René Thom | |
|---|---|
 Thom in 1970 | |
| Born | (1923-09-02)2 September 1923 Montbéliard, France |
| Died | 25 October 2002(2002-10-25) (aged 79) Bures-sur-Yvette, France |
| Alma mater | École Normale Supérieure,University of Paris |
| Known for | Catastrophe theory Cobordism Gradient conjecture Quasi-fibration Splitting lemma Thom conjecture Thom isomorphism Thom space Thom transversality theorem Thom's first isotopy lemma Thom–Porteous formula Thom–Sebastiani Theorem Dold–Thom theorem |
| Children | Françoise Thom |
| Awards | Fields Medal (1958) Brouwer Medal (1970) John von Neumann Lecture Prize (1976) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | University of Strasbourg Université Joseph Fourier Institut des Hautes Études Scientifiques |
| Thesis | Espaces fibrés en sphères et carrés de Steenrod (1951) |
| Doctoral advisor | Henri Cartan |
| Doctoral students | David Trotman |
René Frédéric Thom (French:[ʁənetɔm]; 2 September 1923 – 25 October 2002) was a Frenchmathematician, who received theFields Medal in 1958.
He made his reputation as atopologist, moving on to aspects of what would be calledsingularity 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 the founder ofcatastrophe theory (later developed byChristopher Zeeman).[1][2][3][4][5]
René Thom grew up in a modest family inMontbéliard,Doubs and obtained aBaccalauréat in 1940. After theGerman invasion of France, his family took refuge inSwitzerland and then inLyon. In 1941 he moved to Paris to attendLycée Saint-Louis and in 1943 he began studying mathematics atÉcole Normale Supérieure, becomingagrégé in 1946.[6]
He received his PhD in 1951 from theUniversity of Paris. His thesis, titledEspaces fibrés en sphères et carrés de Steenrod (Sphere bundles and Steenrod squares), was written under the direction ofHenri Cartan.[7]
After a fellowship atPrinceton University Graduate College (1951–1952), he becameMaître de conférences at the Universities ofGrenoble (1953–1954) andStrasbourg (1954–1963), where he was appointed Professor in 1957. In 1964 he moved to theInstitut des Hautes Études Scientifiques, inBures-sur-Yvette, where he worked until 1990.[8]
In 1958, Thom received theFields Medal at theInternational Congress of Mathematicians inEdinburgh for the foundations ofcobordism theory, which were already present in his thesis.[9] He wasinvited speaker at the International Congress of Mathematicians two more times: in 1970 inNice[10] and 1983 inWarsaw (which he did not attend).[11]
He was awarded theBrouwer Medal in 1970,[12] theGrand Prix Scientifique de la Ville de Paris in 1974, and theJohn von Neumann Lecture Prize in 1976.[13] He became the first president, together withLouis Néel, of the newly establishedFondation Louis-de-Broglie In 1973[14] and was elected Member of theAcadémie des Sciences of Paris in 1976.[15]
Salvador Dalí paid homage to René Thom with the paintingsThe Swallow's Tail andTopological Abduction of Europe.[16]
While René Thom is most known to the public for his development ofcatastrophe theory between 1968 and 1972,[17] his academic achievements concern mostly his mathematical work on topology.[18][19]
In the early 1950s, it concerned what are now calledThom spaces,characteristic classes,cobordism theory, and theThom transversality theorem. Another example of this line of work is theThom conjecture, versions of which have been investigated usinggauge theory. From the mid 1950s he moved intosingularity 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 ofstratified sets and stratified maps, proving a basic stratified isotopy theorem describing the local conical structure ofWhitney stratified sets, now known as theThom–Mather isotopy theorem. Much of his work on stratified sets was developed so as to understand the notion oftopologically stable maps, and to eventually prove the result that the set of topologically stable mappings between two smooth manifolds is adense set.
Thom's lectures on the stability of differentiable mappings, given at theUniversity of Bonn in 1960, were written up byHarold Levine and published in the proceedings of a year long symposium on singularities atLiverpool University during 1969–70, edited byC. T. C. Wall. The proof of the density of topologically stable mappings was completed byJohn Mather in 1970, based on the ideas developed by Thom in the previous ten years. A coherent detailed account was published in 1976 by Christopher Gibson, Klaus Wirthmüller, Andrew du Plessis, andEduard Looijenga.[20]
During the last twenty years of his life Thom's published work was mainly in philosophy and epistemology, and he undertook a reevaluation ofAristotle's writings on science. In 1992, he was one of eighteen academics who sent a letter toCambridge University protesting against plans to awardJacques Derrida an honorary doctorate.[21]
Beyond Thom's contributions to algebraic topology, he studied differentiable mappings, through the study ofgeneric properties. In his final years, he turned his attention to an effort to apply his ideas about structural topography to the questions of thought, language, and meaning in the form of a "semiophysics".
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