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D'Alembert, Lagrange, and Reduction of Order - Appendix: D'Alembert and Controversy

Sarah Cummings (Wittenberg University) and Adam E. Parker (Wittenberg University)

Here, we discuss the controversies d'Alembert alluded to in Figure 6.  The first seemed to stem from a competition with Alexis Clairaut.  Clairaut was elected to the Academy of Sciences in 1731 at the age of 18, and d'Alembert followed in 1741 at the age of 24.  The competition started in 1742 when d'Alembert began to present his Traité de Dynamique (Treatise on Dynamics), which he refered to in Figure 5.  A month later, Clairaut presented his own work on dynamics, Quelques Principles qui Donnent la Solution de Plusieurs Problèmes de Dynamique (Some Principles Which Give the Solution to Many Problems in Dynamics).  D'Alembert must have been intimidated by the title and content in Clairaut's early lectures.  Fearing losing his claim to priority, he immediately took his work to the Secretary of the Academy of Sciences to acknowledge it was complete.  He then rushed to private publishers so that it would appear before the issue of Mèmoires of the Paris Academy which contained Clairaut's work [8, p. 30-31].  Not surprisingly, the work was unready for publication.  According to Amir Alexander in Duel at Dawn, “The result is a work that has been much praised for its insights, but also much criticized for being obscure and unreadable” [1, p. 27].  The competition escalated and became unprofessional, with each making petty, condescending insults to the other, often in press.   

Thomas Hankins, in Jean D’Alembert: Science and the Enlightenment [8], gave an excellent description of the entire feud between d'Alembert, Clairaut, and the Academy in general, complete with a fine bibliography.  He noted [8, p. 40]:

As with most scientific controversies it is difficult to say who was right and who was wrong.  Public opinion was with Clairaut, because he had correctly predicted the comet's return, while d'Alembert merely quibbled over an incomprehensible mathematical theory.  Also d'Alembert's ‘public image’ was at a low point because of the collapse of the Encyclopèdie and the hostility of many journalists who were receiving the favor of the court.

As such, d'Alembert fell out with many of his colleagues at the Academy and publishing there ceased to be an option, even though he remained a member and in fact was elected perpetual secretary from 1772 until his death in 1783 [13]. 

Clairaut died on May 17, 1765, and one month later d'Alembert complained bitterly to Lagrange that Clairaut's pension (of 9000 to 10000 francs) had not been passed to himself quickly enough.  He felt it was his “vested right as the oldest member."  He said he was used to being treated poorly by the academy, but acknowledged, “The academy, who must fear losing me, finally wrote the minister to ask that the pension go to me."  Several months later the pension was indeed passed to him [12, p. 38].

The disagreement with the Berlin Academy is no less petty, though perhaps a bit more clear.  Euler was the mathematical titan of his day, if not of all time.  He was the chief mathematician at the Academy of Berlin from 1741 to 1765.  Inevitably, he and d'Alembert worked on some of the same problems, including the three body problem that interested Clairaut as well.  Indeed, given d'Alembert's propensity to publish prematurely,

... his chief innovations all appeared in much clearer and more accurate form in the works of Euler. …  It was d'Alembert's fate to see most of his ‘inventions' adopted by Euler and given a much more satisfactory treatment than he himself was capable of giving them.  [8, p. 42]

Given d'Alembert's personality, he fought hard to make sure that his original ideas were recognized as such, even forcing Euler to issue an apology stating that he “did not make the slightest pretension to the glory that was due to d'Alembert" [1, p. 28].

D'Alembert couldn't compete with Euler mathematically.  However, he did compete politically.  King Frederick II was the patron of the Berlin Society and he was enamored with the high society of Paris and France.  In fact, he hired Pierre-Louis Moreau de Maupertius away from the Paris Academy to be the President of the Berlin Academy in 1746 [1, p. 29].  Maupertius was an early advocate for d'Alembert in Paris, and his departure certainly caused d'Alembert's relationship with the Academy to deteriorate.  However, his arrival in Berlin created an ally for d'Alembert to Frederick. 

Even before Maupertius left Berlin in 1756, Frederick attempted to hire d'Alembert as the President of the Berlin Society.  This position would naturally have gone to Euler and in fact many of the responsibilities did.  However, none of the “benefits or honors" were bestowed [1, p. 30].  D'Alembert declined Frederick's offer, seemingly because of a genuine desire to stay in the more cosmopolitan Paris from which he rarely traveled.  Euler, however, thought his declination was merely an attempt to negotiate a larger salary from Frederick, at which time Euler essentially banned d'Alembert from the competitions and journals of the Berlin Society.  According to Amir Alexander [1, p. 30]:

This last was a particularly severe blow because, thanks in large part to Euler, the Berlin Histoire has become the leading scientific journal in Europe, and d'Alembert has long preferred it to the Paris Academy's Mémoires de l'Académie Royale des Sciences.  With no place to publish his work, d'Alembert resorted to publishing his mathematical papers in his own series Opuscules Mathématiques.

Sarah Cummings (Wittenberg University) and Adam E. Parker (Wittenberg University), "D'Alembert, Lagrange, and Reduction of Order - Appendix: D'Alembert and Controversy," Convergence (September 2015)