Calderón’s report presents a well-rounded, clearly written, and nontechnical description of many major aspects of the Maya mathematical system. Since he has had to reconstruct a segment of a prehistoric culture using fragmentary surviving data, many of his conclusions are necessarily speculative. Despite this difficulty Calderón has presented a logically arranged series of observations based upon a wide survey of available evidence. For the general reader the many diagrams and illustrations aid greatly in understanding this complex system. The one major gap in the report is the failure to discuss correlations between the Maya and European calenders.

The first chapter summarizes the methods of writing the basic units and multiples of the system, using for counters symbols such as two-colored grains of corn and stones or sticks. In annotation the relative position of the symbols also has mathematical value. Although the Maya had a symbol for “zero,” Calderón considers this unit to represent “completeness” or “totality” rather than “absence” or “nothing.” The next four chapters discuss the methods whereby the Maya were able to perform basic arithmetic, such as addition or division, by moving a series of counters over a tablet marked by a series of squares.

In his chapter on the calender system Calderón accepts the theory of G.I. Sánchez that the cycles were based upon 18 units rather than 20, as generally concluded by archaeologists. His succeeding discussion on the systems of Linear measurements utilizes frequency tables compiled with actual measurements of Maya structures. The last portion of the text offers various theories regarding the relationship between numbers and the pantheon of Maya deities.

Perhaps the most controversial aspect of the book is Calderón’s hypothesis that the Maya mathematical system not only antedates those of the Old World, but may have been the source of the latter. Such a conclusion can be resolved only by archaeological evidence in many other aspects of culture.