Editing René Thom (section)

== Research ==
While René Thom is most known to the public for his development of [[catastrophe theory]] between 1968 and 1972,<ref>[[E.C. Zeeman]], [http://www.gaianxaos.com/pdf/dynamics/zeeman-catastrophe_theory.pdf Catastrophe Theory], ''[[Scientific American]]'', April 1976; pp. 65–70, 75–83</ref> his academic achievements concern mostly his mathematical work on topology.<ref>{{Cite book |last=Hopf |first=Heinz |url=https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1958/ICM1958.ocr.pdf |title=The Work of R. Thom |publisher=[[Cambridge University Press]] |year=1960 |editor-first= |location=Cambridge |pages=X - XIV |language=de |author-link=Heinz Hopf}}</ref><ref>{{Cite web |date=2019-12-09 |title=René Thom - Scholars |url=https://www.ias.edu/scholars/ren%C3%A9-thom |access-date=2022-04-10 |publisher=[[Institute for Advanced Study]] |language=en}}</ref>

In the early 1950s it concerned what are now called [[Thom space]]s, [[characteristic class]]es, [[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 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 between 1960 and 1969 developed the theory of [[topologically stratified space|stratified sets]] and stratified maps, proving a basic stratified isotopy theorem describing the local conical structure of [[Whitney conditions|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 map]]s, 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 the [[University of 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 [[C. T. C. Wall]]. The proof of the density of topologically stable mappings was completed by [[John Mather (mathematician)|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 Christopher Gibson, Klaus Wirthmüller, Andrew du Plessis, and [[Eduard Looijenga]].<ref name="Gibson Wirthmüller Du Plessis Looijenga">{{cite book | last=Gibson | first=Christopher G. | last2=Wirthmüller | first2=Klaus | last3=Du Plessis | first3=Andrew | last4=Looijenga | first4=E. | title=Topological stability of smooth mappings | publisher=Springer-Verlag | publication-place=Berlin | date=1976 | isbn=3-540-07997-1 | oclc=2705384 | page=}}</ref>

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. In 1992, he was one of eighteen academics who sent a letter to [[Cambridge University]] protesting against plans to award [[Jacques Derrida]] an honorary doctorate.<ref>{{cite web|url=http://ontology.buffalo.edu/smith/derridaletter.htm|title=Derrida Letter, The Cambridge Affair, 1992}}</ref>

Beyond Thom's contributions to algebraic topology, he studied differentiable mappings, through the study of [[Generic property|generic 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".