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, structure, space, models, and change.
History
On ...
, who received the Fields Medal in 1958.
He made his reputation as a topologist, moving on to aspects of what would be called singularity 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 founder of catastrophe theory (later developed by Erik Christopher Zeeman).
Life and career
René Thom grow up in a modest family in Montbéliard,
Doubs
Doubs (, ; ; frp, Dubs) 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 German invasion of France, his family took refuge in
Switzerland
). Swiss law does not designate a ''capital'' as such, but the federal parliament and government are installed in Bern, while other federal institutions, such as the federal courts, are in other cities (Bellinzona, Lausanne, Luzern, Neuchâtel ...
and then in
Lyon
Lyon,, ; Occitan: ''Lion'', hist. ''Lionés'' also spelled in English as Lyons, is the third-largest city and second-largest metropolitan area of France. It is located at the confluence of the rivers Rhône and Saône, to the northwest of ...
. In 1941 he moved to Paris to attend
Lycée Saint-Louis
The lycée Saint-Louis is a highly selective post-secondary school located in the 6th arrondissement of Paris, in the Latin Quarter. It is the only public French lycée exclusively dedicated to providing '' classes préparatoires aux grandes ...
and in 1943 he began studying mathematics at
École Normale Supérieure
École may refer to:
* an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée)
* École (river), a tributary of the Seine flowing in région Île-de-France
* École, S ...
, becoming agrégé in 1946.
He received his PhD in 1951 from the
University of Paris
, image_name = Coat of arms of the University of Paris.svg
, image_size = 150px
, caption = Coat of Arms
, latin_name = Universitas magistrorum et scholarium Parisiensis
, motto = ''Hic et ubique terrarum'' (Latin)
, mottoeng = Here and a ...
. 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
The Graduate College at Princeton University is a residential college which serves as the center of graduate student life at Princeton. Wyman House, adjacent to the Graduate College, serves as the official residence of the current Dean of the Gr ...
Strasbourg
Strasbourg (, , ; german: Straßburg ; gsw, label= Bas Rhin Alsatian, Strossburi , gsw, label= Haut Rhin Alsatian, Strossburig ) is the prefecture and largest city of the Grand Est region of eastern France and the official seat of the ...
Edinburgh
Edinburgh ( ; gd, Dùn Èideann ) is the capital city of Scotland and one of its 32 Council areas of Scotland, council areas. Historically part of the county of Midlothian (interchangeably Edinburghshire before 1921), it is located in Lothian ...
for the foundations of cobordism theory, which were already present in his thesis. He was
invited speaker at the International Congress of Mathematicians
This is a list of International Congresses of Mathematicians Plenary and Invited Speakers. Being invited to talk at an International Congress of Mathematicians has been called "the equivalent, in this community, of an induction to a hall of fame." ...
two more times: in 1970 in
Nice
Nice ( , ; Niçard: , classical norm, or , nonstandard, ; it, Nizza ; lij, Nissa; grc, Νίκαια; la, Nicaea) is the prefecture of the Alpes-Maritimes department in France. The Nice agglomeration extends far beyond the administrative ...
and 1983 in
Warsaw
Warsaw ( pl, Warszawa, ), officially the Capital City of Warsaw,, abbreviation: ''m.st. Warszawa'' is the capital and largest city of Poland. The metropolis stands on the River Vistula in east-central Poland, and its population is officiall ...
John von Neumann Lecture Prize
The John von Neumann Prize (until 2019 named John von Neumann Lecture Prize) was established in 1959 with funds from IBM and other industry corporations, and is awarded for "outstanding and distinguished contributions to the field of applied ma ...
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
The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. It was at ...
of Paris in 1976.
Salvador Dalí
Salvador Domingo Felipe Jacinto Dalí i Domènech, Marquess of Dalí of Púbol (; ; ; 11 May 190423 January 1989) was a Spanish Surrealism, surrealist artist renowned for his technical skill, precise draftsmanship, and the striking and bizarr ...
paid homage to René Thom with the paintings ''
The Swallow's Tail
''The Swallow's Tail — Series of Catastrophes'' (french: La queue d'aronde — Série des catastrophes) was Salvador Dalí's last painting. It was completed in May 1983, as the final part of a series based on the mathematical catastrophe theo ...
'' 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
In mathematics, cobordism is a fundamental equivalence relation on the class of compact manifolds of the same dimension, set up using the concept of the boundary (French '' bord'', giving ''cobordism'') of a manifold. Two manifolds of the same d ...
Thom conjecture
In mathematics, a smooth algebraic curve C in the complex projective plane, of degree d, has genus given by the genus–degree formula
:g = (d-1)(d-2)/2.
The Thom conjecture, named after French mathematician René Thom, states that if \Sigma is ...
, 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 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.
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 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 (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of ...
's writings on science. In 1992, he was one of eighteen academics who sent a letter to
Cambridge University
, mottoeng = Literal: From here, light and sacred draughts.
Non literal: From this place, we gain enlightenment and precious knowledge.
, established =
, other_name = The Chancellor, Masters and Schola ...
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".
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), .
Reeb graph
A Reeb graphY. Shinagawa, T.L. Kunii, and Y.L. Kergosien, 1991. Surface coding based on Morse theory. IEEE Computer Graphics and Applications, 11(5), pp.66-78 (named after Georges Reeb by René Thom) is a mathematical object reflecting the evolutio ...