Cultures of computation and quantification in the ancient world: An introduction (in dialogue with Agathe Keller and Christine Proust)

Résumé En

This introduction pleads for resuming research on the history of numbers and computation: topics in the history of mathematics that, to many, seem exhausted. One of the main reasons for revisiting these topics is the problematic division of the historiography of number into two branches: on the one hand, the history of the concept of number and, on the other, the history of numerical signs designed to express integers and the history of computations that relied on these inscriptions. Upon closer examination, this split — which has hitherto been unquestioned in the literature — looks untenable, and the book offers evidence showing the actual intertwinement between the history of the concept of number and that of numeration systems and computations. The book further aims at developing a contextualized approach to systems of numeration and computation, which the introduction discusses. To this end, the introduction argues why, in most social contexts of the ancient world, numbers cannot be discussed independently from measurement values, and it explains how the various authors of this book share the goal of identifying, in these social contexts, different ‘cultures of computation and quantification’. Thanks to this effort of contextualization, the book yields a better understanding of both the contexts of emergence and the diversity of uses of place-value numeration systems, which the introduction synthesizes.