View source for Biography:Christopher Zeeman

{{Short description|British mathematician (1925–2016)}}
{{Infobox scientist
 | honorific_prefix  = Sir
 | image             = Christopher Zeeman.jpeg
 | image_size        = 150px
 | caption           = Zeeman in 1980
 | birth_name        = Erik Christopher Zeeman
 | birth_date        = {{Birth date|1925|2|4|df=y}}
 | birth_place       = Japan
 | death_date        = {{death date and age|2016|2|13|1925|2|4|df=y}}
 | death_place       = Woodstock, England
 | citizenship       = British
 | nationality       =
 | ethnicity         =
 | field             = Mathematics
 | work_institutions = [[Organization:University of Cambridge|University of Cambridge]] <br /> [[Organization:University of Warwick|University of Warwick]] <br />[[Organization:University of Oxford|University of Oxford]] <br /> Gresham College
 | alma_mater        = Christ's College, Cambridge
 | doctoral_advisor  = [[Biography:Shaun Wylie|Shaun Wylie]]
 | doctoral_students = Peter Buneman <br /> [[Biography:David B. A. Epstein|David Epstein]] <br /> Jenny Harrison <br /> Ray Lickorish <br />Tim Poston <br /> [[Biography:Colin P. Rourke|Colin Rourke]] <br /> David Trotman <br /> [[Biography:C. T. C. Wall|Terry Wall]] <br /> Charlotte Watts 
 | known_for         = [[Catastrophe theory]]<br />[[Geometric topology]]<br />[[Singularity theory]]<br/>[[Zeeman conjecture]]<br/>[[Zeeman's comparison theorem]]<br/>[[Stallings–Zeeman theorem]]
 | thesis_title = Dihomology
 | thesis_year = 1955
 | thesis_url  = 
 | religion          =
 | footnotes         = Fellow of the Royal Society
}}

'''Sir Erik Christopher Zeeman''' FRS<ref>{{Cite journal |last=Rand |first=David A. |date=2022 |title=Sir Erik Christopher Zeeman. 4 February 1925—13 February 2016 |url=https://royalsocietypublishing.org/doi/10.1098/rsbm.2022.0012 |journal=Biographical Memoirs of Fellows of the Royal Society |volume=73|pages=521–547 |doi=10.1098/rsbm.2022.0012 |s2cid=251447255 |doi-access=free }}</ref> (4 February 1925 – 13 February 2016), was a British mathematician,<ref name="oxford-times">{{cite news| url=http://www.oxfordtimes.co.uk/news/obits/obituaries/14301547.Obituary_____Remarkable____maths_professor_Sir_Christopher_Zeeman_remembered/?ref=rss | title=Obituary: 'Remarkable' maths professor Sir Christopher Zeeman remembered [Sir Christopher Zeeman: Mathematics professor and former college principal] | first=Megan | last=Archer | newspaper=Oxford Times | page=86 | date=25 February 2016 | accessdate=8 March 2016 }}</ref> known for his work in [[Geometric topology|geometric topology]] and [[Singularity theory|singularity theory]].

==Overview==
Zeeman's main contributions to mathematics were in [[Topology|topology]], particularly in [[Knot theory|knot theory]], the [[Piecewise linear manifold|piecewise linear]] category, and dynamical systems.

His 1955 thesis at the [[Organization:University of Cambridge|University of Cambridge]] described a new theory termed "dihomology", an algebraic structure associated to a [[Topological space|topological space]], containing both [[Homology (mathematics)|homology]] and [[Cohomology|cohomology]], introducing what is now known as the Zeeman [[Spectral sequence|spectral sequence]]. This was studied by Clint McCrory in his 1972 Brandeis thesis following a suggestion of [[Biography:Dennis Sullivan|Dennis Sullivan]] that one make "a general study of the Zeeman [[Spectral sequence|spectral sequence]] to see how singularities in a space perturb [[Poincaré duality]]". This in turn led to the discovery of [[Intersection homology|intersection homology]] by [[Biography:Robert MacPherson (mathematician)|Robert MacPherson]] and [[Biography:Mark Goresky|Mark Goresky]] at [[Organization:Brown University|Brown University]] where McCrory was appointed in 1974.

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|catastrophe theory]], which was due initially to another topologist, [[Biography:René Thom|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.

==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 in Horsham, West Sussex, he served as a Flying Officer with the {{wipe|Royal Air Force}} from 1943 to 1947.<ref name="oxford-times"/> 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 [[Biography:Shaun Wylie|Shaun Wylie]]) from the University of Cambridge, and became a Fellow of Gonville and Caius College where he tutored [[Biography:David Fowler (mathematician)|David Fowler]] and [[Biography:John Horton Conway|John Horton Conway]].<ref>The Guardian, [https://www.theguardian.com/news/2004/may/03/guardianobituaries.research Obituary: David Fowler], 3 May 2004</ref>

==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]] for all dimensions above four.<ref>'The generalised Poincaré conjecture', Bull. Amer. Math. Soc. 67:270 (1961)</ref><ref>'The Poincaré conjecture for n greater than or equal to 5', Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961), 198–204, Prentice–Hall, 1962</ref>

After working at [[Organization:University of Cambridge|Cambridge]] (during which he spent a year abroad at [[Organization:University of Chicago|University of Chicago]] and [[Organization:Princeton University|Princeton]] as a Harkness Fellow) and the [[Organization:Institut des Hautes Études Scientifiques|Institut des Hautes Études Scientifiques]], he founded the Mathematics Department and Mathematics Research Centre at the new [[Organization:University of Warwick|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.''<ref>E.C.Zeeman, Mathematical Association President's report, 2004, [http://www.m-a.org.uk/annual_reports/annual_report_200304/ M-A.org.uk]</ref>

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 [[Organization:University of California, Berkeley|University of California at Berkeley]], after which his research turned to dynamical systems, inspired by many of the world leaders in this field, including [[Biography:Stephen Smale|Stephen Smale]] and [[Biography:René Thom|René Thom]], 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.<ref name="Causality">{{cite journal |last1=Zeeman |first1=E. C. |title=Causality Implies the Lorentz Group |journal=Journal of Mathematical Physics |date=1 April 1964 |volume=5 |issue=4 |pages=490–493 |doi=10.1063/1.1704140 |bibcode=1964JMP.....5..490Z |issn=0022-2488}}</ref> 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]]. 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,<ref>D.J.A.Trotman and E.C.Zeeman, The classification of elementary catastrophes of codimension less than or equal to 5, in Structural stability, the theory of catastrophes, and applications in the sciences. Proceedings of the Conference held at Battelle Seattle Research Center, Seattle, Wash., 21–25 April 1975. Edited by P. Hilton. Lecture Notes in Mathematics, Vol. 525. Springer-Verlag, Berlin-New York, 1976</ref> and in a 1977 collection of papers on catastrophe theory by Zeeman.<ref>E. C. Zeeman, Catastrophe theory. Selected papers, 1972–1977. Addison–Wesley Publishing Co., Reading, Mass.–London–Amsterdam, 1977</ref> In 1974 Zeeman gave an invited address at the International Congress of Mathematicians in Vancouver, about applications of catastrophe theory.

[[File:Christopher Zeeman 2009.jpg|thumb|upright|Zeeman at the Warwick Mathematics Institute in December 2009]]
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.<ref name="gresham">{{cite web| url=http://www.gresham.ac.uk/professors-and-speakers/sir-christopher-zeeman | title=Sir Christopher Zeeman | publisher=Gresham College | location=London, UK | accessdate=8 March 2015 }}</ref>

In 1978, Zeeman gave the televised series of Christmas Lectures at the Royal Institution.<ref>{{Cite web
 | title = Mathematics into Pictures, 1978 Royal Institution Christmas Lectures
 | url = https://www.rigb.org/christmas-lectures/watch/1978/mathematics-into-pictures/
 | access-date = 7 February 2022
 }}</ref> 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.<ref>{{Cite web
 | title = Royal Institution Maths and Engineering Masterclasses
 | url = http://www.rigb.org/education/masterclasses
 | access-date = 22 August 2012
}}</ref>

 |title       = Honours and Awards Newsletter
 |author      = London Mathematical Society
 |url         = http://www.lms.ac.uk/newsletter/352/352_03.html
 |access-date = 8 July 2007
 |url-status     = dead
 |archiveurl  = https://web.archive.org/web/20071012060300/http://www.lms.ac.uk/newsletter/352/352_03.html
 |archivedate = 12 October 2007}}</ref> The medal is awarded triennially, and Zeeman was the second ever recipient of the award.<ref>{{Cite web
 | title = List of IMA-LMS Prizewinners
 | author = London Mathematical Society
 | url = http://www.lms.ac.uk/prizes/list-ima-lms-prize-winners
 | access-date = 10 December 2014
}}</ref> He died on 13 February 2016.<ref>{{Cite web
 | title = Sir Christopher Zeeman FRS (1925–2016) 
 | publisher = Mathematics Institute, [[Organization:University of Warwick|University of Warwick]]
 | url = http://www2.warwick.ac.uk/fac/sci/maths/general/news/new/?newsItem=094d434552cfc0810152eaf835027917
 | date = 16 February 2016 | access-date = 16 February 2016
}}</ref>

==The Zeeman Medal==
The ''{{ill|Christopher Zeeman Medal for Communication of Mathematics|WD=Q97515862}}''<ref>{{Cite web|url=https://ima.org.uk/awards-medals/christopher-zeeman-medal/|title=Christopher Zeeman Medal}}</ref> 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".

==See also==
* [[Biography:Mary Lou Zeeman|Mary Lou Zeeman]], Zeeman's daughter, also a mathematician
* Nicolette Zeeman, Zeeman's daughter, a literary scholar
* Samuel C. Zeeman, Zeeman's son, a plant biologist

== References ==
{{Reflist}}

== External links ==
* {{MacTutor Biography |id = Zeeman }}
* [https://web.archive.org/web/20040514135922/http://at.yorku.ca/i/a/a/h/14.htm Interview in ''CIM Bulletin'' 2001]
* [http://www-groups.dcs.st-and.ac.uk/~history/References/Zeeman.html Three references for further reading]
* [http://zakuski.math.utsa.edu/~gokhman/ecz/bib.cgi Bibliography]
* Zeeman's Catastrophe Machine
** [https://archive.today/20121211093251/http://lagrange.physics.drexel.edu/flash/zcm Zeeman's Catastrophe Machine in Flash]
** [https://www.ams.org/featurecolumn/archive/cusp1.html AMS — The Catastrophe Machine]
** [http://www.math.sunysb.edu/~tony/whatsnew/column/catastrophe-0600/cusp4.html Doctor Zeeman's Original Catastrophe Machine]
**[https://www.youtube.com/watch?v=L2qa1NTS4-I 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, 1981. {{ISBN|978-0-85533-293-8}}
* {{MathGenealogy |id = 24417 }}
* [https://www.rigb.org/christmas-lectures/watch/1978/mathematics-into-pictures Mathematics into pictures], Christopher Zeeman's 1978 Royal Institution Christmas Lectures
* [https://manchesterhistory.net/architecture/2000/zeeman.html Zeeman building], [[Organization:University of Warwick|University of Warwick]]
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{{s-aca}}
{{s-bef|before=[[Biography:Geoffrey Warnock|Geoffrey Warnock]]}}
{{s-ttl|title=[[Social:Principal (academia)|Principal]] of [[Organization:Hertford College, Oxford|Hertford College, Oxford]]|years=1988–1996}}
{{s-aft|after=Walter Bodmer}}
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{{DEFAULTSORT:Zeeman, Christopher}}
[[Category:Topologists]]

{{Sourceattribution|Christopher Zeeman}}