 The rapid development of mathematical analysis in the eighteenth century had not concealed the fact that its underlying concepts not only lacked rigorous definition, but were even (e.g., in the case of differentials and infinitesimals) of doubtful logical character. The lack of precision in the notion of continuous function—still vaguely understood as one which could be represented by a formula and whose associated curve could be smoothly drawn—had led to doubts concerning the validity of a number of procedures in which that concept figured. For example it was often assumed that every continuous function could be expressed as an infinite series by means of Taylor’s theorem. Early in the nineteenth century this and other assumptions began to be questioned, thereby initiating an inquiry into what was meant by a function in general and by a continuous function in particular.