Mathematics in Ancient Iraq: A Social History.

• Author: Montelle, Clemency
• Position: Book review

Mathematics in Ancient Iraq: A Social History. By ELEANOR ROBSON. Princeton: PRINCETON UNIVERSITY PRESS, 2008. Pp. xxiii + 441, illus. $49.50.

"The cuneiform mathematics of ancient Iraq," writes Eleanor Robson, "... can be divided into three phases: numerate apprenticeship, metrological justice, and divine quantification" (p. 263). Indeed, Robson's authoritative pen, with its characteristic flourish and flair, has undertaken the task of assembling into a single definitive work a new perspective on the mathematics of ancient Iraq that has been growing in recent decades. Responding to the standard accounts of the mathematics in this area that have been largely entrenched in three aspects--the sexagesimal system of numeration, the ingenious approximation to the square-root of two, and the famous mathematical tablet Plimpton 322--Robson presents an irresistible challenge to this orthodoxy. She insists upon a revitalization of the field by broadening the scope of inquiry and demands that this earliest mathematical culture be contextualized by locating it in its wider social and intellectual setting. Robson's stewardship in a burgeoning field is none too soon. The result, a study of impressive scope and quality.

Robson convinces us that this field is rich and far from the Ozymandian wasteland that some have maintained. While she acknowledges the many challenges for a historian of mathematics working in this area, she reminds us that cuneiform evidence is "concrete, immediate, and richly contextualised" (p. 290), with many sources that are personally signed and dated, (of recent times) archaeologically provenanced, and relatable to broader social trends, traditions, and contexts. Furthermore, Robson shows us how this particular mathematical tradition stands in a complete and nuanced way to other mathematical cultures and in turn, from her approach, much can be learnt and applied to the ways in which new generations of scholars will explore and study other mathematical cultures.

Robson declares her intentions from the outset, seeking to combine "close attention to textual and linguistic detail, as well as material and archaeological evidence to situate ancient mathematics within the socio-intellectual worlds of the individuals and communities who produced and consumed it" (p. 1). To undertake this, she champions the array of expertise required, drawing on leading research in history of mathematics, philosophy, mathematics education, material culture, ethnomathematics, contemporary ethnography, geography, and archaeology, among other disciplines. She pays attention to all aspects of her field, considering the visual, textual, and numerical paired with significant attention to mathematical, linguistic, and artifactual detail (p. 9). She is mindful of the different backgrounds of her readers and presents a thorough account of the physical features of cuneiform tablets and the script and languages that were used, as well as an eloquent discussion of the representation of numbers both in presentation and content, not limited to the dominant sexagesimal system but including the other instances of numerical bases. She grapples with the conceptual processes behind mathematical operations presented in these documents and insists upon contextualizing these artifacts as complex cultural assemblages (p. 21), including details on find-spots, provenance, prosopography, paleography, orthography, social history, even relevant comments on the trade of antiquities (p. 26). Her analysis is...