Jean le Rond d’Alembert


Jean-Baptiste Le Rond d”Alembert


The child of an illegitimate love between the writer Marquise Claudine Guérin de Tencin and Duke Leopold Philippe d”Arenberg, d”Alembert was born on November 16, 1717, in Paris. Destouches was abroad at the time of d”Alembert”s birth, who, a couple of days later, was abandoned by his mother on the steps of the chapel of Saint-Jean-le-Rond in Paris, pertaining to the north tower of Notre-Dame Cathedral. As tradition dictated, he was named after the chapel”s patron saint and became Jean le Rond.

First placed in an orphanage, he soon found a foster family: he was taken into the care of a glazier”s wife. The knight Destouches, although he did not officially acknowledge his paternity, secretly watched over his education and granted him an annuity.


At first, d”Alembert attended a private school. The Chevalier Destouches, upon his death in 1726, left him an annuity of 1,200 lire. Under the influence of the Destouches family, at the age of twelve d”Alembert entered the Jansenist College of the Four Nations (also known as the Mazarin College) where he studied philosophy, law and fine arts, earning his baccalauréat in 1735.

In his later years, d”Alembert mocked the Cartesian principles that had been imparted to him by the Jansenists: “physical pre-motion, innate ideas, and the vortices.” The Jansenists steered d”Alembert toward an ecclesiastical career, trying to dissuade him from pursuing poetry and mathematics. However, theology was “rather flimsy fodder” for him. He attended law school for two years, becoming a lawyer in 1738.

Later he became interested in medicine and mathematics. At first he enrolled in these courses under the name Daremberg, then changed it to d”Alembert, a name he kept for the rest of his life.


In July 1739 he presented his first contribution to the field of mathematics, pointing out the errors he had found in Charles René Reynaud”s L”analyse démontrée, a book published in 1708, in a communication addressed to the Académie des Sciences. At the time, L”analyse démontrée was a classic work, on which d”Alembert himself had studied the basics of mathematics.

In 1740 he proposed his second scientific work in the field of fluid mechanics, Mémoire sur le refraction des corps solides, which was acknowledged by Clairaut. In this work d”Alembert theoretically explained refraction. In addition, he exposed what is now called d”Alembert”s paradox: the resistance to motion exerted on a body immersed in a non-viscous, incompressible fluid is equal to zero.

The celebrity he achieved with his work on integral calculus enabled him to enter the Académie des Sciences in May 1741 at the age of 24, and he became its adjoint, later receiving the title of associé géometre in 1746. He also entered the Berlin Academy at age 28, for a paper on the cause of winds. Frederick II twice offered him the presidency of the Berlin Academy, but d”Alembert, because of his shy and reserved character, always refused, preferring the tranquility of his studies.

In 1743 he published the Traité de dynamique in which he expounded the result of his research on the quantity of motion.

He was a frequent visitor to various Parisian salons, such as that of the Marquise Thérèse Rodet Geoffrin, that of the Marquise du Deffand and, above all, that of Mademoiselle de Lespinasse. It was here that he met Denis Diderot in 1746, who recruited him for the Encyclopédie project; the following year they undertook the direction of the project together. D”Alembert took charge of the sections on mathematics and the sciences.

In 1751, after five years of work by more than two hundred contributors, the first tome of the Encyclopédie appeared. The project continued until a series of problems temporarily halted it in 1757. D”Alembert wrote more than a thousand articles, in addition to the very famous Preliminary Discourse (in it we can also see those elements of sensible empiricism, derived from Francis Bacon and John Locke, that d”Alembert would later popularize in the Éléments de philosophie (1759). The Encyclopédie”s article on Geneva provoked a polemical reaction from Rousseau (Lettre à d”Alembert sur les Spectacles, 1758), to which d”Alembert responded with a paper of his own. In 1759, due to disagreements with Diderot, d”Alembert abandoned the project.

Alongside his scientific activity, he also developed a rich activity as a philosopher and scholar: Mélanges de littérature, de philosophie et d”histoire, 1753; Réflexions sur la poésie et sur l”histoire, 1760; Éloges, 1787.

In 1754 d”Alembert was elected a member of the Académie française and became its Perpetual Secretary on April 9, 1772.

He left his adoptive family in 1765 to experience platonic love with Julie de Lespinasse, the Parisian writer and salonnière with whom he cohabited in an apartment.

He was a great friend of Joseph-Louis Lagrange, who proposed him in 1766 as Euler”s successor at the Berlin Academy.

Academic rivalries

His great rival in mathematics and physics at the Académie des Sciences was Alexis Claude Clairaut. In fact, in 1743 D”Alembert, after working on various problems in rational mechanics, had published his famous Traité de dynamique. He had written it rather hastily in order to prevent the loss of scientific priority; this was because his colleague Clairaut was working on similar problems. His rivalry with Clairaut, which continued until Clairaut”s death, however, was only one of many in which he was involved over the years.

Indeed, another academic rival was the distinguished naturalist Georges-Louis Leclerc de Buffon. Certainly strained relations were also with the celebrated astronomer Jean Sylvain Bailly. D”Alembert, in fact, had been encouraging Bailly since 1763 to practice a style of literary composition popular at the time, that of éloges, in the prospect, one day, that he might have valid literary references so that he could become Perpetual Secretary of the Academy of Sciences. Six years later, however, D”Alembert had given the same suggestion, and perhaps held out the same hopes, to a promising young mathematician, Marquis Nicolas de Condorcet. Condorcet, following the advice of his patron D”Alembert, quickly wrote and published éloges on the early founders of the Academy: Huyghens, Mariotte and Rømer.

In early 1773, the then Perpetual Secretary, Grandjean de Fouchy, asked that Condorcet be appointed his successor upon his death on the condition, of course, that he survive him. D”Alembert strongly supported this candidacy. In contrast, the distinguished naturalist Buffon supported Bailly with equal energy; Arago reports that the Academy “for some weeks presented the appearance of two enemy camps.” There was finally a hotly contested electoral battle: the result was the appointment of Condorcet as de Fouchy”s successor.

The anger of Bailly and his supporters found vent with accusations and terms “of inexcusable harshness.” It was said that D”Alembert had “lowly betrayed the values of friendship, honor, and the main principles of probity” alluding to the promise of protection, support, and cooperation made with Bailly dating back ten years.

In fact, it was more than natural that D”Alembert in having to pronounce his support for one between Bailly and Condorcet, gave his preference to the candidate who was more concerned with high mathematics than the other, and thus to Condorcet.

D”Alembert also criticized Bailly”s writings and his conception of history, going so far as to write in a letter to Voltaire, “Bailly”s dream about an ancient people who would teach us everything except their own name and existence seems to me one of the emptiest things man has ever dreamed.”

Bailly”s admission to the Académie française was also somewhat problematic. Bailly failed three times before finally being admitted. He knew for a fact that these results unfavorable to him were the effect of open hostility from D”Alembert, who was very influential as Perpetual Secretary. In one of the votes for admission to the academy Bailly obtained 15 votes against, once again, D”Alembert”s protégé Condorcet, who was elected with 16 votes thanks to a maneuver by which D”Alembert got him the vote of Count de Tressan, a physicist and scientist. Opposition to D”Alembert”s Bailly ended only with the latter”s death.

Latest works

D”Alembert was also a noteworthy Latin scholar; in the latter part of his life he worked on a superb translation of Tacitus, which earned him wide praise including that of Diderot.

Despite his enormous contributions to the fields of mathematics and physics, d”Alembert is also famous for incorrectly assuming, in Croix ou Pile, that the probability of a coin toss yielding heads increases for each time the toss results in tails. In gambling, the strategy of decreasing the bet as wins increase and increasing the bet as losses increase is therefore called the “d”Alembert system,” a type of martingale.

In France, the fundamental theorem of algebra is called the “d”Alembert-Gauss theorem.”

He also created his own criterion for testing whether a number series converges.

He entertained correspondence of scientific importance, particularly with Euler and Joseph-Louis Lagrange, but only part of it has been preserved.

Like many other Enlightenmentists and encyclopedists, D”Alembert was a Freemason, a member of the Paris “Nine Sisters” Lodge of the Grand Orient of France, in which Voltaire was also initiated.

He was elected a foreign member of the Academy of Sciences, Letters and Arts on June 15, 1781.

He suffered from ill health for many years and died of bladder disease. Being a known unbeliever, d”Alembert was buried in a common grave with no headstone.

Until his death in 1783 at age 66, he continued his scientific work by disappearing at the height of his fame, thus taking a resounding revenge on his unfortunate birth. In accordance with his last wishes, he was buried without a religious funeral in an anonymous grave in the old Porcherons Cemetery; with the cemetery”s closure in 1847, the bones were first moved to the West Ossuary and finally, in 1859, to the catacombs at the height of rue Faubourg-Montmartre.


In 1745 d”Alembert, who was a member of the Académie des sciences at the time, was commissioned by André Le Breton to translate the Cyclopaedia of Englishman Ephraim Chambers into French.

From a simple translation, the project turned into the writing of an original and unique work: the Encyclopédie ou dictionnaire raisonné des sciences, des arts et des métiers. D”Alembert would later write the famous Preliminary Discourse, as well as most of the articles concerning mathematics and the sciences.

“Penser d”après soi” and “penser par soi-même,” formulas that have become famous, are d”Alembert”s; they are found in the Preliminary Discourse, Encyclopédie, tome 1, 1751. These formulations are a reprise of ancient maxims (Hesiod, Horace).


In the Traité de dynamique he stated d”Alembert”s theorem (also known as Gauss-d”Alembert”s Theorem), which says that any polynomial of degree n with complex coefficients possesses exactly n roots in C } (not necessarily distinct; the number of times a root is repeated must be taken into account). This theorem was not proved until the 19th century by Carl Friedrich Gauss.

Let it be ∑ u n {displaystyle sum u_{n}} a series with strictly positive terms for which the ratio u n + 1 u n {frac {u_{n+1}}{u_{n}}}} tends toward a limit L ≥ 0 {displaystyle L {u_{geq 0} . Then:

In a game where you win twice the stake with a 50% probability (for example, at roulette, playing pair

With this procedure, the game is not necessarily winning, but one increases the chances of winning (a little) at the price of increasing the possible (but rarer) loss. For example, if by bad luck you win only on the tenth time after losing 9 times, you need to have bet and lost 1+2+4+8+16+32+64+128+256+512 = 210-1 units to win 1024, with a final balance of only 1. You also need to be prepared to possibly bear a loss of 1023, with a weak probability (1

Finally, one should refrain from playing again after a win, as this has the reverse effect of the martingale: increasing the probability of the loss.

There are other famous types of martingales, all of which feed the false hope of a sure win.

It should be noted that the attribution of this martingale to d”Alembert is subject to reservation; in fact, some argue that it is actually the equally famous martingale practiced at the St. Petersburg Casino and which gave rise to the famous St. Petersburg paradox, invented by Nicolas Bernoulli and first presented by his cousin Daniel. The same Casino, which allowed limitless losing bets on red and black, later gave its name to another tragic and deadly challenge: Russian roulette. The uppercut suggested by d”Alembert, on the other hand, concretized, with lavish gain (50 percent) the return to equilibrium of a chance that had the probability of 50 percent. It consists of observing a hit, after which bet 1 is made on the opposite event. In case of a win you start over, and in case of a loss you increase the bet by 1 unit. Every time you run into a hit you decrease, on the other hand, by 1 unit. By increasing by 1 when you lose and decreasing by 1 when you win, what happens is that when, for example, after 100 hits the ones guessed will be 50, 50 will be the pieces won, just 50 percent profit, as with 1 in 2, 5 in 10 or 500 in 1,000. There are many intermediate solutions; however, in roulette, which involves a 1.35 percent tax, this technique succumbs to the symmetry of the discards, which due to the tax make equilibrium unattainable, even theoretically.


He studied the equinoxes and the three-body problem, to which he applied his principle of dynamics, thus succeeding in explaining the precession of the equinoxes and the nutation of the axis of rotation.


In Traité de dynamique (1743) he enunciated the principle of quantity of motion, which is sometimes called “D”Alembert”s Principle.”

“If we consider a system of material points bound together so that their masses acquire different respective velocities depending on whether they move freely or jointly, the quantities of motions acquired or lost in the system are equal.”

He also studied differential equations and partial derivative equations. In addition, he established the cardinal equations of the equilibrium of a rigid system.

He was among the first, along with Euler and Daniel Bernoulli, to study the motion of fluids, analyzing the resistance encountered by solids in fluids and formulating the so-called d”Alembert paradox. He studied the motion of gravities and the law of resistance of the medium.

In 1747 he found the second-order partial derivative equation of waves (d”Alembert”s or vibrating string equation).


D”Alembert discovered philosophy at the College of the Four Nations (now Académie française), founded by Mazarin and governed by Jansenist and Cartesian clerics. In addition to philosophy, he became interested in ancient languages and theology (he wrote on St. Paul”s Letter to the Romans). Upon leaving the college, he put theology aside for good and threw himself into the studies of law, medicine and mathematics. Of his early years of study he preserved a Cartesian tradition that, integrated with Newtonian concepts, would later pave the way for modern scientific rationalism.

It was the Encyclopédie, on which he collaborated with Diderot and other thinkers of his time, that gave him the opportunity to formalize his philosophical thought. The Encyclopédie”s Preliminary Discourse, inspired by the empiricist philosophy of John Locke and published at the beginning of the first volume (1751), is often rightly considered a genuine manifesto of Enlightenment philosophy. He asserts therein the existence of a link between the progress of knowledge and social progress.

A contemporary of the Age of Enlightenment, a determinist and atheist (at least a deist), d”Alembert ascribed a purely practical value to religion: it is not meant to enlighten the minds of the people, but rather to regulate their morals. d”Alembert”s “secular catechism” aimed to teach a morality that would enable people to recognize evil as a detriment to society, and to take responsibility; punishments and rewards are thus distributed according to social harm or benefit. The principle governing human life is that of utility; consequently, it is preferable to turn to the sciences rather than religion, as the former have more immediate practical utility.

D”Alembert was one of the leading figures, along with his friend Voltaire, in the struggle against religious and political absolutism that was denounced by him in the numerous philosophical articles he wrote for the Encyclopédie. The collection of his spiritual analyses of each domain of human knowledge covered by the Encyclopédie constitutes a true philosophy of the sciences.

In the Philosophie expérimentale, d”Alembert defined philosophy thus, “Philosophy is nothing but the application of reason to the different objects on which it can be exercised.”


D”Alembert, like other encyclopedists (his text Éléments de musique of 1754 outlines the theory of harmony and dictates the main rules of basso continuo composition and performance. Despite claiming in the title of the work to follow the harmonic principles enunciated by Jean-Philippe Rameau, he along with the other encyclopedists (especially Rousseau) had a polemical attitude toward the great French composer through a dense exchange of polemical pamphlets.

A lunar crater bears his name.


  1. Jean Baptiste Le Rond d”Alembert
  2. Jean le Rond d”Alembert
  3. ^ Joseph Bertrand, d”Alembert, Librairie Hachette et Cie, 1889.
  4. ^ Edwin Burrows Smith, Jean Sylvain Bailly: Astronomer, Mystic, Revolutionary (1736-1798), American Philosophical Society (Philadelphia, 1954); p. 449.
  5. ^ a b c d e f g Biography of Jean-Sylvain Bailly by François Arago (english translation) – Chapter VI
  6. Cette graphie, conforme aux conventions typographiques de Wikipédia, est en outre celle retenue par les principales références bibliographiques françaises : Le Petit Robert des noms propres, édition 2019, p. 45 (qui classe la notice sous la lettre A et mentionne explicitement « Jean Le Rond d’Alembert ») ; l”Académie française dans sa notice biographique ; Le Petit Larousse, 2008 (ISBN 978-2-03-582503-2), sous la lettre A, p. 1104 ; l’Encyclopædia Universalis, février 1985, vol. 1, p. 693 ; le Lagarde et Michard. Voir aussi le Quid, 2001, p. 262.
  7. Le Petit Robert des noms propres, édition 2019, p. 45 (qui classe la notice sous la lettre A et mentionne explicitement « Jean Le Rond d’Alembert ») ;
  8. l”Académie française dans sa notice biographique ;
  9. Le Petit Larousse, 2008 (ISBN 978-2-03-582503-2), sous la lettre A, p. 1104 ;
  10. l’Encyclopædia Universalis, février 1985, vol. 1, p. 693 ;
  11. ^ Autorii contemporani preferă grafia „D’Alembert”, întrucât particula nu denotă nici originea, nici vreun titlu de proprietate; de asemenea, D-ul nu se poate disocia, neexistând numele Alembert. Prin urmare, ei îl așează alfabetic la litera D.
  12. ^ His last name is also written as D”Alembert in English.
  13. ^ “Jean Le Rond d”Alembert | French mathematician and philosopher”. Encyclopedia Britannica. Retrieved 26 June 2021.
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