Mathematics, Administrative and Economic Activities in Ancient Worlds

1. Front Matter

   Pages i-vi

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

   • Cécile Michel, Karine Chemla

   Pages 1-48

3. Mathematical Writings, Regulations, Laws and Norms

   1. Front Matter

      Pages 49-49

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   2. A Comparative Study of Prices and Wages in Royal Inscriptions, Administrative Texts and Mathematical Texts in the Old Babylonian Kingdom of Larsa

      • Cécile Michel, Robert Middeke-Conlin, Christine Proust

      Pages 51-80

   3. Computation in the Arthaśāstra

      • Mark McClish

      Pages 81-124

   4. Official Salaries and State Taxes as Seen in Qin-Han Manuscripts, with a Focus on Mathematical Texts

      • Hao Peng 彭浩

      Pages 125-155

4. Quantifying Spatial Extension, Quantifying Work

   1. Front Matter

      Pages 157-157

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   2. Insights into the Administration of Ancient Irrigation Systems in Third Millennium BCE Mesopotamia

      • Stephanie Rost

      Pages 159-200

   3. Mathematical Computations in the Management of Public Construction Work in Mesopotamia (End of the Third and Beginning of the Second Millennium BCE)

      • Martin Sauvage

      Pages 201-237

   4. The Use of Volume in the Measurement of Grain in Early Imperial China

      • Karine Chemla 林力娜, Biao Ma 馬彪

      Pages 239-279

5. Quantifying Land and Surfaces

   1. Front Matter

      Pages 281-281

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   2. The Measurement of Fields During the Pre-sargonic Period

      • Camille Lecompte

      Pages 283-344

   3. Early-Dynastic Tables from Southern Mesopotamia, or the Multiple Facets of the Quantification of Surfaces

      • Christine Proust

      Pages 345-395

6. Prices, Rates, Loans and Interests

   1. Front Matter

      Pages 397-397

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   2. Computation Practices of the Assyrian Merchants During the Nineteenth Century BCE

      • Cécile Michel

      Pages 399-433

   3. Connecting a Disconnect Can Evidence for a Scribal Education Be Found in a Professional Setting During the Old Babylonian Period?

      • Robert Middeke-Conlin

      Pages 435-462

   4. Loans and Interest in Sanskrit Legal and Mathematical Texts

      • Sreeramula Rajeswara Sarma, Takanori Kusuba

      Pages 463-501

   5. Computational Practices Around Coins and Coinage: John of Murs’ Quadripartitum Numerorum and French Money Changers’ Books

      • Marc Bompaire, Matthieu Husson

      Pages 503-531

7. Back Matter

   Pages 533-568

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This book focuses on the ancient Near East, early imperial China, South-East Asia, and medieval Europe, shedding light on mathematical knowledge and practices documented by sources relating to the administrative and economic activities of officials, merchants and other actors. It compares these to mathematical texts produced in related school contexts or reflecting the pursuit of mathematics for its own sake to reveal the diversity of mathematical practices in each of these geographical areas of the ancient world. Based on case studies from various periods and political, economic and social contexts, it explores how, in each part of the world discussed, it is possible to identify and describe the different cultures of quantification and computation as well as their points of contact. The thirteen chapters draw on a wide variety of texts from ancient Near East, China, South-East Asia and medieval Europe, which are analyzed by researchers from various fields, including mathematics, history, philology, archaeology and economics. The book will appeal to historians of science, economists and institutional historians of the ancient and medieval world, and also to Assyriologists, Indologists, Sinologists and experts on medieval Europe.

• Ancient Mathematics
• Ancient Administration
• Economic history
• Old Babylonian Kingdom of Larsa
• Qin-Han Taxes
• Arthaśāstra
• Ancient Irrigation Systems
• Quadripartitum Numerorum

“Mathematics, Administrative and Economic Activities in Ancient Worlds fills a longstanding need to situate mathematics into its context of administration in which it originated and developed in various societies. … These publications attest to the lively and active community of historians of science working on ancient sources and the potential to learn about the origin and early development of sciences … within societies which–judging by recent developments–has become a point of concern in many parts of the world.” (Annette Imhausen, NTM, Vol. 30 (3), September, 2022)

“As an economist, I thoroughly enjoyed and was impressed at the many details and analysis of those examples of these activities in the varied places during these early time periods. … The is book is very comprehensive in its discussion. Math formulas explaining different ways of computing interest and many other types of financial economic analysis are given. Each chapter has an ample number of references.” (Paul Gentle, HEI History of Economic Ideas, Vol. 29 (2), 2021)

• CNRS, Paris 1 Panthéon-Sorbonne, Université Paris Nanterre, Ministère de la Culture, ArScAn, UMR 7041, Nanterre, France

  Cécile Michel

• CNRS, Université de Paris - Paris Diderot, SPHERE, UMR 7219, Paris, France

  Karine Chemla

Cécile Michel is a Senior Researcher at the laboratory ArScAn, at the French National Center for Scientific Research (CNRS), (CNRS, Université Paris 1 Panthéon-Sorbonne, Université Paris Nanterre, Ministère de la Culture) and a Professor at Hamburg University. An Assyriologist, she works on Assyrian and Babylonian cuneiform texts from the 2nd millenium BC and conducts research on social and economic history, gender studies, material culture, education, mathematics and literacy. She is a member of the international team in charge of the decipherment of the private archives of Assyrian merchants excavated in central Anatolia. Her publications include Correspondance des marchands de Kaniš au début du IIe millénaire av. J.-C. (Le Cerf, 2001), Women in Aššur and Kaneš from the private archives of Assyrian merchants of the early 2nd millennium BC (SBL, in press), Richesse et sociétés (ed. with C. Baroin, De Boccard 2013), Wool Economy in the Ancient Near East and the Aegean: from the Beginnings of Sheep Husbandry to Institutional Textile Industry (ed. with C. Breniquet, Oxbow Books 2014), and The Role of Women in Work and Society in the Ancient Near East (ed. with B. Lion, Walter de Gruyter 2016).


Karine Chemla is a Senior Researcher at the French National Center for Scientific Research (CNRS), laboratory SPHERE (CNRS & Université de Paris. Her research focuses the historical anthropological aspects of the relationship between mathematics and the various cultures in the context of which it is practiced. Chemla published Les Neuf Chapitres (with Guo Shuchun, Dunod, 2004), and edited The History of Mathematical Proof in Ancient Traditions (Cambridge University Press, 2012); Texts, Textual Acts and the History of Science (with J. Virbel, Springer, 2015); The Oxford Handbook of Generality in Mathematics and the Sciences (with R. Chorlay and D. Rabouin, Oxford University Press, 2016); Numerical Tables and Tabular Layouts in Chinese ScholarlyDocuments (Special issues of East Asian Science, Technology and Medicine, 43 (2016, March 2017) & 44 (2016, April 2017)); and Cultures without culturalism: The making of scientific knowledge (with Evelyn Fox Keller, Duke University Press, 2017). Chemla is a member of the Deutsche Akademie der Naturforscher Leopoldina (2005), of the Academia Europaea (2013), and of the American Philosophical Society (2019).

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