## Pembroke Mathematicians

The College has housed a number of eminent mathematicians over the centuries. For example, in the eighteenth Century there was Roger Long, who was Lowndean Professor in the University and Master of the College, while in the nineteenth Century Sir George Stokes, FRS (1819-1901) held the Lucasian Professorship for over 60 years, and was also Master during the last few months of his life. William Burnside, FRS, a noted group theorist, was another distinguished mathematician from the late nineteenth Century. However, in this article I shall be concerned with members from the present century.

George Birtwhistle was the College’s Fellow and teacher in Mathematics from 1900 to his death in 1929. He had been bracketed Senior Wrangler, and was a successful teacher. Although not distinguished in research, he was one of the earliest to write a text book on the new quantum theory in the late 1920s, at a time when quantum theory was considered to be rather abstruse. Birtwhistle’s successor was J. M. Whittaker, the son of the distinguished Edinburgh mathematician E. T. Whittaker. However, Whittaker was appointed Professor of Pure Mathematics at Liverpool University in 1934. He was subsequently Vice-Chancellor of Sheffield University, and an FRS.

Whittaker was in turn succeeded by W. V. D. Hodge. Hodge had studied initially at his home university of Edinburgh, where he was much influenced by E. T. Whittaker and was a classmate of J. M. Whittaker. Then he came to St John’s College, Cambridge to take the Mathematical Tripos. After a few years at Bristol and one year at Princeton he returned to Cambridge, and was made University Lecturer in 1933. He was therefore a very natural choice to succeed to the teaching position at Pembroke in 1934. His time in that position was short-lived, however; for such was his distinction that he was elected to the Lowndean Chair in 1936. Fortunately the College elected him to a Professorial Fellowship, which he held until his election to the Mastership in 1958. Hodge’s subject was algebraic geometry and also to some extent differential geometry. His great work was done in the 1930s, when the modern versions of those subjects were being created under the new influence of topology. One result of modern differential geometry is that it is possible to write down, in a very concise way, the generalization of Stokes’ theorem to a manifold of any number of dimensions. I well remember Hodge writing this down for me one evening in Parlour. He liked to regard himself as a successor to Stokes in several ways, as University Professor, as Master of Pembroke, and as Secretary of the Royal Society. During the war years he was necessarily diverted into administration, to which as a result he devoted much of his energies in the later part of his career. He did much work for the Royal Society, of which he had become a Fellow in 1938, and is of course well remembered in Pembroke for his Mastership (1958-1970) in which he presided during the great years of University expansion. He was also the founding Head of the Department of Pure Mathematics and Mathematical Statistics in the University. He received a knighthood in 1958. During the 1950s, he enjoyed fruitful collaboration with his star graduate student, Michael Atiyah of Trinity, of whom more later. He died in 1975.

Hodge’s election to the Lowndean Professorship meant that Pembroke had again to find a College teacher in Mathematics. This time they chose Robert Stoneley, a theoretical seismologist, some 7 years senior to Hodge. Like Hodge, he came from St John’s College, and had been appointed University Lecturer a year before joining Pembroke. His work concerned the propagation of elastic waves in the Earth’s crust, and the interpretation of the records of earthquakes. He was elected FRS in 1935. He directed studies for Pembroke until his retirement in 1961; meanwhile he had been appointed Reader in Theoretical Geophysics in 1949. Stoneley was one of the very small number of the mathematics staff who stayed in Cambridge during the war years. Although the number of students was then rather small also, such staff as there were had still to cover all the topics taught in lectures as well as provide supervisions; I remember Stoneley describing to me the horrendous number of teaching hours that had then to be worked. After his retirement he spent 4 years in the United States, during which he enjoyed an Indian summer in his research activities. Unfortunately it was only after his return that I got to know him personally. I found him still to be a man full of zest for life and of great geniality. He died in 1976.

Among Stoneley’s pupils who pursued mathematical careers were C. Domb, R. Hill, P. Chadwick and G. H. Toulmin.

In 1958, no doubt with Stoneley’s retirement on the horizon, and having regard also to the increasing complexity and range of choice in the Mathematical Tripos, the College decided to appoint a Teaching Fellow in Pure Mathematics. They elected M. F. Atiyah, mentioned above. Among the pupils taught by him and Stoneley in the next 3 years were two who form part of our story, J. F. C. Kingman and W. B. R. Lickorish. Another was J. A. Bather, now Professor of Statistics at Sussex University. However, like his predecessors in the 1930s, Atiyah gained rapid promotion which prevented him from teaching for Pembroke for very long. In 1961 he was attracted to a Readership at Oxford, and in 1963 was elected to the Savilian Professorship of Geometry there. In 1969 he left Oxford to become Professor of the Institute for Advanced Study, Princeton, but returned to Oxford as Royal Society Research Professor in 1973. Among his many honours is a Knighthood in 1983, and an Honorary ScD at Cambridge in 1984. His work has ranged widely over contemporary pure mathematics, especially geometry and topology, with connections to mathematical physics.

The retirement of Stoneley in 1961, and the departure of Atiyah for Oxford in the same year, were responsible for my own migration from my original college of Sidney Sussex to Pembroke; I had become Assistant Lecturer in Applied Mathematics in the University that year. It was somewhat daunting to succeed those two people. On my first day in College I was mistaken by the College secretary for a new graduate student, but I was relieved when, a few days later at the admission of new Fellows, I observed a Research Fellow looking younger even than myself. He was John Kingman, already publishing papers although he had graduated only the previous year. He also became Assistant Lecturer next year, and gave me considerable assistance with the teaching, on the Pure side, in those early years. However, true to form, he left Pembroke in 1965 for promotion, going to the University of Sussex as a Reader, becoming Professor there the next year. In 1969 he moved again, being elected to a newly established Chair at Oxford. He became FRS in 1971 at the age of 31. His subject is probability theory and statistics, in which he has produced several noted books. More recently, he became Chairman of the Science and Engineering Research Council in 1981, thus finding himself deeply involved in the leadership of the country’s science at a time of diminished resources. However, while on secondment from his Oxford Chair to serve at SERC he resigned it to accept the Vice-Chancellorship of Bristol University in 1985. He was also knighted in that year.

Luckily the College was in a sense already prepared for Kingman’s departure, as W. B. R. Lickorish had returned to Cambridge in 1964 as University Lecturer in Pure Mathematics after one year at Sussex University, and the College had elected him Fellow. For the next two decades, he and I have, with occasional help from others, endeavoured to keep the Pembroke mathematical ship on course. Some of our pupils from the 1960s and 1970s may perhaps be mentioned. Brandon Carter (1961) now FRS, was a Fellow of the College for several years, and University Lecturer in Mathematics, but has for some time worked in Paris. His subject is cosmology. Peter Jupp (1963) was a geometer rather in the Hodge tradition, although he subsequently migrated to statistics. He was Research Fellow in 1971-1974. S. J. Nickell (1962) became a mathematical economist, and was Professor at the London School of Economicsfrom 1979 until his recent move to Oxford to head an institute there. V. P. Snaith (1963) was a Fellow of Emmanuel for several years, and A. G. Tristram is now Senior Tutor at Churchill. S. T. C. Siklos (1968) teaches at Newnham and for the Faculty. Three members of the intake of 1960 are teaching at other Universities in the U.K.: M. Rowan-Robinson, M. K. Wallis and F. J. Yeadon, as also are J. P. Miles (1962) and A. M. Davie (1964).

Perhaps the most notable of all is Simon Donaldson (1976) who was first introduced to topology and geometry through the teaching of Raymond Lickorish at Pembroke. After graduating with every kind of distinction, he moved to Oxford, where he pursued research for his doctorate under the supervision of Sir Michael Atiyah. Tales of his research prowess reached us here from time to time. His story finally reached the Sunday newspapers early in 1985 when Oxford University announced that the successor to Sir John Kingman, in the Chair now named the Wallis Professorship of Mathematics, had been elected; the new professor was Simon Donaldson at age 27. This year (1986) he has been elected also to the Royal Society. Meanwhile, another mathematician joined the College as Professorial Fellow in 1979, M. J. D. Powell, (FRS 1983), whose subject is numerical analysis. Among his research pupils has been Yuan Ya-xiang, who is also a member of the College and has recently been elected to a Research Fellowship at Fitzwilliam College. D. J. Allwright and J. R. Partington have also held Research Fellowships at Pembroke in recent years and are now Fellows of King’s and Fitzwilliam respectively.

Dr J P Dougherty

*Pembroke Annual Gazette*, Volune 60 (1986), pp. 33-36

##### Pembroke Mathematicians – A Supplement

In a *Gazette* article of 1986 I gave an account of the mathematicians who taught or were taught (or both) at Pembroke in the period 1900-1986. Here I continue the story to the present day.

A major event that just missed inclusion was the award of the Fields Medal to Simon Donaldson (1976) in 1986. A small digression about the Fields Medal is appropriate. The scheme for Nobel Prizes does not include the subject of mathematics. An American, Professor Fields, sought to remedy this gap by endowing the Fields Medals, shortly before the Second World War. The Medals are awarded at the International Congress of Mathematicians, convened at four-year intervals. On recent occasions, four medals have been awarded each time. Recipients must be below the age of 40 at the time of the award. The Fields Medal is the highest honour there is in mathematics. Simon’s accomplishments also include a sailing Blue in 1980. He moved from Oxford to Imperial College, London in 1998.

The previous article omitted to mention that Sir Michael Atiyah had been awarded a Fields Medal in 1966. After a long absence from Cambridge, Sir Michael returned in 1990 as Master of Trinity College (to 1997), becoming in the same year President of the Royal Society (to 1995) and the first Director of the Isaac Newton Institute (to 1996). The Isaac Newton Institute was only a building site in 1990, and opened its doors for academic work in 1992. It conducts sessions, mostly lasting six months, of research on specific topics, endeavouring to collect the world’s experts together for that time. Its award-winning building on Clarkson Road occupies one corner of the site which has subsequently been used to house the new buildings for the University Departments of Mathematics (Pure and Applied), together with the new Betty and Gordon Moore Library. The Institute has this year completed 10 years of very successful operation. Sir Michael, who became an OM in 1992, retired to Edinburgh.

After many years as Director of Studies in the College, Raymond Lickorish (I957) stepped down from that position in 1991, the year in which he was awarded the Senior Whitehead Prize of the London Mathematical Society for his work on Knot Theory. He became a Professor ad hominem in 1996, and undertook the post of Head of the Department of Pure Mathematics and Mathematical Statistics in 1997, thus finding himself a successor to Hodge, the founding Head. Whereas Hodge had to concern himself with the move into the Mill Lane premises, Raymond had to oversee the move out of Mill Lane into the new Buildings referred to above. A great success for the Department occurred in 1998, when two members (both of Trinity) were awarded Fields Medals.

Raymond’s successor as Director of Studies is Dennis Barden, a geometer. The College has been very successful in its undergraduate work in the 1990’s, attracting a much increased field of applicants and securing a high standard in Tripos results.

Professor Michael Powell (1978) was awarded the Gold Medal of the Institute of Mathematics and its Applications in 1996 and the Senior Whitehead Prize of the London Mathematical Society in 1999. He received the rare distinction of becoming a Foreign Associate of the U.S. National Academy of Sciences in 2001.

I retired from Directing Studies in Applied Mathematics in 1996, after doing it on and off since 1961, an activity I have much enjoyed. I take the opportunity to thank all my former pupils and colleagues. My immediate successor was Niall MacKay, who was already Stokes Fellow in the College. However, (like so many of his predecessors: see my 1986 article) he was soon on the move, and left in 1998. He is now on the staff of Durham University. Another Research Fellow who gave considerable help in teaching in that epoch was Shahn Majid, who left in the same year to take a Readership at Queen Mary College, London.

Martin Baxter (1986), was both undergraduate and graduate student here, and was elected to a Research Fellowship in 1993. He found time to write a text on the fashionable subject of Financial Calculus; unfortunately for academia it was too fashionable and he left in 1997 to work in the City. Perhaps he will have crossed paths with S.J. Nickell (1962), who is now back at the London School of Economics as Professor, and a Member of the Bank of England’s Monetary Policy Committee. Continuing in the financial field, several of our alumni became actuaries, notably Chris Daykin (1967), now the Government Chief Actuary. He received a CB in 1993, was President of the Institute of Actuaries 1994-96, and was awarded the Institute’s Gold Medal in 1997.

Our alumni also include academics in senior posts. A.J.Mann (1975) is Head of Pure Mathematics at Greenwich University. With Peter Neumann (hisformer D.Phil. supervisor at Queen’s College, Oxford) he organised in 1997 a commemorative meeting for Burnside, the nineteenth century Pembroke mathematician (see my 1986 article); together they are editing Burnside’s papers. M.R.Yeadon (1964) is Professor of Computer Simulation in Sport at Loughborough University. P.D.Straffin (1965) is Professor of Mathematics at Beloit College, Wisconsin, and the author of a book on the Theory of Games. V.P.Snaith (1963) is Professor of Mathematics at the University of Southampton, after spending many years in Canada, where he became an FRSC. Ya-xiang Yuan (1982) is the Director of the Institute of Computational Mathematics and Scientific/Engineering Computing of the Chinese Academy of Sciences. J.R.Partington (Drapers Research Fellow 1980) is professor of Applied Functional Analysis at Leeds University.

I apologise for any omissions from the above list, and indeed from the article generally. Early in 2001, the College elected Dr Nilanjana Datta into a Teaching Fellowship to have charge of Applied Mathematics. She comes from Calcutta, via a Research post in Geneva.

Professor Powell and I both retired from our University posts on 30 September 2001.

We must return to the Isaac Newton Institute. Following Sir Michael Atiyah’s departure, the post of Director was filled by the appointment of my Departmental Colleague Professor Keith Moffatt for 5 years to 2001, by secondment from the Department. The nature of the Institute’s activity is to be transitory, but it has been unsatisfactory that it had no established University posts at all, even for the Director. This has been remedied through the endowment of the N.M.Rothschild and Sons Professorship of Mathematical Sciences. This is a Chair not assigned to either Department, and to which the post of Director is attached. Sir John Kingman (1961) has been elected to be the first N.M. Rothschild and Sons Professor from 1 October 2001 and, relinquishing the Vice-Chancellorship of Bristol University after 16 years, has rejoined Pembroke as a Professorial Fellow. He will also be President of the European Mathematical Society during 2003-2006.

Two centenaries will occur in 2003: the death of Sir George Stokes and the birth of Sir William Hodge. Both will be celebrated in appropriate manner, both in Pembroke and more widely.

Dr J P Dougherty

*Pembroke Annual Gazette*, Volume 76 (2002), pp. 45-47