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Strictly speaking, this book is not about the history of mathematics, except indirectly. Rather, it is devoted to commentaries, a specific textual form that many practitioners of mathematics, like other scholars active in a variety of other domains, have sometimes chosen in order to carry out their inquiries. To the modern reader, commentaries might look like a rather odd phenomenon: but until early modern times, for an author to write a commentary on a base text of any sort was quite a common choice of genre, and the practice has certainly not disappeared in our own age. By “commentary,” here, we do not mean merely the activity of jotting down one’s thoughts for oneself while reading a text or afterwards, but, instead, deciding to compose not only for oneself but above all for other readers (known and unknown students, colleagues, and others) a kind of text that complies with a base text but remains ancillary to it.
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.