The Mathematics of Egypt, Mesopotamia, China, India, and Islam

Fernando Q. Gouvêa at the Mathematical Association of America website:

OldmathsourcebookThis is an essential book for anyone interested in the early history of mathematics. Go thou and buy thyself a copy.

It is also an impressive editorial achievement. Victor Katz has put together five experts: Annette Imhausen on Egypt, Eleanor Robson on Mesopotamia, Joe Dauben on China, Kim Plofker on India, and Len Berggren on Islam. These are all well-known historians, and several of them are writing or have written books on the mathematics of these cultures. They have done a wonderful job of selecting, annotating, and contextualizing sources.

Apart from the Greek mathematical tradition, these five are the best-documented and most impressive pre-modern mathematical cultures. (Well, one could argue that one is missing: the Medieval European tradition, which has also been too little studied, as Menso Folkerts points out.) At least a few translations of primary sources for the Greek tradition are available, including several sourcebooks. That is not the case for Egypt, Mesopotamia, India, China, and Islam: a few items have been published here and there, but this is the first systematic collection of such translations; in fact, several of the sources presented here have been newly translated. The editors include detailed introductions emphasizing the current state of knowledge about each area and period.

There are two ways to introduce readers to a new mathematical tradition: the expert can act as a tour guide, pointing out the sights at every point, or can give us an overall idea of the layout of the terrain, and then allow us to go out an explore on your own. It is the second approach that characterizes a “sourcebook”: after some general orientation, we are left to study the sources on our own.

More here.