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

## The tradition of rivalry with Cambridge

Oxford has always maintained a close relationship with the University of Cambridge, which came into existence at around the same time; their histories have many features in common. The very similarity has from the start provoked attempts to create or characterize differences between the two universities, although the most measured judgement must be that of J. I. Catto and Ralph Evans that `Together, in tandem or in counterpoint, the two collegiate universities would eventually form a single, empirical tradition of ideas.' The free flow and interchange of scholars between the universities over the centuries are evidence of that. Nonetheless, attempts have long persisted to contrast Oxford and Cambridge. As recently as 1952, the music critic of The Times perceived a difference in how mathematics was viewed:

*At Redbrick they treat mathematics as an instrument of technology; at Cambridge they regard it as an ally of physics and an approach to philosophy; at Oxford they think of it as an art in itself having affinities with music and dancing.*

It is certainly interesting to compare the development of mathematical studies at the two universities, since the overall historical record here is somewhat at variance with popular impression and belief. It has been long and widely felt that there is a marked difference of quality: that mathematics at Cambridge is a much more serious study than at Oxford; that Cambridge is the place to study mathematics, while Oxford's genius lies more in the humanities. Thus when foundation appointments were to be made in the 1820s to the new London University, the first English university to be founded since the Middle Ages, The Times reported that `it is known to be the intention to choose classical professors at Oxford, and mathematical at Cambridge', although in the event the classical appointees were from Cambridge too. This judgement has not been without some justification, but is hardly a timeless truth.

Over the past eight centuries, taken as a whole, the alleged mathematical superiority of Cambridge seems mainly to be an artefact of nineteenth-century circumstance. During that century, it happened that the purpose of studying mathematics at the two universities was rather different, as were the conditions and framework within which it was done. While being attentive to the role of mathematics in a liberal education, Cambridge developed, from the mid-eighteenth century onwards, a highly competitive examination culture geared towards ranking students on a mathematical examination, after prolonged coaching. Furthermore, until mid-century no student could go on to take the classical tripos who had not taken, and done well in, the mathematics tripos. This system produced, for more than a century, many young men whose mathematical abilities made a real contribution in, and for, later life: the ranks of the Senior Wrangler and others high in the listings include many of the best mathematicians and scientists of the nineteenth century, as well as some of the best lawyers, clergymen, and other professionals. Oxford, by contrast, did not place such a high premium on competitiveness in the mathematical sphere--for example, honours classifications were never individually ranked--nor indeed were all students expected to study mathematics. Since 1831 Oxford has had University scholarships in mathematics, the senior one of which corresponded in effect to Cambridge's `Smith's prize', but these were not at first awarded for original work and did not play such an important role in the world outside Oxford.

Although the Cambridge system in its most competitive form was dropped in the early twentieth century, the impression lived on for some time that Oxford mathematical training, and the calibre of people involved, was markedly inferior. Such a belief had a selffulfilling quality. The effect of this can be seen in the rueful reflections in 1912 of Arthur Joliffe, Fellow and tutor at Corpus Christi College from 1891 to 1920, upon the evidence presented by candidates for Oxford entrance scholarships:

*it is undeniable that the average candidate is not as good as the average candidate at Cambridge. The genius from the small grammar school, the promising student from a provincial university, the ablest boy at the large public school, all are sent to Cambridge in preference to Oxford as a rule. Some of the candidates sent to Oxford from large public schools are occasionally so bad that one can only suppose that their masters think that a willingness to come to Oxford is a sufficient qualification for a Mathematical Scholarship there.*

In developing his analysis of how Oxford mathematics suffered in comparison with that at Cambridge, Joliffe put his finger on the way low expectations, both of people and of career prospects for mathematicians at Oxford, dampened down the whole process. Nor was this comparison with Cambridge purely abstract. Oxford colleges themselves believed in Oxford's relative mathematical weakness, to the extent of sending their more promising students over to Cambridge to receive special coaching for Oxford examinations.

In the course of the twentieth century, Oxford mathematics made huge strides away from the melancholy picture painted by Joliffe, to such an extent that at one stage in the 1980s three holders of the internationally prestigious Fields Medal were teaching at Oxford. As early as the 1920s, Mary Cartwright, one of the country's leading mathematicians of the twentieth century and the first woman mathematician to be elected a Fellow of the Royal Society, was an undergraduate at Oxford. Again, one of the most famous mathematicians of the 1990s, Andrew Wiles (the Princeton professor who proved Fermat's last theorem) studied at Oxford as an undergraduate, later returning as a Royal Society Research Professor. These individual examples provide evidence both for the quality of the undergraduate intake and for the quality of mathematical training provided. Perhaps Oxford need no longer feel an automatic sense of mathematical inferiority in comparison with Cambridge.

next section, previous section