At the Chalkdust issue 06 launch party, we brought along a challenge for our guests: we connected two people up with ropes and challenged them to separate themselves. To make things interesting, they weren’t allowed to remove the ropes from their hands, cut the ropes or untie the knots. Although the trick is 250 years old, it was made popular by Sir Erik Christopher Zeeman who used it as an interactive way to demonstrate topology, hence the challenge became known as Zeeman’s ropes.
Erik Christopher Zeeman was born in 1925 in Japan to a Danish father, Christian Zeeman, and a British mother, Christine Bushell. A year after his birth they moved to England. Zeeman was educated at Christ’s Hospital, an independent boarding school in Horsham, West Sussex. He did not enjoy the experience, feeling it was a prison in which he lost his self-esteem.
In 1943–1947, Zeeman served in the RAF as a flying officer. In his own words:
“I 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 was 60% 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.”
During his service, Zeeman forgot much of his school maths. But this didn’t stop him from going on to study maths at Christ’s College, Cambridge, where he earned his MA.
Zeeman stayed on in Cambridge for his PhD, in which he wrestled with unknotting spheres in 5 dimensions, spinning knots in 4 dimensions, as well as trying (and failing) to solve the Poincaré conjecture (which would only be resolved in 2005 by Gregori Perelman). He was supervised by Shaun Wylie, who had worked with Alan Turing at Bletchley Park during the war on projects including deciphering a German teleprint cipher called Tunny.
In 1963, Zeeman was invited to join the newly established University of Warwick as the foundation professor of mathematics. He initially declined, since he believed Cambridge to be “the centre of the mathematical world”. However, after “a sleepless night”, Zeeman changed his mind and made the biggest move of his life in 1964.
At Warwick, Zeeman was determined to “combine the flexibility of options that are common in most American universities, with the kind of tutorial care to be found in Oxford and Cambridge”. Initially, he recruited lecturers in three main branches of mathematics: analysis, algebra and topology. Legend has it that those he invited to Warwick all declined their offer; his response was to encourage them by telling them that all the others had accepted his invitation. Later on, Zeeman also appointed six lecturers in applied mathematics.
His leadership style was informal, which helped produce an atmosphere in which mathematical research flourished. By the time Warwick accepted its first students in October 1965, the department was already competing with other universities at an international level. The glass building it is now housed in is named after Zeeman in honour of his tremendous effort in founding the department.
Zeeman left Warwick in 1988, and was made an honorary professor there upon his departure. He moved on to become the principal of Hertford College, Oxford and Gresham professor of geometry at Gresham College, London. He retired from these two positions in 1995 and 1994 respectively.
From 1966 to 1967, Zeeman was a visiting professor at the University of California, Berkeley. Shortly after his return to Warwick, a dynamical systems symposium was held, attended by many of the world leaders in dynamical systems, including Stephen Smale and René Thom. They inspired his change of discipline from topology to dynamical systems, and prompted Zeeman to spend a sabbatical with Thom in Paris, where he grew fascinated with what came to be known as catastrophe theory.
He is famous for inventing a catastrophe machine, consisting of a circular disc that can rotate freely about its centre, and two elastic bands of identical length attached on the edge of the disc The other end of one piece of elastic is fixed, while that of the second elastic is free to move on the plane. Zeeman’s machine has some surprising behaviour: as the free end moves around, the disc would do something unexpected: it flips to a drastically different position. The flipping action is a vivid example of a catastrophe: a discontinuous effect resulting from a continuous change of forces. You can plot the set of points at which the disc flips, called the bifurcation set, which takes on a diamond-like shape consisting of four concave edges and four cusps.
According to Hirsch, Zeeman once tried to take his machine with him to the USA. As soon as he mentioned the name of his machine, US customs cleared the room and had Zeeman arrested!
Zeeman played a huge role in making catastrophe theory a hot topic in the 70s. He was keen to apply it in numerous contexts such as nerve impulses, the collapse of bridges, stock markets and even prison riots. On returning to Warwick, he taught a course in catastrophe theory for undergraduates, which soon became extremely popular.
Outreach and the Royal Institution
Zeeman was not only passionate about his research, he was also heavily engaged in promoting mathematics to the general public. He was the first mathematician to present the Royal Institution Christmas lectures, in 1978. Going by the title of Mathematics into pictures and including a mix of pure and applied mathematics, Zeeman inspired his live audience with the aid of various demonstrations, including his own catastrophe machine. His lectures sparked plenty of enthusiasm; among the live audience was Marcus du Sautoy, a budding young mathematician who would go on to deliver his own Christmas lectures in 2006.
But that was not the only result from Zeeman’s Christmas lectures—they also served as the inspiration behind the Royal Institution masterclasses for both mathematics and engineering. Starting from 1981, the masterclasses were designed to inspire keen schoolchildren across the UK. When I attended them as a schoolgirl in 2005, I had no idea about the history behind the masterclasses at the time!
Awards and positions
In 1975, Zeeman was elected a fellow of the Royal Society and was president of the London Mathematical Society (LMS) from 1986 to 1988. He also took up many other positions and received various awards—too many to list in one article.
Zeeman was knighted in 1991 for his “mathematical excellence and service to British mathematics and mathematics education”. More recently, the Institute of Mathematics and its Applications (IMA) and the LMS jointly set up the Zeeman medal in his honour to recognise those who “have excelled in promoting mathematics and engaging with the general public”. And you don’t have to be a seasoned professor to earn the medal—the 2016 Zeeman medal was won by author Rob Eastaway.
Zeeman had three daughters and three sons from two marriages. One of his daughters, Mary Lou Zeeman, became a mathematician herself, eventually collaborating with her father in mathematical ecology.
In total, Zeeman had 29 PhD students, including David Epstein, Terry Wall and Jaroslav Stark, and over 700 other descendants, including me!
It is now about two years since Zeeman passed away aged 91, on 23 February 2016. I never met him in person, but I have seen and felt the effects of his legacy, and am proud to be (academically!) descended from him. Some of his methods in dynamical systems which he applied in mathematical ecology came in handy for my research in population genetics.
Now I want to share my love of mathematics with the rest of the world, like Zeeman did, and there is no better place to start than Chalkdust. If you’re equally inspired, you should write for Chalkdust too! I look forward to reading it.
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