Peter Swinnerton-Dyer interviewed by Alan Macfarlane 12th May 2008 0:09:07 Born in Northumberland in 1927; maternal grandfather was a Newcastle business man; my paternal great-grandfather was managing director of Armstrong Whitworth; grandfather lost much by investing in bogus Australian gold mines; father was more successful in business and I went to Eton; in due course the elder branch of the family died out and I inherited the baronetcy; I earned a knighthood as Chairman of the U.G.C.; father was by training an engineer; I am the first in the male line ever to have gone to a university; mother was interested in everything, very lively and vigorous, and ran anything she got her hands on; she was much more interested in academic things than my father; we moved to Shropshire when I was about five; we lived in the depths of the countryside where I did roam around though never became really interested in natural history; I was a reader and from a very early age it was clear that I would become a mathematician; my mother said that, from the age of two, the only way to keep me quiet in the bath was to give me sums; the first school I went to was what in earlier days would have been called a Dame School in Church Stretton, about six miles away; then I went to the Dragon School in 1935; I was influenced by the maths teacher, Geoffrey Meister; played games but not very successfully; I loathed cricket so in my last year at the Dragon I was allowed to play tennis; at Eton I rowed as that was the only alternative to cricket; fairly enthusiastic about music but the only thing I play is the gramophone; enjoy opera more than anything else and eighteenth century orchestral music; quite enjoyed Eton; there were some reasonably good mathematicians; had to take Latin, Greek, French, a small amount of German, history, divinity, a certain amount of science - physics and biology, but oddly, not chemistry; of these, have a continuing interest in history; memories of Geoffrey Elton; at Eton did public exams but they were privately marked; can't remember exactly what I did for 'A' level but probably mathematics and physics 10:32:09 Got a Major Scholarship to Trinity, Cambridge; my father and the school said it was the right place for me to go; Hardy was there in my first year as an undergraduate but I never spoke to him; Littlewood was my research supervisor; the other outstanding mathematician of that generation was Besicovitch; Littlewood was one of the greatest mathematician of the twentieth century in a distinctly old-fashioned way; I was brought up as an old-fashioned analyst and number theorist; since I was primarily a number theorist my natural research supervisor would have been Mordell but he was a devoted and very bad bridge player and if he had been my supervisor I would have had to play bridge with him about once a week and the prospect did not attract me; Littlewood's technique with research students was simple; he gave you a list of some twenty or thirty problems and told you to come back when you had done one of them; I only later learnt that the way the list was compiled was that they were all problems which a mathematician who he respected had seriously tried and failed to do; I did do one of them so I got a research fellowship at the end of my second year; he had a list of much easier problems that you got given in the third year if necessary; I never saw that list; I had four years as a research fellow and then got a Commonwealth Fund Fellowship and went to Chicago intending to work under Zygmund whom I knew as he had been in Cambridge for one of my years as a research fellow; within twenty-four hours I was kidnapped by André Weil, again one of the great mathematicians of the twentieth century, but as far removed in style from Littlewood as you can conceivably imagine, so mathematically I have been schizophrenic ever since; Littlewood's interests were in old-fashioned methods whereas Weil was very modern; that related to the problems they were interested in; Weil wanted me as by definition anyone with a Commonwealth Fund scholarship was very good; they were difficult to get at that time because they required you to spend three months of the Summer travelling around the U.S.; although that was in theory to travel to other universities where there was a colleague with shared interests, in practice, for most fellows it meant going from one National Park to another 15:22:16 I came to Cambridge in 1945; Dirac was still at St John's but I never met him; I never acquired an interest in applied mathematics; I never seriously thought of staying in America; I came back to a teaching fellowship in Trinity; if you are a bachelor, a teaching fellowship in Trinity is a very comfortable place; got to know Jack Gallagher, the Indian historian, who was my closest friend at high table; Eric Barnes, the mathematician, was elected the same year as me; David Wheeler, a computer scientist, elected the following year; knew Peter Laslett reasonably well; Trevelyan was Master when I got a research fellowship; I scarcely had any conversation with him as he didn't have much interest in the scientists; outside Trinity spent time with David Wheeler in the Computing Lab.; at that time I couldn't get a University assistant lectureship; I lost out once to Michael Atiyah and once to Christopher Zeeman; there was pressure at the time for anyone with a College fellowship to get a University job as well to relieve the financial pressure on the college; in due course, unable to get a position in pure mathematics I got one in the Computing Lab.; I spent about ten years there and had I not been there I don't think the Birch Swinnerton-Dyer conjectures would ever have happened because they couldn't have been made credible without the use of a computer; in those very early days it was only privileged people who got the use of a computer; Cambridge's EDSAC1 was on some criteria the first working computer every built; it was the first British computer to run a program correctly though not the first to run; the Manchester computer beat it by a few days but there was a bug in the program; Bryan Birch was a research fellow in Trinity at that time; he came a few years later than me, partly because he had done National Service and I hadn't; we worked together as we were both pure mathematician, indeed, number theorists, and both in Trinity, and got on together 21:48:20 The question - suppose you have a cubic curve in a plane and you know a rational point on it, then it turns out that the set of all points on it form an abelian group in a natural way; the question is the structure of that group; it had been well known for a long time that the torsion part of it was finite and by now everything is known about the torsion part; it was proved by Mordell that there are only finitely many generators of infinite order; the great problem is, how many generators of infinite order; that was at that time regarded as one of those questions to which there could not be a sensible answer, partly because it appeared to most of the people who worked in that area that there was nothing in terms of which to express it; we found conjecturally that there was a sensible answer and stated it in some detail; but there is a very big gap between conjecture and proof; it has never been proved; special cases are now proved but really only very special cases; it is one of the Clay Institute $1,000,000 problems; I think it is solvable but don't expect it to happen in my lifetime, indeed I rather hope it doesn't as I should have to understand the proof and I am too old for that; computers will not help to solve it; John Coates is one of the people who has proved special cases, but the special cases all depend on a very special property which certainly does not generalize 25:25:03 I was never exclusively involved in mathematics; I captained the University chess team as an undergraduate and was also dragged into becoming President of the University bridge club; discovered that I played bridge rather well and would probably have been rated as one of the ten top players in the country; I played in the European championships twice representing Britain; I gave it up eventually, partly because it was taking up too much time and partly because, out of pure curiosity, I became interested in University affairs; the only body that was at all easy to get onto was the Council of the Senate; became deeply involved in University affairs in the 1960's; by the troubles of 1968 I was regarded as the only member of the Council who talked to undergraduates; probably the only one who was really sympathetic to them; St Catharine's, who hadn't had a Vice-Chancellor for more than 150 years, when they had a vacancy decided I was a good bet; they elected me Master; another thing that worked in my favour was that I was a bachelor and the classic quarrel in a College is apt to be between the Bursar and the Master's wife, which had happened before in St Catharine's; I duly was elected Vice-Chancellor; I did enjoy being Master; it seemed to me that getting to know the undergraduates was crucial but not every Head of House has taken that view; St Catharine's being famously a games playing College meant a good deal of touchline duty, but you can think about mathematics while standing there and cheering your team on; job needs patience, letting the Senior Tutor and Bursar run the College; the fault of some Masters is they think they can override their principle officers; the Vice-Chancellorship in those days was a position of dignity rather than power; it was a two year job; not his job to get his own way or formulate policies; if you wanted to get things done you did that before you were Vice-Chancellor; even Arthur Armitage who must have been the most formidable figure as Vice-Chancellor got his way before and not as Vice-Chancellor; he then went off to Manchester to be a proper Vice-Chancellor; in those days you chaired the Council of the Senate, the General Board and the Financial Board; apart from that, sundry minor committees; I was on the Council of the Senate in 1968 when they besieged the Old Schools when the Council was sitting; I was the member who was sent out to tell them that they were not going to get what they wanted; they treated me better than Paris undergraduates would have greeted a corresponding figure; St Catharine's was a very old-fashioned College; at one time under my predecessor in 1968 some undergraduates came into hall where he was dining and blew a trumpet under his nose; I was still in Trinity when the Garden House affair blew up though on the Council of the Senate; I was not sympathetic 34:06:20 I was on the University Grants Committee for five and a half years and then for three years on the Universities Funding Council; I was head of the former and Chief Executive of the latter; all my time was under Margaret Thatcher; I had considerable sympathy with her views on universities which were widely held in the top ranks of the Civil Service as well who remembered the university from the days when they had been undergraduates and thought there was an awful lot of rubbish that needed cleaning out; indeed there was; for confirmation of that read my farewell speech as Vice-Chancellor; included people neglecting their duties and not being thrown out; but being rather loved and admired; an extreme reluctance to take decisions or answer questions in a hurry; reforming Government of 1832 wrote to Oxford suggesting they updated their statutes to which the University replied that they had had a thorough examination of their statutes in the 1630's and they thought it would be premature to do it again; that I think was a widespread attitude and so a lot of my job was to convince universities that they were in the late twentieth century under a Prime Minister whose deepest urge was spring cleaning; the need to persuade vice-chancellors that it was their job to lead the university, not just to make good after-dinner speeches; the need to shift power from senates to councils; none of that applies to Oxford and Cambridge who have a different and peculiar structure, but there, too, the need to recognise reality; indeed, all universities have greatly changed; had really rather little dealing with Margaret Thatcher but I liked her; I suppose in her latter days she got madder but I never saw her then; the principle dealings I had were with Keith Joseph who was Secretary of State for Education most of my time at the U.G.C. and who was a lovely man, very courteous, reasonable, prepared to think through any problem very thoroughly, and very reluctant actually to do anything as a result of thinking through it; he was someone who esteemed academics; memory of Robert Rhodes-James 40:13:01 I Still did a certain amount of mathematics while administering the U.G.C.; once I retired from the U.F.C. I have been able to go back to mathematics and I am still doing good research; I was involved in two major enquiries; I chaired the London University enquiry where they said the smaller colleges were not going to be viable under increased financial pressures and had to be merged into bigger ones, which happened; also on the committee that was set up to merge the Ulster Polytechnic and the New University of Ulster; I have never been an administrator but have been a policy maker; the two most important things are to judge what are the limits of the practical and to put yourself in the other peoples' minds; there is a saying in S.J. Simons 'Why You Lose at Bridge', a book that in some ways has influenced me more than any other, which says that you should seek for the best result possible not the best possible result; the Duke of Wellington's answered when asked the secret of his success was that he always tried to know what was going on on the other side of the hill; I did this by saying what I would think if I were in their shoes and held their opinions; it is probably the same talent that was developed by my years as a bridge player for which putting yourself in the other man's shoes is also crucial; I married at the very end of my Mastership at St Catharine's; my wife, Harriet Crawford, is an archaeologist so I have to take an interest in her subject because it is cultural but she doesn't have to take an interest in mine; she used to dig in Mesopotamia before we were married, after that she moved first to Bahrain and then to Kuwait 44:48:23 On mathematical ability and age, find I have less energy than I used to, not necessarily less ability; the statement that mathematicians do their best work when young is really based on two famous cases of two of the greatest nineteenth century mathematicians who died in their thirties; one was Abel, a Norwegian, the other was Galois; Abel died of consumption, Galois, in a duel; Littlewood was still doing good research in his eighties; he finally had to give it up, not because he had run out of ability, but because he could no longer read his own handwriting; Oxford claim I don't understand it as I believe it is just the same as Cambridge, which is not true, but I don't understand Oxford; I did understand Cambridge as well as anyone but it has changed quite a bit and I have not really kept up with the changes; Cambridge is like the children's game grandmother's footsteps, you can never observe it changing but can observe that it has changed; Oxford is different as you can watch it changing or refusing to change, the latter so under the present Vice-Chancellor; to the question, where is the University, now there are so many buildings on the other side of the river I think it is essentially there; in terms of distributed power, the great scientific departments, probably, and they represent a permanent pressure for progress whereas the classical humanities represent a permanent pressure for stasis; part of the difference between Oxford and Cambridge is that the balance between the two is very different; in Cambridge the sciences dominate because they always have whereas in Oxford the classics and humanities dominate; Oxford more conservative; balance of power between the Colleges and University, that is Departments, show Colleges as more important in Oxford; here there is a tension between them but it works tolerably well; for encouraging creative thought this structure works, though why it works is a sociologist's problem, not a mathematician's, but empirically it does seem to work pretty well; I think Harvard works better but I doubt if there is any university within Britain that I know well enough, apart from Cambridge, to say that; on giving advise to a research student in mathematics, chose to go somewhere that has somebody really good in the topic that interests you, that is far more important than the overall reputation of the university; mentoring is usually, though not always, important; garden in Thriplow