This is a wonderful book, one of the best examples I know of writing about mathematics and its history for the general public.
Until early in the 20th century, it was common for Archimedes scholars to lament the loss of "The Method," a text in which Archimedes was said to have explained how he figured out the answers to many of the problems he solved. In the existing manuscripts, one mostly had elaborate proofs by exhaustion, but with little indication of how Archimedes had known what to prove. For example, Archimedes' "On Sphere and Cylinder" includes a proof that the surface area of a sphere is four times the area of the largest circle within it; but how did he figure that out?
Then, in the early 1900s, J. L. Heiberg reported on an amazing discovery: an old prayer book in a Constantinople monastery turned out to have been written on used parchment sheets. (Such manuscripts are called "palimpsests.") The sheets had been washed and new text had been written on them, but one could still (with difficulty) read the underlying older text. And that text was mostly by Archimedes. It included some known works plus "The Method."
This was, of course, an important and much-celebrated discovery. (One can get the flavor of the reaction by looking at the Dover edition of Heath's The Works of Archimedes, which includes an appendix with a translation of the newly-found "Method.") A few years later, however, the prayer book that Heiberg had worked on went missing, presumably sold to some private collector.
Then, in 1998, Christie's made the sensational announcement that the Archimedes Palimpsest was up for sale. It would be sold at auction on Thursday, October 29. That auction is the opening scene in the story told by Netz and Noel.
The book ended up being sold to another private collector, a wealthy American whose identity remains a secret. But this time it didn't disappear into some private vault. Instead, the new owner entrusted the manuscript to the Walters Art Museum in Baltimore and provided funds for it to be properly studied.
The authors of The Archimedes Codex have been directly involved in that study. William Noel is the curator of manuscripts at the Walters, while Reviel Netz is Professor of Classics at Stanford, a leading Archimedes scholar and translator . Noel and Netz write alternate chapters, Noel telling the story of the manuscript and Netz discussing the contents. Both stories are fascinating.
In Noel's chapters, we follow the efforts made to preserve, protect, and finally read the manuscript. He tells us about parchment codices and how they were made and about palimpsests in general. Then he discusses the history of this particular codex. But the really juicy part is the story of how this delicate and damaged book was handled and how technology was brought into play to read it. It is an exciting intellectual detective story.
Netz's chapters focus on Archimedes and his mathematics. In particular, he tells us exactly what is in the manuscript, explains its significance and importance, and discusses what new things we have learned about Archimedes' work. These chapters are a little harder to read than Noel's, mostly because they contain bits of mathematics. Their presence, however, lifts the book above the average "popular science" text, giving it some real meat.
Both authors are very good at conveying their excitement, which will help readers through some of the harder bits. The book includes many photos, including high-tech images of the text that demonstrate just how difficult it is to read. One leaves the book with a heightened sense of both the difficulty and the fascination of scholarship — and, of course, of the genius of Archimedes.
Scholars will, of course, want to know more, and wait impatiently for the critical edition and the many technical papers that are sure to come. Meanwhile, this is a must-read for anyone interested in the history of Greek mathematics.
Fernando Q. Gouvêa is the editor of MAA Reviews.