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SF-01 (1-27) 9/5/00 9:40 AM Page Viii SF-01 (1-27) 9/5/00 9:40 AM Page 1 SF-01 (1-27) 9/5/00 9:40 AM Page viii SF-01 (1-27) 9/5/00 9:40 AM Page 1 800 years of mathematical traditions John Fauvel If the Elizabethan antiquary William Camden is to be believed, the teaching of mathematics at Oxford, along with the foundation of the University itself, dates from the time of Alfred the Great in the ninth century: In the year of our Lord 886, the second year of the arrival of St. Grimbald in England, the University of Oxford was begun … John, monk of the church of St. David, giving lectures in logic, music and arithmetic; and John, the monk, colleague of St. Grimbald, a man of great parts and a universal scholar, teaching geometry and astronomy before the most glorious and invincible King Alfred. By such a reckoning, we could now be celebrating over 1100 years of mathematical traditions at Oxford. Alas, the founding of the University by King Alfred is but one of the stories of Oxford’s mythical past for which there is now considered to be insufficient historical evidence. The University of Oxford can, however, safely trace its existence back over at least 800 years, which confirms its respectable antiquity while recognizing it as younger than the universities of Bologna and Paris. The University seems to have come into being gradually during the twelfth century, as groups of scholars gathered to learn and study together at ‘that catarrhal point of the English Midlands where the rivers Thames and Cherwell soggily conjoin’, in the evocative words of Jan Morris. In 1188, the historian Gerald of Wales visited Oxford and recorded the existence of several faculties of study. This date may stand for the start of the University as well as any, not least because it happily matches that of a major fund-raising appeal by the modern University launched in 1988. Throughout the succeeding eight centuries, the The earliest mathematical book to be published in Oxford was Compotus manualis ad mathematical arts and sciences have been pursued at Oxford, taught, usum Oxoniensium, printed by Charles used, and explored in a variety of ways. Kyrforth in February 1520. Slight and unoriginal in mathematical content, its opening image records astronomical instru- The medieval heritage ments as well as bearing evidence of the scribal culture upon which Oxford built its From its early years, Oxford has drawn upon mathematical influences traditions of scholarship. on its ways of thinking. By comparison with the University of Paris, SF-01 (1-27) 9/5/00 9:40 AM Page 2 Oxford figures Oxford in the Middle Ages was more strongly influenced by a tradition of Christian Neoplatonism. In this tradition (as for Plato himself) mathematics played an important role, as revealing God’s design for the universe. An early Oxford teacher, and Chancellor of the University, was Robert Grosseteste. In what amounts to a research programme for investigating the world through mathematical, specifically geometrical, modelling, he wrote: The usefulness of considering lines, angles and figures is the greatest, because it is impossible to understand natural philosophy without these … For all causes of natural effects have to be expressed by means of lines, angles and figures, for otherwise it would be impossible to have knowledge of the reason concerning them. Oxford scholars of succeeding generations would, in effect, attempt to put this programme into practice. Grosseteste’s most famous admirer, the Franciscan friar Roger Bacon, went even further in proclaiming the Portrait of Robert Grosseteste, Oxford’s first importance of mathematics: Chancellor and a strong influence on the early He who knows not mathematics cannot know the other sciences nor the intellectual life of the University, from a fourteenth-century manuscript. things of this world … And, what is worse, those who have no knowledge of mathematics do not perceive their own ignorance and so do not look for a cure. Conversely a knowledge of this science prepares the mind and raises it up to a well-authenticated knowledge of all things. It was at Oxford in the next century that some of the most sophisticated mathematical discussions of the Middle Ages took place, in which math- ematics was used and developed along the lines of the programme that Grosseteste and Bacon had advocated. By this time there was also a strong Aristotelian influence upon Oxford’s mathematical studies. Most of the scholars concerned with this development were Fellows of Merton College, founded in 1264. Prominent in this group was Thomas Bradwardine, who showed, in effect, how the programmatic utterances of Grosseteste and Bacon could bear real fruit in the math- ematical analysis of nature: ‘it is mathematics which reveals every genuine truth, for it knows every hidden secret’. In the hands of Roger Bacon’s study on Folly Bridge later Bradwardine and his fellow scholars, the mathematization of mag- became a place of pilgrimage for scientists. nitudes went beyond anything thought of in Greek geometry. Mem- Samuel Pepys visited it in 1669, remarking: bers of the Merton School attempted to quantify intensities of light, ‘So to Friar Bacon’s study: I up and saw it, and gave the man 1s … Oxford mighty fine place.’ heat, sound, hardness, and density, as well as magnitudes that math- It was pulled down in the eighteenth century ematicians have still not managed to quantify effectively: knowledge, for road widening. certitude, charity, and grace. How far such developments would have gone we cannot know. Bradwardine died of bubonic plague (the ‘Black Death’) in 1349. Many other Oxford scholars and at least a third of the population of England died of the same cause over those terrible years, and the University rapidly fell into a decline mirroring that of the country. Despite the ravages and devastation of the Black Death and other social and political miseries, teaching and learning did continue, albeit in a rather SF-01 (1-27) 9/5/00 9:40 AM Page 3 | years of mathematical traditions depressed state, but not for three centuries did Oxford even begin to regain the intellectual vigour of its glorious early days. Merton College’s fourteenth-century Mob Quad has seen six centuries of mathematical activity. The tradition of the mathematical sciences If one had to nominate the single most influential event of Oxford’s long mathematical history, it would be the founding by Sir Henry Savile of two endowed Chairs in 1619. Through the Savilian Chair of Geometry and the Savilian Chair of Astronomy a conception of the breadth of the mathematical sciences, as well as a tradition of how to teach and study and further them, was passed down from generation to generation. Although in an institutional sense the Chairs began to drift apart in the nineteenth century, under the pressure of exam- inations and shifting faculty alliances, research into pure mathematics and applied and cosmological mathematics has remained a notable dimension of Oxford activity up to the present day. Throughout much of the period after the founding of the Savilian Chairs, the two roles seem to have been more or less interchangeable: a leading Oxford mathematician would generally be appointed to the next Chair to fall vacant and could tilt his interests accordingly, or indeed carry on regardless. It can be surprising now to notice the range of many of the Savilian professors, able to write as knowledgeably on music theory as on architecture, and observe an eclipse as attentively as preparing scholarly mathematical editions for the press. To some extent this breadth, shown also in the interchangeability of Chairs, reflects the breadth achieved by any well-trained professional mathematician of the time. One would find the same set of interests among leading math- SF-01 (1-27) 9/5/00 9:40 AM Page 4 Oxford figures Oxford almanac for 1344, with notes on ematicians throughout Europe, so that is not in itself exceptional— square numbers written by the Mertonian Simon Bredon. Owners of the manuscript except that the size and continuity of the Oxford tradition has enabled have included John Dee and Thomas Allen. the tradition of the mathematical sciences to flourish, with more or less vigour, over such a long period. The early seventeenth century saw also the founding by Sir William Sedley of an endowed Chair in Natural Philosophy; this is, in effect, what we would now call physics, or perhaps applied mathematics. Holders of the Sedleian Chair—the first, Edward Lapworth, was appointed in 1621—contributed further to the range of mathematical sciences taught in Oxford, notably in the eighteenth century when they shared in promoting Newtonian science alongside the Savilian pro- fessors: indeed, for the latter part of that century Thomas Hornsby managed to fill both the Sedleian Chair and the Savilian Chair of Astronomy, as well as various other positions, for a period of nearly 30 years. Over the past century the Sedleian professor has been a distin- guished applied mathematician, to give leadership to that side of Oxford’s mathematical teaching and research activity. Besides the Sedleian Chair, scientific principles were taught from the early eighteenth century onwards by a reader in experimental philo- sophy, a function discharged for over a hundred years, from 1730 to SF-01 (1-27) 9/5/00 9:40 AM Page 5 | years of mathematical traditions 1838, by one or other of the Savilian professors who tended to accumu- late offices so long as professorial income was derived largely from student fees. It was while David Gregory was Savilian Professor of Astronomy in the 1690s that the style was developed in Oxford of teaching Newtonian science demonstratively through experiments, with lectures given in a room on the first floor of the Ashmolean Museum, now the Museum of the History of Science.
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