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.

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.

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.

Thompson's attitude was one of bringing your unsolved problems to him, and in a cloud of pipe smoke he would outline a solution.

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.

At New York University I began reading the papers of Roger Penrose on zero rest-mass field equations in relativity.

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.

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.

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.

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 ...

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.

... for his work in Differential Geometry;

... for his paper 'The self-duality equations on a Riemann surface' (1987);

... 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;

... for his fundamental and enormously influential contributions to geometry, as well as for his wider contributions to the development of mathematics and mathematical physics;

... 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.

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.

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.

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.