The vibrating string controversy

Abstract

In the mid-1700s a debate raged between Jean d’Alembert, Leonhard Euler, and Daniel Bernoulli concerning the proper solution to the classical wave equation. This controversy was partially solved by Lagrange and, more conclusively, by Fourier (50 years later) and it provides an interesting case study for the role of mathematics in the modeling of physical phenomena. Of particular note in this debate, was the meaning of boundary conditions. The controversy is summarized from the point of view of this mathematical physics perspective.