A Versatile Mind
Violet Moller applauds a scholarly journey through the work of the most mysterious of ancient mathematicians
Benjamin Wardhaugh, The Book of Wonders: The Many Lives of Euclid’s Elements. London: William Collins 2020. Pp. 336. £25. ISBN 9780008299903
Euclid grasping his mathematical studies as imagined by Jusepe de Ribera in Spain, c. 1630–5, oil on canvas (Digital Image Courtesy of the Getty’s Open Content Program)
Universally acclaimed as the most influential non-religious book of all time, Euclid’s Elements has been the foundation of mathematics since it was written 23 centuries ago. In The Book of Wonders, Benjamin Wardhaugh, a Fellow of All Soul’s, Oxford, takes the reader on an exhilarating ride through the long and complex history of this seminal text.
Euclid lived and worked in Alexandria during the third century BC – that is pretty much all the information we have about his personal life, although anecdotes were told. Wardhaugh navigates these skilfully: both the ‘no royal road to geometry’ story, which has Euclid telling King Ptolemy that hard work is the only way to succeed in maths, and the one where a pupil asks Euclid what he can profit by studying geometry, only to have a few coins thrown in his face. Both stories paint Euclid as someone who was passionate about the subject. This certainly isn’t an unreasonable assumption to make about him. Wardhaugh, however, discounts these stories as embellishments added by later writers, understandably keen to add some detail and colour to this mysterious figure.
While it would be interesting to know more about him, Euclid’s personal anonymity doesn’t really matter. He has achieved immortality through The Elements, a text that has been studied and discussed by people in every age and every corner of the world. These ‘many lives’ are the subject of The Book of Wonders, and they are presented thematically, so that each of Euclid’s many incarnations is studied in turn. In ‘Author’ we see the typical journey of a classical text down the ages, while ‘Sage’ reveals the philosophical tradition of The Elements by introducing readers whose interests lay in the mental gymnastics it offered. Next up is ‘Hero’, which focuses on the many practical applications Euclid’s geometry inspired, nicely highlighting the age-old tension between lofty pure maths and its gritty, practical counterpart. In the final section, ‘Shadow and mask’, we see the darker side of the story, the backlashes and challenges the text has faced over more recent centuries. This approach highlights the multitude of ways The Elements has been read and used during the two millennia it has been in circulation. Clever and imaginative, it does, however, result in some zigzagging backwards and forwards, which may feel rather discombobulating to some readers.
Wardhaugh’s chatty, informal style makes the complex history of the Elements easy to understand. It’s the kind of book that is perfect for dipping in and out of, each anecdote a little jewel-like glimpse into another world. We see Euclid in many different guises: in the novels of George Eliot and the paintings of Piero della Francesca; hewn in stone on the façade of Chartres Cathedral; floating in space, in music, in Hebrew and in Urdu; on the stage; behind the walls of a medieval convent and in the luggage of a Jesuit scholar arriving in Beijing at the dawn of the 17th century. It isn’t surprising that Wardhaugh describes Euclid’s Elements as ‘a shape-shifter capable of almost anything,’ who bids us farewell. We watch as it goes, ‘dancing on into the future, never fully grasped by any one of the cultures it touches.’
The secret to this adaptability is simplicity. Euclid begins the text, ‘a point is that which has no part.’ He precisely defines even the most basic elements, starting at the very beginning and assuming nothing on the part of the reader. This makes the text accessible to anyone with the requisite patience to work through it. Euclid’s clarity is crucial to his longevity. He was not a mathematician of brilliant originality like Archimedes. In fact, everything he put into The Elements had been worked out by previous generations of mathematicians. His book is, in fact, a survey of mathematical knowledge at that point. Euclid’s importance lies in his ability to organise and express the material so clearly. He was the scientific communicator par excellence. Once The Elements was on offer, scholars stopped bothering to recopy other similar texts – only one survives that predates it. This gave Euclid total cultural dominance, paving the way for centuries of commentary, translation and transmission.
The history of every ancient text can be divided into two parts: before and after printing. The manuscript history of Euclid’s great book is extremely complex and full of unsolved mysteries. Every copy made in the first 18 centuries or so of its existence was unique, copied out by hand with varying degrees of accuracy and skill, in various languages. Wardhaugh takes us to some of the most important moments in the story of its transmission: Alexandria in the fourth century AD when the mathematician Theon wrote his influential commentary; Baghdad in the ninth century when it was translated into Arabic for the first time, founding a new and prolific branch of mathematical development that spread as far as al-Andalus in Spain and all the way up the Silk Roads to the borders of China. In 1582 The Elements arrived in the Venetian printshop of Erhardt Ratdolt, the German genius who devised a way to print the diagrams that tumble down the margins of the text and publish them for the first time. This heralded the beginning of a new chapter in the book’s story. From that moment on, its survival was guaranteed, thanks to the hundreds of copies in circulation. In the following decades, new translations were made into the vernacular European languages, introducing the genius of Euclid to a much larger audience than ever before and vastly increasing the opportunity for its practical application.
As the last section of The Book of Wonders shows, Euclid’s story is not one of universal triumph. There have been moments when his mathematics have been criticised and his methods questioned, but these are as interesting and important for understanding his contribution to culture as the periods of adulation. It is also worth noting that many of the other great scientific theories inherited from the classical past – Ptolemaic astronomy and Galenic medicine, for example – have been disproved and disregarded in the intervening period. But Euclid’s Elements remains as true today as when it was written 23 centuries ago, and that really is a breath-taking thought. The Book of Wonders is the latest in the long and distinguished tradition of literature about The Elements, a joyful celebration of its epic journey down to us, in the 21st century.
