This 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.
Mostly, this is what we get here. In the case of Egypt, the sources are so scanty that we end up getting a mixed approach. In the other sections, however, we get a real chance to explore for ourselves, which leads to a much deeper experience. By reading extended texts, one can come to a better feel for how each culture "did" mathematics.
To help distinguish what is source material and what is commentary, the publisher has used different typefaces: translated sources are printed in sans serif, the modern historian's commentary in a serifed font. This works, but it does require the reader to pay attention and to have sharp eyes. The book is a well-made, sturdy hardcover. At over 680 large pages, you want it in hardcover. (If Princeton ever decides to make a paper edition, I'd actually suggest five little volumes, one for each tradition, instead of a big paperback that will inevitably fall apart.) Given the overall package, the price seems quite reasonable.
There is much here that we who teach history can use in class, and there is much more that will greatly enrich our presentation of these mathematical traditions. I wouldn't use the book as a text, at least not for a first course in the history of mathematics. (On the other hand, it would be a spectacular resource for a student wanting to do independent study on one of these traditions.) I'm sure Princeton University Press would be happy to authorize reproduction of certain sections for use in class (for an appropriate fee, of course). I plan to take advantage of this next time I teach the course.
Examining the non-Greek pre-modern mathematical traditions is both fascinating and important. This book is now the best place to start.
Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College and the co-author, with William P. Berlinghoff, of Math through the Ages.