The Values of Simplicity and Generality in Chasles’s Geometrical Theory of Attraction

Abstract

French mathematician Michel Chasles (1793–1880), a staunch defender of pure geometrical methods, is now mostly remembered as the author of the Apercu historique (1837). In this book, he retraced the history of geometry in order to expound epistemological theses on what constitutes a virtuous practice of geometry. Amongst these stands out the assertion that the values of generality and simplicity in mathematics are intimately connected. In this paper, we flesh out this claim by analysing Chasles’s geometrical solutions to the century-old problem of the attraction of the ellipsoids. We show how these solutions echo Chasles’s evaluation of the relative strengths of geometrical and analytical methods, and how they embody a set of normative rules for the geometer’s practice whose observance Chasles deemed necessary and sufficient for the development of general methods and theories.