Sir Erik Christopher Zeeman FRS (4 February 1925 – 13 February 2016), was a British mathematician, known for his work in

geometric topology In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another. History Geometric topology as an area distinct from algebraic topology may be said to have originated i ...

and

singularity theory In mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold, if one neglects its thickness. A singularity can be made by balling it up, dropping it ...

Overview

Zeeman's main contributions to mathematics were in

topology In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...

, particularly in

knot theory In the mathematical field of topology, knot theory is the study of knot (mathematics), mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are ...

, the piecewise linear category, and

dynamical systems In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a p ...

. His 1955 thesis at the

University of Cambridge , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...

described a new theory termed "dihomology", an algebraic structure associated to a

topological space In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance. More specifically, a topological space is a set whose elements are called points ...

, containing both

homology Homology may refer to: Sciences Biology *Homology (biology), any characteristic of biological organisms that is derived from a common ancestor * Sequence homology, biological homology between DNA, RNA, or protein sequences *Homologous chrom ...

and

cohomology In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be viewe ...

, introducing what is now known as the Zeeman

spectral sequence In homological algebra and algebraic topology, a spectral sequence is a means of computing homology groups by taking successive approximations. Spectral sequences are a generalization of exact sequences, and since their introduction by , they hav ...

. This was studied by Clint McCrory in his 1972 Brandeis thesis following a suggestion of

Dennis Sullivan Dennis Parnell Sullivan (born February 12, 1941) is an American mathematician known for his work in algebraic topology, geometric topology, and dynamical systems. He holds the Albert Einstein Chair at the City University of New York Graduate Ce ...

that one make "a general study of the Zeeman

to see how singularities in a space perturb

Poincaré duality In mathematics, the Poincaré duality theorem, named after Henri Poincaré, is a basic result on the structure of the homology and cohomology groups of manifolds. It states that if ''M'' is an ''n''-dimensional oriented closed manifold (compact a ...

". This in turn led to the discovery of

intersection homology In topology, a branch of mathematics, intersection homology is an analogue of singular homology especially well-suited for the study of singular spaces, discovered by Mark Goresky and Robert MacPherson in the fall of 1974 and developed by them ove ...

by Robert MacPherson and

Mark Goresky Robert Mark Goresky is a Canadian mathematician who invented intersection homology with his advisor and life partner Robert MacPherson. Career Goresky received his Ph.D. from Brown University in 1976. His thesis, titled ''Geometric Cohomology a ...

Brown University Brown University is a private research university in Providence, Rhode Island. Brown is the seventh-oldest institution of higher education in the United States, founded in 1764 as the College in the English Colony of Rhode Island and Providenc ...

where McCrory was appointed in 1974. From 1976 to 1977 he was the

Donegall Lecturer in Mathematics The Donegall Lecturership at Trinity College Dublin, is one of two endowed mathematics positions at Trinity College Dublin (TCD), the other being the Erasmus Smith's Chair of Mathematics. The Donegall (sometimes spelt Donegal) Lectureship was e ...

Trinity College Dublin , name_Latin = Collegium Sanctae et Individuae Trinitatis Reginae Elizabethae juxta Dublin , motto = ''Perpetuis futuris temporibus duraturam'' (Latin) , motto_lang = la , motto_English = It will last i ...

. Zeeman is known among the wider scientific public for his contribution to, and spreading awareness of

catastrophe theory In mathematics, catastrophe theory is a branch of bifurcation theory in the study of dynamical systems; it is also a particular special case of more general singularity theory in geometry. Bifurcation theory studies and classifies phenomena cha ...

, which was due initially to another topologist,

René Thom René Frédéric Thom (; 2 September 1923 – 25 October 2002) was a French mathematician, who received the Fields Medal in 1958. He made his reputation as a topologist, moving on to aspects of what would be called singularity theory; he became w ...

, 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 behavioural sciences.

Early life

Zeeman was born in Japan to a Danish father, Christian Zeeman, and a British mother. They moved to England one year after his birth. After being educated at

Christ's Hospital Christ's Hospital is a public school (English independent boarding school for pupils aged 11–18) with a royal charter located to the south of Horsham in West Sussex. The school was founded in 1552 and received its first royal charter in 1553 ...

Horsham Horsham is a market town on the upper reaches of the River Arun on the fringe of the Weald in West Sussex, England. The town is south south-west of London, north-west of Brighton and north-east of the county town of Chichester. Nearby to ...

, West Sussex, he served as a Flying Officer with the

Royal Air Force The Royal Air Force (RAF) is the United Kingdom's air and space force. It was formed towards the end of the First World War on 1 April 1918, becoming the first independent air force in the world, by regrouping the Royal Flying Corps (RFC) and ...

from 1943 to 1947. He studied mathematics at

Christ's College, Cambridge Christ's College is a constituent college of the University of Cambridge. The college includes the Master, the Fellows of the College, and about 450 undergraduate and 170 graduate students. The college was founded by William Byngham in 1437 as ...

, 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 Shaun Wylie (17 January 1913 – 2 October 2009 Gonville and Caius College Gonville and Caius College, often referred to simply as Caius ( ), is a constituent college of the University of Cambridge in Cambridge, England. Founded in 1348, it is the fourth-oldest of the University of Cambridge's 31 colleges and one of th ...

where he tutored David Fowler and

John Horton Conway John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions to many branches ...

Academic career

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 In the mathematics, mathematical field of geometric topology, the Poincaré conjecture (, , ) is a theorem about the Characterization (mathematics), characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dim ...

for all dimensions above four. After working at

Cambridge Cambridge ( ) is a university city and the county town in Cambridgeshire, England. It is located on the River Cam approximately north of London. As of the 2021 United Kingdom census, the population of Cambridge was 145,700. Cambridge bec ...

(during which he spent a year abroad at

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park neighborhood. The University of Chicago is consistently ranked among the b ...

and

Princeton Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the nine ...

as a

Harkness Fellow The Harkness Fellowship (previously known as the Commonwealth Fund Fellowship) is a program run by the Commonwealth Fund of New York City. This fellowship was established to reciprocate the Rhodes Scholarships and enable Fellows from several coun ...

) and the

Institut des Hautes Études Scientifiques The Institut des hautes études scientifiques (IHÉS; English: Institute of Advanced Scientific Studies) is a French research institute supporting advanced research in mathematics and theoretical physics. It is located in Bures-sur-Yvette, just ...

, he founded the Mathematics Department and Mathematics Research Centre at the new

University of Warwick The University of Warwick ( ; abbreviated as ''Warw.'' in post-nominal letters) is a public research university on the outskirts of Coventry between the West Midlands (county), West Midlands and Warwickshire, England. The university was founded i ...

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 supervisions 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 The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant univ ...

, after which his research turned to dynamical systems, inspired by many of the world leaders in this field, including

Stephen Smale Stephen Smale (born July 15, 1930) is an American mathematician, known for his research in topology, dynamical systems and mathematical economics. He was awarded the Fields Medal in 1966 and spent more than three decades on the mathematics facult ...

and

, who both spent time at Warwick. 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

. 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 David John Angelo Trotman (born 27 September 1951) is a mathematician, with dual British and French nationality. He is a grandson of the poet and author Oliver W F Lodge and a great-grandson of the physicist Sir Oliver Lodge. He works in an ar ...

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 This is a list of International Congresses of Mathematicians Plenary and Invited Speakers. Being invited to talk at an International Congress of Mathematicians has been called "the equivalent, in this community, of an induction to a hall of fame." ...

in Vancouver, about applications of catastrophe theory. Christopher Zeeman 2009

Zeeman was elected as a

Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...

in 1975, and was awarded the Society's Faraday Medal in 1988. He was the 63rd President of the

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ...

in 1986–88 giving his Presidential Address on 18 November 1988 ''On the classification of dynamical systems''. He was awarded the

Senior Whitehead Prize The Senior Whitehead Prize of the London Mathematical Society (LMS) is now awarded in odd numbered years in memory of John Henry Constantine Whitehead, president of the LMS between 1953 and 1955. The Prize is awarded to mathematicians normally ...

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 Gresham College is an institution of higher learning located at Barnard's Inn Hall off Holborn in Central London, England. It does not enroll students or award degrees. It was founded in 1596 under the will of Sir Thomas Gresham, and hosts ove ...

. 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 centres in the United Kingdom. In 1988, Zeeman became Principal of

Hertford College, Oxford Hertford College ( ), previously known as Magdalen Hall, is a colleges of the University of Oxford, constituent college of the University of Oxford in England. It is located on Catte Street in the centre of Oxford, directly opposite the main ga ...

. The following year he was appointed an honorary fellow of

. He received a

knighthood A knight is a person granted an honorary title of knighthood by a head of state (including the Pope) or representative for service to the monarch, the church or the country, especially in a military capacity. Knighthood finds origins in the Gr ...

in the

1991 Birthday Honours The Birthday Honours 1991 for the United Kingdom and the other Commonwealth realms of Antigua and Barbuda, Bahamas, Belize, Grenada, New Zealand, Saint Lucia, Saint Vincent and the Grenadines, Solomon Islands, Tuvalu, were announced on 14 June 19 ...

for "mathematical excellence and service to British mathematics and mathematics education". He was invited to become President of

The Mathematical Association The Mathematical Association is a professional society concerned with mathematics education in the UK. History It was founded in 1871 as the Association for the Improvement of Geometrical Teaching and renamed to the Mathematical Association in ...

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

in 2006. In September 2006, the

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

The '' Christopher Zeeman Medal for Communication of Mathematics'' of the

and the Institute of Mathematics and its Applications is named in Zeeman's honour. The award aims "to honour mathematicians who have excelled in promoting mathematics and engaging with the general public. They may be academic mathematicians based in universities, mathematics school teachers, industrial mathematicians, those working in the financial sector or indeed mathematicians from any number of other fields".

References

External links

*
Interview in ''CIM Bulletin'' 2001

Bibliography
* Zeeman's Catastrophe Machine *
Zeeman's Catastrophe Machine in Flash
*

*

Video illustrating Zeeman's Catastrophe Machine
* "The Cusp of Catastrophe: René Thom, Christopher Zeeman and Denis Postle" in ''Maps of the Mind'' Charles Hampden-Turner.

Collier Books Crowell-Collier Publishing Company was an American publisher that owned the popular magazines '' Collier's'', ''Woman's Home Companion'' and ''The American Magazine''. Crowell's subsidiary, P.F. Collier and Son, published ''Collier's Encyclopedia, ...

, 1981. *
Mathematics into pictures
Christopher Zeeman's 1978

Royal Institution The Royal Institution of Great Britain (often the Royal Institution, Ri or RI) is an organisation for scientific education and research, based in the City of Westminster. It was founded in 1799 by the leading British scientists of the age, inc ...

Christmas Lectures The Royal Institution Christmas Lectures are a series of lectures on a single topic each, which have been held at the Royal Institution in London each year since 1825, missing 1939–1942 because of the Second World War. The lectures present sc ...

Zeeman building