When looking at the major accomplishments of societies in ancient times, one can divide the examination into two main categories: what they did, and how they did it. While so much that was built has not survived the passage of the centuries, what remains is extremely impressive. Whether you see them in person or just see pictures and read facts, the pyramids of Egypt and Mexico are stunning. It is clear to everyone that the societies that constructed them knew engineering and project management.

This book is about an achievement that is just as impressive: the ability of the Babylonians to predict the future locations of the heavenly bodies that alter their position in short periods of time. Rather than having us look at a big structure and be awed, the author pieces together the contents of tablets, sometimes incomplete, in order to describe how capable the Babylonian astronomers/astrologists were. However, the structure that is made is no less awe-inspiring.

To mathematical readers, the most interesting chapter will no doubt be the second one, where the mathematical concepts used by the Babylonians are explained. Babylonian astronomy was developed between 450 BCE and 350 BCE; it is the earliest known form of mathematical astronomy. The Babylonian wording is given, and although it takes a bit of thought to follow (for example, there were three different verbs for addition), all of the explanations of the computational algorithms can be easily understood. The terms that the Babylonians used for all of the operations are included.

The next section of the book is a listing of 102 Babylonian tablets with museum designations, descriptions of their contents and explanations and critical and philological notes. This is where the book gets deeply into the details, which, quite frankly, can overwhelm the uninformed or casual reader. I plowed my way through several of them and did appreciate the scholarly work that went into the analysis, though I had to do it in discrete segments.

For nearly all of us, this is a work best examined from on high rather than in the sentence-by-sentence details. I came away from the book once again impressed by what the ancients accomplished. There were geniuses among them and it is unfortunate that more is not known. We talk now about how complex modern projects are. While I know that is true, I have my doubts about historical comparisons with some of the things done on the other side of the BCE/CE divide.

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing *The Journal of Recreational Mathematics*. In his spare time, he reads about these things and helps his daughter in her lawn care business.