# Oxford Figures, Chapter 1: 800 years of mathematical traditions

## The mathematical research tradition

While the early days of medieval Oxford represent a golden age of mathematical research on an international level, it was only in the seventeenth century that research began to be developed as an explicit activity in which dons and the better students might be expected to join. A research dimension was implicit in Henry Savile's statutes for the Savilian Chairs, since the professors were expected to develop their subjects alongside their teaching duties, and the early Savilian professors set a high standard in this respect.

John Wallis, in particular, Savilian Professor of Geometry throughout the second half of the seventeenth century, created in effect the first mathematical research school at the University since the Middle Ages, in the sense that he actively encouraged his younger colleagues and former students to solve problems that arose from work he was doing, and found means to publish and publicize their solutions. Younger mathematicians whose work he promoted in this way included Christopher Wren, William Neile, and William Brouncker. Throughout his life Wallis was forthright in ensuring that the work of others was published for the good of the wider mathematical community, and even reprimanded Isaac Newton for not making his work more readily available. Indeed, the contrast with Newton points up the great achievement of Wallis in creating his research school. Newton did not, on the whole, gather round him younger scholars whose work he assisted and promoted--although he was effective in later years in supporting the career aspirations of young men whose work he admired--but had a far more complex and anguished relationship with his contemporaries.

Notwithstanding the strong state in which Wallis left Oxford mathematics, and the capable mathematicians who were his immediate successors, research activity seemed to run into the ground from 1720 or so, and little more is heard in this respect until well into the next century.

Although nineteenth-century Oxford had some distinguished mathematical researchers--notably, two Savilian professors, Henry Smith and James Sylvester--there was never a widespread research school, and such an ethos did not move far below the professorial level. There were two societies that fulfilled some of the functions of a research seminar, the Ashmolean Society from 1828, where scientific researchers could discuss and share their work, and the Oxford Mathematical Society from 1888. But new creative mathematical activity was fairly restricted. To some extent, sheer overloading of the college tutors and lecturers might be thought responsible: their teaching and examining duties would preclude time for research, particularly if there was not seen to be any point or advantage in it. Research, including explicit training in research techniques, did not seem particularly relevant. In a 1925 talk to the Oxford Mathematical and Physical Society (as the Oxford Mathematical Society became), the retired Waynflete professor Edwin Elliott recalled the frame of mind in which he taught as a young don in the 1870s and 1880s, teaching an effective syllabus of which he was proud:

*But how about research and original work under this famous system of yours, I can fancy someone saying. You do not seem to have promoted it much. Perhaps not! It had not yet occurred to people that systematic training for it was possible.*

At the time that Elliott gave this talk the Savilian professor was G. H. Hardy, who had come over from Cambridge after the First World War. Hardy succeeded in stimulating the research activity that Sylvester had hoped to encourage, and also urged the formation of a Mathematical Institute to embody such aspirations. By the time that a new purpose-built Mathematical Institute finally came about, in 1966, the research activity to fill it was already strongly under way.

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