René Frédéric Thom
(September 2, 1923 – October 25, 2002) 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 founder of
catastrophe theory (later developed by
Erik Christopher Zeeman). He
received the
Fields Medal in
1958.
Biography
René Thom
was born in Montbéliard, Doubs.
He was
educated at the Lycée Saint-Louis and the École Normale
Supérieure, both in Paris. He received his PhD in
1951 from the University of
Paris. His thesis, titled
Espaces fibrés en
sphères et carrés de Steenrod (
Sphere bundles and Steenrod
squares), was written under the direction of
Henri Cartan. The foundations of
cobordism theory, for which he received the Fields
Medal at Edinburgh in 1958, were already present in his
thesis.
After a
fellowship in the United
States, he went on to teach at the Universities of
Grenoble (1953-1954) and Strasbourg (1954-1963), where he
was appointed Professor in 1957. In 1964, he moved to
the Institut des Hautes Études
Scientifiques, in Bures-sur-Yvette. He was awarded the
Grand Prix
Scientifique de la Ville de Paris in 1974, and became a Member
of the
Academie des Sciences
of Paris in 1976.
While René Thom is most known to the public for his development of
catastrophe theory between 1968 and 1972, his earlier work was on
differential topology. In the
early 1950s it concerned what are now called
Thom spaces,
characteristic classes,
cobordism theory, and the
Thom transversality theorem.
Another example of this line of work is the
Thom conjecture, versions of which have been
investigated using
gauge theory. From
the mid 50's he moved into
singularity theory, of which catastrophe
theory is just one aspect, and in a series of deep (and at the time
obscure) papers between 1960 and 1969 developed the theory of
stratified sets and stratified maps,
proving a basic stratified isotopy theorem describing the local
conical structure of
Whitney
stratified sets, now known as the Thom-Mather isotopy theorem.
Much of his work on
stratified sets
was developed so as to understand the notion of topologically
stable maps, and to eventually prove the result that the set of
topologically stable mappings between two smooth manifolds is a
dense set.
Thom's lectures on the stability of
differentiable mappings, given at Bonn in 1960, were written up by
Harold Levine and published in the
proceedings of a year long symposium on singularities at Liverpool
University during 1969-70, edited by Terry Wall. The proof of the density of
topologically stable mappings was completed by
John Mather in 1970, based on the ideas
developed by Thom in the previous ten years. A coherent detailed
account was published in 1976 by C. Gibson, K. Wirthmuller, E.
Looijenga and A. du Plessis.
During the last twenty years of his life Thom's published work was
mainly in philosophy and epistemology, and he undertook a
reevaluation of Aristotle's writings on science.
Beyond Thom's contributions in algebraic topology, his influence on
modern differential geometry, through the intensive study of
generic properties, can hardly be
exaggerated.
Thom died on October 25, 2002, in Bures-sur-Yvette.
Bibliography
- "Espaces fibrés en sphères et carrés de
Steenrod", Annales Scientifiques de l'École Normale
Supérieure (3) 69, (1952), 109—182.
- "Ensembles et morphismes stratifiés", Bulletin of the
American Mathematical Society 75 (1969),
240—284.
- "Semio Physics: A Sketch", Addison Wesley, (1990), ISBN
0-201-50060-4
- Structural Stability and Morphogenesis, W. A. Benjam,
(1972), ISBN 0-201-40685-3.
References
- David Aubin, " Forms of Explanations in the Catastrophe Theory of
René Thom: Topology, Morphogenesis, and Structuralism," in
Growing Explanations: Historical Perspective on the Sciences of
Complexity, ed. M. N. Wise, Durham: Duke University Press,
2004, 95-130.
- Martin Weil, French Mathematician René Thom Dies,
Washington Post, November 17 (2002),
p. C10
External links