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Henry Peter Francis Swinnerton-Dyer

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Born
2 August 1927
Throckley, Northumberland, England
Died
26 December 2018
Thriplow, Cambridge, England
Summary
Peter Swinnerton-Dyer was an outstanding mathematician best known for the Birch-Swinnerton-Dyer Conjecture. He also served as Master of St Catharine's College, Cambridge, Vice-Chancellor of Cambridge University, chair of the University Grants Committee, and chief executive of the Universities Funding Council.
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Biography

Peter Swinnerton-Dyer was the son of Sir Leonard Schroeder Swinnerton-Dyer (1898-1975) and Barbara Winifred Brackenbury (1905-1990). The Dyer Baronetcy had been created in 1678 for William Dyer who had married Thomazine, the daughter and heiress of Thomas Swinnerton, himself the heir of Sir John Swinnerton, lord mayor of London. Sir Leonard Schroeder Swinnerton-Dyer, the 15th Baronet, was an engineer and businessman. Many of Sir Leonard's ancestors were officers in the navy or army and indeed he had served as a lieutenant in the Royal Field Artillery during the First World War. He married Barbara Brackenbury on 16 June 1925 in Cramlington Church, Northumberland. Barbara was the daughter of Hereward Irenius Brackenbury (1871-1938), a department manager of the mechanical engineering firm Armstrong Whitworth & Co, and his wife Winifred Isabel Browne (1872-1943). Sir Leonard and Barbara had two children, Henry Peter Francis Swinnerton-Dyer, the subject of this biography born 1927, and a younger daughter.

We note that Henry Peter Francis Swinnerton-Dyer is now known as Peter Swinnerton-Dyer although when he travelled to the United States in the 1950s he gives his name as Henry Swinnerton-Dyer or Henry P F Swinnerton-Dyer and his papers are mostly published under the name H P F Swinnerton-Dyer up to the 1980s after which they are published under the name Peter Swinnerton-Dyer. He spoke about his early years in [23]:-
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.
Peter Swinnerton-Dyer began his schooling at a kindergarten in Church Stretton, a town about six miles from his home. He attended this school from the age of five up to eight. After that, in 1935, he went to the Dragon School in Oxford. At this school he was very much influenced by the mathematics teacher Gerald Meister. Meister had been a housemaster at Sedbergh School for fifteen years before deciding to become a preparatory school teacher. He taught at Stratton Park near Bletchley, then at Wellington College before teaching at the Dragon School. He was an outstanding mathematics teacher and gave Swinnerton-Dyer a passion for the subject. Swinnerton-Dyer was also fond of music and, although he did not play an instrument, he auditioned for the chorus at the Dragon School. The school was keen to encourage their pupils to play sports and they were expected to play cricket. Swinnerton-Dyer played some games but hated cricket so in his final year he was allowed to play tennis instead of cricket.

After the Dragon School, Swinnerton-Dyer studied at Eton, the famous independent school. He studied Latin, Greek, French, and also a small amount of German, history, divinity, physics and biology up to GCSE level. Among his A level subjects were, of course, mathematics and physics but, following the standard practice at Eton, he did not sit the public examinations. At Eton the only alternative to cricket was rowing and so Swinnerton-Dyer rowed, a sport he was quite good at. He also played tennis, real tennis and squash well but was an outstanding chess player and bridge player. Perhaps his greatest mathematical achievement while at Eton was having the paper A solution of A4+B4=C4+D4A^{4} + B^{4} = C^{4} + D^{4} published in the Journal of the London Mathematical Society. He published it under the name P S Dyer and submitted it to the Society on 2 October 1942 when fifteen years old. He ends the paper with the Acknowledgement [13]:-
I should like to thank Prof Mordell for his kindness in giving me the necessary references.
When he wrote the paper A4+B4=C4+D4A^{4} + B^{4} = C^{4} + D^{4} revisited in 1968, which he dedicated to "Professor L J Mordell on his 80th birthday, he wrote [41]:-
My first piece of research was to obtain some non-trivial rational solutions of the equation in the present title. That this work was written up and published, I owe entirely to the efforts of Professor Mordell; and it is a pleasure to be able to acknowledge his kindness to me both on that occasion and subsequently.
Bryan Birch writes about this first paper of Swinnerton-Dyer's in [3]:-
It is very appropriate that his first paper was on the arithmetic of surfaces, the theme that recurs most often in his mathematical work; indeed, for several years he was almost the only person writing substantial papers on the subject; and he is still writing papers about the arithmetic of surfaces sixty years later.
Both Eton College and his father urged Swinnerton-Dyer to apply to Trinity College, Cambridge University since, they said, it was the best place to study mathematics. It was the only university application he made and he was awarded a Major Scholarship. He began his studies in 1945.

At Cambridge Swinnerton-Dyer made an instant impression as an outstanding mathematician and chess player. He played for the Cambridge University Chess Club in 1946, 1947, 1948 and 1949 being top board in 1948 and 1949. He began to become very interested in playing bridge and after the award of his B.A. in 1948 his choice of research advisor was influenced by this. He said [23]:-
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.
He therefore chose John Littlewood as his research advisor. He never submitted his thesis for a doctorate, instead in 1950 he was awarded a Prize Fellowship at Trinity based on his thesis on van der Pol's equation. In addition to his outstanding work in mathematics, he reached international level as a bridge player. In October 1950 the Acton Gazette reported [14]:-
International bridge player Mr Norman Smart, son of Dr J Ewart Smart, Acton Education Officer, and his partner, Mr P Swinnerton-Dyer, are England's youngest international contract bridge players. ... They have been selected to play for England in the next Camrose Trophy match. The pair were members of the Cambridge University team which beat Oxford last year and this year. ... after this, Mr Swinnerton-Dyer was disqualified from membership of the Cambridge team by being elected to a Fellowship ...
On 30 October 1950, Swinnerton-Dyer submitted the paper On a conjecture of Hardy and Littlewood which was published in 1952. In the paper he writes:-
I should like to express my gratitude to Prof Littlewood, both for originally suggesting the problem and for his advice and assistance in preparing this paper.
Three other papers by Swinnerton-Dyer were published in 1952. Two are joint work with Eric Stephen Barnes (1924-2000). These are major pieces of work, the first The Inhomogeneous Minima of Binary Quadratic Forms (I) being a 65-page paper with the following acknowledgement:-
... we should like to express our gratitude to Dr J W S Cassels, Prof L J Mordell and Dr C A Rogers, who have offered detailed criticisms of our manuscript and helped to remove several obscurities.
The second of these joint papers with Barnes is the 38-page paper The Inhomogeneous Minima of Binary Quadratic Forms (II) which has the acknowledgement:-
We wish to express our indebtedness to Dr J W S Cassels for his criticisms and encouragement.
Bryan Birch, in his Memories of Peter Swinnerton-Dyer, writes [2]:-
During his Prize Fellowship Peter worked on various problems of number theory, which included a massive collaboration with E S Barnes on the inhomogeneous minima of binary quadratic forms; in particular they determined which real quadratic fields are norm Euclidean.
During the years 1950-54 while he held the Prize Fellowship at Trinity College he represented England at bridge in the Camrose Trophy. He played vs Republic of Ireland in 1951, vs Wales in 1953 and vs Northern Ireland in 1954. He was partnered by Dimmie Fleming in the European Open teams championship in 1953 coming second out of fifteen teams.

On 15 September 1954, he sailed from Southampton in the Cunard Steam Ship Company's Caronia arriving in New York on 22 September. He had been awarded a Commonwealth Fund Fellowship to undertake research at the University of Chicago where he planned to study analysis with Antoni Zygmund. He had known Zygmund who had spent a year in Cambridge while Swinnerton-Dyer was a research fellow. Once in Chicago, however, he worked with André Weil who knew of Swinnerton-Dyer's reputation as an outstanding mathematician and was keen to work with him. This was to prove an important step in the direction Swinnerton-Dyer's research was to take for Weil converted him to algebraic geometry, particularly over the rationals. Birch writes [2]:-
Weil's influence on Peter's mathematics was paramount; from that time on, Peter remained an arithmetic geometer, albeit with an unexpected affection for second order differential equations.
Swinnerton-Dyer spent the summer of 1955 travelling round the United States, which was a requirement of the Commonwealth Fund Fellowship. He returned to England on the Queen Elizabeth, sailing from New York on 14 September 1955 and arriving in Southampton on 20 September. He gave his address in England as Westhope Cottage, Craven Arms, Shropshire.

Back at Cambridge he was appointed as a Teaching Fellow at Trinity College. Trinity put pressure on their teaching fellows to have, in addition, a university position so Swinnerton-Dyer applied for an Assistant Lectureship in Pure Mathematics. He failed to get the first two such jobs. The first position that arose went to Michael Atiyah while the second one went to Christopher Zeeman. Swinnerton-Dyer did not mind losing out to Atiyah but was rather unhappy that he lost out to Zeeman. Failing to obtain a position in Pure Mathematics, he applied for a post in the Cambridge Computing Laboratory and was appointed. This, in fact, led to the mathematical result for which he is most famous, namely the Birch-Swinnerton-Dyer Conjecture. We discuss this below.

Bryan Birch first met Swinnerton-Dyer in the autumn of 1953 while a Cambridge undergraduate and began research in the geometry of numbers advised by Ian Cassels when Swinnerton-Dyer was in Chicago. Birch writes that after Swinnerton-Dyer returned from Chicago to take up the Trinity position [2]:-
... as a teaching fellow I got to know him well; he taught me to love opera (I have happy memories of sitting on the floor listening to his recording of Callas singing Casta Diva) ...
They undertook some joint work and submitted the paper On the inhomogeneous minimum of the product of n linear forms in October 1955. Birch, like Swinnerton-Dyer, was awarded a Commonwealth Fund Fellowship and spent 1957-58 at Princeton. When he returned to Cambridge he discovered that Swinnerton-Dyer was working in the Computing Laboratory. They submitted a second joint paper, Note on a problem of Chowla, in April 1959.

For some time Birch and Swinnerton-Dyer worked on elliptic curves. In May 1962 they submitted the paper Notes on elliptic curves I and explained the background to their paper in the Introduction [5]:-
Siegel has shown that the density of rational points on a quadric surface can be expressed in terms of the densities of p-adic points; which for almost all primes p depends directly on the number of solutions of the corresponding equation in the finite field with p elements. More recently, Siegel's work has been fruitfully extended and simplified by Tamagawa and independently by Martin Kneser [son of Hellmuth Kneser.]

It is natural to hope that something similar will happen for the elliptic curve

          Γ:y2=x3−Ax−B\Gamma : y^{2} = x^{3} - Ax - B

where A, B are rational. In particular, one hopes that if for most p the curve has unusually many points in the finite field with p elements, then it will have a lot of rational points.

Several years ago we carried out by hand some calculations which tended to support these hopes. Since then, we have used the Cambridge University electronic computer EDSAC 2 for extensive calculations on elliptic curves. As a result, we have been able to put our conjectures into an exact form and support them with a good deal of numerical evidence. However, it has become clear to us that we are unlikely to be able to prove these conjectures.

We therefore feel it best to publish the material we have obtained, in a series of short notes. Much of the information in these notes is the result of machine computation; however the theoretical basis of these computations is not always trivial.
Two years later, in May 1964, they submitted Notes on elliptic curves II which continues their investigation and contains what today is known as the Birch- Swinnerton-Dyer Conjecture. In 1999 the Clay Mathematics Institute listed this Conjecture as one of their seven $1m Millennium Prize Problems. They write [4]:-
Supported by much experimental evidence, this conjecture relates the number of points on an elliptic curve mod p to the rank of the group of rational points. Elliptic curves, defined by cubic equations in two variables, are fundamental mathematical objects that arise in many areas: Wiles' proof of the Fermat Conjecture, factorisation of numbers into primes, and cryptography, to name three.
...
When the solutions [of an elliptic equation] are the points of an abelian variety, the Birch and Swinnerton-Dyer conjecture asserts that the size of the group of rational points is related to the behaviour of an associated zeta function ζ(s)\zeta (s) near the point s=1s = 1. In particular this amazing conjecture asserts that if ζ(1)\zeta (1) is equal to 0, then there are an infinite number of rational points (solutions), and conversely, if ζ(1)\zeta (1) is not equal to 0, then there is only a finite number of such points.
John Coates writes in [2]:-
The conjecture discovered jointly by Peter Swinnerton-Dyer and Bryan Birch in the early 1960s both surprised the mathematical world, and also forcefully reminded mathematicians that computations remained as important as ever in uncovering new mysteries in the ancient discipline of number theory. Although there has been some progress on their conjecture, it remains today largely unproven, and is unquestionably one of the central open problems of number theory. It also has a different flavour from most other number-theoretic conjectures in that it involves exact formulae, rather than inequalities or asymptotic questions.
Swinnerton-Dyer was appointed as a Cambridge University Lecturer in Mathematics in 1960, then promoted to Professor of Mathematics in 1971. He had spent the year 1970-71 as a visiting professor at Harvard University. He served as Dean of Trinity College from 1963 to 1970 and then, in 1973, he became Master of St Catharine's College, Cambridge. He continued to hold this position until 1983 and, during that period, he served as Vice-Chancellor of Cambridge University from 1979 to 1981. He also became a member of the Advisory Board for Research Councils in 1977, continuing in that role until 1990.

The position of Vice-Chancellor did not stop him enjoying sports [10]:-
Student squash and tennis enthusiasts at St Catharine's might be forgiven for thinking that their Master's two-year stint at the top will leave them less competition for places in college teams. Not so. Sir Peter intends to play harder to retain his place and pre-eminence. "I cannot but do otherwise if I am to remain at all fit. I simply must play and train harder to compensate for all the dinners I am going to be required to attend and to give over the next two years," he explained.
You can read two newspaper articles, the first as he was about to be installed as Vice-Chancellor at THIS LINK and the second immediately after he gave his retiring speech, at THIS LINK.

In 1983 Swinnerton-Dyer resigned as Master of St Catharine's College and on 25 May of that year he married his second cousin, the archaeologist Harriet Crawford. Harriet Elizabeth Walston Browne, the daughter of Rt Hon Sir Patrick Reginald Evelyn Browne and Evelyn Sophie Alexandra Walston, was born on 13 May 1937. She had married Iain A Crawford in 1960. She was a Senior Fellow at the McDonald Institute for Archaeological Research, University of Cambridge and an Honorary Visiting Professor at the Institute of Archaeology, University College, London.

The reason he resigned as Master in 1983 was to take up the position of chair of the University Grants Committee (UGC). It is likely that he was chosen for this role by the Government of the day because of the views he had expressed regarding the need for universities to change. He expressed these views in the article [42] entitled Prospects for Higher Education.
We give a version of the article at THIS LINK.

He served as chair of the UGC until 1989 when the government replaced the UGC by the Universities Funding Council (UFC). Swinnerton-Dyer became chief executive of the UFC and continued in that role until 1991. In these roles he wanted to see major changes to British universities. He said in the interview [23]:-
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. ... 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. ... [There was a] need to persuade vice-chancellors that it was their job to lead the university and not just to make good after-dinner speeches. [There was a] need to shift power from senates to councils ...
We should note that he resigned as chief executive of the UFC in 1991 after a serious argument with the Commons Public Accounts Committee following the prediction that over half of British universities would have large financial deficits.

We have found over 350 newspaper articles concerning Swinnerton-Dyer, most of which relate to his time at chair of the UGC and chief executive of the UFC. We have selected some which refer to his interaction with Scottish universities, in particular with Aberdeen University.
You can read some of these articles at THIS LINK.

Despite the heavy workload that his work on the UGC and UFC involved, Swinnerton-Dyer was still able to publish on average about one mathematics paper per year during this period. After 1991 he returned to full-time mathematical work in Cambridge and was able to devote more time to research, increasing his publication rate.

He has published two books, the first Analytic theory of abelian varieties (1974) was quite early in his career, while the second A brief guide to algebraic number theory (2001) was late in his career.
You can see some details about these two works at THIS LINK.

As a mathematician, Swinnerton-Dyer was broad in his interests and in his expertise. When discussing proof in his article The Justification of Mathematical Statements he wrote [43]:-
I am usually regarded as a number theorist, and therefore, as a pure mathematician of the most uncompromising kind. On the other hand, I also work at the more vulgar end of the study of ordinary differential equations; indeed for years I was the only pure mathematician in Cambridge who had a visa to enter the Department of Applied Mathematics. And for a substantial part of my career I was employed not as a mathematician but as a computer scientist. In these three roles, my attitudes to what should be regarded as a proof have been quite different.
His breadth as a mathematician was also demonstrated in his lecturing at Cambridge where he gave advanced courses on a wide variety of topics. His students regarded him as an outstanding lecturer.

Swinnerton-Dyer was elected a fellow of the Royal Society in 1967, succeeded his father as 16th baronet in 1975 and was knighted in 1987. He won the Sylvester medal of the Royal Society in 2006 [40]:-
For his fundamental work in arithmetic geometry and his many contributions to the theory of ordinary differential equations.
Also in 2006 he was awarded the Polya Prize by the London Mathematical Society.

He was made an Honorary Fellow of Worcester College, Oxford, in 1980, an Honorary Fellow of St Catharine's College, Cambridge in 1983, and an Honorary Fellow of Trinity College, Cambridge in 1983. He was awarded an Honorary DSc from the University of Bath in 1981; an Honorary DSc from the University of Wales in 1991; an Honorary ScD from the University of Ulster in 1991; an Honorary ScD from the University of Birmingham in 1992; an Honorary ScD from the University of Nottingham in 1992 and an Honorary LLD from the University of Aberdeen in 1991.

Alex May writes in [26]:-
Swinnerton-Dyer was known for his gregariousness, hospitality, interest in other people (including especially students), wry humour, and self-deprecatory wit as well as his fierce intelligence. For many years he lived with his wife, Harriet, in Thriplow, between Royston and Cambridge, where he enjoyed tending his garden.
Swinnerton-Dyer died at Thriplow on 26 December 2018 at the age of 91. A memorial service was held for Sir Peter Swinnerton-Dyer in the Trinity College Chapel, Cambridge on Monday 1 July 2019. A four-day meeting was hosted by the Isaac Newton Institute on 17-20 May 2021 to commemorate his achievements in number theory. Because of COVID-19, this was an online event.

You can read Swinnerton-Dyer's own description of his life, which he gave in an interview on 12 May 2008, at THIS LINK.
Other Mathematicians born in England
A Poster of Peter Swinnerton-Dyer

References (show)

  1. A tribute to Peter Swinnerton-Dyer (1927-2018), The Isaac Newton Institute for Mathematical Sciences (8 January 2019).
    https://www.newton.ac.uk/news/ini-news/a-tribute-to-peter-swinnerton-dyer-1927-2018/
  2. B Birch, J Coates, J-L Colliot-Thélène and A Skorobogatov, Peter Swinnerton-Dyer (1927-2018), Notices of the American Mathematical Society 66 (7) (2019), 1058-1067.
  3. B J Birch, J-L Colliot-Thélène, G K Sankaran, M Reid and A Skorobogatov, In lieu of Birthday Greetings, in M Reid and A Skorobogatov (eds.), Number Theory and Algebraic Geometry: to Peter Swinnerton-Dyer on his 75th Birthday (Cambridge University Press, 2003). 1-22.
    https://api.pageplace.de/preview/DT0400.9781139238724_A23867149/preview-9781139238724_A23867149.pdf
  4. Birch and Swinnerton-Dyer Conjecture, Clay Mathematics Institute (2025).
    https://www.claymath.org/millennium/birch-and-swinnerton-dyer-conjecture/
  5. B J Birch and H P F Swinnerton-Dyer, Notes on elliptic curves I, Journal für die Reine und Angewandte Mathematik 212 (1963), 7-25.
  6. B J Birch and H P F Swinnerton-Dyer, Notes on elliptic curves II, Journal für die Reine und Angewandte Mathematik 218 (1965), 79-108.
  7. Bridge experts met, Western Mail, Cardiff (5 November 1952), 7.
  8. J Campbell, Sir Peter Swinnerton-Dyer, Bridge Winners (4 January 2019).
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  9. B Christie, 'Anti-Scottish' remarks spark academic row, The Scotsman (Friday 19 May 1989), 9.
  10. M Deaves, Sir Peter: man for the 1980s, Cambridge Evening News (Thursday 27 September 1979), 21.
  11. Dons warned: You may have to take cuts in salaries, Cambridge Evening News (Thursday 1 October 1981), 9.
  12. J Duckers, Dons' Campaign 'Waste of Time', Press and Journal (Wednesday 3 June 1987), 1.
  13. P S Dyer, A solution of A4+B4=C4+D4A^4 + B^4 = C^4 + D^4, Journal of the London Mathematical Society 18 (1) (1943), 2-4.
  14. England's youngest international contract bridge players, Acton Gazette Ealing (27 October 1950), 1.
  15. H P F Swinnerton-Dyer, Polya Prize, London Mathematical Society (2025),
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  16. (Henry) Peter (Francis) Swinnerton-Dyer, Supplement to The London Gazette (Tuesday, 30 December 1986).
  17. A Jackson, Swinnerton-Dyer Receives Sylvester Medal, Notices of the American Mathematical Society 53 (9) (2006), 1062.
    https://www.ams.org/notices/200609/people.pdf
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  19. Lord Dyer's son honoured, Shropshire Star (Tuesday 7 February 1978), 3.
  20. J Lund, Remembering Sir Michael Atiyah and Sir Peter Swinnerton-Dyer, Cambridge Core blog (25 January 2019).
    https://www.cambridge.org/core/blog/2019/01/25/remembering-sirs-michael-atiyah-and-peter-swinnerton-dyer/
  21. C MacDonald, Gloom over campus cash, Press and Journal (Tuesday 23 June 1987), 1.
  22. C MacDonald, Double boost on university crisis, Press and Journal (Thursday 8 December 1988), 3.
  23. A Macfarlane, Peter Swinnerton-Dyer, YouTube (7 August 2025).
    https://www.youtube.com/watch?v=nwCiBTJPe3A
  24. A Macfarlane, Peter Swinnerton-Dyer, Interview Text (7 August 2025).
    https://www.alanmacfarlane.com/DO/filmshow/swinnerton-dyertx.htm
  25. Marriages, The Times (26 May 1983).
  26. A May, Dyer, Sir (Henry) Peter Francis Swinnerton- (1927–2018), Oxford Dictionary of National Biography (8 August 2024).
    https://doi.org/10.1093/odnb/9780198614128.013.90000380602
  27. J McLeish, Lectures' fury at attack on teaching, Evening Express (Friday 15 April 1988), 3.
  28. D McLeod, Facing up to the university challengers, The Scotsman (Tuesday 8 September 1987), 11.
  29. Memorial Service for Sir Peter Swinnerton-Dyer, The London Mathematical Society (2019).
    https://www.lms.ac.uk/news-entry/07052019-1358/memorial-service-sir-peter-swinnerton-dyer
  30. W Narkiewicz, Review: A brief guide to algebraic number theory, by H P F Swinnerton-Dyer, Mathematical Reviews MR1826558 (2002a:11117).
  31. Peter Swinnerton-Dyer, The English Bridge Union (2025).
    https://www.ebu.co.uk/biographies/peter-swinnerton-dyer
  32. Peter Swinnerton-Dyer, Academia Europaea (14 June 2021).
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  33. W Pickard, Ignorance beggaring belief, Scotland on Sunday (21 May 1989), 10.
  34. Professor Sir Peter Swinnerton-Dyer Bt DSc FRS*, University of Bath (2025).
    https://www.bath.ac.uk/corporate-information/honorary-graduates-1980-to-1989/
  35. Professor Sir Peter Swinnerton-Dyer Bt KBE FRS (1927-2018), St Catharine's College, Cambridge (Friday, 28 December 2018).
    https://www.caths.cam.ac.uk/about-us/news-and-events/professor-sir-peter-swinnerton-dyer-bt-kbe-frs-1927-2018
  36. Professor Sir Peter Swinnerton-Dyer, The Times (11 January 2019).
  37. Professor Sir Peter Swinnerton-Dyer, expert on number theory who was co-creator of the 'beautiful' Birch and Swinnerton-Dyer Conjecture - obituary, The Telegraph (31 December 2018).
  38. M Reid, Sir Peter Swinnerton-Dyer obituary, The Guardian (Wednesday, 9 January 2019).
  39. Sir Peter Swinnerton-Dyer, Honorary Graduates since 1985, Ulster University (2025).
    https://www.ulster.ac.uk/about/ous/committeeservices/honorary-graduates/honorary-graduates-conferred-since-1985
  40. Sir Peter Swinnerton-Dyer Bt KBE FRS, Sylvester Medal, The Royal Society (2025).
    https://royalsociety.org/medals-and-prizes/sylvester-medal/
  41. H P F Swinnerton-Dyer, A4+B4=C4+D4A^4 + B^4 = C^4 + D^4 revisited, Journal of the London Mathematical Society 43 (1968), 149-151.
  42. P Swinnerton-Dyer, Prospects for Higher Education, London Review of Books 3 (21) (1981).
  43. P Swinnerton-Dyer, The Justification of Mathematical Statements, Philosophical Transactions of the Royal Society: Mathematical, Physical and Engineering Sciences 363 (2005), 2437-2447.
  44. P Swinnerton-Dyer, Diophantine equations: Progress and problems, in B Poonen and Yu Tschinkel (eds.), Arithmetic of Higher-dimensional Algebraic Varieties (Birkhäuser, Boston, Cambridge, MA, 2004), 3-35.
    https://link.springer.com/content/pdf/10.1007/978-0-8176-8170-8_1.pdf
  45. Swinnerton-Dyer, Sir (Henry) Peter Francis, Bt, KBE, MA, FRS, International who's who 2004 (Europa, London, 2003), 1639.
  46. Ten years of 'pain', Aberdeen Evening Express (5 July 1991).
  47. F Urquhart, Voices of discontent as Sir Peter gets degree, Aberdeen Evening Express (6 July 1991).

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Written by J J O'Connor and E F Robertson
Last Update December 2025