Abstract

Greek mathematics is usually seen as having reached its height in a “golden age” around 300 b.c., after which it declined, reaching a rather sad stage in late antiquity. In this latter period Pappus of Alexandria stands out as one of the last competent mathematicians, although even his Mathematical Collection has been valued by historians mainly for its wealth of information on earlier mathematical achievements. In her readable book, Serafina Cuomo sets out to correct the conventional view of mathematics in late antiquity: her general goal is “to show that the mathematics of late antiquity deserves a place both in the history of science and in the history of antiquity” . To that end she focuses on Pappus's Collection, for which she attempts “to produce a historical analysis … and at the same time to explore its wider cultural contexts” . Thus her text is not intended primarily as a discussion of the mathematics contained in the Collection; instead Cuomo looks into the historical circumstances in which Pappus produced this work and the image he wanted to convey both of mathematics and of himself.The first chapter presents some general background on the public's perception of mathematics and its practitioners in late antiquity. Emphasizing evidence “apart from what we find in the books of the famous mathematicians” , Cuomo looks at astrological treatises such as the Mathesis by Julius Firmicus Maternus and considers the social and fiscal status of various “technical” professions, such as those of land surveyor, architect, and public administrator. She uses Diocletian's edict on wages and salaries and examines the role of mathematics in education to show that, “far from being invisible or confined to ivory towers” , mathematics was perceived as an integral part of life and regarded positively. All this material is very interesting, but how relevant is it? Cuomo's broadening of the perspective to include more than just the works of famous mathematicians is certainly commendable. But should one equate the mere skill of calculating with numbers, or even that of applying some “higher” mathematics, with theoretical, philosophical, mathematical thought? Of course, Cuomo is aware of this problem. Taking it to be irrelevant for her purpose, she makes a good point: claiming affiliation with mathematics to enhance one's status, as those professional practitioners would do, presupposes a positive image of mathematics among the public . Nevertheless, such evidence would probably not have swayed previous historians' opinion of the decline of mathematics in late antiquity.Chapters 2–4 are devoted to Book 5 of the Collection, which covers isoperimetric problems and Platonic solids; Book 8, on mechanics; Book 3, on cube duplication; and Book 4, on special curves and their classification. In Chapter 2 Cuomo argues that Pappus used the widely known problems discussed in Book 5 to address a general audience so as to promote mathematics and show that “mathematicians are better qualified than philosophers … to talk about isoperimetry and the five Platonic bodies” . At the same time, pointing out the complementarity of mathematics and mechanics , Pappus stresses the usefulness of mathematics in educational and material matters. In Chapter 4 Cuomo examines how Pappus, addressing experts, “marks out his territory within the mathematical field itself” .In the final chapter Cuomo tries “to get a clearer grasp of Pappus' mathematical agenda” . She concludes that Pappus is not just a compiler admiring the past; rather, he selected his subjects and manipulated the mathematical tradition to serve his own immediate goals in the present.This book contains an abundance of interesting historical material, although, regrettably, the mathematical examples are only roughly sketched. Cuomo shows that we can learn much from looking at Pappus's Collection in its own right. Her book deserves careful study