The d’alembert-euler rivalry

Abstract

Jean le Rond D'Alembert and Leonhard Euler were two towering figures in the firmament of 18th century mathematical physics. They both made significant contributions to the growth and maturing of mathematics and of theoretical science. There is no question about the extraordinary genius and prolific creativity of Euler. And D'Alembert, who boldly initiated and attempted problems that interested that Swiss prodigy, often provoked Euler's unfriendly reaction. A spirit of rivalry naturally arose between the two giants. Daniel Bernoulli, another outstanding genius of the age, was also involved in some of the controversies and misunderstandings between Euler and D'Alembert. Even if profound insights and germinal ideas are sometimes credited to D'Alembert, he is usually referred to as not only creatively inferior to Euler, but even unworthy of the fame and recognition that he received. Historians of science have not been very sympathetic to D'Alembert. As specific instances of this we may mention Todhunter 's "History of Probability" in which the chapter on D'Alembert is one long enumeration of his mistakes, told in a vein that is intended to provoke pity and ridicule. In referring to the voluminous correspondence between Euler and D'Alembert in connection with the logarithm of negative numbers Cajori remarked, "D'Alembert proceeds to advance arguments of meta-physical, analytical and geometrical nature which shrouded the subject further, ''1 ignoring the fact that such arguments were quite common in 18th century discussions. Ravetz, in his s tudy of the vibrating string problem, refers to D'Alembert's "priggishness as a mathematician," and finds his opuscules "a bewildering jumble. ''2 But the dean of all D'Alembert despisers is Truesdell. This eminent scholar and historian, having edited parts of Euler's complete works, seems to have inherited his idol's antipathies for D'Alembert. Indeed they are so magnified in his writings that it is doubtful if even Euler would concur with him on all points. Here, for example, is how he describes the reading of D'Alembert's works: "One searches for the little solid matter, as a sparrow pecks out a few nutritious seeds from a d u n g h e a p a task not altogether savory. "'3 On the other hand the prodigious genius of Euler has been adequately recorded. From the fable in which Diderot is made a fool by Euler in Catherine's court 4 to E. T. Bell's fascinating sketch of Analysis Incarnate only superlat ives have been used to paint Euler 's achievements. And all the encomiums that Euler has received for his own creativity are well deserved. In this year of the 200th death anniversary of D'Alembert it will be of some interest to look a little more closely into D'Alembert's standing vis-a-vis Euler, and to see how far some of the damaging remarks against