Mechanics

Abstract

The ambiguous title reflects the dual purpose of this section: to give a brief survey of the mechanics that came before calculus and to introduce the thesis that mechanics was psychologically, if not logically, a prerequisite for calculus itself. The remainder of the chapter will expand on this thesis, demonstrating how several important fields in calculus (and beyond) originated in the study of mechanical problems. Lack of space, not to mention lack of expertise, prevents my venturing far into the history of mechanical concepts, so I shall assume some understanding of time, velocity, acceleration, force, and the like, and concentrate on the mathematics which emerged from reflection on these notions. These mathematical developments will be pursued as far as the nineteenth century. More details may be found in Dugas [1957, 1958] and Truesdell [1954, 1960]. In our own century, mathematics seems to have been the motivation for mechanics rather than the other way round. The outstanding mechanical concepts of the twentieth century—relativity and quantum mechanics—would not have been conceivable without nineteenth-century advances in pure mathematics, some of which we shall discuss later.