Nigel James Hitchin

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2 August 1946
Holbrook, Derbyshire, England

Nigel Hitchin is a British mathematician who has made many contributions to geometry and mathematical physics. He has won many awards including the Pólya Prize and the Shaw Prize.


Nigel Hitchin was born in Holbrook but grew up in nearby Duffield, which is about 5 km north of Derby. His father was an industrial chemist who worked at the British Celanese chemical factory at Spondon, just to the east of Derby. British Celanese was founded 1916 and became a subsidiary of Courtaulds in 1957. Nigel's father had worked there from the time he left school, but after he marriage, his wife persuaded him to study for an external London University degree. Nigel's mother, the daughter of a baker, had left school at fourteen and helped in her father's bakery until her marriage. Nigel attended the local Duffield primary school but even before that his brother, who was four year older than him, had taught him to read.

In 1957, when he was eleven years old, Nigel entered Ecclesbourne School. This secondary school opened in Duffield in the year Nigel began his studies there. The headmaster of the school was Donald Redfearn, who was a rugby fanatic, so the boys played rugby, not soccer. In [12] we learn about Redfearn from one of Hitchin's fellow pupils:-
Our headmaster was Mr Redfearn, known from a fairly early stage as 'the Beak' because of his dictatorial and magisterial manner. He was a formidable creature and a strict disciplinarian who imposed his will with a rod of iron on pupils and teachers alike. To his credit, he wanted everyone to achieve high standards; in fact, it went beyond that. He wanted the school to quickly move into the big league of academia. From day one, 'the Beak' introduced a timetable of 40, 40-minute lessons per week and homework built up from a gentle half hour per evening in year one to a burdensome three hours per night in the sixth form.
In his first year at Ecclesbourne School, Hitchin was taught mathematics by the French teacher and the PE teacher. Things improved markedly in Hitchin's second year when Norman Else (1932-2023) was appointed to teach mathematics. He had graduated with a degree in mathematics from the University of Nottingham in 1953 and was keen to answer pupils' questions. Although mathematics was one of Hitchin's favourite subjects throughout his school studies, he expected to go on to have a career in engineering. At the start of his sixth form, however, he had a major appendix operation, missed time at school and dropped one of his intending A-levels, deciding to concentrate on mathematics and physics. That meant that he would apply to study mathematics at university.

Donald Redfearn, the Ecclesbourne School headmaster, was ambitious and wanted to see as many of the first intake into the school win places at Oxford or Cambridge. Redfearn himself was a mathematician who, in the 1930s, he been offered a place to study mathematics at Jesus College, Oxford, but lacked the financial support to accept. He was keen that Hitchin should apply to study mathematics at Jesus College, Oxford, motivated, perhaps, at his own sadness at having to turn down a place there. On the basis of his A-level results, Hitchin was offered a place at Jesus College to start in October 1964. Following advice given at his interview, he decided to take the scholarship examinations and delay entry for a year. He returned to Ecclesbourne School but, when informed that he was awarded an Open Scholarship in December 1964, he immediately left the school and decided to spend the first nine months of 1965 gaining some work experience and earning some money.

The Rolls Royce Engineering Company opened its factory in Derby in 1908. There the Merlin engine which powered both the Spitfire and Hurricane planes during World War II were designed and built. Rolls Royce was one of the largest employers in Derby and was a natural choice for Hitchin to look for his 'gap year' employment. Donald Redfearn contacted the company and, after being interviewed, Hitchin was given a job as a trainee programmer in the Engineering Computing Department. In the interview [23] Hitchin said:-
I learned Fortran and I was given various jobs. The skills needed were organisational and combinatorial: for example, finding a pattern of mixing nozzle guide vanes in a jet engine to avoid the natural frequency of the turbines, without using months of computer time: I knew nothing of Fourier analysis at the time, but eventually realised why I was doing this.
I also absorbed too much pie and chips in the canteen, and put on a lot of weight! I returned for a couple of periods of vacation work and they told me that there would always be a job for me if I wanted one after graduation. When things got difficult as a research student I considered it, but by then I really wanted to widen my horizons and not return to Derby.
In October 1965 Hitchen became a resident of Jesus College, Oxford, in a comfortable, reasonably warm room overlooking Ship Street. He was one of eight first year mathematics students entering Jesus College that year. At the College there were two mathematics tutors, Edward Crossley Thompson (1919-1991) and Christopher J Bradley (1938-2013).

Christopher Bradley was a popular and effective Fellow and Tutor in Mathematics at Jesus College from 1964 to 1977, after which he entered school teaching, notably at Clifton College, near Bristol. For many years he served as Deputy Leader of the British Mathematical Olympiad team and as Secretary of the British Mathematical Olympiad Committee. He produced elegant Olympiad problems. Hitchin said [23]:-
Bradley was happy to give more individual attention. I liked his approach to applied mathematics, which was very clean, and he introduced me, for example, to tensors. He was happy to give up time to explain things outside the syllabus.
Edward Thompson had studied mathematics at New College Oxford from 1937 to 1940, and then undertook decoding work at Bletchley Park during World War II. He was Fellow and Mathematics Tutor of Jesus College from 1945 to 1986. He tutored pure mathematics [23]:-
Thompson's attitude was one of bringing your unsolved problems to him, and in a cloud of pipe smoke he would outline a solution.
In Hitchin's first year, Oxford University experimented with starting the mathematics course with top lecturers giving demanding courses. Michael Atiyah taught the algebra course going through material very quickly, starting with set theory and reaching Galois groups by the end of the term. Charles Coulson taught applied mathematics and John Hammersley taught analysis. Hammersley caused difficulties since his problem sheets were very difficult so even college tutors were struggling and phoning each other up for help. Hitchin enjoyed this challenging start, but most students gave up. As his undergraduate studies progressed, Hitchin found there were courses he liked and those he did not. For example he did not like probability and statistics, and so avoided these topics. He did a little fluid dynamics but then gave it up. Eventually he found that he loved the courses on topology, algebraic geometry, commutative algebra and functional analysis. In his final year Brian Steer gave him tutorials in topology and differential geometry. He gradually came to feel that these were the topics for him. He graduated with a BA with First Class Honours in Mathematics in 1968 and was awarded an Oxford University Junior Mathematical Prize. It is worth noting at this point that, although Hitchin has made outstanding contributions to research on the boundary between mathematics and theoretical physics, he never took any applied mathematics or physics courses during his undergraduate studies - in fact he actively avoided them.

Hitchin began his graduate studies at Jesus College, with Brian Steer at Hertford College as his advisor. Brian Steer had graduated from the University of Oxford with a D.Phil. on algebraic topology in 1961 having been advised by John Henry Constantine Whitehead and Ioan Mackenzie James. Steer had been a member of the Institute for Advanced Study at Princeton from September 1962 to April 1963 before returning to Hertford College Oxford. Hitchin took graduate courses and was awarded a Diploma in Advanced Mathematics in 1969. His attempts to find the right research topic, however, did not go well at first. Warwick University was running a year long Symposium on Differential Equations and Dynamical Systems with a Summer School in July 1969. Hitchin attended the Summer School with the thoughts that Dynamical Systems might be a good research topic but it did not appeal to him. Steer suggested he look at a K-theory problem but he made little progress, then he was given a paper by André Lichnerowicz about the Dirac operator. After reading papers on the Atiyah-Singer index theorem, he found an extension of Lichnerowicz's results which formed the basis of the dissertation required to transfer to the D.Phil. degree.

After this year of graduate studies at Jesus College, in 1969 he moved to Wolfson College, Oxford. When he started producing results which Steer thought would interest Atiyah he asked Atiyah if he would supervise Hitchin while he (Steer) was on sabbatical leave for a term. After Steer returned to Oxford, Hitchin continued to be informally supervised by Atiyah. This was not too easy since Atiyah was not based in Oxford at this time but on the Faculty of the Institute for Advanced Study at Princeton but returned to Oxford each summer. Hitchin said [23]:-
Supervisions were very lively, with Atiyah offering suggestions, sketching out the background on the blackboard, informing me about the essentials of a subject and not asking me to get a book to read about it. It was difficult to recall everything and to try and write it down afterwards, but it was an amazing experience.
Atiyah was on the Faculty of the School of Mathematics at the Institute for Advanced Study at Princeton and, in 1971, Hitchin moved to Princeton as Atiyah's research assistant. He continued to work on his Oxford D.Phil. and was awarded the degree in 1972 for his thesis Differentiable Manifolds: The Space of Harmonic Spinors. The paper [16], Harmonic Spinors, published in 1974, was based on this thesis. For an extract from the Introduction to that paper, see THIS LINK.

Hitchin was two years at Princeton as Atiyah's assistant. Shing-Tung Yau was at Princeton for part of this time and they had many useful discussions about the Calabi Conjecture. While at Princeton he met Nedda who was visiting the Institute for Advanced Study because her cousin was a visitor there. Nigel and Nedda Hitchin married in 1973 and they moved to New York where Nedda was studying. Hitchin spent a year as an Instructor at the Courant Institute, New York University. He writes in [5]:-
At New York University I began reading the papers of Roger Penrose on zero rest-mass field equations in relativity.
The American Mathematical Society held a Differential Geometry Symposium at Stanford University in California from 30 July to 17 August 1973. Hitchin contributed the paper On the curvature of rational surfaces which was published in the Proceedings of the Symposium. In the paper he found certain rational surfaces which admit a Hodge metric of positive scalar curvature.

In 1974 he came back to Oxford with his wife and for the next three years was a Science Research Council Research Assistant at Oxford University and a Junior Research Fellow at Wolfson College. When this ended in 1977 he was awarded a Science Research Council Advanced Research Fellowship at Oxford University, and was a Research Fellow at Wolfson College. He held these positions until 1979. He writes [5]:-
When I returned to Oxford as a postdoc the following year Penrose had recently been appointed to a Chair and I began to learn that, through his newly-developed twistor theory, the Riemannian geometry I was interested in and the geometry of relativity were both put on the same footing. It meant that questions about Einstein's equations which were occupying me at the time made sense in this new setting. This was perhaps the first occasion I realised that there was an interface between my own interests and physics which I could exploit.
Hitchin was looking at these questions when Isadore Singer came from the Massachusetts Institute of Technology to spend a term in Oxford. He was working on a problem on instantons (Euclidean versions of the Yang-Mills equations of particle physics) which, although it dealt with concepts that Hitchin was looking at, asked quite different questions. Physicists had constructed some solutions to the problem that Singer was working on but there was much to be done. Hitchin became involved since he had relevant ideas from looking at Penrose's zero rest-mass field equations in relativity but had never written them up as a paper. The outcome was the 2-page paper Deformations of instantons (1977) with Atiyah, Hitchin and Singer as co-authors. This was Hitchin's fourth paper and the first of eight which he co-authored with Atiyah. This paper only announced results without giving details of proofs. These were given in the 37-page paper Self-duality in four-dimensional Riemannian geometry (1978) with the same three co-authors. This 1978 paper did more than give full details of the results announced in the previous paper, for it also gave an account of the Penrose transform in the Riemannian setting.

Atiyah and Hitchin continued to work together on the construction of instantons and made a breakthrough described by Atiyah in [3]:-
I would like to mention our work on instantons which became known as the ADHM construction (M F Atiyah, V G Drinfeld, N J Hitchin and Yu I Manin, Construction of instantons, 'Phys. Lett. A' 65 (1978), 185-187). One morning, after a long struggle, we finally saw the light. We adjourned to lunch in St Catherine's College euphoric at our success, though post‐prandial analysis often punctures premature celebration. On this occasion there was no unseen error but instead there was a letter from Manin informing us that he and Drinfeld had just reached the same conclusion! This was the genesis of the four‐author paper and it was some years later before Nigel or I met Drinfeld.
This is now known as the ADHM (Atiyah-Hitchin-Drinfeld-Manin) construction of instantons. Hitchin received many invitations to speak about the ADHM construction and made many visits to give lectures. This, he remarked, was unfortunate for his wife Nedda since their first child was born around this time.

For the next eleven years, 1979-1990, Hitchin was a Fellow and Tutor in Mathematics and a Common University Fund Lecturer at St Catherine's College, University of Oxford. This was a major change for him since he had held research positions up to this time. The teaching duties were heavy even though St Catherine's College tried to ease them a little. He explained [23]:-
I worked in the Mathematical Institute in the mornings and often, since Michael Atiyah was a professorial fellow at the same college, we would walk together across the University Parks from the Institute for lunch and exchange ideas then. The constraints I felt were more that teaching time took away the opportunity to go to seminars or conferences, both in Oxford and elsewhere.
In 1990 Atiyah left Oxford to become Master of Trinity College, Cambridge. Warwick University was advertising to fill the position which became vacant when Christopher Zeeman left to become Principal of Hertford College, Oxford. Hitchin felt that it was time for a change and applied for the chair at Warwick. He took up the chair at Warwick in 1990 and became involved in dealing with departmental issues which he had avoided up to that time. He was also slightly surprised to find that he had to give tutorials as well as lectures. There were, however, many positive things for him being in a friendly and very active environment. His election as a fellow of the Royal Society of London in 1991 involved him in committee work so, when it was suggested to him that he should apply to become Rouse Ball Professor of Mathematics at Cambridge University following the retirement of John Thompson, he took the opportunity.

In 1994 Hitchin was appointed Rouse Ball Professor of Mathematics at the University of Cambridge and as a Professorial Fellow at Gonville and Caius College. He was only there for three years since the position for the Savilian Professor of Geometry at Oxford University became vacant. Ioan James had retired as the Savilian Professor of Geometry in 1995 and Richard Taylor was appointed to fill the vacant chair on 1 October 1995. After one year, Richard Taylor moved to the United States when he was appointed as a Professor at Harvard University and in 1997 Hitchin was appointed as Savilian Professor of Geometry at the University of Oxford and a Professorial Fellow at New College.

During September 2005 he was appointed as a Clay Senior Scholar to participate in 'Mathematical Aspects of String Theory' at the Kavli Institute for Theoretical Physics which is a research institute of the University of California, Santa Barbara.

To celebrate Hitchin's 60th birthday, a conference took place at the Consejo Superior de Investigaciones Científicas in Madrid during the week of 4-8 September 2006. The book [43] is the Proceedings of that conference. The Publisher's information about the book includes the following:-
Nigel Hitchin's mathematical influence has been enormous, and his work is frequently cited in widely different branches of mathematics. In accordance with the book's title, his work concerns not just differential geometry, but strikes at the heart of algebraic geometry, complex analysis, Lie groups, as well as abstract algebra and topology. The present contributions reflect his work on four‐manifolds, monopoles and instantons, Nahm's equations, hyperkähler manifolds, Higgs bundles, integrable systems, the geometrical structure of moduli spaces, gerbes, harmonic forms, reduced holonomy, special Lagrangian submanifolds, and generalised complex structures. Still this list is not exhaustive ...
The book contains the paper [3] by Michael Atiyah on Hitchin's mathematical work. It begins:-
It was a great pleasure for me to take part in the 60th birthday celebration for Nigel Hitchin. I have known him ever since he was a graduate student in Oxford and subsequently as my assistant at the institute in Princeton and then as a colleague and collaborator. I have watched him mature mathematically over the years and gradually establish a unique niche for himself on the frontier between differential geometry and theoretical physics. This is now a very popular and active field but Nigel occupies a singular place in it by virtue of the many important and beautiful ideas he has introduced.

It has been said that the real measure of a mathematician's contribution is how long it would have taken the community to discover these results in his absence. In Nigel's case it is clear that he would score highly by this criterion, since many of his results have been somewhat neglected on their first appearance and their significance has only become apparent some years later.

Nigel has a large output with many beautiful papers which deserve to be read and re‐read.
In [15] Hitchin gives an overview of his work. A more general look at the interactions of geometry and physics is contained in the paper [4] by Michael Atiyah, Robbert Dijkgraaf and Nigel Hitchin. For an extract from this paper, see THIS LINK.

Hitchin has received many awards for his remarkable contributions. These include: the Junior Whitehead Prize (1981):-
... for his work in Differential Geometry;
the Senior Berwick Prize (1990):-
... for his paper 'The self-duality equations on a Riemann surface' (1987);
the Royal Society of London's Sylvester Medal (2000):-
... for his important contributions to many parts of differential geometry combining this with complex geometry, integrable systems and mathematical physics interweaving the most modern ideas with the classical literature;
the Pólya Prize (2002):-
... for his fundamental and enormously influential contributions to geometry, as well as for his wider contributions to the development of mathematics and mathematical physics;
and the Shaw Prize in Mathematical Sciences (2016):-
... for his far-reaching contributions to geometry, representation theory and theoretical physics. The fundamental and elegant concepts and techniques that he has introduced have had wide impact and are of lasting importance.
For more information on all five of these awards, see THIS LINK.

We mentioned above that Hitchin was elected a fellow of the Royal Society of London in 1991. He was also elected an Ordinary Member of the Academia Europaea (Academy of Europe) in 1993, and a Fellow of the American Mathematical Society in 2013.

Hitchin published two books, the first being Monopoles, minimal surfaces and algebraic curves (1987). Krzysztof Galicki writes in the review [10]:-
The volume under review is based on lectures that Nigel Hitchin gave at the University of Montreal in 1985. Its purpose is to provide a unifying framework for a number of different nonlinear differential equations: from the four-dimensional self-dual Yang-Mills equations through the monopole and the vortex equations to harmonic maps of a 2-torus into the Lie group. All of these equations are of interest to those engaged in many areas of modern physics.
The second book, jointly authored with Michael Atiyah, is based on the Milton Brockett Porter Lectures which Atiyah delivered at Rice University in January 1987. Atiyah writes in the Preface:-
This provided me with the opportunity of presenting, at some length, the results on magnetic monopoles which Nigel Hitchin and I have been investigating over the past few years. This book, written jointly, is an expanded version of the lectures and it contains a full and detailed treatment of the essentially new results. Although dependent on earlier work by many authors we have endeavoured to make it more self-contained by adding some introductory and background material.
For more information about these two books, see THIS LINK.

In September 2016 three events were organised to celebrate Hitchin's 70th birthday. The first was a workshop on 'Differential Geometry and Quantization', held at the Centre for Quantum Geometry of Moduli Spaces, Aarhus University, followed by a meeting at the Mathematical Institute, University of Oxford, then finally a workshop on 'Celebrating 30 years of Higgs bundles and 15 years of generalized geometry' held at the Instituto de Ciencias Matemáticas, Madrid [14]:-
The workshops in Aarhus and Madrid provided a unique opportunity for researchers and current PhD students to learn about recent exciting developments and exchange ideas in some of the areas most closely associated with Hitchin's name and most influenced by his work. The speakers at the Oxford event included towering figures in mathematics whose own research has been influenced by Hitchin's.

References (show)

  1. About the Laureates: Nigel Hitchin, The Shaw Prize Lecture in Mathematical Sciences 2016, The Shaw Prize (31 May 2016).
  2. An Essay on the Prize, The Shaw Prize Lecture in Mathematical Sciences 2016, The Shaw Prize (27 September 2016).
  3. M Atiyah, Mathematical work of Nigel Hitchin, in Jean Pierre Bourguignon, Oscar Garcia-Prada and Simon Salamon (eds.), The Many Facets of Geometry: A Tribute to Nigel Hitchin (Oxford University Press, Oxford, 2010), 11-16.
  4. M Atiyah, R Dijkgraaf and N Hitchin, Geometry and physics, in Philosophical Transactions: Mathematical, Physical and Engineering Sciences 368 (1914), Personal perspectives in the physical sciences for the Royal Society's 350th anniversary (13 March 2010), 913-926.
  5. Autobiography of Nigel J Hitchin, The Shaw Prize Lecture in Mathematical Sciences 2016, The Shaw Prize (27 September 2016).
  6. Conference: Hitchin 70 (Aarhus), Centre for Quantum Geometry of Moduli Spaces, Aarhus University (24 November 2025).
  7. Congratulations to Nigel Hitchin, winner of the 2016 Shaw Prize in Mathematical Sciences, Simons Center for Geometry and Physics (31 July 2016).
  8. Contribution of Nigel J Hitchin, The Shaw Prize Lecture in Mathematical Sciences 2016, The Shaw Prize (31 May 2016).
  9. Curriculum Vitae, Nigel James Hitchin, The Academy of Europe.
  10. K Galicki, Review: Monopoles, minimal surfaces and algebraic curves, by Nigel Hitchin, American Scientist 78 (6) (1990), 574.
  11. Geometry Conference: 50 years of Nigel Hitchin's Mathematics, Institute of the Mathematical Sciences of the Americas, University of Miami (December 2023).
  12. J Goddard, Diamond milestone for school made in image of visionary headmaster, Derby Telegraph (14 August 2017).
  13. P R Goody. 1981 Prizes, London Mathematical Society Newsletter 82 (October 1981), 1.
  14. Hitchin 70, Clay Mathematics Institute (September 2016).
  15. N Hitchin, Geometry and physics: a personal view, in Jean Pierre Bourguignon, Oscar Garcia-Prada and Simon Salamon, The Many Facets of Geometry: A Tribute to Nigel Hitchin (Oxford University Press, Oxford, 2010), 1-10.
  16. N Hitchin, Harmonic Spinors, Advances in Mathematics 14 (1974), 1-55.
  17. J Hurtubise Review: The geometry and dynamics of magnetic monopoles, by Michael Atiyah and Nigel Hitchin, American Scientist 77 (3) (1989), 296-297.
  18. M Itoh, Review: Monopoles, minimal surfaces and algebraic curves, by Nigel Hitchin, Mathematical Reviews MR0935967 (89h:58043).
  19. E Kehoe, Hitchin Awarded Shaw Prize, Notices of the American Mathematical Society 63 (8) (2016), 940-941.
  20. G M Khenkin, Review: The geometry and dynamics of magnetic monopoles, by Michael Atiyah and Nigel Hitchin, Mathematical Reviews MR0934202 (89k:53067).
  21. C LeBrun, Review: The geometry and dynamics of magnetic monopoles, by Michael Atiyah and Nigel Hitchin, American Scientist 78 (1) (1990), 70-71.
  22. M Mazzocco, Hitchin wins Shaw Prize, Mathematics Today (August 2016), 161.
  23. M McCartney, Interview with Nigel Hitchin, in Robin Wilson (ed.), Oxford's Savilian Professors of Geometry (Oxford University Press, Oxford, 2022), 207-220.
  24. Nigel Hitchin, Clay Mathematics Institute (2024).
  25. Nigel Hitchin: Fellow, The American Mathematical Society.
  26. Nigel Hitchin, Academia Europaea.
  27. Nigel Hitchin, The Royal Society.
  28. Nigel Hitchin, University of Oxford.
  29. Nigel Hitchin and Ngô Bao Châu Laboratory, Instituto de Ciencias Matemáticas, Madrid, Spain (2021).
  30. Nigel Hitchin reflects: Interview with Martin Bridson,
  31. Nigel Hitchin awarded Honorary Doctorate by Warwick University, Mathematical Institute, University of Oxford (14 August 2014).
  32. Preface, in Jean Pierre Bourguignon, Oscar Garcia-Prada and Simon Salamon, The Many Facets of Geometry: A Tribute to Nigel Hitchin (Oxford University Press, Oxford, 2010).
  33. Prof Nigel Hitchin, Mathematical Institute, University of Oxford.
  34. Professor Nigel Hitchin BA (Oxford) DPhil (Oxford) FRS, Gonville & Caius, University of Cambridge.
  35. Professor Nigel Hitchin's Commendation Video Transcript, The University of Derby (July 2023).
  36. Professor Nigel Hitchin FRS: Commendation, The University of Derby (July 2023).
  37. Publications of Nigel Hitchin, University of Oxford.
  38. Research Students of Nigel Hitchin, University of Oxford.
  39. Savilian Professor Nigel Hitchin reflects, Mathematical Institute, University of Oxford (20 October 2016).
  40. C Series, Oration for Nigel Hitchin awarded Honorary Doctorate by Warwick University, University of Warwick (Friday 18 July 2014).
  41. R Y Sharp, LMS 1990 Prizes, London Mathematical Society Newsletter 174 (July 1990), 1.
  42. R S Ward, Review: The geometry and dynamics of magnetic monopoles, by Michael Atiyah and Nigel Hitchin, Bulletin of the American Mathematical Society 20 (2) (1989), 230-231.
  43. J P Bourguignon, O Garcia-Prada and S Salamon (eds.), The Many Facets of Geometry: A Tribute to Nigel Hitchin (Oxford University Press, Oxford, 2010).

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Written by J J O'Connor and E F Robertson
Last Update March 2024