Review of Mathematics in Ancient Egypt: A Contextual History

Mathematics in Ancient Egypt: A Contextual History, Annette Imhausen, 2016. 248 pp. illustrations, tables, bibliography and index. $45 hardcover, ISBN: 978-0-691-11713-3. Princeton, NJ: Princeton University Press.

Any historian of mathematics must also be a detective seeking out clues: societal, cultural, and contextual information on and about the events and concepts they are trying to record and understand. The extent to which factual history must and should be supplemented by relevant contextual history is determined both by the particular scholarly philosophy of the recorder/researcher and the actual amount and quality of available subject matter. Since the extant sources of information on Ancient Egyptian mathematics are extremely limited and problematic, one could, and perhaps should, expect a stronger reliance on contextual substance to round out any historical investigation of this subject.

In accomplishing her task of reporting on the content and applications of mathematics in Ancient Egypt, Professor Annette Imhausen (Goethe University, Frankfurt) treads a judicious path in balancing the contextual setting of mathematics with its specific substance. Imhausen is a specialist in the history of science with particular research interests in the mathematics of Ancient Mesopotamia and Egypt. She has consulted all available papyri and her epigraphic evidence varies from inscribed flints to clay fragments to tomb walls. The research is thorough, well documented, and supported by ample footnotes and an excellent bibliography. A chronological order is followed, proceeding from the unification of Egypt as a state, ca. 3000 BCE, to the period of Greco-Roman domination, ca. 30 BCE, a span of 3000 years, a long period of time. A reader is introduced to Egyptian numeral notation and to systems of metrology for measuring capacity and distance. Time measurement focuses on calendric reckoning and excludes units smaller than a day. The nuisances of Egyptian unit fractions are discussed in detail. The use of mathematical tables is explained and basic computation and its place in problem solving is examined. Fundamentals of a concrete geometry are revealed. Throughout these discussions, the appropriate Egyptian terminology is introduced and analyzed. Mathematics is sought out in administrative and ritual literature, architecture, and art. The education and training of scribes is considered. A fascinating and informative feature of this research is the use of scribal correspondence to provide glimpses of the scribes’ tasks and work with mathematics (Chapters 13 and 14). Helpful summaries of the material covered are dispersed throughout the text. What emerges from these encounters is the impression that mathematical activities were very much the exclusive, bureaucratic prerogative of the state.

This is a well-written and well-researched work. A feature of any good book is that while it answers questions, it also generates questions. For this reviewer, Mathematics in Ancient Egypt leaves me wondering:

• Did Egyptian trade and commerce have any influence on mathematical developments?
• What geometry is revealed in the ancient water conservation systems of dikes and canals?
• Did the Egyptians use “shadow reckoning” techniques in their astronomy and land surveying as implied by legends of Thales of Greece?

A map of Egypt referencing the locations and regions discussed would have been a helpful addition, as would have been a “Timeline” illustration.

Professor Imhausen wisely ends by saying that much more research must be done to better understand the development and use of mathematics in Ancient Egypt. However, up until this point in time, historic information on Egyptian mathematics has been sparse and widely dispersed. Mathematics in Ancient Egypt: A Contextual History has temporarily solved this problem. It is a wonderful resource, highly readable, and I strongly recommend it to anyone seeking a knowledge and understanding of the development of mathematics in the Land of the Nile.

See also the MAA Review by Calvin Jongsma.