René Thom (English)
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René Thom René Frédéric Thom ( French: [ʁəne tõ]; September 2, 1923 – October 25, 2002) was a French mathematician. He made his reputation as a topologist, moving on to as- pects of what would be called singularity theory; he be- came world-f amous among the wider academic commu- nity and the educ ated gene ral pub lic f or one aspect of this latter interest, his work as founder of catastrophe theory (later developed by Erik Christopher Zeeman ). He re - ceived the Fields Medal in 1958. 1 Bi ography René Thom was born in Montbéliard, Doubs. He was ed- ucated 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, ti tled 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 Pro- fe ssor in 195 7. In 1964, he moved to the Institut des Hautes Étude s Scie ntifi que s, in Bures-sur-Yvette . He wa s awarded the Brouwer Medal in 1970, the Grand Prix Sci- enti fi qu e de la Vil le de Pa ris in1974 , and be ca mea Mem- ber 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 differentia l topology. In the early 1950s it concerned what are now called Thom spaces, characteristic classes , cobordism theory, and the Thom transversality theorem. Anoth er ex ampl e of this line of work is the Thom conjecture, versions of which have been investigated using gauge theory. Fr om the mid 1950s 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 betwee n 1960 and 1969 developed the theory of stratified sets and stratified maps, proving a basic stratified isotopy theorem describ- ing the local conical structure of Whitney stratified sets , now known as the Thom-Mather isotopy theorem. Much ofhisworkon stratified sets wa s de ve lo ped so as to und er- sta nd the not io n of top ol ogi ca ll y stable ma ps, andto ev en- tually 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 map- pings, 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 dur- ing 1969-70, edited by Terry Wall. Th e pr oof of th e 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. Wirth- muller, E. Looijenga and A. du Plessis. During the last twenty years of his lif e Thom’s published work was mainly in philosophy and epistemology, and he undertook a reevaluation of Aristotle's writings on sci- enc e. In 1992, he was one of ei ghte en acade mics who sent a letter to Cambridge University protesting against plans to award Jacques Derrida an honorary doctorate. Beyond Thom’s contributions to algebraic topology, he studied diff ere ntia ble map ping s, thro ugh the stud y of generic properties. 2 See also • Dold–Thom theorem • Quelques propriétés globales des variétés differen- tiables • Thom isomorphism • Pontryagin-Thom construction • Thom–Porteous formula 3 Biblio gra ph y • “Espaces fibrés en sphères et carrés de Steenrod” , Annales Scientifiques de l'École Normale Supérieure (3) 69, (1952), 109–182. • Thom, René (1954), “Q ue lq ues pr o- pri été s gl oba le s de s va rié tés di ff ér entia bl es ” , Commentar ii Math emati ci Hel vetici 28: 17–86, doi :10.1007/BF02566923, MR 0061823 • “Ensembles et morphismes stratifiés”, Bulletin of the American Mathematical Society 75 (1969), 240– 284. • “Se mi o Ph ys ics: A Sketc h”, Ad dis on Wes le y, (1990), ISBN 0-201-50060-4 1
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René Thom
René Frédéric Thom (French: [ʁəne tõ]; September 2,1923 – October 25, 2002) was a French mathematician.He made his reputation as a topologist, moving on to as-pects of what would be called singularity theory; he be-came world-famous among the wider academic commu-nity and the educated general public for one aspect of thislatter interest, his work as founder of catastrophe theory(later developed by Erik Christopher Zeeman). He re-ceived the Fields Medal in 1958.
1 Biography
René Thom was born in Montbéliard, Doubs. He was ed-ucated at the Lycée Saint-Louis and the École NormaleSupérieure, both in Paris. He received his PhD in 1951from the University of Paris. His thesis, titled Espaces fibrés en sphères et carrés de Steenrod (Sphere bundlesand Steenrod squares), was written under the directionof Henri Cartan. The foundations of cobordism theory,for which he received the Fields Medal at Edinburgh in1958, were already present in his thesis.
After a fellowship in the United States, he went on toteach at the Universities of Grenoble (1953–1954) andStrasbourg (1954–1963), where he was appointed Pro-fessor in 1957. In 1964, he moved to the Institut desHautes Études Scientifiques, in Bures-sur-Yvette. He wasawarded the Brouwer Medal in 1970, the Grand Prix Sci-entifique de la Ville de Paris in 1974, and became a Mem-ber of the Academie des Sciences of Paris in 1976.
While René Thom is most known to the public for hisdevelopment of catastrophe theory between 1968 and1972, his earlier work was on differential topology. Inthe early 1950s it concerned what are now called Thomspaces, characteristic classes, cobordism theory, and theThom transversality theorem. Another example of thisline of work is the Thom conjecture, versions of whichhave been investigated using gauge theory. From themid 1950s he moved into singularity theory, of whichcatastrophe theory is just one aspect, and in a series ofdeep (and at the time obscure) papers between 1960 and1969 developed the theory of stratified sets and stratifiedmaps, proving a basic stratified isotopy theorem describ-ing the local conical structure of Whitney stratified sets,now known as the Thom-Mather isotopy theorem. Muchofhisworkon stratified setswas developedso as to under-
stand thenotion of topologically stable maps, and to even-tually prove the result that the set of topologically stablemappings between two smooth manifolds is a dense set.
Thom’s lectures on the stability of differentiable map-pings, given at Bonn in 1960, were written up by HaroldLevine and published in the proceedings of a year longsymposium on singularities at Liverpool University dur-ing 1969-70, edited by Terry Wall. The proof of thedensity of topologically stable mappings was completedby John Mather in 1970, based on the ideas developedby Thom in the previous ten years. A coherent detailedaccount was published in 1976 by C. Gibson, K. Wirth-muller, E. Looijenga and A. du Plessis.
During the last twenty years of his life Thom’s publishedwork was mainly in philosophy and epistemology, and heundertook a reevaluation of Aristotle's writings on sci-ence. In 1992, he was one of eighteen academics whosent a letter to Cambridge University protesting againstplans to award Jacques Derrida an honorary doctorate.
Beyond Thom’s contributions to algebraic topology, hestudied differentiable mappings, through the study ofgeneric properties.
2 See also
• Dold–Thom theorem
• Quelques propriétés globales des variétés differen-tiables
• Thom isomorphism
• Pontryagin-Thom construction
• Thom–Porteous formula
3 Bibliography• “Espaces fibrés en sphères et carrés de Steenrod”,
Annales Scientifiques de l'École Normale Supérieure(3) 69, (1952), 109–182.
• Thom, René (1954), “Quelques pro-priétés globales des variétés différentiables”,Commentarii Mathematici Helvetici 28: 17–86,doi:10.1007/BF02566923, MR 0061823
• “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
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2 5 EXTERNAL LINKS
• Structural Stability and Morphogenesis, W. A. Ben-jamin, (1972), ISBN 0-201-40685-3.
4 References
• Logos et Théorie des Catastrophes: à partir del’oeuvre de René Thom, ed. Jean Petitot. Colloquede Cerisy-la-Salle 1982 (Patiño, Geneva 1996),ISBN 9782882130105
• David Aubin, "Forms of Explanations in the Catas-trophe Theory of René Thom: Topology, Morpho-genesis, and Structuralism,” in Growing Explana-tions: Historical Perspective on the Sciences of Com- plexity, ed. M. N. Wise, Durham: Duke UniversityPress, 2004, 95-130.
• Brian J. Reilly, “René Thom,” in The ColumbiaHistory of Twentieth-Century French Thought . ed.Lawrence D. Kritzman. New York: Columbia Uni-versity Press, 2006. pp. 663–666.
• Martin Weil, French Mathematician René ThomDies, Washington Post, November 17 (2002), p.C10
5 External links
• O'Connor, John J.; Robertson, Edmund F., “René
Thom”, MacTutor History of Mathematics archive,University of St Andrews.
• René Thom at the Mathematics Genealogy Project
• Washington Post Online edition (free registration)
• Meeting René THOM
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