Forward … to the nineteenth century: Historiographic concerns about Reviel Netz's ‘The Place of Archimedes in World History’

Abstract

In this response I argue that Netz’ essay adopts nineteenth-century theses on the history of mathematics, one of the uses of which was to highlight an alleged difference between Europe and “the others”. The debasement of certain facets of mathematical work devoted to numbers and computation has played a key role in perpetuating these theses. Such a devaluation applies notably to decimal place-value numeration systems, which Reviel perceives as representing no “significant contribution to mathematical science.” I counter this view by showing the continued theoretical impact that numeration systems of this type have had. I also discuss two historiographic operations that I identify in Reviel's argument and whose use requires revision: selecting and purifying. My conclusion emphasizes how in the post World War II period historians such as Lucien Febvre invited their colleagues to focus, in contrast, on the hybrid character of cultural artefacts.