Introduction

Abstract

The question of the nature of change in the development of mathematics was systematically discussed for the first time in the second half of the nineteenth century in connection with the discovery of non-Euclidean geometries. This discussion was evidence of a fundamental change in the perception of mathematics. Even at the beginning of the eighteenth century it was still common for mathematicians to try to give legitimacy to, and to underline the importance of, their discoveries by ascribing them to ancient authorities. In doing so they implicitly assumed that mathematical theorems express eternal and permanent truths and thus a discovery is only an incidental event when someone becomes aware of these eternal truths. This strategy of ascribing his own discoveries to ancient authors was used even by Newton. According to the testimony of Nicolas Facio de Drivillier, Newton was convinced that all important theorems of his Philosophiae Naturalis Principia Mathematica were known already to Plato and Pythagoras (Rattansi 1993, p. 239).