hankins 1990, p. 26.
8. ^ "Library and Archive Catalogue". Royal Society. Retrieved 3 December 2010.
9. ^
10. ^ a b
11. ^ [1] Archived 31 May 2012 at the Wayback Machine.
12. ^ Smith Richardson 1858, pp. 8–9.
13. ^ "Book of Members, 1780–2010: Chapter A" (PDF). American Academy of Arts and Sciences. Retrieved 14 April 2011.
14. ^ a b Christensen 1989, p. 415.
15. ^
16. ^ The New Grove Dictionary of Music and Musicians, 2nd ed., s.v. "Alembert, Jean le Rond d'"
17. ^ D'Alembert 1995, p. 38.
18. ^ D'Alembert 1995, p. 69.
19. ^ D'Alembert 1995, p. 100.
20. ^ 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."
21. ^ 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."
22. ^ 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."

## References

• Bernard, Jonathan W. (1980). "The Principle and the Elements: Rameau's Controversy with D'Alembert". Journal of Music Theory. 24 (1): 37–62.
• Briggs, J. Morton (1970). "Jean le Rond d'Alembert". Dictionary of Scientific Biography. 1. New York: Charles Scribner's Sons. pp. 110–117. ISBN 0-684-10114-9.
• Christensen, Thomas (1989). "Music Theory as Scientific Propaganda: The Case of D'Alembert's Élémens [sic] De Musique". Journal of the History of Ideas. 50 (3): 409–27.
• Crépel, Pierre (2005). "Traité de dynamique". In Grattan-Guinness, I. Landmark Writings in Western Mathematics. Elsevier. pp. 159–67.