Most mathematicians, if they have heard of Pappus at all, know him as the author of a famous theorem about solids and surfaces of revolution. People interested in the history of mathematics may have heard a little more about him, and particularly about his role as a recorder and transmitter of the Greek mathematical tradition. Most historians don't give the man much credit. Cuomo quotes Alexander Jones, for example, who says that during Pappus's time (the fourth century AD) Greek mathematics had "experienced a deep and permanent decline" and describes Pappus as an "author in this degenerate tradition" whose reputation is high only because of the large volume of his work, the large percentage of that work which is still extant, and the fact that he preserves important bits of earlier tradition.
Cuomo sets out to change this impression, not so much by arguing for Pappus as a creative mathematician as by trying to see him in the context of his time. The book is too short for the author to investigate Pappus's work in depth (there is a lot of it), but she does a good job of describing how mathematics fit into late Hellenistic culture and how Pappus can be seen as a great mathematician in this context. Cuomo does a few close readings of material from Pappus, and these are the most interesting parts of the book. The result is readable, interesting, and an eye-opener for those who have only met Greek mathematics at a superficial level. This little book in the "Cambridge Classical Series" is one that mathematicians interested in the history of their subject will want to read.
[This book is now (2007) available also in a paperback edition .]
Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College. He is the editor of FOCUS, the news magazine of the MAA.
1. The outside world
2. Bees and philosophers
3. Inclined planes and architects
4. Altars and strange curves
5. The inside story