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 Pṛthūdaka's Vāsanābhāṣya 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 Enūma Anu Enlil 14 and Šumma Sîn ina Tāmartišu 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.
Karine Chemla is Senior Researcher at the Centre national de la recherche scientifique (CNRS), in the laboratory SPHERE (CNRS & University of Paris) and focuses, from the viewpoint of historical anthropology, on the relationship between mathematics and the various cultures in the context of which it is practiced. Glenn. W. Most retired in November 2020 as Professor of Greek Philology at the Scuola Normale Superiore di Pisa. He remains a regular Visiting Professor on the Committee on Social Thought at the University of Chicago and an External Scientific Member of the Max Planck Institute for the History of Science in Berlin.
