Abstract

We discuss the differences between the ancient and the modern notion of mathematical continuity. We focus on three ancient approaches to the continuum, namely the monist, the atomist and the Aristotelian approach. Afterwards, we analyze the construction of real numbers by Dedekind, Weierstrass and Cantor. The modern continuum is characterized by these constructions, but is a more general notion. We compare the ancient conception of continuity and the modern approach in order to show that the modern concept of mathematical continuity cannot be interpreted as part of the ancient theoretical framework, or as some kind of extension of this framework.