Erik Christopher Zeeman

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Sir Erik Christopher Zeeman (born February 4 1925), is a Japanese-born British mathematician known for work in geometric topology and singularity theory.

Technical skill is mastery of complexity while creativity is mastery of simplicity.

'Catastrophe Theory', 1977.


Zeeman was born in Japan to a Danish father and a British mother. He and his parents moved to England one year after his birth. After being educated at Christ's Hospital School 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 high-school mathematics while serving for the air force. He received an MA and PhD (the latter under the supervision of Shaun Wylie, who had spent the war at Bletchley Park) from the University of Cambridge. 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 Etudes Scientifiques, he founded the Mathematics Department and Mathematics Research Centre at the new University of Warwick in 1964.


Zeeman's style of leadership was informal, but inspirational, and he rapidly took Warwick to international recognition for the quality of its mathematical research. 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".

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 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. 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 Mathematics and Statistics building was renamed the Zeeman building in his honour.

Zeeman's main contribution to mathematics was in topology, particularly in the piecewise linear category, and dynamical systems. However, he is better known for his contribution to, and spreading awareness of catastrophe theory, which was due initially to another topologist René Thom. He was especially active encouraging the application of mathematics, and catastrophe theory in particular, to biology and behavioural sciences.

Catastrophe Theory

"For the general public, catastrophe theory (or CT) has become the biggest thing in mathematics. René Thorn and Christopher Zeeman are the two leaders of this field. L'Express (October 14-30, 1974) asserts that the "new Newton" is French (i.e. Thorn). An announcement of Zeeman's lecture at Northwestern University in the spring of 1977 contains a quote describing catastrophe theory as the most important development in mathematics since the invention of calculus 300 years ago. Newsweek has given similar comparisons. Zeeman juxtaposes Newton and Thorn in the volume under review (briefly ZCT), p. 623. Thorn writes " . . . CT is-quite likely-the first coherent attempt (since Aristotelian Logic) to give a theory on analogy" [p. 637, ZCT]. On the back cover of Thorn's book, Structural stability and morphogenesis [English translation, Benjamin, 1975 or Thorn's SSM], is the quote from the London Times review, "In one sense the only book with which it can be compared is Newton's Principia.

Recently however, the importance of CT has been sharply and publicly challenged by Hector Sussman and subsequently by Sussman and Raphael Zahler... A critical story on CT by Gina Kolata in "Science", April 15, 1977, is headed: Catastrophe theory: The emperor has no clothes..." Steven Smale, November 197, [1]

Begun by the French mathematician Rene Thom in the 1960s, catastrophe theory is a branch of dynamical systems theory. It studies and classifies phenomena characterized by abrupt changes in behavior that arise from small, continuous changes in circumstances. Catastrophes in this sense are bifurcations between different equilibria, or fixed point attractors. Given certain assumptions, catastrophes can be classified based on how many control variables are involved. The simplest interesting catastrophe, the "cusp" catastrophe, can arise when there are two control variables. If, however, there are more than five controls, there is no classification.

The apparent beauty and power of catastrophe theory as expounded by Zeeman was its ability to elegantly express apparently complex behaviours in a very simple, intuitively appealing geometric manner, in a way which exposed analogies with many apparently unrelated phenomena, and in a manner which stimulated fresh theories and inspired new hypotheses. Thus, Zeeman applied catastrophe theory to many different phenomena, including the heartbeat and nervous impulse, the stability of ships and bridges, embryyological development, the fight-or-flight behavior of animals, and prison riots.

Catastrophe theory is securely founded in rigorous mathematics, but Zeeman was often understood to be saying that if a complex behaviour has a simple explanation then that simple explanation must be correct. However, sadly, often complex phenomena arise from ugly complex causes not elegant and simple ones. In fact, Zeeman was a magnificent provocateur, like Karl Popper, he saw the goal of science as being to generate simple, elegant theories and then to test them, and catastrophe theory as a wonderful engine to generate elegant theories.

For an often naive audience though, catastrophe theory itself was something that was either true or false, and when some of the applications came under fire, its popularity faded, although it remains an important part of mathematics. In some ways Zeeman's brilliance as a lecturer contributed to this downfall, he had the gift of persuading people that they understood things when they did not.

References

  1. Steven Smale, reviewing Catastrophe theory: Selected papers, 1972-1977 by E. C. Zeeman, 1977[http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.bams/1183541477 Bull Am Math Soc 84: November 1978