Mathematics in Ancient Egypt: A Contextual History by Annette Imhausen (review)

In Mathematics in Ancient Egypt: A Contextual History, historian of science Annette Imhausen has written a well-researched introduction to Egyptian mathematics in antiquity by tracing its development over more than the last 3000 years, from the foundation of the dynasties to the rise of Alexandria as a global hub of ideas during Greek and Roman times. At the core of this book is the author's careful recitation of solutions to the practical mathematical problems that occupied the Egyptian mind. In this way the reader learns how ancient Egyptians approached mathematics. It is important to note, as Imhausen does, that only a minority of Egyptians, the elite scribes, had mastered numbers and written language so that the problems of mathematics applied to a select few.

Imhausen organizes Mathematics in Ancient Egypt into the familiar divisions of Egypt's past: prehistory and the early dynasties, the Old Kingdom, the Middle Kingdom, the New Kingdom, and the Greek and Roman period. These large divisions are the signposts that guide the reader through ancient Egypt and its mathematics. Not all sections are of equal length or importance due to the state of preservation of artifacts. The references to mathematics are less numerous in prehistory and the early dynasties, for example, than in the Middle Kingdom. Imhausen found it necessary, therefore, to cover the Middle Kingdom in more detail than prehistory and the early dynasties. In introducing ancient Egyptian mathematics to the reader, Imhausen's most significant conclusion may be that these mathematics were preoccupied with practicality. Egypt's number system may have originated in the need to count cattle and tabulate other economic data. In this instance Egyptian mathematics seems to have been every bit as functional as the mathematics that developed in Mesopotamia about the same time. Basic numeracy, essential to life in ancient Egypt seems to be as old as written language. That is, the invention of numbers seems to have occurred at the moment of the invention of a written script.

The audience for Mathematics in Ancient Egypt seems to be the general reader, though some knowledge of mathematics is essential because the author does not define the terms integer, numerator, denominator, and absolute value. In the case of integer, numerator, and denominator, Imhausen is probably safe to expect the reader to understand these terms, though her presentation of numerator and denominator seems strange because she arranges the pair alphabetically whereas mathematics textbooks order the numerator first and denominator second because in a fraction the numerator appears above the denominator. With absolute value a brief definition would probably be best. The absolute value of a number is always positive such that one might think of absolute value as a machine that transforms every negative number into its positive counterpart so that the absolute value of |-1| is 1, |-2| is 2 and so forth. Moreover the author inadvertently may create confusion in representing a fraction analogous to ancient Egyptian practices with a bar above a number so that 2, for example, represents the fraction ½. This notation may confuse because a bar above a number, at least where a decimal is represented, means the repetition of that part of the decimal so that 0.2, for example, means 0.2222222… In the limitless universe of the imagination the 2 repeats to infinity. The reader must also have some basic knowledge of Egypt because Imhausen does not define Upper and Lower Egypt, places integral to the geography of the region. Yet the reader need not be omniscient because the author begins every section of the book with an overview of ancient Egypt's society, economy, and politics. These sections are particularly well written and informative.

Mathematics in Ancient Egypt is no blind repetition of past scholarship. Whereas early works on ancient Egyptian mathematics said little about the Greek and Roman period, Imhausen includes this time as a section of its own. Moreover early works on ancient Egyptian mathematics...