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René Frédéric Thom (; 2 September 1923 – 25 October 2002) was a French
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
, who received the
Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of Mathematicians, International Congress of the International Mathematical Union (IMU), a meeting that takes place e ...
in 1958. He made his reputation as a topologist, moving on to aspects of what would be called
singularity theory In mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold, if one neglects its thickness. A singularity can be made by balling it up, dropping it ...
; 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 of catastrophe theory (later developed by Christopher Zeeman).


Life and career

René Thom grew up in a modest family in Montbéliard,
Doubs Doubs (, ; ; ) is a department in the Bourgogne-Franche-Comté region in Eastern France. Named after the river Doubs, it had a population of 543,974 in 2019.Baccalauréat in 1940. After the German invasion of France, his family took refuge in
Switzerland Switzerland, officially the Swiss Confederation, is a landlocked country located in west-central Europe. It is bordered by Italy to the south, France to the west, Germany to the north, and Austria and Liechtenstein to the east. Switzerland ...
and then in
Lyon Lyon (Franco-Provençal: ''Liyon'') is a city in France. It is located at the confluence of the rivers Rhône and Saône, to the northwest of the French Alps, southeast of Paris, north of Marseille, southwest of Geneva, Switzerland, north ...
. In 1941 he moved to Paris to attend Lycée Saint-Louis and in 1943 he began studying mathematics at
École Normale Supérieure École or Ecole may refer to: * an elementary school in the French educational stages normally followed by Secondary education in France, secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing i ...
, becoming agrégé in 1946. He received his PhD in 1951 from the
University of Paris The University of Paris (), known Metonymy, metonymically as the Sorbonne (), was the leading university in Paris, France, from 1150 to 1970, except for 1793–1806 during the French Revolution. Emerging around 1150 as a corporation associated wit ...
. His thesis, titled ''Espaces fibrés en sphères et carrés de Steenrod'' (''Sphere bundles and Steenrod squares''), was written under the direction of Henri Cartan. After a fellowship at Princeton University Graduate College (1951–1952), he became Maître de conférences at the Universities of
Grenoble Grenoble ( ; ; or ; or ) is the Prefectures in France, prefecture and List of communes in France with over 20,000 inhabitants, largest city of the Isère Departments of France, department in the Auvergne-Rhône-Alpes Regions of France, region ...
(1953–1954) and
Strasbourg Strasbourg ( , ; ; ) is the Prefectures in France, prefecture and largest city of the Grand Est Regions of France, region of Geography of France, eastern France, in the historic region of Alsace. It is the prefecture of the Bas-Rhin Departmen ...
(1954–1963), where he was appointed Professor in 1957. In 1964 he moved to the
Institut des Hautes Études Scientifiques The Institut des hautes études scientifiques (IHÉS; English: Institute of Advanced Scientific Studies) is a French research institute supporting advanced research in mathematics and theoretical physics (also with a small theoretical biology g ...
, in Bures-sur-Yvette, where he worked until 1990. In 1958 Thom received the
Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of Mathematicians, International Congress of the International Mathematical Union (IMU), a meeting that takes place e ...
at the
International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...
in
Edinburgh Edinburgh is the capital city of Scotland and one of its 32 Council areas of Scotland, council areas. The city is located in southeast Scotland and is bounded to the north by the Firth of Forth and to the south by the Pentland Hills. Edinburgh ...
for the foundations of cobordism theory, which were already present in his thesis. He was
invited speaker at the International Congress of Mathematicians An invitation system is a method of encouraging people to join an organization, such as a Club (organization), club or a website. In regular society, it refers to any system whereby new members are chosen; they cannot simply apply. In relation to w ...
two more times: in 1970 in
Nice Nice ( ; ) is a city in and the prefecture of the Alpes-Maritimes department in France. The Nice agglomeration extends far beyond the administrative city limits, with a population of nearly one millionWarsaw Warsaw, officially the Capital City of Warsaw, is the capital and List of cities and towns in Poland, largest city of Poland. The metropolis stands on the Vistula, River Vistula in east-central Poland. Its population is officially estimated at ...
(which he did not attend). He was awarded the Brouwer Medal in 1970, the Grand Prix Scientifique de la Ville de Paris in 1974, and the John von Neumann Lecture Prize in 1976. He become the first president, together with Louis Néel, of the newly established Fondation Louis-de-Broglie In 1973 and was elected Member of the Académie des Sciences of Paris in 1976.
Salvador Dalí Salvador Domingo Felipe Jacinto Dalí i Domènech, Marquess of Dalí of Púbol (11 May 190423 January 1989), known as Salvador Dalí ( ; ; ), was a Spanish Surrealism, surrealist artist renowned for his technical skill, precise draftsmanship, ...
paid homage to René Thom with the paintings '' The Swallow's Tail'' and ''Topological Abduction of Europe''.


Research

While René Thom is most known to the public for his development of catastrophe theory between 1968 and 1972, his academic achievements concern mostly his mathematical work on 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 In physics, a gauge theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, does not change under local transformations according to certain smooth families of operations (Lie groups). Formally, t ...
. From the mid 1950s he moved into
singularity theory In mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold, if one neglects its thickness. A singularity can be made by balling it up, dropping it ...
, 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 In topology and related areas of mathematics, a subset ''A'' of a topological space ''X'' is said to be dense in ''X'' if every point of ''X'' either belongs to ''A'' or else is arbitrarily "close" to a member of ''A'' — for instance, the ...
. Thom's lectures on the stability of differentiable mappings, given at the
University of Bonn The University of Bonn, officially the Rhenish Friedrich Wilhelm University of Bonn (), is a public research university in Bonn, North Rhine-Westphalia, Germany. It was founded in its present form as the () on 18 October 1818 by Frederick Willi ...
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 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. 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 Aristotle (; 384–322 BC) was an Ancient Greek philosophy, Ancient Greek philosopher and polymath. His writings cover a broad range of subjects spanning the natural sciences, philosophy, linguistics, economics, politics, psychology, a ...
's writings on science. In 1992, he was one of eighteen academics who sent a letter to
Cambridge University The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...
protesting against plans to award Jacques Derrida an honorary doctorate. Beyond Thom's contributions to algebraic topology, he studied differentiable mappings, through the study of 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".


Bibliography

* * *
Ensembles et morphismes stratifiés
, ''
Bulletin of the American Mathematical Society The ''Bulletin of the American Mathematical Society'' is a quarterly mathematical journal published by the American Mathematical Society. Scope It publishes surveys on contemporary research topics, written at a level accessible to non-experts. ...
'' 75 (1969), 240–284. * "Semio Physics: A Sketch", Addison Wesley, (1990), * ''Structural Stability and Morphogenesis'', W. A. Benjamin, (1972), .


See also

*" Quelques propriétés globales des variétés differentiables" * Reeb graph


References

* * * * * *


External links

*
Washington Post Online edition
(free registration)

{{DEFAULTSORT:Thom, Rene 1923 births 2002 deaths Scientists from Montbéliard 20th-century French mathematicians École Normale Supérieure alumni Recipients of the National Order of Scientific Merit (Brazil) Fields Medalists Brouwer Medalists French semioticians Members of the French Academy of Sciences Institute for Advanced Study visiting scholars Theoretical biologists Topologists Lycée Saint-Louis alumni Academic staff of the University of Strasbourg University of Paris alumni French lecturers 20th-century French philosophers