In the introduction to this book, Michael Deakin expresses surprise that there have been so few full-length treatments of the life and work of Hypatia, and that, in particular, most such accounts have had very little to say about her mathematics. But in fact it is not surprising at all. In one of the appendices of this book, Deakin collects all the primary sources on Hypatia and her life. He is quite generous, including material that is only tangentially related but helps to set the context and also including some mentions that may well be secondary, dependent on other sources in his appendix. It all fills only 21 pages, and almost all of it is about Hypatia's death. None of it is material written by Hypatia, and none of it contains any mathematics at all.
Given how little information this actually is, why write about Hypatia at all? Well, because she is a useful figure. The manner of her death was used, from the 18th century to the early 20th, in various kinds of propaganda: anti-clerical, anti-Catholic, and anti-Christian, in roughly chronological order. The fact that she is one of the last active mathematicians in the Ancient Greek tradition makes her death in the hands of a mob an excellent symbol of the end of that tradition, particularly for those, from Gibbon onwards, who want to blame the rise of Christianity for the decline of Classical culture. The fact that she was a woman has made her useful again, from the late 19th century onwards, as a feminist icon. Were it not for this usefulness, there would be even fewer books about Hypatia, and there would be none, like this one, aimed at the "general public."
Given the paucity of sources on her life and the politically and ideologically charged currents that surround the story of her death, the main question to ask of a book about Hypatia has to do with how much care has been used to be both precise and impartial. It is important to properly distinguish fact from conjecture, to have recourse to the best scholarship, and to attempt to put oneself into the mindset of the times and to avoid, to the extent possible, letting one's ideological bias skew the picture. Deakin does pretty well on the first count, less well on the others.
As mentioned above, Deakin does the reader the great favor of including English translations of all the important sources on Hypatia's life and work. As befits the "popular" nature of the book, they are presented in an appendix. In the text, he discusses these sources in some detail and explains his reasons for accepting some and rejecting others. These are generally cogent, though one discerns a slight tendency to prefer those sources that paint a positive picture of Hypatia. Deakin is quick to note, for example, the biases of those sources that have some reason to admire Cyril of Alexandria, but not so quick to highlight the biases of those who might have reason to be negative about him. This is par for the course in such a book, and the presence of the actual sources puts the reader in a good position to assess Deakin's choices. In fact, the best strategy is probably to read the chapters on the historical, religious, and philosophical context first, then Appendix D, and then go on to the chapters on Hypatia herself.
The chapters setting the context are a mixed bag. One finds a pretty good account of what 4th century Alexandria was like, but a few pages later one finds an account of Trinitarian doctrine that seems both confused and different from any theologian's point of view. Later, when he wants to present a more elaborate and careful account, he gives us Augustine's take on the Trinity. This is a bad call, since Augustine was very much a Western, Latin-speaking Christian, while Alexandria was very much an Eastern, Greek-speaking city. The Latin and Greek traditions were already beginning to diverge at this point. Deakin also seems to miss the point that the controversies of the time were more Christological than Trinitarian. In general, he seems unaware of recent scholarship on the patristic period. For example, he does not cite any recent study of Cyril of Alexandria (there were at least five such studies published since 2000).
Deakin's account of Greek mathematics is not too bad, but it also seems to ignore much recent scholarship. For example, Deakin mentions several times that Theon and Hypatia mostly wrote commentaries on older mathematical works. This would seem to call for some discussion of what Reviel Netz calls the "deuteronomistic" nature of late Greek mathematics, but Netz's work does not even appear in the bibliography. Deakin's description of Hypatia as "not a research mathematician" is a consequence of this: it is not only anachronistic, it also shows very little feel for what Greek mathematics (in fact, Greek intellectual work in general) was like at this time. Similarly, Deakin discusses Pappus in some detail, and even includes an appendix on Pandrosion (the woman mathematician mentioned in one of his books), but seems unaware of Cuomo's recent book on Pappus .
The account of Hypatia's life is necessarily quite thin, since we know very little. The chapter on her death is, of course, the most interesting. It is a pity, however, that Deakin spends so much time on the question of whether Cyril was to blame. Who cares? Perhaps only people who are members of churches that consider Cyril a saint or those who want to cast aspersions on such churches. But those churches respect Cyril because of his theological and devotional writing, not because of any belief that he was morally perfect. Many saints were pretty abrasive characters! (Think Ignatius Loyola or even Francis of Assisi — not the sort of people one would invite to a dinner party.)
By comparison, Deakin spends very little time on the gender-related aspects of her death. Consider, however, that the one story that has been preserved about Hypatia's life has to do with virginity and a sanitary napkin. And the accounts of her death all mention details that relate to her being a woman. It seems to me that there's much more of a case to be made for Hypatia as an "uppity woman" victimized by violent men than there is a case for Hypatia as a "pagan martyr" killed at the hands of Christians. One should note, however, that the majority of ancient sources do not seem interested in either aspect; instead, they emphasize the nature of politics in Alexandria, where disputes seem to have often been resolved by force. Deakin does compare 4th century Alexandria to current trouble spots such as Baghdad and Malaysia, but then reverts to the "pagan martyr" approach.
Since we do not have access to any of Hypatia's mathematics or philosophy, the chapters on her work have to be mostly context and conjecture. The chapter on Hypatia's philosophy is mostly about neo-Platonism. The chapter on her mathematics focuses on what the sources tell us, namely, that she wrote commentaries on Ptolemy and Diophantus. So we get accounts of those works and some speculation on whether some of the surviving manuscripts of those works preserve some of her work. Deakin misses a trick here. His account of Diophantus' work does not really emphasize how strange it is, how far out of the mainstream of Greek mathematics. (David Fowler once pointed out that if manuscripts of Diophantus had not survived we would never have guessed that Greek mathematics included anything of the sort!) Given the uniqueness of Diophantus, surely the fact that Hypatia wrote a commentary on the Arithmetica says something about her mathematical sagacity!
Every so often, one discerns a tendency to anachronism. Deakin's use of the concept of a "research mathematician," noted above, is an example. So is his argument that the reason Theon and Hypatia did not (as far as we know) write commentaries on Ptolemy's Tetrabiblos was that they realized that astrology did not have the same scientific status as observational astronomy.
Deakin's overall assessment of Hypatia's work and significance is pretty much on target, though it could have been made more precise by taking into account the nature of intellectual work in her cultural context. About her mathematics, he seems to have said all that can be said, barring some spectacular manuscript discovery.
Overall, this is a useful book, particularly given the fact that the sources are included. The actual text, minus appendices and notes, has only 113 pages, so it can easily be read and digested by students. It is certainly much better than certain accounts that float around on the internet. I cannot help wishing, however, that Deakin had written a more careful and scholarly account.
Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College. He is the editor of FOCUS, the news magazine of the MAA, and of MAA Reviews.