Mathematical Commentaries in the Ancient World
A Global Perspective

Comparative analysis of the techniques and procedures of important mathematical commentaries in five ancient cultures from China to Greece.

Karine Chemla (Edited by), Glenn W. Most (Edited by)

9781108839570, Cambridge University Press

Hardback, published 9 June 2022

448 pages
25.1 x 17.5 x 3.1 cm, 0.991 kg

This is the first book-length analysis of the techniques and procedures of ancient mathematical commentaries. It focuses on examples in Chinese, Sanskrit, Akkadian and Sumerian, and Ancient Greek, presenting the general issues by constant detailed reference to these commentaries, of which substantial extracts are included in the original languages and in translation, sometimes for the first time. This makes the issues accessible to readers without specialized training in mathematics or in the languages involved. The result is a much richer understanding than was hitherto possible of the crucial role of commentaries in the history of mathematics in four different linguistic areas, of the nature of mathematical commentaries in general, of the contribution that the study of mathematical commentaries can make to the history of science and to the study of commentaries in general, and of the ways in which mathematical commentaries are like and unlike other kinds of commentaries.

1. Introduction: Why study mathematical commentaries? Karine Chemla and Glenn W. Most
Commentators at Work: 2. Philosophical commentaries on mathematical texts: The case of Proclus' commentary on the first book of Euclid's Elements Orna Harari
3. Characterizing a Sanskrit mathematical commentary: An exploration of P?th?daka's V?san?bh??ya on progressions Agathe Keller
4. Calling out Zheng Xuan (127–200 CE) at the crossroads of ritual, mathematics, sport, and classical commentary Daniel Patrick Morgan
Comparing Commentaries: 5. Astral commentaries within the Mesopotamian received tradition: The Commentary to En?ma Anu Enlil 14 and Šumma Sîn ina T?martišu Zackary Wainer and John Steele
6. Contrasting commentaries and contrasting subcommentaries on mathematical and Confucian canons. Intentions and mathematical practices Karine Chemla and Zhu Yiwen.

Subject Areas: History of mathematics [PBX], Philosophy of mathematics [PBB], History of ideas [JFCX], Classical history / classical civilisation [HBLA1]