Mathematics in Ancient Iraq: A Social History (review)

In this monumental book, the author includes all 957 cuneiform tablets (published before 2007) that in some way or other are concerned with mathematics in a broad sense: accounts, metrological lists, arithmetical lists or tablets, calculations and diagrams, and all kinds of mathematical exercises (word problems or model documents) as well as mathematical astronomy. By so doing, Eleanor Robson for the first time traces the origins and the development of mathematics in the ancient Middle East from its earliest beginnings in the fourth millennium b.c., continuing through six epochs to the mathematical and astronomical texts written during the late first millennium b.c., when cuneiform writing was gradually abandoned. The book witnesses a new and inspiring approach to the vast field of cuneiform mathematics. It does not replace former works but it presents their results from a new point of view, introducing mathematics as developed parallel to the development of writing and societies—as an integral and powerful component of cuneiform culture. The investigation includes linguistic considerations combined with analysis of the contents, methods, and concepts behind the mathematical tablets. Curriculum and teaching in the scribal schools during the different periods are analyzed, and new insight is gained from analysis of scribe families, mentioned in colophons. In addition, Robson treats the clay tablets as archaeological objects, where material and form give important information, not to speak of the whereabouts they were found and which other tablets were found near them (for the lucky cases where location and circumstances of the excavated tablets are known).

When cuneiform mathematics was deciphered for the first time around 1930—a pioneering work that deserves our respect and admiration—only the internal, mathematical content was (and could be) considered. In this first approach the mathematical content of (mostly Old Babylonian, OB from now on) mathematical texts were reproduced in modern algebraic notation. Algebraic translations of the texts were treated further, and it became evident that OB mathematics was versatile and, for example, able to solve second-degree equations. In the 1980s, Jens Høyrup started analyzing the language used in “algebraic” texts from Old Babylonian time. He pointed at the fact that two different words were used for addition, and he succeeded in demonstrating that some geometrical figures had guided the “algebraic” calculations. It was not some known algebraic formulas or identities that determined the operations, but rather a geometric cut-and-paste technique that was utilized for many different mathematical exercises.¹

Instead of concentrating on mathematics from the important OB period, from which 712 mathematical cuneiform tablets have come down to us, the author has taken a wider view of mathematics and numeracy and asked new questions. Seeking to trace mathematical thinking in the Mesopotamian culture, she has analyzed tablets from all periods of Mesopotamian history, searching for mathematical thoughts and practices within its social, religious, cultural, and historical context.

Chapter 1 gives an excellent and general introduction to the topic—a great help to all newcomers not familiar with Assyriology. Chapters 2–4 and 6–8 examine the six epochs into which the author has structured the cuneiform mathematics. Each chapter begins with background information and then presents texts and figures, representative for the period, followed by its arrangement into sociohistorical context. Three concentric circles or domains are analyzed: the inner zone is the scribal school with its teaching and methods, the middle zone is the sphere of practical work (utilizing techniques learned in the schools), and the outer zone goes beyond mathematical practices and includes for example ethno-mathematics or reliefs and Sumerian hymns. For each time period, the conclusions drawn from the material presented in the chapter are repeated in condensed form at the end of the chapter.

History is not “what happened” but an interpretation of the past, arisen in the brain of the historian. The questions asked and the point of view taken by the historian determine the answers one gets. Jens Høyrup explained the fact...