Zeeman is one of the founders of engulfing theory in piecewise linear topology and is credited with working out the engulfing theorem (independently also worked out by John Stallings), which can be used to prove the piecewise linear version of the
Poincaré conjecture for all dimensions above four. After working at
Cambridge (during which he spent a year abroad at
University of Chicago and
Princeton as a
Harkness Fellow) and the
Institut des Hautes Études Scientifiques, he founded the Mathematics Department and Mathematics Research Centre at the new
University of Warwick in 1964. In his own words :
I was 38 and had developed some fairly strong ideas on how to run a department and create a Mathematics Institute: I wanted 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. Zeeman's style of leadership was informal, but inspirational, and he rapidly took Warwick to international recognition for the quality of its mathematical research. The first six appointments he made were all in topology, enabling the department to immediately become internationally competitive, followed by six in algebra, and finally six in analysis and six in applied mathematics. He was able to trade four academic appointments for funding that enabled PhD students to give undergraduate supervision in groups of two for the first two years, in a manner similar to the tutorial system at Oxford and Cambridge. He remained at Warwick until 1988, but from 1966 to 1967 he was a visiting professor at the
University of California at Berkeley, after which his research turned to dynamical systems, inspired by many of the world leaders in this field, including
Stephen Smale and
René Thom, who both spent time at Warwick. In 1963, Zeeman showed that causality in special relativity expressed by the preservation of partial ordering is given exactly and only by the
Lorentz transforms. Zeeman subsequently spent a sabbatical with Thom at the Institut des Hautes Études Scientifiques in Paris, where he became interested in
catastrophe theory. On his return to Warwick, he taught an undergraduate course in Catastrophe Theory that became immensely popular with students; his lectures generally were "standing room only". In 1973 he gave an MSc course at Warwick giving a complete detailed proof of Thom's classification of elementary catastrophes, mainly following an unpublished manuscript, "Right-equivalence" written by
John Mather at Warwick in 1969.
David Trotman wrote up his notes of the course as an MSc thesis. These were then distributed in thousands of copies throughout the world and published both in the proceedings of a 1975 Seattle conference on catastrophe theory and its applications, and in a 1977 collection of papers on catastrophe theory by Zeeman. In 1974 Zeeman gave an
invited address at the International Congress of Mathematicians in Vancouver, about applications of catastrophe theory. Zeeman was elected as a
Fellow of the Royal Society in 1975, and was awarded the Society's Faraday Medal in 1988. He was the 63rd President of the
London Mathematical Society in 1986–88 giving his Presidential Address on 18 November 1988
On the classification of dynamical systems. He was awarded the
Senior Whitehead Prize of the Society in 1982. He was the Society's first Forder lecturer, involving a lecture tour in New Zealand, in 1987. Between 1988 and 1994 he was the
Professor of Geometry at
Gresham College. In 1978, Zeeman gave the televised series of
Christmas Lectures at the Royal Institution. From these grew the Mathematics and Engineering Masterclasses for both primary and secondary school children that now flourish in forty centers in the United Kingdom. In 1988, Zeeman became Principal of
Hertford College, Oxford. The following year he was appointed an honorary fellow of
Christ's College, Cambridge. He received a
knighthood in the
1991 Birthday Honours for "mathematical excellence and service to British mathematics and mathematics education". He was invited to become President of
The Mathematical Association in 2003 and based his book
Three-dimensional Theorems for Schools on his 2004 Presidential Address. On Friday 6 May 2005, the University of Warwick's new Mathematics and Statistics building was named the Zeeman Building in his honour. He became an Honorary Member of
The Mathematical Association in 2006. In September 2006, the
London Mathematical Society and the
Institute of Mathematics and its Applications awarded him the
David Crighton medal in recognition of his long and distinguished service to mathematics and the mathematical community. The medal is awarded triennially, and Zeeman was the second-ever recipient of the award. He died on 13 February 2016. ==The Zeeman Medal==