In its first five hundred years Oxford University had many fine mathematicians, astronomers and philosophers – from the Merton scholars of the early 14th century to the newly appointed Savilian Professors of Geometry and in the 17th century. Early mathematics in Oxford -line

1150 –120 0 Oxford University comes into being c.1224 Robert Grosseteste becomes Chancellor of Oxford University c.1238 Roger Bacon comes to Oxford 1249–64 University, Balliol and Merton Colleges founded 1300–49 The Merton School flourishes 1320s Richard of Wallingford in Oxford 1349 Black Death: death of Thomas Bradwardine c.1360 The Merton astrolabe 1391 Chaucer’s Treatise on the Astrolabe 1520 Oxford’s first printed mathematics book, the Compotus Manualis 1522 Cuthbert Tunstall’s De Arte Supputandi c.1537 Richard Benese’s Boke of Measuryng of Lande 1543 Robert Recorde’s Grounde of Artes 1557 Recorde introduces the equals sign 1570 Henry Billingsley’s English edition of Euclid’s Elements 1581 Pelican sundial erected in Corpus Christi College 1585–86 Thomas Harriot’s expedition to North America 1613–24 Schools Quadrangle built 1619 Henry Savile endows the Savilian Chairs of Geometry and Astronomy Henry Briggs appointed the first Savilian Professor of Geometry 1621 Edward Lapworth appointed the first Sedleian Professor of Natural Philosophy John Killingworth (c.1410–45), the best of the Merton 1624 Henry Briggs’s Arithmetica School astronomers, is remembered on a memorial brass Logarithmica in Merton College Chapel. 1631 Death of Henry Briggs Early mathematics in Oxford Beginnings

Although its actual origins are obscure, the University of Oxford can trace its existence back over at least eight hundred years.

Grosseteste and Bacon The Merton School

Some of the most sophisticated mathematical discussions of the Middle Ages took place at Oxford in the 14th century, where mathematics was used and developed along the lines of the programme that Grosseteste and Bacon had advocated. Most of the scholars concerned with this development were Fellows of Merton College, founded in 1264, and the Merton School became celebrated throughout Europe.

Prominent among the Merton scholars was Thomas Bradwardine, Robert Grosseteste Roger Bacon Bradwardine’s Geometria the most important English Speculativa, written in Oxford mathematician of the 14th century, The University of Oxford seems Grosseteste’s famous associate, as an aid to students who showed how the utterances to have come into being gradually the Franciscan friar Roger Bacon, of Grosseteste and Bacon could during the 12th century as groups known as Dr Mirabilis, went In the hands of Bradwardine bear real fruit in the mathematical of scholars gathered to learn and even further in proclaiming the and his fellow scholars the analysis of nature: study together. From its early years importance of mathematics: mathematisation of magnitudes ‘It is mathematics which reveals every Oxford drew upon mathematical ‘He who knows not mathematics went beyond anything thought of genuine truth, for it knows every influences on its ways of thinking. cannot know the other sciences in Greek geometry. Members of hidden secret… Whoever then has A seat of Franciscan teaching, it nor the things of this world… And, the Merton School attempted to the effrontery to study physics while was influenced by a tradition of what is worse, those who have no quantify intensities of light, heat, neglecting mathematics should Christian Neoplatonism, and in knowledge of mathematics do sound, hardness and density, and know from the start that he will this tradition mathematics played not perceive their own ignorance even unlikely ‘magnitudes’ such as never make his way through the an important role as revealing and so do not look for a cure. knowledge, charity and grace. portals of wisdom.’ God’s design for the Universe. Conversely a knowledge of this science prepares the mind and In 1349 Bradwardine (along with An early Oxford teacher was Robert raises it up to a well-authenticated many other Oxford scholars and Grosseteste, who may have been knowledge of all things.’ at least a third of the population of the University’s first Chancellor England) succumbed to the bubonic around 1224. In what amounts Bacon’s study and observatory later plague – the ‘Black Death’ – shortly to a research programme for became a place of pilgrimage for after being appointed Archbishop of investigating the world through scientists. Samuel Pepys visited it Canterbury. Teaching and learning mathematical (and specifically on 9 June 1668, remarking: continued in Oxford, but in a rather geometrical) modelling, he wrote: ‘So to Friar Bacon’s study: I up depressed state, and it was some ‘The usefulness of considering and saw it, and gave the man 1s… three centuries before Oxford lines, angles and figures is the Oxford mighty fine place. . .’ regained any of the intellectual greatest, because it is impossible It was pulled down in 1779 for road vigour of its glorious early days. to understand natural philosophy widening. without these… For all causes of natural effects have to be expressed by means of lines, angles and figures…’

Bacon’s study on Folly Bridge Merton College library (late 13th century) Early mathematics in Oxford Instruments

Throughout the 14th century Oxford witnessed a great advance in the development of mathematical instruments for use in astronomy.

Richard of Wallingford Astrolabes

An astrolabe is an instrument that In Oxford a number of colleges own was widely used by astronomers, astrolabes named after them. The navigators and surveyors in the following picture shows the Merton Europe of the Middle Ages. Once astrolabe, dating from about 1360. fully developed, it could be used for finding and predicting the positions of the Sun, and stars, for calculating latitude, and for carrying out calculations. The invention of the astrolabe can be traced back to ancient Greece, and during the Islamic age the instrument came into its own, when angular and numerical scales appeared around the rim and a sighting bar was added for Richard of Wallingford at work A reconstruction of Richard of use in astronomy. dividing a brass disc Wallingford’s astronomical in St Albans Abbey Richard of Wallingford studied at Oxford in the 1320s. Perhaps the scholar, and was influential best English mathematician and throughout Europe for several astronomer of the Middle Ages, his centuries to come. Geoffrey Chaucer achievements included the design of an albion, a sort of After leaving Oxford he became Geoffrey Chaucer had a deep interest Chaucer also wrote A Treatise on or planetary computer. This Abbot of St Albans, where he built in mathematical and astronomical the Astrolabe, in which he instructs complicated instrument contained a vast and intricate astronomical instruments. In The Canterbury ‘Lowys, my son’ to whom he has over sixty scales of various sorts, clock, the first mechanical clock Tales he tells of Nicholas, a poor given ‘A suffisant Astrolabie as for and carried a universal astrolabe of which we have any detailed Oxford scholar who kept in his our orizonte [horizons], compowned and an eclipse computer. knowledge and far surpassing lodgings a copy of Ptolemy’s after the latitude of Oxenforde’. most others for the next two Almagest, an astrolabe, and counters In mathematics Richard of centuries. for making calculations (‘augrim- Wallingford wrote one of the first stones’): comprehensive trigonometrical His Almageste and bokes grete texts in Europe. After his death his Richard of Wallingford’s treatise and smale, work on the albion was revised by on the theory, construction and His astrelabie, longinge for his art, Simon Tunsted, another Oxford use of the albion His augrim-stones layen faire a-part On shelves couched at his beddes heed.

Chaucer also provided the definitive image of an Oxford academic, the Clerk of Oxenford: Of studie took he most cure and most hede. Noght o word spak he more than was nede, And that was seyd in forme and reverence, And short and quik, and ful of A page from a 1392 manuscript on hy sentence. the equatorium – probably Souninge in moral vertu was by Chaucer his speche, And gladly wolde he lerne, and gladly teche. Early mathematics in Oxford The 16th century

In this century Oxford University helped to provide the practical mathematics needed for navigation, map-making, astronomy and trade expansion.

Sundials and surveying Books

Several Oxford scholars of the 16th century were involved with land- surveying. The first surveying book in English, The Boke of Measuryng of Lande (c. 1537) was written by Richard Benese, an Augustinian friar who had supplicated for an Oxford law degree in 1519. Books such as this provided the quantitative skills needed for opening up the Tudor land market.

Cardinal Wolsey’s portable gilt Title page of the Compotus Tunstall’s De Arte Supputandi brass sundial, probably made by Manualis Nicolaus Kratzer in Oxford There were also increasing numbers With the invention of printing in of mathematical texts in the English Around 1520 King Henry VIII the mid-15th century, mathematics language. Notable Oxford authors and Cardinal Wolsey wished to books began to be widely available included Robert Recorde, who wrote encourage the teaching of the at a reasonable price. Some were several highly popular textbooks, mathematical sciences. Wolsey in Latin, such as the Compotus and Henry Billingsley, who published founded a mathematical lecture Manualis ad Usum Oxoniensium of the first English edition of Euclid’s at Oxford, given by Nicolaus 1520, Oxford’s earliest publication Elements in 1570. Kratzer, a Munich-born scholar with any mathematical content, who became a Fellow of Corpus which taught its readers how to Christi College and ‘Deviser of calculate the dates of the Church the King’s Horloges’. The ‘pelican calendar on one’s fingers.Cuthbert sundial’, designed for that college Tunstall, who had studied in by Charles Turnbull, was erected Oxford, wrote De Arte Supputandi, in its front quadrangle in 1581. the first arithmetic text to be published in England.

Robert Recorde’s arithmetic text, The Grounde of Artes (1543)

The title page and a picture of the Greek astronomer Ptolemy from Richard Benese’s The Boke of Measuryng of Lande

The ‘pelican sundial’ at Corpus Cuthbert Tunstall

The ‘equals’ sign made its first appearance in Recorde’s algebra text The Whetstone of Witte (1557) Early mathematics in Oxford Around 1600

Around 1600 teaching and research were developing in Oxford, while other practitioners were involved with such concerns as navigation.

People Instruments

At this time of important advances In 1559 Gemini made a splendid in navigation and astronomy, the gilt brass astrolabe for Queen need for mathematical instruments Elizabeth I, who had recently of high quality was paramount. ascended to the throne; it is now in The chief instrument makers Oxford’s Museum of the History used by Oxford scholars for their of Science. Gemini may have teaching and research were mainly had Cole as a pupil, who in 1568 based in London, the pre-eminent made an astronomical gilt brass instrument-making centre of compendium containing a number Europe. Prominent among of measuring instruments. Among these were Thomas Gemini and the towns whose latitude is given is Humphrey Cole. Oxford (51° 50').

Thomas Allen Ralph Kettell

Thomas Allen was one of the most One of Oxford’s greatest influential Oxford scholars from mathematicians was Thomas the 1560s until his death in 1632. Harriot, ‘by birth and by education An avid collector of mathematical an Oxonian’. After taking his B.A. books and manuscripts, he degree at Oriel College, he joined contributed to the build-up of the Walter Ralegh’s colonising ventures Bodleian Library’s fine collection of to Virginia and North Carolina, medieval mathematics and science. advising him on navigation, astronomy and surveying. Ralph Kettell, President of Trinity College, was one of Oxford’s Harriot was a highly original thinker eccentrics. Disliking long hair he who left over 8000 manuscript pages walked around Hall at dinner time of his researches into geometry, cutting any student’s over-long locks algebra, optics, mechanics, Thomas Gemini’s gilt brass Humphrey Cole’s astronomical with a pair of scissors hidden in his astronomy and navigation. He was astrolabe compendium muff. Intervening in a geometry also the first astronomer to use a tutorial he announced: telescope to map the Moon. Only in I will shew you how to inscribe a recent years have his writings been triangle in a quadrangle. Bring a pig studied in great detail. into the quadrangle, and I will sett The Schools Quadrangle the colledge dog at him, and he will One of Harriot’s achievements was take the pig by the eare; then come to find the length of an equiangular I and take the Dog by the tayle, and spiral by approximating it by the hog by the tayle, and so there a polygon, cutting it up, and you have a triangle in a quadrangle: rearranging the pieces into a triangle quod erat faciendum. whose dimensions can be calculated.

Entrance to the School of Geometry and Arithmetic in the Schools Quadrangle

The Schools Quadrangle of the The Savilian Professors of Geometry Bodleian Library was built under lectured in the first floor to the the inspiration of Thomas Bodley south of the central tower, while the between 1613 and 1624. The pillars Professors of Astronomy lectured decorating the central tower of the in the first floor to the north. The Schools Quadrangle correspond tower itself was fitted out as an to the five classical orders of observatory by John Bainbridge, architecture. the first Astronomy Professor. Early mathematics in Oxford The world of Henry Savile

Oxford mathematics from the 1620s was dominated by the legacy of Sir Henry Savile, Warden of Merton College.

Henry Savile Henry Briggs, the first professor

Some logarithms from Henry Briggs’s Arithmetica Logarithmica

In 1614 John Napier of Edinburgh The appointment of Henry Briggs introduced logarithms as an aid to as the first Savilian Professor of mathematical calculation, designed Geometry was not a foregone to replace lengthy computations conclusion. The practitioner involving multiplications and Edmund Gunter had devised divisions by simpler ones using a number of mathematical additions and subtractions. instruments, including the Gunter sector and a quadrant, and according Unfortunately, they were awkward to the Oxford antiquary John Aubrey, to use, since they corresponded to Henry Savile sent for Gunter, the equation: ‘who came and brought with him Savile’s memorial in Merton College shows him flanked by Ptolemy log ab = log a + log b – log 1, his sector and quadrant, and fell to and Euclid, whose work he expounded in his Oxford lectures where log 1 had an awkward value. resolving of triangles and doeing a great many fine things. Said the Henry Savile was renowned both The Savilian Chairs of Geometry Henry Briggs was a Yorkshireman grave knight, “Doe you call this for his mathematical abilities and and Astronomy that Henry Savile who graduated from Cambridge reading of Geometrie? This is for his encyclopaedic knowledge of endowed in 1619, towards the end before becoming the first Gresham showing of tricks, man!” and so ancient texts. A student of Brasenose of his life, had an unparalleled Professor of Geometry in London. dismisst him with scorne, and sent College, he was elected a fellow of influence on the institutional Excited by Napier’s logarithms, for Briggs, from Cambridge.’ Merton College in 1565 and became structure of Oxford mathematics. Briggs felt that they could be Warden in 1585, later concurrently The statutes that he composed redefined so that log 1 = 0 and he Henry Briggs was appointed in holding the position of Provost of for these two Chairs not only twice visited Napier in Scotland 1619, along with John Bainbridge, Eton College. He was also a tutor in provided for their maintenance and to discuss the matter. On returning the first Savilian Professor of Greek to Queen Elizabeth I. administration, but also gave very to London he devised his ‘logs to Astronomy. Briggs occupied the precise details of how the subjects base 10’, for which: Geometry Chair for eleven years. Savile was a prolific lecturer and were to be taught. Through these log ab = log a + log b He died in 1631 and is buried in the extensive notes of his lectures statutes he did more than anyone Merton College Chapel. on mathematics and astronomy, else to influence the course and In 1624, by which time he had are an invaluable source of attitudes style of future mathematics teaching moved to Oxford, Briggs produced towards these subjects in Oxford. in Oxford. his Arithmetica Logarithmica, an At a time when mathematics was extensive book containing the widely suffering a period of neglect, Two years after the Savilian logarithms of no fewer than 30,000 and when many colleges had ceased professorships were founded, Sir numbers, each calculated by hand to teach it, Savile kept the teaching of William Sedley endowed a Chair to fourteen decimal places These the subject alive and well at Merton. in Natural Philosophy. Its first proved to be of immense value in His teaching of astronomy ranged occupant was Edward Lapworth. navigation and astronomy and led from lectures on Ptolemy’s Almagest Several early Sedleian professors to the development of mathematical to the earliest public teaching in held degrees in medicine, while instruments based on a logarithmic Oxford of the new Copernican recent holders have been applied scale, such as the slide rule. system of planetary motion. mathematicians.

These posters were written by Robin Wilson and Raymond Flood, with the assistance of Dyrol Lumbard and Graham Diprose. The text is based on writings by Allan Chapman, Robert Goulding, Willem Hackmann, the late John North and the late John Fauvel.