Sir Peter Swinnerton-Dyer, 1927–2018

The College is saddened by the death of Honorary Fellow, Professor Sir Peter Swinnerton-Dyer Bt KBE FRS, on 26 December 2018 at the age of 91.

Sir Peter’s long association with Trinity began in 1945 when he came up from Eton to read mathematics. He would turn into a leading number theorist of his generation. His research was supervised by J. E. Littlewood, whom Sir Peter described as ‘one of the greatest mathematicians of the twentieth century in a distinctly old-fashioned way’ (interview with social anthropologist and Fellow of King’s College, Alan Macfarlane, May 2008, available to view online at https://sms.cam.ac.uk/media/1131073)

After a Research Fellowship at Trinity, he spent a formative year in Chicago as a Commonwealth Fund Fellow where he was ‘kidnapped’ (his word) by another great mathematician, André Weil. He returned to Trinity in 1955 as a College Lecturer in Mathematics where he also served as Dean from 1963 to 1970. He was elected to an Honorary Fellowship in 1981.

Initially unsuccessful in achieving a University post in Mathematics (on one occasion being pipped by future Master, Sir Michael Atiyah), he found a position in the Computer Laboratory. In the autumn of 1958 he began collaborating with Bryan Birch, another Trinity mathematician, in experiments on the early EDSAC computers that led to their famous joint ‘Conjecture’. Birch describes the next four years as ‘probably the best of my life […] We were under no pressure to publish: we both had Fellowships, and knew we could get another job whenever we needed one’.

John Coates –– who would go on to become Sadleirian Professor of Pure Mathematics at Cambridge from 1986 to 2012 –– vividly remembers as a young graduate student in Paris and Cambridge the sensation caused by the publication of their work. He explains the aim of their experiments:

to uncover numerical evidence for the existence of some kind of analogue for elliptic curves of the mysterious exact formulae proven by Dirichlet for the class number of binary quadratic forms, and powerfully extended to all quadratic forms by Siegel. Even though Siegel’s work had been actively developed for linear algebraic groups by others, it was Birch and Swinnerton-Dyer alone who first sought, and later found striking evidence for, an analogue for elliptic curves. The international echoes of their work were enormous …

Coates comments that Andrew Wiles’s proof of Fermat’s Last Theorem ‘had its roots in Birch and Swinnerton-Dyer’s discovery’. And further, that although ‘some partial results in the direction of their conjecture have been proven, the general case remains open and full of mystery’.

In 2000 the Conjecture was nominated one of the seven Millennium Prize Problems by the Clay Mathematics Institute with a reward of $1 million for its solution. Sir Peter thought that it could eventually be solved but hoped this would not be in his lifetime. In the meantime robbing a bank would be easier.

In 1973 Sir Peter was elected Master of St Catharine’s College, and six years later served as Vice-Chancellor of the University for what was then still a two-year term. In 1983 he left St Catharine’s to act as Chair of the University Grants Committee, and then Chief Executive of the University Funding Council. This meant working with Mrs Thatcher, with whose enthusiasm for ‘clearing rubbish out’, he subsequently expressed some sympathy.

He returned to mathematical work, noting that his mentor Littlewood had continued research into his 80s. In 2006 Sir Peter was awarded the Royal Society’s Sylvester Medal for ‘his fundamental work in arithmetic geometry and his many contributions to the theory of ordinary differential equations’.

University Reader in Number Theory and Fellow of Trinity, Dr Tom Fisher, describes Sir Peter as his ‘academic great-grandfather (i.e. supervisor’s supervisor’s supervisor)’. He confirms the energy with which Sir Peter maintained surprisingly diverse research interests, including more recently the arithmetic of surfaces. ‘All the time I have known him, he has been past retirement age, and yet still doing entirely original innovative research, unafraid to tackle hard problems of the sort it would be too risky to give to a graduate student.’

Sir Partha Dasgupta, Professor Emeritus of Economics and Honorary Fellow, remembers with gratitude an earlier incarnation. He writes:

Peter was Dean of Trinity when I arrived in 1962, and he supervised me in pure mathematics in my first two years. Because I was an overseas student, I had nowhere to go during vacations. In those days, Trinity was a lonely place during vacations –– there were no East Asians jostling on the streets in those days! –– so from time to time Peter would invite me and one or two others in residence like me, for sherry and conversation. Over the years I have come to realize that he had a profound influence on me. Shy to the point of being non-communicative, he nevertheless responded to intellectual queries with a dazzle that can only come from someone who is a master of his own field but knows how connected enquiries are across disciplines. I had never come across quite that ability before. I have been privileged to come into close contact with minds of a similar bent but my attraction to that style of intellectual enquiry has its roots in Peter’s mentoring.

His recreations included bridge (to an internationally competitive level), chess (one of the top ten in the country), tennis and squash. Particularly influential on his thinking, he said, was S. J. Simon’s Why You Lose at Bridge. A younger Fellow of Trinity recalls regularly losing games of squash in the 1970s to ‘the most ferociously competitive opponent’ he ever encountered.

Asked in 2008 how to understand Cambridge University, Sir Peter responded that it was a bit like the children’s game of ‘Grandmother’s Footsteps’. ‘You can never observe it changing. You can observe that it has changed.’