If I asked you to give me the name of a sixteenth century mathematician I would expect that you could, after a pause, produce one or two, but I would not be surprised, nor would you forfeit my respect, if you could not. If I asked you for a quick survey of sixteenth-century mathematics I would be very surprised if you could think of anything except, maybe, the solution of the cubic. Robert Goulding’s interesting book will prepare you for the next time you encounter such an unpleasant interrogator as I.

Its emphasis is the history of mathematics in the sixteenth century. During the European middle ages the history of mathematics, if it was thought of at all, was thought to be irrelevant. The renaissance, with its emphasis on the humanistic topics of rhetoric, literature, and history, threatened to diminish the already not-too-large stature of mathematics in the universities. Perhaps as a reaction to this, mathematicians took more interest in the history of their subject, possibly trying to show that it was worth consideration along with the humanities.

*Defending Hypatia* focuses on two people of the time, the Frenchman Peter Ramus (Pierre de la Ramée in French, Petrus Ramus in Latin, 1515–1572) and the Englishman Henry Savile (1549–1622).

Ramus is a person whose biography I would dearly love to read, but Charles Desmaze’s 1864 *Petrus Ramus* has not been translated into English. He taught philosophy at the University of Paris until 1544 when he was forbidden to teach it by the university authorities. He had friends in high places and by 1551 he was back at the university. He had turned to mathematics, though he did not find it easy: “I burst out in rage against mathematics because it tortures so cruelly those who love it and are eager for it.” He was evidently a person of large charisma. His lectures, it is said, attracted audiences of more than a thousand, and he left behind a school of Ramists. He became a Protestant and, partly as a result, had his life ended by murder.

He published an edition of Euclid’s *Elements* leaving out the proofs, which he saw as defects. He had the idea, which seems strange to us now, that mathematics should develop naturally, out of things like the observations of artisans. Proofs, I think, reminded him of the sterile treatment of Aristotelian logic that played such a large part in medieval universities and to which he, and the humanists, was opposed. His view could have arisen from the lateness of his coming to mathematics and the unadvanced state of the subject in his day.

Savile lectured on Ptolemy’s *Almagest* at Oxford and had the proper view that teaching should consist of more than reading a book aloud, which was not universal at the time. Mathematics was at a low ebb: Savile told his class that members of it who could not add or subtract should withdraw immediately. Three years before his death he founded the Savilian professorships of astronomy and geometry at Oxford.

The history of mathematics was in a sorry state in the sixteenth century. Stories about how the extended lifetimes of the biblical patriarchs (969 years for Methuselah) were needed so that they could develop mathematics, which Abraham transmitted to the Egyptians, were taken more or less seriously. It was generally thought that Theon of Alexandria *created* the proofs in his fourth-century edition of Euclid’s *Elements*. Proclus, the fifth-century author of a *Commentary* on the *Elements* was placed by some in the second century. Euclid of Megara was thought to be the same person as Euclid of Alexandria. Correcting the errors and getting things straight was neither quick nor easy. Knowledge is hard won!

Goulding ranges widely and considers many topics. His book is scholarly, but the writing is very clear and there are flashes of wit. I found it fascinating.

Its title, designed to catch the eye, is a bit far-fetched. You will have to read the book to see if you think it is appropriate.

Woody Dudley taught mathematics for a living in each of six different decades and has eight books for sale on Amazon, but expects to be rapidly forgotten by history.