Differences: Chaos in the History of the Sciences

Abstract

In this paper from the book Les origines de la géométrie (The origins of geometry), subtitled tiers livre des fondations (third book of foundations) (Serres, 1993, Flammarion, Paris), I argue that the history of the sciences and, in particular, the history of mathematics cannot be written using the tools and models of traditional historiography. Rather, I claim that there is a need for a science of history that takes seriously what I see as a radical contemporaneity or copresence of the archaic and the contemporary. The model of history that I propose attempts to seek a degree of congruence between a model of time that is not chronological but rather percolating and filtering the ways that the mathematical tradition is reinvented. There exists—or seems to exist—a structural similitude between mathematics itself and the form or model of historiography required to write its history.