A Peter Swinnerton-Dyer interview

Peter Swinnerton-Dyer was interviewed by Alan Macfarlane on 12 May 2008.
The interview is on YouTube. See THIS LINK.

There is also an extensive summary of the interview at THIS LINK.

Below we present the text of the interview almost in its entirety. We have not given it in the form of an interview, however, since we have not recorded the questions and have made slight changes to Peter Swinnerton-Dyer's replies so that they make sense when the question does not appear.

Peter Swinnerton-Dyer talks about his career.

I was born in Northumberland in 1927. The Swinnerton-Dyer name came about in the following way. My family picked the wrong side in the civil war and lost all their money. The heir married the only daughter of the Lord Mayor of London who was called Swinnerton. As long as the money lasts we shall be called Swinnerton-Dyer.

My maternal grandfather was a Newcastle business man. My paternal great-grandfather was managing director of Armstrong Whitworth. My grandfather unfortunately had no talent for gaining or even keeping money and lost much by investing in bogus Australian gold mines. My father was more successful in business and left me well off so, for example, I was sent 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.

My father, a successful business man, a country gentleman, was by training an engineer. I am the first in the male line ever to have gone to a university though I'm not a typical first generation university entrant since I come from a well-off middle-class family. My mother was interested in everything, very lively and very vigorous, and ran anything she got her hands on. She was a kind mother and much more interested in academic things than my father.

We moved to Shropshire when I was about five, so I think of myself as growing up in Shropshire and not in Northumberland. 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; very simple sums but even so.

The first school I went to was what in earlier days would have been called a Dame School in Church Stretton, which is a town about six or seven miles away. Then I went to the Dragon School in 1935 where I was influenced by the maths teacher, Gerald Meister. At that school I was very enthusiastic about mathematics. I played games but not very successfully, I loathed cricket and continue to do so. So in my last year at the Dragon I was allowed to play tennis instead of cricket. At Eton I rowed as that was the only alternative to cricket and being large I was a reasonably good oar. I am fairly enthusiastic about music and at the Dragon School I was auditioned for the chorus but since I have a voice like a corncrake I didn't in fact get very far. Although enthusiastic about music the only thing I play is the gramophone. I enjoy opera more than anything else and eighteenth century orchestral music running from Bach to Beethoven and Schubert. I quite enjoyed Eton as much as I would have enjoyed any public school, probably more than most. I wasn't influenced by the teachers as much as at the Dragon School but there were some reasonably good mathematicians. I had to take all subjects up to GCSE level but being Eton you didn't take any public examinations at all. I 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. I'm not at all a linguist but, of these, I have a continuing interest in history which I continue to read with enthusiasm but take some pleasure in that I don't have to be a professional historian. It looks like really hard work grubbing in archives. Geoffrey Elton said that the best friends of historians were fire, water and rats. I knew Geoffrey, he was about my age. He was a formidable university politician and I got on very well with him; I think largely because we disliked the same people. I used to describe myself as one of the few Thatcherites in the Labour party but now they're very common. At Eton we did public exams but they were privately marked. I can't remember exactly what I did for 'A' level but probably mathematics and physics.

I only applied to Trinity, I got a Major Scholarship, that was well before you had to start applying anywhere else. I applied to Trinity because of its reputation in mathematics. My father and the school said it was the right place for me to go to so, as a dutiful youth, I went. Hardy was there in my first year as an undergraduate, I saw him sitting out in Great Court 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 and so 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 very 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 but 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 but 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 interest and 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's interests were in very modern methods and that related to the problems they were interested in as well. Weil wanted me since I had a certain reputation and by definition anyone with a Commonwealth Fund scholarship was extremely good. They were jolly difficult to get but at that time very attractive because they required you to spend three months of the Summer travelling around the States. Although that was in theory to travel to other universities where there was a colleague who shared interests with you, in practice, for most Commonwealth Fund fellows it meant going from one National Park to another.

I came up to Cambridge in 1945 so during the war I was at Eton. Paul Dirac was still at St John's but I never met him and I never acquired an interest in applied mathematics. I never seriously thought of staying in America, I had a research fellowship for a limited term and one had to come back. I never thought of going there permanently. I came back to a teaching fellowship in Trinity and, if you are a bachelor, a teaching fellowship in Trinity is a very comfortable place. I got to know Jack Gallagher, the Indian historian, who was certainly my closest friend at high table. Other friends were Eric Barnes, the mathematician, who was elected the same year as me, and David Wheeler, a computer scientist, elected the following year. I knew Peter Laslett reasonably well.

Trevelyan was Master when I got a research fellowship. He was a very illustrious man but I scarcely had any conversation with him as he didn't have much interest in the scientists. Indeed the Fellowship Admission Dinner where the Master makes a long speech explaining about the qualities of the research fellows just selected, he devoted more time to George Carey, the one humanist, than to the six scientists put together. I don't resent that - it's to be expected.

Outside Trinity I spent time with David Wheeler in the Computing Lab. I came back to a teaching fellowship in Trinity but I couldn't get a University assistant lectureship. I lost out twice, once to Michael Atiyah, which was certainly the right decision, and once to Christopher Zeeman which was less clearly the right decision. These were lectureships in pure mathematics. There was pressure in those days for anyone with a College fellowship to get a University job as well to relieve the financial pressure on the college. In due course, in fact, unable to get a position in pure mathematics I got a position 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 and in those very early days it was only privileged people who got the use of a computer.

Cambridge had the EDSAC1 which was, on some criteria, the first working computer every built. It's a very delicate criteria. It was the first British computer to run a program correctly though not the first to run a program. 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 mathematicians, indeed, number theorists, and both in Trinity, and got on together. The question to which this is the answer - 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 and 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 and it was proved by Mordell that there are only finitely many generators with 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 now 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 seven Clay Institute $1,000,000 problems so if you solve it you get $1,000,000 but robbing a bank is really easier. I think it is soluble but don't expect it to happen in my lifetime, indeed I rather hope it doesn't in my lifetime as I should have to try 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 generalise.

I was never exclusively involved in mathematics. I captained the University chess team as an undergraduate and I got dragged into being President of the University bridge club by someone who wanted to run it but, since he was only about to enter their second year, became secretary and wanted a front man to become president. I discovered gradually that I played bridge rather well and I would probably have been rated as one of the ten top players in the country. I certainly played in the European championships twice representing Britain. I gave it up eventually, partly because it was taking up too much time travelling to London all the 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. Its good advice for a career always to enter everything at the top. One way or another the force was with me as it were and I got deeper and deeper involved into 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. I was 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 to be Vice-Chancellor so they elected me. I was a fellow of Trinity and I hadn't had any contacts with St Catharine's at all but 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 in spades. I duly was elected Vice-Chancellor. I did enjoy being Master of St Catharine's College although it had its difficult moments. It seemed to me that getting to know the undergraduates was crucial but not every Head of House has taken that view over the years. St Catharine's being famously a games playing College, that meant a good deal of touchline duty, but you can think about mathematics while standing on the touchline and cheering your team on so that wasn't too bad. The job needs patience, letting the Senior Tutor and the Senior Bursar run the College, that's the fault of some other Masters. They think they can override their principle officers. I had good officers when I was at St Catharine's.

The Vice-Chancellorship in those days was a position of dignity rather than power. It was a two year job because lasting any longer than two years you would have got into trouble. It was not the Vice-Chancellorship's job to get his own way or formulate his own 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 during my time at Cambridge 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 and, apart from that, sundry minor committees. I was on the Council of the Senate already in 1968 and involved when they besieged the Old Schools while the Council was sitting. I was the member of the Council 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 King's undergraduates came into hall where he was dining and blew a trumpet under his nose. I was still in Trinity then so I only heard about this second hand. When the Garden House affair blew up I was still in Trinity though on the Council of the Senate; I was not sympathetic.

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 U.G.C. and Chief Executive of the Funding Council. All my time was under Margaret Thatcher. I had considerable sympathy with Margaret Thatcher's 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 clearing out. Indeed there was - if you want a confirmation of that read my farewell speech as Vice-Chancellor. There were people potentially neglecting their duties and not being thrown out but being rather loved and admired. There was an extreme reluctance to take decisions or even to answer questions in a hurry. You know the story of the great reforming Government of 1832 and their communication to Oxford. Among other things they wrote to Oxford saying that perhaps it was about time they updated their statutes to which the University of Oxford replied that they had had a careful and 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. Women are devoted to spring cleaning and Mrs Thatcher more than most. The need to persuade vice-chancellors that it was their job to lead the university and 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 and not just say all this is nonsense, they'll get over it in due course, Oxford and Cambridge are wonderful and deserve to remain untouched. Indeed, all universities have greatly changed.

I had really rather little dealing with Margaret Thatcher but I liked her. I suppose in her latter days she got madder and madder but I never saw her in her latter days. The principle dealings I had were with Keith Joseph who was Secretary of State for Education for most of my time at the U.G.C. and who was a lovely man, very courteous, very 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 - he had been a fellow of All Souls.

Robert Rhodes-James was the Conservative Member of Parliament for Cambridge. I knew him quite well. He was very nice, very reasonable, sympathetic to universities, very much on the left wing of the party, scarcely at all a Thatcherite. Indeed when the Social Democrats split from the Labour Party, I tried to persuade him to join the Social Democrats with whom he had considerable sympathy but not sufficient to do that.

I still did a certain amount of mathematics while administering the U.G.C. and once I retired from the U.F.C. I have been able to go back to mathematics and I'm 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. I was also on the committee that was set up to merge the Ulster Polytechnic and the New University of Ulster, the only shotgun marriage that needed two shotguns! In both cases it was successful.

I would distinguish between an administrator and a policy maker. I have never been an administrator and I think I'd be rather bad at it. I have been a policy maker and 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 probably, which says that you should always seek for the best result possible not the best possible result - the art of the possible. Of course there is the Duke of Wellington's famous answer when he was asked what was the secret of his military success. He said 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 mentioned several times that I was a bachelor but 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 is also my second cousin. She used to dig in Mesopotamia before we were married, after that she moved first to Bahrain and then to Kuwait. She's now settled on being a senior figure and going round commenting on what is in museums.

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 they're 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 died 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 claims I don't understand Oxford 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 of course Cambridge 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. It's refusing to change under the present Vice-Chancellor but then his technique of reform is not skilled.

To the question, where is the University, now there are sufficiently 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 is more conservative and, for various reasons, the balance of power between the Colleges and the University, that is essentially the Departments, show Colleges as much more important in Oxford. In Cambridge 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 pure mathematics, chose to go somewhere that has somebody really good in the topics that interests you, that is far more important than the overall reputation of the university. Mentoring is usually, though not always, important in mathematics.

The cultivated part of our garden in Thriplow is my wife's work. It has about four acres of wood at the back of it that once was elm and has therefore become dead elm, nettles and elder. I'm gradually trying to reduce that to order. You know Thriplow has a daffodil weekend at which most gardens are open including ours. The lady a few years back came up to my wife and said, "I see you like a wild garden." My wife was furious!

Last Updated December 2025