Erik Christopher Zeeman
Encyclopedia
Sir Erik Christopher Zeeman FRS (born 4 February 1925), is a Japanese-born 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.
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
. 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
". 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.
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 behavioural sciences.
He and his parents moved to England
one year after his birth. 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
.
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
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, 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, 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 which became immensely popular with students; his lectures generally were "standing room only". In 1973 he gave an M.Sc. 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
, then aged 21, attended this course, and wrote up his notes as his M.Sc. 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.
In 1978, Zeeman gave the televised series of Christmas Lectures at the Royal Institution
. From these grew the 'Mathematics Master classes' for 13-year old children that now flourish in forty centres 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 1991 for "mathematical excellence and service to British mathematics and mathematics education". On Friday 6 May 2005, the University of Warwick's new Mathematics and Statistics building was named the Zeeman building in his honour. In September 2006, it was announced that the London Mathematical Society
and the Institute of Mathematics and its Applications
will award 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 will be the second ever recipient of the award.
The Christopher Zeeman Medal for Communication of Mathematics of the London Mathematical Society
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'.
Geometric topology
In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another.- Topics :...
and singularity theory
Singularity theory
-The notion of singularity:In mathematics, singularity theory is the study of the failure of manifold structure. A loop of string can serve as an example of a one-dimensional manifold, if one neglects its width. What is meant by a singularity can be seen by dropping it on the floor...
.
Zeeman's main contributions to mathematics were in topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
, particularly in knot theory
Knot theory
In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined together so that it cannot be undone. In precise mathematical language, a knot is an embedding of a...
, the piecewise linear
Piecewise linear manifold
In mathematics, a piecewise linear manifold is a topological manifold together with a piecewise linear structure on it. Such a structure can be defined by means of an atlas, such that one can pass from chart to chart in it by piecewise linear functions.An isomorphism of PL manifolds is called a PL...
category, and dynamical systems.
His 1955 thesis at the University of Cambridge
University of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...
described a new theory termed "dihomology", an algebraic structure associated to a topological space
Topological space
Topological spaces are mathematical structures that allow the formal definition of concepts such as convergence, connectedness, and continuity. They appear in virtually every branch of modern mathematics and are a central unifying notion...
, containing both homology
Homology (mathematics)
In mathematics , homology is a certain general procedure to associate a sequence of abelian groups or modules with a given mathematical object such as a topological space or a group...
and cohomology
Cohomology
In mathematics, specifically in algebraic topology, cohomology is a general term for a sequence of abelian groups defined from a co-chain complex. That is, cohomology is defined as the abstract study of cochains, cocycles, and coboundaries...
, introducing what is now known as the Zeeman spectral sequence
Spectral sequence
In homological algebra and algebraic topology, a spectral sequence is a means of computing homology groups by taking successive approximations...
. This was studied by Clint McCrory in his 1972 Brandeis thesis following a suggestion of Dennis Sullivan
Dennis Sullivan
Dennis Parnell Sullivan is an American mathematician. He is known for work in topology, both algebraic and geometric, and on dynamical systems. He holds the Albert Einstein Chair at the City University of New York Graduate Center, and is a professor at Stony Brook University.-Work in topology:He...
that one make "a general study of the Zeeman spectral sequence
Spectral sequence
In homological algebra and algebraic topology, a spectral sequence is a means of computing homology groups by taking successive approximations...
to see how singularities in a space perturb Poincaré duality
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...
". This in turn led to the discovery of intersection homology by Robert MacPherson and Mark Goresky
Mark Goresky
Robert Mark Goresky is a Canadian mathematician who invented intersection homology with Robert MacPherson.He received his Ph.D. from Brown University in 1976. His thesis, titled Geometric Cohomology and Homology of Stratified Objects, was written under the direction of MacPherson...
at Brown University
Brown University
Brown University is a private, Ivy League university located in Providence, Rhode Island, United States. Founded in 1764 prior to American independence from the British Empire as the College in the English Colony of Rhode Island and Providence Plantations early in the reign of King George III ,...
where McCrory was appointed in 1974.
Zeeman is known among the wider scientific public for his contribution to, and spreading awareness of catastrophe theory
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....
, which was due initially to another topologist, René Thom
René Thom
René Frédéric Thom was a French mathematician. He made his reputation as a topologist, moving on to aspects of what would be called singularity theory; he became world-famous among the wider academic community and the educated general public for one aspect of this latter interest, his work as...
, 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.He and his parents moved to England
England
England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west, with the North Sea to the east and the English Channel to the south separating it from continental...
one year after his birth. After being educated at Christ's Hospital
Christ's Hospital
Christ's Hospital is an English coeducational independent day and boarding school with Royal Charter located in the Sussex countryside just south of Horsham in Horsham District, West Sussex, England...
in Horsham
Horsham
Horsham is a market town with a population of 55,657 on the upper reaches of the River Arun in the centre of the Weald, West Sussex, in the historic County of Sussex, England. The town is south south-west of London, north-west of Brighton and north-east of the county town of Chichester...
, West Sussex
West Sussex
West Sussex is a county in the south of England, bordering onto East Sussex , Hampshire and Surrey. The county of Sussex has been divided into East and West since the 12th century, and obtained separate county councils in 1888, but it remained a single ceremonial county until 1974 and the coming...
, he served as a Flying Officer
Flying Officer
Flying officer is a junior commissioned rank in the Royal Air Force and the air forces of many countries which have historical British influence...
with the Royal Air Force
Royal Air Force
The Royal Air Force is the aerial warfare service branch of the British Armed Forces. Formed on 1 April 1918, it is the oldest independent air force in the world...
from 1943 to 1947. He studied mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
at Christ's College
Christ's College, Cambridge
Christ's College is a constituent college of the University of Cambridge.With a reputation for high academic standards, Christ's College averaged top place in the Tompkins Table from 1980-2000 . In 2011, Christ's was placed sixth.-College history:...
, Cambridge
University of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...
, but had forgotten much of his school mathematics while serving for the air force. He received an MA
Master of Arts (Oxbridge)
In the Universities of Oxford, Cambridge and Dublin, Bachelors of Arts of these universities are admitted to the degree of Master of Arts or Master in Arts on application after six or seven years' seniority as members of the university .There is no examination or study required for the degree...
and PhD
PHD
PHD may refer to:*Ph.D., a doctorate of philosophy*Ph.D. , a 1980s British group*PHD finger, a protein sequence*PHD Mountain Software, an outdoor clothing and equipment company*PhD Docbook renderer, an XML renderer...
(the latter under the supervision of Shaun Wylie
Shaun Wylie
Shaun Wylie was a British mathematician and World War II codebreaker.-Early life:Wylie was born in Oxford, England, the fourth son of Sir Francis Wylie, later the first Warden of Rhodes House in Oxford. He was educated at Dragon School and then Winchester College...
) from the University of Cambridge
University of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...
, and became a Fellow of Gonville and Caius College where he tutored David Fowler
David Fowler (mathematician)
David Herbert Fowler was a historian of Greek mathematics who published work on pre-Eudoxian ratio theory...
and John Horton Conway
John Horton Conway
John Horton Conway is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory...
.
Academic career
Eric Christopher 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 piece-wise linear version of the Poincaré conjecturePoincaré conjecture
In mathematics, the Poincaré conjecture is a theorem about the characterization of the three-dimensional sphere , which is the hypersphere that bounds the unit ball in four-dimensional space...
for all dimensions above four.
After working at Cambridge (during which he spent a year abroad at University of Chicago
University of Chicago
The University of Chicago is a private research university in Chicago, Illinois, USA. It was founded by the American Baptist Education Society with a donation from oil magnate and philanthropist John D. Rockefeller and incorporated in 1890...
and Princeton
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
as a Harkness Fellow
Harkness Fellowship
The Harkness Fellowships are a programme run by the Commonwealth Fund of New York City. They were established to reciprocate the Rhodes Scholarships and enable Fellows from several countries to spend time studying in the United States...
) and the Institut des Hautes Études Scientifiques
Institut des Hautes Études Scientifiques
The Institut des Hautes Études Scientifiques is a French institute supporting advanced research in mathematics and theoretical physics...
, he founded the Mathematics Department and Mathematics Research Centre at the new University of Warwick
University of Warwick
The University of Warwick is a public research university located in Coventry, United Kingdom...
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, after which his research turned to dynamical systems, inspired by many of the world leaders in this field, including Stephen Smale
Stephen Smale
Steven Smale a.k.a. Steve Smale, Stephen Smale is an American mathematician from Flint, Michigan. He was awarded the Fields Medal in 1966, and spent more than three decades on the mathematics faculty of the University of California, Berkeley .-Education and career:He entered the University of...
and René Thom
René Thom
René Frédéric Thom was a French mathematician. He made his reputation as a topologist, moving on to aspects of what would be called singularity theory; he became world-famous among the wider academic community and the educated general public for one aspect of this latter interest, his work as...
, who both spent time at Warwick, Zeeman subsequently spent a sabbatical with Thom at the Institut des Hautes Études Scientifiques in Paris, where he became interested in catastrophe theory
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....
. On his return to Warwick, he taught an undergraduate course in Catastrophe Theory which became immensely popular with students; his lectures generally were "standing room only". In 1973 he gave an M.Sc. 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 Trotman
David John Angelo Trotman is a mathematician, with dual British and French nationality. He was born on September 27, 1951 in Plymouth, Devon, England, a grandson of the poet and author Oliver W F Lodge and a great-grandson of the physicist Sir Oliver Lodge...
, then aged 21, attended this course, and wrote up his notes as his M.Sc. 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
International Congress of Mathematicians
The International Congress of Mathematicians is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union ....
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
London Mathematical Society
-See also:* American Mathematical Society* Edinburgh Mathematical Society* European Mathematical Society* List of Mathematical Societies* Council for the Mathematical Sciences* BCS-FACS Specialist Group-External links:* * *...
in 1986–88 giving his Presidential Address on 18 November 1988 On the classification of dynamical systems. He was awarded the Senior Whitehead Prize
Senior Whitehead Prize
The Senior Whitehead Prize of the London Mathematical Society is currently 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 resident in the United Kingdom on 1 January of the...
of the Society in 1982. He was the Society's first Forder lecturer, involving a lecture tour in New Zealand, in 1987.
In 1978, Zeeman gave the televised series of Christmas Lectures at the Royal Institution
Royal Institution Christmas Lectures
The Royal Institution Christmas Lectures are a series of lectures on a single topic, which have been held at the Royal Institution in London each year since 1825. The lectures present scientific subjects to a general audience, including young people, in an informative and entertaining manner....
. From these grew the 'Mathematics Master classes' for 13-year old children that now flourish in forty centres in the United Kingdom.
In 1988, Zeeman became Principal of Hertford College, Oxford
Hertford College, Oxford
Hertford College is one of the constituent colleges of the University of Oxford in England. It is located in Catte Street, directly opposite the main entrance of the original Bodleian Library. As of 2006, the college had a financial endowment of £52m. There are 612 students , plus various visiting...
. The following year he was appointed an honorary fellow of Christ's College, Cambridge
Christ's College, Cambridge
Christ's College is a constituent college of the University of Cambridge.With a reputation for high academic standards, Christ's College averaged top place in the Tompkins Table from 1980-2000 . In 2011, Christ's was placed sixth.-College history:...
. He received a knighthood in 1991 for "mathematical excellence and service to British mathematics and mathematics education". On Friday 6 May 2005, the University of Warwick's new Mathematics and Statistics building was named the Zeeman building in his honour. In September 2006, it was announced that the London Mathematical Society
London Mathematical Society
-See also:* American Mathematical Society* Edinburgh Mathematical Society* European Mathematical Society* List of Mathematical Societies* Council for the Mathematical Sciences* BCS-FACS Specialist Group-External links:* * *...
and the Institute of Mathematics and its Applications
Institute of Mathematics and its Applications
The Institute of Mathematics and its Applications is the UK's chartered professional body for mathematicians and one of the UK's learned societies for mathematics ....
will award 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 will be the second ever recipient of the award.
The Christopher Zeeman Medal for Communication of Mathematics of the London Mathematical Society
London Mathematical Society
-See also:* American Mathematical Society* Edinburgh Mathematical Society* European Mathematical Society* List of Mathematical Societies* Council for the Mathematical Sciences* BCS-FACS Specialist Group-External links:* * *...
and the Institute of Mathematics and its Applications
Institute of Mathematics and its Applications
The Institute of Mathematics and its Applications is the UK's chartered professional body for mathematicians and one of the UK's learned societies for mathematics ....
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'.
External links
- Interview in CIM Bulletin 2001
- Three references for further reading
- Bibliography
- Zeeman's Catastrophe Machine
- "The Cusp of Catastrophe: René Thom, Christopher Zeeman and Denis Postle" in Maps of the Mind Charles Hampden-Turner. Collier BooksCollier BooksCollier Books was a publisher established by the Collier family. It later become part of Crowell-Collier Publishing, which merged with Macmillan Publishing to become Macmillan, Inc.....
, 1981. ISBN 978-0855332938