Christopher Zeeman

Sir Erik Christopher Zeeman FRS (4 February 1925 – 13 February 2016), was a British mathematician, known for his work in geometric topology and singularity theory.

Zeeman's main contributions to mathematics were in topology, particularly in knot theory, the piecewise linear category, and dynamical systems.

After being educated at Christ's Hospital in Horsham, West Sussex, he served as a Flying Officer with the Royal Air Force from 1943 to 1947.

He studied mathematics at Christ's College, Cambridge, but had forgotten much of his school mathematics while serving for the air force.

He received an MA and PhD (the latter under the supervision of Shaun Wylie) from the University of Cambridge, and became a Fellow of Gonville and Caius College where he tutored David Fowler and John Horton Conway.

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.

His 1955 thesis at the University of Cambridge described a new theory termed "dihomology", an algebraic structure associated to a topological space, containing both homology and cohomology, introducing what is now known as the Zeeman spectral sequence.

In 1963, Zeeman showed that that causality in special relativity expressed by 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".

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

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 supervisions in groups of two for the first two years, in a manner similar to the tutorial system at Oxford and Cambridge.

This was studied by Clint McCrory in his 1972 Brandeis thesis following a suggestion of Dennis Sullivan that one make "a general study of the Zeeman spectral sequence to see how singularities in a space perturb Poincaré duality".

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.

This in turn led to the discovery of intersection homology by Robert MacPherson and Mark Goresky at Brown University where McCrory was appointed in 1974.

In 1974 Zeeman gave an invited address at the International Congress of Mathematicians in Vancouver, about applications of catastrophe theory.

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.

Zeeman was elected as a Fellow of the Royal Society in 1975, and was awarded the Society's Faraday Medal in 1988.

From 1976 to 1977 he was the Donegall Lecturer in Mathematics at Trinity College Dublin.

Zeeman is known among the wider scientific public for his contribution to, and spreading awareness of catastrophe theory, which was due initially to another topologist, René Thom, and for his Christmas lectures about mathematics on television in 1978.

He was especially active encouraging the application of mathematics, and catastrophe theory in particular, to biology and behavioral sciences.

Zeeman was born in Japan to a Danish father, Christian Zeeman, and a British mother.

They moved to England one year after his birth.

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.

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.

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.

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.

Between 1988 and 1994 he was the Professor of Geometry at Gresham College.

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.