In my response to Reviel Netz’s essay ‘The Place of Archimedes in World History’, I argue that the essay adopts quite a few nineteenth-century theses on the history of mathematics, one of the central uses of which is to highlight an alleged difference between Europe and the rest of the world. In my view, the debasement of certain facets of mathematical work devoted to numbers and computation has played a key role in perpetuating these theses for several centuries. 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 indicating conceptual advancements that numeration systems of this type have inspired and by showing the continued theoretical impact that they have had in mathematics. Broadening my focus, I discuss two historiographic operations that I identify in Reviel’s argument and whose use, I believe, requires revision: selecting and purifying. My conclusion reflects on how in the immediate post-World War II period, historians such as Lucien Febvre invited their colleagues to focus, in contrast, on the hybrid character of most cultural artefacts.