Reading Mathematics in Early Modern Europe: Studies in the Production, Collection, and Use of Mathematical Books ed. by Philip Beeley, Yelda Nasigoglu and Benjamin Wardhaugh (review)

alone among the disciplines, mathematics is often regarded as the search for absolute truth, as possessing what Bertrand Russell called the cold and austere beauty of a sculpture. The editors of Reading Mathematics in Early Modern Europe seem determined to demolish any such idealistic representation, preferring instead Russell’s later assessment (in Mysticism and Logic) of ‘the subject in which we never know what we are talking about, nor whether what we are saying is true.’ The volume’s contributors analyse books of mathematics not as printed sources of incontrovertible pure knowledge, but as valuable handwritten records of continuous debates, revisions, mistakes, and uncertainties. While schoolchildren bequeathed their names, inky thumbprints and personal comments to posterity, more dedicated users might remain anonymous yet engage in longitudinal, well-informed conversa- tions between successive owners.

Reading mathematics was an active process that also entailed writing, drawing, and copying. As books’ readers (who were overwhelmingly male) strove to translate diagrams and symbols on the printed page into valuable fodder for their own minds and methods, they repeatedly pointed out logical flaws, added their own arguments, corrected printers’ errors, drew diagrams in the margins, pasted in printed extracts, and even left traces of workshop sawdust. Isaac Newton composed his Principia Mathematica (1687) in Euclidean geometry because he regarded it as the finest of mathematical languages, yet the pages of his own copy of Euclid’s Elements reveal how he challenged the Greek original by converting its theorems into algebra. Such annotating and customizing of mathematical texts seems to have been encouraged, although unfortunately for this type of research, librarians have often preferred to acquire relatively clean copies.

Collectively, the eleven excellent yet independent papers in this volume demon- strate that regarding books as material objects can bring fresh insights into what is supposedly the most abstract of subjects. Through close reading of annotated texts and manuscripts, the authors reconstruct controversies and practices that were previously near-invisible. The standard is uniformly high, which is why I have refrained in this review from singling out particular articles. On the other hand, although they complement one another, their approaches and topics are diverse, and demand differing levels of mathematical expertise. The three editors (also contribu- tors) have provided only a short introduction and no conclusion, although they have attempted to impose coherence by organizing this disparate collection into three loose groups, which focus in turn on classical texts, on the two English universities, and on less highbrow treatments intended for schools and workplaces.

The umbrella title is all-embracing if somewhat misleading: only one article (on an erroneous diagram by Tycho Brahe) ventures outside England, while ‘early modern’ ranges here from around 1500 to 1750. Moreover, ‘mathematics’ is used in several different senses, often anachronistically. Several authors discuss how the discipline’s significance changed over this extended time period, and did not necessarily enjoy a high status. When Theology was Queen of the Sciences, no subject called ‘mathematics’ (or ‘science’, for that matter) featured on the syllabus at either Oxford or Cambridge, where educators stressed the importance of all- round learning to equip students for participating in civil life, rather than for burying themselves in abstruse scholarship. Henry Savile makes several appearances in this volume, but his campaign to boost mathematics teaching at Oxford resulted in the Savilian chairs of astronomy and geometry, both subjects on the medieval curriculum. In contrast, the more practical aspects of mixed mathematics— chronology, surveying, accountancy—fell outside the gentlemanly domain.

This publication originated in an Oxford-based project to explore Euclid, so unsurprisingly, several participants discuss editions and interpretations of his enormously influential Elements. Their research...