Dark end of Egypt's star philosopher

At the close of the 4th century, Alexandria was a turbulent city, riven by religious strife, its cultural life in steep decline, and it was about to lose its secular intellectual tradition. In this dismal landscape the world's two best living mathematicians, father and daughter, taught mathematics and astronomy to a dwindling coterie of trainee natural philosophers.

Theon of Alexandria, the last director of the Museum, wrote a famed commentary of Ptolemy's Almagest that would serve as the introductory textbook of computational astronomy until the end of the Middle Ages. His daughter Hypatia, who was the more able of the two mathematicians, gave significant assistance in his second edition by improving the didactic style and producing efficient algorithms for handling long division.

Sparse original sources describe Hypatia as a woman of striking physical beauty who donned the mantle of scholar to expound publicly on the philosophy of Plato and Aristotle. The character of her teaching and her dignified deportment led to her becoming a public figure who was much admired as a skilled expositor. The chief magistrates and city administrators sought her counsel, and she had frequent interviews with the Roman civil governor.

Hypatia's lifestyle was devotedly celibate: as a Neoplatonist committed to transcending the natural world, this made sense. She saw off a priapic student by thrusting at him a menstrual napkin as evidence of her unclean nature.

As Michael Deakin reminds us, Hypatia is the first woman in the history of mathematics of whom we have reasonably detailed knowledge, to which a measure of informed speculation is added. She wrote a commentary on conic sections, but no direct copy of that survives. There are scholars who believe that novel elements in the Arabic texts of the Arithmetic of Diophantus are due to Hypatia. It is possible that she had a hand in transmitting knowledge of the astrolabe to her most famous pupil, Synesius of Cyrene, who corresponded with her on both the astrolabe and the hydroscope.

Religious turmoil in Alexandria claimed her life in 415 or 416 when she was brutally murdered by Christian zealots; Christians and Jews were then at each other's throats. For any fundamentalist mob wanting to single out a public figure, the pagan Hypatia, a prominent adviser to the civil powers, presented an easy target. Fanatics blocked the homeward path of her chariot, hauled her into a church, stripped her naked, battered her to death with roofing tiles, then tore her corpse limb from limb.

Deakin is outspoken in his criticism of his predecessors whose biographies are based on unreliable sources. Novelist Charles Kingsley published Hypatia in 1853 as a work of fiction. But from 1860 he was regius professor of history at Cambridge, so it is understandable that his fiction migrated first to legend and then to inference that became generally accepted. Deakin strikes a modern note by roundly condemning hits from Google searches that cite such sources.

This is a work of outstanding scholarship. All biographers of Hypatia have struggled with meagre primary sources that by turns duplicate and conflict with each other. Deakin weighs the evidence with great skill. His examination of the reliability of the sources is meticulous, with the result that his biography is scrupulous in its distinction between solid evidence and inference. Appendices and endnotes make up half the book, a decision that has contributed greatly to its readability, and will lighten the load of future scholars.

Simon Mitton is a fellow of St Edmund's College, Cambridge.