From the Theory of Waves to the Theory of Light

Abstract

Mathematical physics, like teaching, was an extremely fruitful source of inspiration for Cauchy. The study of various physical phenomena, of course, provided a natural setting for many difficult mathematical problems. The challenge facing Cauchy was to develop and articulate new mechanical models consistent with the experimental facts and to solve the equations of equilibrium and motion derived from them. In these areas, Cauchy undertook fundamental research work, which required a great deal of time and effort. His main contribution to mathematical physics remains today the continuum theory of elasticity; however, his longest and most ambitious research efforts centered on the molecular theory of light. In fact, the purely mathematical theories, such as the theory of elliptic functions and the theory of algebraic equations, having few physical applications, never particularly interested Cauchy. So, apart from his arithmetical works, most of his studies dealt with mechanics or mathematical physics in one way or another, especially those on linear differential equations, complex function theory, and linear algebra. In this chapter, we will adopt the current tensorial notation with the summation convention.1 This unimportant anachronism simplifies the involved mathematical writing that Cauchy used in his papers on mechanics.