# Oxford Figures

*By Robin Wilson and Raymond Flood*

The University has recently opened the Andrew Wiles Building, the magnificent new Mathematical Institute in the Radcliffe Observatory Quarter. Named in celebration of one of Oxford's most distinguished mathematicians, the official opening took place on on 3 October 2013.

The new building provides a workspace for over 500 mathematical researchers and support staff, and a centre for the academic life of almost 900 undergraduates. But while its presence is a major milestone, it’s important to remember that it is the latest event in over eight centuries of incredible mathematical activity in Oxford. Here, we plot a line through the history of mathematics at the University — right through to the construction of the new building.

### Oxford Origins

In 1214 Oxford University elected its first Chancellor, Bishop Robert Grosseteste. For mathematics, this was a fortunate decision, as he was founder of the tradition of scientific thought in medieval Oxford and particularly interested in geometry. He once wrote:

*'The usefulness of considering lines, angles and figures is the greatest, because it is impossible to understand natural philosophy without them. By the power of geometry, the careful observer of natural things can give the causes of all natural effects.'*

Indeed, Grosseteste’s most famous admirer was Roger Bacon, whose Folly Bridge observatory became a place of pilgrimage for scientists. Centuries later, Samuel Pepys would note, after visiting Bacon’s study, that Oxford was a ‘mighty fine place’.

By the early 14th century scholars were organising themselves into colleges — and Merton College in particular became pre-eminent in scientific studies, becoming famous throughout Europe as its members tried to quantify natural phenomena such as heat, light, and colour. Most important was Thomas Bradwardine, the greatest English mathematician of the time, who in 1349 he became Archbishop of Canterbury, but died of the Black Death soon after.

Back then, Oxford’s students arrived in their early teens and were assigned tutors who were responsible for their moral behaviour. The curriculum comprised the seven liberal arts: the trivium, a 4-year course on grammar, rhetoric and dialectic, followed by the 3-year quadrivium, the Greek mathematical arts of arithmetic, music, astronomy and geometry.

Not long after the invention of printing, a press was set up in Oxford, which eventually became the Oxford University Press. The first mathematical book to emerge from the press was the 1520 Compotus Manualis, which showed how to calculate the date of Easter on one’s fingers. Later, Robert Recorde’s 1557 algebra text The Whetstone of Witte, contained the first appearance of what we now know as the equals sign — two parallel lines, because, as the book explains, ‘noe.2. thynges, can be moare equalle’.

### Step Change

In 1619, Sir Henry Savile, Warden of Merton, founded the Savilian Professorships of Geometry and Astronomy — in reaction to what he viewed at the time as the terrible state of Oxford mathematics. The first geometry professor was Henry Briggs, who improved Napier’s new logarithms, calculating by hand extensive tables of base-10 logs to fourteen decimal places, an incredibly laborious, but astonishingly useful, process, as his logs became incorporated into the newly invented slide rule.

After the Civil War, the mathematical scene moved to Wadham College. In 1648 its Warden John Wilkins gathered a group of brilliant men — known as the Oxford Philosophical Society — to discuss what they termed ‘philosophical experiments’. Wilkins’s group included John Wallis (Savilian Professor of Geometry), Robert Boyle, Robert Hooke and Christopher Wren. Members of this illustrious group went on to form the Royal Society in London.

Wallis’s successor as Savilian Professor of Geometry was Edmond Halley. While still an undergraduate he sailed to St Helena to catalogue the Southern stars. Among his achievements were cajoling Newton to write Principia Mathematica, becoming Astronomer Royal and predicting the return of the comet that now bears his name.

### Sustained Growth

Throughout the 18th century Newtonian philosophy flourished in the Old Ashmolean Building, now the Museum of the History of Science, in Broad Street. The first public museum in England, it also contained the first science teaching rooms and teaching laboratory. Many scientific lectures were given there by the Savilian professors. One of these, Thomas Hornsby, was responsible for the Radcliffe Observatory, then Europe’s best-equipped astronomical observatory, now housed in Green Templeton College and just a stone’s throw from the new Andrew Wiles Building.

Decline in the University’s fortunes led to significant changes in the 19th century, when science degrees were introduced, examinations began to include written papers, and the University Museum was built. There were three notable Savilian Professors of Geometry at this time. Baden Powell wrote texts in geometry and calculus and was a populariser of science (one of his sons, incidentally, went on to found the Boy Scout movement). Powell’s successor was Henry Smith, who made major contributions to algebra and number theory. Smith died relatively young and was succeeded by James Joseph Sylvester who, being a Jew, had been unable to secure an Oxbridge post. After the rules changed in 1871, Sylvester became professor at age 69.

### Prime of Its Life

In 1900 there were three mathematics chairs — in geometry, natural philosophy, and the new Waynflete Chair in Pure Mathematics. A major boost to Oxford’s mathematics was G. H. Hardy’s appointment to the geometry chair. Mainly remembered as a Cambridge man, he spent eleven fruitful years in Oxford, publishing over 100 papers and establishing a world-famous school in analysis and number theory. Another important influence was Waynflete professor Henry Whitehead, whose school of topology attracted scholars from around the world; a keen pig farmer, he claimed to derive mathematical inspiration by scratching his pigs’ backs for an hour every afternoon. A third popular figure was Charles Coulson, who at various times held professorships in three universities in three subjects (mathematics, physics, and chemistry). A well-known lay preacher, Coulson was involved with the founding of OXFAM in 1942.

Hardy, Whitehead and Coulson were all energetic advocates for a Mathematical Institute, and after occupying various buildings, the Mathematics Faculty acquired its own home in St Giles in 1966. Meanwhile, Oxford continued to attract many distinguished figures. Three Oxford mathematicians were awarded Fields Medals, the mathematical equivalent of the Nobel Prize. Andrew Wiles, after whom the Institute’s new building is named, famously proved Fermat’s Last Theorem — unproved for 250 years — and was a Merton undergraduate who later received an Oxford honorary doctorate, when the Public Orator described him as ‘the Archimedes of our time, the outstanding master of numbers, the incomparable unriddler of the Last Theorem’. Wiles has since returned to Oxford.

Recent expansion in Oxford’s mathematical activity has been spectacular. Syllabuses have continually changed, and new joint degrees have been introduced, with philosophy, statistics, and computer science. There are now centres for mathematical biology, financial mathematics, industrial applied mathematics, and much else besides. Oxford mathematics continues to go from strength to strength – and the Andrew Wiles building is a fine celebration of all that has come before and with great promise for the future.

**Read more:** John Fauvel, Raymond Flood, and Robin Wilson (eds.), Oxford Figures: Eight Centuries of the Mathematical Sciences (Second edition), OUP, 2013.