Jouve, Guillame (Author)
Between 1749 and 1752, D'Alembert published three papers on the problem of vibrating strings in the volumes of the Berlin Academy. In the first two texts, he used a new mathematical tool to determine the position at every moment of a vibrating stretched string: the partial differences calculus. Both papers are now considered to form the foundation of the first theory of partial differential equations worthy of the name. The third paper is itself the starting point of a long polemic with Euler about the conditions to impose on arbitrary functions appearing in the solution of the problem of vibrating strings. This quarrel, which a few years later also involved Daniel Bernoulli and Lagrange, helped to change the mathematical notions of function and continuity in the following decades. We will show in this article that recent researches on D'Alembert's correspondence allow us to understand better his initial thoughts on the subject as well as those of Euler, and to apprehend more precisely the genesis and chronology of their first papers.
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