René Thom

Infobox Scientist
name=René Thom


caption=René Thom
birth_date = birth date|1923|09|02
birth_place= Montbéliard, France
alma_mater= University of Paris
doctoral_advisor= Henri Cartan
death_date = death date and age|2002|10|25|1923|09|02
field = Mathematics
prizes=Fields Medal in 1958
known_for= topology

René 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 celebrated for one aspect of this latter interest, his work as founder of catastrophe theory (later developed by Christopher Zeeman). He received the Fields Medal in 1958.

Biography

René Thom was born in Montbéliard, France. He was educated at the Lycée Saint-Louis and the École Normale Supérieure. 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 later received the Fields Medal, 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.

While he is most known to the public for his development of catastrophe theory between 1968 and 1972, his earlier work was on differential topology. 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. He then moved into singularity theory, of which catastrophe theory is just one aspect, and 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. This result was proved by John Mather in 1970, based on the ideas developed by Thom in the previous ten years. 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

* [http://archive.numdam.org/article/ASENS_1952_3_69__109_0.pdf "Espaces fibrés en sphères et carrés de Steenrod"] , "Annales Scientifiques de l'École Normale Supérieure" (3) 69, (1952), 109--182.
*citation|id=MR|0061823| title=Quelques propriétés globales des variétés différentiables|journal= Commentarii Mathematici Helvetici |volume= 28|year= 1954|pages= 17–86 |url=http://retro.seals.ch/digbib/view?did=c1:389597&sdid=c1:389960| doi=10.1007/BF02566923
* "Ensembles et morphismes stratifiés", Bulletin of the Americam Mathematical Society,vol. 75 (1969), 240-284
* "Semio Physics: A Sketch", Addison Wesley, (1990), ISBN 0201500604
* "Structural Stability and Morphogenesis", W. A. Benjam, (1972), ISBN 0201406853.

References

* David Aubin, " [http://www.institut.math.jussieu.fr/~daubin/publis/2004a.pdf 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

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* [http://www.washingtonpost.com/wp-dyn/articles/A64970-2002Nov16.html Washington Post Online edition] (free registration)
* [http://www.pedagopsy.eu/meeting_rene_thom.htm Meeting René THOM]