Mathematics, Administrative and Economic Activities in Ancient Worlds: An Introduction

Abstract

The chapter outlines a research program on the relationships between mathematics, administrative and economic activities in ancient worlds, and it draws on the various chapters in the book to illustrate the benefits that can be derived from this program. The overall goal is to provide a better understanding of the role mathematical knowledge and practices played in allowing various types of practitioners to carry out managerial and economic activities in the ancient worlds. Moreover, the purpose is to provide a more precise understanding of how, and the extent to which the bodies of knowledge and the practices of mathematics reflected by these administrative and economic sources were linked to those attested by more strictly mathematical sources. To fulfil these aims, we suggest focusing on the practices of quantification and computation attested to in specific administrative and economic activities, and also on the contexts in which they were carried out. After a survey of the sources on which the chapters of the book draw, and some of the social milieus considered, we present the specific activities on which the book concentrates. First, we argue that the practice of regulations, laws and norms, as attested to by texts produced in various milieus, highlights the intimate relationship that ties some more strictly mathematical sources and documents of practice (Sect. 1.4). We then deal with various ways in which documents of practice reflect the quantification of spatial entities and, in particular, of work (Sect. 1.5). We also show how more strictly mathematical sources allow us to interpret these practices of quantification. Subsequently, we turn to the quantification of land and other surfaces, and underline the diversity of mathematical practices to which various sources attest to carry out this task (Sect. 1.6). Finally, an examination of the quantification and computation of prices, loans and interest, and the assessment of the values of coins allows us to shed light on the diversity of mathematical cultures embraced by the various actors who engaged in these activities (Sect. 1.7).

The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007–2013)/ERC Grant agreement No. 269804, Mathematical Sciences in the Ancient World. This book is one of the two volumes deriving from the three-month workshop on ‘Cultures of computation and quantification’ and its final conference (https://sawerc.hypotheses.org/workshops/workshop-cultures-of-computation, accessed 2 October 2019). The definitions and founding principles of this collective research are set out in Chemla (2007, 2009, 2010) and also in the introduction to the other volume, see Chemla et al. (forthcoming); both volumes were prepared together and work as a pair. We wish to address our warmest thanks to Matthieu Husson, Agathe Keller and Christine Proust who actively took part in all the editorial meetings linked to the preparation of this book. We wish to thank Martin Sauvage for the maps. It is also our pleasure to thank all the participants in our meetings, and in particular the authors of the different chapters of this book. The referees provided insightful comments that helped us clarify our intentions and results. Christine Mousset and Richard Kennedy have devoted much of their time for the completion of this book. We are happy to express our gratitude to all of them. Needless to say, we take full responsibility for all remaining mistakes.