# Erik Christopher Zeeman

### Born: 4 February 1925 in Japan

Died: 13 February 2016 in Woodstock, Oxfordshire, England

**Chris Zeeman**'s father Christian Zeeman was from Aarhus in Eastern Jutland, Denmark, while his mother was Christine Bushell. He spent the first year of his life in Japa n before his parents returned to England. His first memory of being fascinated by mathematics was when his mother showed him how to solve a problem when he was seven years old. The problem was: given a rectangle 3 by 4, what would be the dimensions of a rectangle inside the given one which was half the area and a left an equal width border all round. Chris still remembers his mother explaining how to solve it by introducing

*x*for twice the width of the border [3]:-

It was the one and only time he remembers discussing mathematics with his mother. Zeeman was educated at Christ's Hospital School in Horsham, West Sussex, England which he did not enjoy, feeling that it was a prison in which he lost his self-esteem. He served as a Flying Officer with the Royal Air Force from 1943 to 1947 [3]:-... it was a revelation to me.

Zeeman's university studies were at Christ's College Cambridge and at first he had to contend with the fact that he had forgotten much of his school mathematics while serving in the Royal Air Force. He received his B.A. from Cambridge and remained there to study for his doctorate under Shaun Wylie. He was awarded his Ph.D. in 1953 for his thesisI was a navigator on bombers, trained for the Japanese theatre, but that was cancelled because they dropped the atomic bomb a week before we were due to fly out. Since the death rate was60% in that theatre it probably saved my life, but at the time I was disappointed not to see action, although relieved not to have to bomb Japan, the land of my birth.

*Dihomology*but he spent the first year as a research student trying unsuccessfully to solve the 3-dimensional Poincaré Conjecture. Zeeman was then awarded a fellowship by Gonville and Cais College Cambridge in 1953. After being awarded a Commonwealth Scholarship he spent the year 1954-55 partly at the University of Chicago and partly at Princeton. Back at Cambridge, he was appointed a College Lecturer in 1955. In 1960 he married Rosemary Gledhill; they had three sons and two daughters. One of the daughters is a mathematician who has collaborated with her father.

During 1962-63 Zeeman was a member of the Institut des Hautes Études Scientifiques. Then in 1964 he made the biggest move of his life when he went to the new University of Warwick in Coventry. Warwick's first Vice-Chancellor Jack Butterworth invited him to become the Foundation Professor of Mathematics in 1963. Zeeman explained [1]:-

At Warwick he lead the setting up of the Department of Mathematics and the Mathematics Research Centre. He decided that the first six appointments he made would be topologists, then the next appointments would be algebraists. Those he initially invited, he encouraged to accept by telling them that the others had all accepted. When the University took in its first undergraduates in October 1965, it seemed as though mathematics at Warwick was already established with an international reputation. This was largely due to Zeeman's remarkable leadership.At first I said "no"; then changed my mind after a sleepless night. ... I had always thought that Cambridge was the centre of things, but I grew as a mathematician at Warwick.

Zeeman's style of leadership at Warwick was a very informal one. It produced an atmosphere in which mathematical research flourished. From 1964 Zeeman remained at Warwick until 1988, although he did spend 1966-67 as a visiting professor at the University of California at Berkeley. His research took a different turn as he explained [3]:-

From 1976 till 1981 he held a senior SERC fellowship which enabled him to concentrate on research. He also held a visiting fellowship at Oxford during 1985-86.During1968-69I learnt about dynamical systems during the Warwick Symposium we ran on the topic, when many of the world leaders including Smale and Thom spent time at Warwick. In the following year I spend a sabbatical with Thom at the Institut des Hautes Études Scientifiques in Paris, where I learnt all about catastrophe theory. So I was very fortunate to get in on the ground floor of such beautiful new subjects.

In 1988 Zeeman left Warwick, although he was made an honorary professor there on leaving. At this point he became Principal of Hertford College, Oxford, and Gresham professor of geometry at Gresham College London. He retired from this post at Gresham College in 1994 and from his position of Principal of Hertford College in 1995.

Zeeman has held important roles within UK mathematics. He served on the SERC Mathematics Committee from 1982 to 1985 and, in 1990, he chaired the committee which set up the Isaac Newton Institute in Cambridge. He continues to serve on the Steering Committee for the Isaac Newton Institute.

Zeeman's research has been in a variety of areas such as topology, in particular PL topology, dynamical systems and mathematical applications to biology and the social sciences. His initial research was in topology and one of his theorems was the unknotting of spheres in five dimensions. Certainly his work in topology would make him one of the leading topologists of all time but he may be known principally for other work.

Perhaps he is best known for his work on catastrophe theory for, although this theory was due initially to René Thom, it was Zeeman who brought it before the general public giving widespread publicity to applications of what was before that time thought of as pure mathematics. In particular Zeeman pioneered the applications of catastrophe theory in the biological and behavioural sciences, as well as the physical sciences. He invented the Zeeman Catastrophe machine which was a mechanical device to illustrate how a small perturbation can give rise to a discontinuous consequence.

Among the books which Zeeman has published are the texts *Catastrophe theory* (1977), *Geometry and perspective* (1987) and *Gyroscopes and boomerangs* (1989). One of his many memorable quotes, from his *Catastrophe theory* text, says much about mathematical philosophy:-

A shorter introduction to catastrophe theory than his 1977 book was given by Zeeman in his beautifully written survey articleTechnical skill is mastery of complexity while creativity is mastery of simplicity.

*Bifurcation and catastrophe theory*[Contemp. Math. (1981)]. The article introduces catastrophe theory in a unified way giving both elementary and non-elementary aspects. There is an elementary discussion of the cusp and the pitchfork and a statement of the classification theorem for elementary catastrophes. Asked what were the highlights of his own research he explained:-

In 1978, Zeeman gave the Christmas Lectures at the Royal Institution, out of which grew the Mathematics Master classes for 13-year old children that now flourishes in forty centres in the United Kingdom. He was the 63I suppose I am particularly fond of having unknotted spheres in5-dimensions, of spinning lovely examples of knots in4-dimensions, of proving Poincaré's Conjecture in5-dimensions, of showing that special relativity can be based solely on the notion of causality, and of classifying dynamical systems by using the Focke-Plank equation. And amongst my applications of catastrophe theory I particularly liked buckling, capsizing, embryology, evolution, psychology, anorexia, animal behaviour, ideologies, committee behaviour, economics and drama.

^{rd}President of the London Mathematical Society in 1986-88 and delivered the Presidential Address to the Society on 18 November 1988

*On the classification of dynamical systems*.

He was awarded the Senior Whitehead Prize of the London Mathematical Society in 1982. During his period as president of the Society, he became the Society's first Forder lecturer in 1987. Elected to the Royal Society of London in 1975, he was awarded the Societies' Faraday Medal in 1988.

Zeeman was knighted in 1991 and he has received many honours in addition to those mentioned above. He has been awarded honorary degrees from many universities including Strasbourg (1974), Hull (1984), Warwick (1988), York (1988), Leeds (1990), Durham (1990) and Hartford (1992).

I [EFR] first met Chris Zeeman in 1965 when I went to Warwick as a postgraduate student. He leapt out of his office to greet the new postgraduates with "Hi, I'm Chris". He is an exceptional lecturer with a remarkable ability to convince his audience that they understand the deep concepts that he is explaining, either in a research seminar of talking to non-mathematicians.

The first year that Warwick opened for undergraduates, all the undergraduates and postgraduates could get into one lecture theatre. There was a course covering all aspects of study including arts, science and mathematics. Chris Zeeman gave the mathematics lectures and explained to an audience, most of whom had no more than a low level school mathematics qualification, knotting and unknotting spheres in high dimensions. The remarkable thing was that everyone said they understood what he was talking about!

Let us end by giving Zeeman's views on a few topics. First when asked about the value of mathematical education he replied that:-

When asked whether he regards mathematics as an art or a science, he replied [1]:-... vocational apprenticeship to the profession of mathematical teaching needs discipline if the student is to master the necessary techniques. And such discipline needs to be taught, needs specialists to teach it, and needs to be supported by research on curriculum reform and the analysis of learning techniques.

Did he consider himself a mathematician or a scientist:-Both. Sometimes you invent it; sometimes you discover it. You have to invent maths to get a solution to a problem but, in the process, I often discover a whole lot more which I didn't expect.

In [1] Arnot writes about Zeeman's interests outside mathematics:-I ... occupied a position halfway between mathematics and science. I wanted to get my hands dirty, and make predictions, and get the experimentalists to test them, because I knew that the scientific community would never take a theory seriously unless it was capable of being tested experimentally. And I was gratified that several of my predictions were confirmed. Some were refuted, and others remain to be tested.

On 2 October 2006 the London Mathematical Society and the Institute of Mathematics and its Applications announced that the 2006 David Crighton Medal for services to Mathematics and to the Mathematics Community was to be awarded to Professor Sir Christopher Zeeman, F.R.S.:-Fine wines are among his pleasures. Fine music and fine art, too. Classical CD collections occupy the few shelves not crammed with tomes on Catastrophe Theory and other pet subjects. Works by Vermeer and Velasquez share a window ledge with a spherical jigsaw, above which dangles a chain made up by nine pairs of spectacles.

The announcement contained a more detailed summary of the reasons that the award was being made. It begins by describing his research contributions in a similar way to what we have written above, and goes on to explain his brilliant achievement setting up mathematics at the University of Warwick. The announcement continues:-... in recognition of his long and distinguished service to mathematics and to the mathematical community in all areas - in research, to mathematics in higher education, to the mathematical societies, and in outreach activities with schools and the public.

On 24 April 2007 Zeeman delivered his David Crighton Award lectureAs chair of the Mathematics Committee of SERC he created the Nonlinear Systems Initiative which went on to become the Applied Nonlinear Systems Initiative. He created HoDoMS - the committee that represents mathematics departments. He chaired the inaugural Scientific Committee of the Newton Institute that oversaw its creation and chose the programmes during its first ten years. He is a past-President of the London Mathematical Society(1986-88)and received the Senior Whitehead Prize of the Society in1982.

He was a pioneer in the area of public engagement with mathematics, and has a strong involvement with school mathematics. As early as1967he was speaking on(the then)BBC Third Programme on topics such as topology. He delivered the1978Royal Institution Christmas Lectures on BBC television - the first time in the150-year history of these lectures, founded by Michael Faraday, that the topic was mathematics. These lectures led Sir Christopher to start the Royal Institution Mathematics Masterclasses for talented young people. He was Gresham Professor of Geometry from1988to1994, delivering an annual series of public lectures. For his work in the public understanding of science he received the prestigious Royal Society Faraday Medal in1988. He served as the President of the Mathematical Association in2003-04, a post to which he brought his customary enthusiasm and ideas, ensuring that the power and beauty of mathematics is at the heart of mathematics education, and that the wider public should have inspirational opportunities to experience this for themselves.

*What's wrong with Euclid Book V*to an audience at the Royal Statistical Society. The London Mathematical Society and the Institute of Mathematics and its Applications further honoured Zeeman by creating the Christopher Zeeman Medal:-

Naming the award for Zeeman was particularly appropriate for a number of reasons: he was first mathematician to deliver the Royal Institution's Christmas Lectures; and his 'Mathematics into Pictures' series is recognised as significantly influencing to young mathematicians. The first award was made in 2008 when Zeeman presented the Christopher Zeeman Medal to Professor Ian Stewart, FRS.... to recognise and acknowledge the contributions of mathematicians involved in promoting mathematics to the public and engaging with the public in mathematics in the UK, and demonstrate that such activities are valued by the societies and the mathematical community at large and are a part of a mathematician's roles and responsibilities.

**Article by:** *J J O'Connor* and *E F Robertson*

**September 2009**

**MacTutor History of Mathematics**

[http://www-history.mcs.st-andrews.ac.uk/Biographies/Zeeman.html]