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Moved page from wikipedia:en:René Thom (history)
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{{short description|French mathematician}}
{{Infobox scientist
{{Infobox scientist
{信息盒科学家
|name=René Thom
|name=René Thom
|name=René Thom
|image=René Thom.jpeg
|image=René Thom.jpeg
|image=René Thom.jpeg
|caption=René Thom in [[Nice]], 1970
|caption=René Thom in Nice, 1970
1970年摄于尼斯
|birth_date = {{birth date|1923|9|2|df=y}}
|birth_date =
出生日期
|birth_place= [[Montbéliard]], France
|birth_place= Montbéliard, France
出生地: 法国蒙贝利亚德
|death_date = {{death date and age|2002|10|25|1923|9|2|df=y}}
|death_date =
死亡日期
|death_place=[[Bures-sur-Yvette]], France
|death_place=Bures-sur-Yvette, France
死亡地点: 伊维特河畔比尔，法国
|nationality = French
|nationality = French
| 国籍: 法国
|workplaces = [[University of Strasbourg]]<br>[[Université Joseph Fourier]]<br>[[Institut des Hautes Études Scientifiques]]
|workplaces = University of Strasbourg<br>Université Joseph Fourier<br>Institut des Hautes Études Scientifiques
约瑟夫傅立叶大学斯特拉斯堡大学法国高等科学研究所
|alma_mater=[[École Normale Supérieure]], [[University of Paris]]
|alma_mater=École Normale Supérieure, University of Paris
|alma_mater=École Normale Supérieure, University of Paris
|doctoral_advisor= [[Henri Cartan]]
|doctoral_advisor= Henri Cartan
博士生导师: Henri Cartan
|doctoral_students=[[David Trotman]]
|doctoral_students=David Trotman
博士生: David Trotman
|thesis_title = Espaces fibrés en sphères et carrés de Steenrod
|thesis_title = Espaces fibrés en sphères et carrés de Steenrod
|thesis_title = Espaces fibrés en sphères et carrés de Steenrod
|thesis_year = 1951
|thesis_year = 1951
论文年份 = 1951
|field = [[Mathematics]]
|field = Mathematics
| field = 数学
|prizes=[[Fields Medal]] in 1958
|prizes=Fields Medal in 1958
1958年菲尔兹奖
|known_for=[[Dold–Thom theorem]]<br>[[Thom isomorphism]]<br>[[Thom space|Pontryagin–Thom construction]]<br>[[Thom–Porteous formula]]
|known_for=Dold–Thom theorem<br>Thom isomorphism<br>Pontryagin–Thom construction<br>Thom–Porteous formula
托姆同构庞特里亚金结构托姆-波特罗公式
}}
}}
}}
'''René Frédéric Thom''' ({{IPA-fr|ʁəne tɔm|lang}}; 2 September 1923 – 25 October 2002) was a French [[mathematician]]. 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]]). He received the [[Fields Medal]] in 1958.
René Frédéric Thom (; 2 September 1923 – 25 October 2002) was a French mathematician. 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). He received the Fields Medal in 1958.
René Frédéric Thom (; 1923年9月2日至2002年10月25日)是一位法国数学家。他作为一个拓扑学家而闻名于世，并开始研究后来被称为奇点理论的一些方面; 他在更广泛的学术界和受过教育的公众中因后一个方面而闻名于世，那就是他作为灾难理论创始人的工作(后来由 Erik Christopher Zeeman 发展)。他于1958年获得菲尔兹奖。
==Biography==
René Thom was born in [[Montbéliard]], [[Doubs]]. He was educated 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, titled ''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 the [[International Congress of Mathematicians]] in [[Edinburgh]] in 1958, were already present in his thesis.
René Thom was born in Montbéliard, Doubs. He was educated 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, titled 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 the International Congress of Mathematicians in Edinburgh in 1958, were already present in his thesis.
René Thom 出生于杜城的蒙贝利亚尔。他在圣路易公立中学和高等师范学校接受教育，都在巴黎。他于1951年在巴黎大学获得博士学位。他的论文名为 Espaces fibres en sphères et carrés de Steenrod (球束和 Steenrod 方块) ，是在亨利 · 卡尔坦的指导下写成的。1958年，他在爱丁堡的国际数学家大会获得了菲尔兹奖，其合作主义理论的基础已经出现在他的论文中。
After a fellowship in the [[United States]], he went on to teach at the Universities of [[Université Joseph Fourier|Grenoble]] (1953–1954) and [[University of Strasbourg|Strasbourg]] (1954–1963), where he was appointed Professor in 1957. In 1964, he moved to the [[Institut des Hautes Études Scientifiques]], in [[Bures-sur-Yvette]]. He was awarded the [[Brouwer Medal]] in 1970, the [[Grand Prix Scientifique de la Ville de Paris]] in 1974, and became a Member of the [[Académie des Sciences]] of Paris in 1976.
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 Professor in 1957. In 1964, he moved to the Institut des Hautes Études Scientifiques, in Bures-sur-Yvette. He was awarded the Brouwer Medal in 1970, the Grand Prix Scientifique de la Ville de Paris in 1974, and became a Member of the Académie des Sciences of Paris in 1976.
在美国获得奖学金后，他继续在格勒诺布尔大学(1953-1954)和斯特拉斯堡大学(1954-1963)任教，并于1957年被任命为教授。1964年，他搬到了法国高等科学研究所伊维特河畔比尔。他于1970年获得布鲁沃奖章，1974年获得 Grand Prix Scientifique de la Ville de Paris 奖章，并于1976年成为巴黎法国科学院委员会成员。
While René Thom is most known to the public for his development of [[catastrophe theory]] between 1968 and 1972, in which he uses his earlier work on [[differential topology]] to develop a general theory of biological form,<ref name="New Kind of Science">{{cite book|last=Wolfram|first=Stephen|title=A New Kind of Science|publisher=Wolfram Media, Inc.|year=2002|page=[https://www.wolframscience.com/nks/notes-8-6--history-of-theories-of-biological-form/ 1003]|isbn=1-57955-008-8|url=https://www.wolframscience.com/nks/}}</ref> his academic achievements concern mostly his mathematical work on topology. 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 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 (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]]. While Thom found general recognition among the general public for the popularized version of his work on biology (later developed by [[Christopher Zeeman]]), this work struggled to gain traction among natural scientists due to the inaccessibility of its mathematics.<ref name="New Kind of Science" />
While René Thom is most known to the public for his development of catastrophe theory between 1968 and 1972, in which he uses his earlier work on differential topology to develop a general theory of biological form, 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. 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. While Thom found general recognition among the general public for the popularized version of his work on biology (later developed by Christopher Zeeman), this work struggled to gain traction among natural scientists due to the inaccessibility of its mathematics.
在1968年到1972年间，rené Thom 因发展了灾难理论而为公众所熟知，在这个理论中，他利用他早期的微分拓扑理论发展了一个生物形态的通用理论，他的学术成就主要是关于拓扑学的数学工作。在20世纪50年代早期，它涉及到现在所谓的 Thom 空间、特征类、协边理论和 Thom 横截性定理。这一系列工作的另一个例子是汤姆猜想，其版本已被用规范理论研究。从20世纪50年代中期开始，他进入了奇点理论，突变理论只是其中的一个方面，在1960年到1969年间，他发表了一系列深入的论文，发展了分层集合和分层映射理论，证明了描述惠特尼分层集合的局部锥形结构的基本分层同位定理，现在被称为---- 马瑟同位定理。他关于分层集的大部分工作都是为了理解拓扑稳定映射的概念，并最终证明两个光滑流形之间的拓扑稳定映射集是一个稠密集。的关于可微映射稳定性的演讲，于1960年在波恩大学上发表，由 Harold Levine 撰写，并于1969-1970年间在利物浦大学关于奇点的长达一年的研讨会上发表，由 C.T.c. Wall 编辑。1970年，John Mather 完成了拓扑稳定映射密度的证明，该证明基于 Thom 在过去十年中发展的思想。1976年，Klaus Wirthmüller，Andrew du Plessis 和 Eduard Looijenga 发表了一份详细的克里斯·吉布森。虽然 Thom 发现他的生物学工作(后来由 Christopher Zeeman 开发)的普及版本得到了公众的普遍认可，但由于数学难以获得，这项工作难以在自然科学家中获得吸引力。
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 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".
除了 Thom 对代数拓扑的贡献之外，他还通过研究通用性质来研究可微映射。在他生命的最后几年，他把注意力转向努力将他关于结构地形学的思想以“半物理学”的形式应用到思想、语言和意义的问题上。
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".
==Bibliography==
* {{citation|mr=0054960| last=Thom| first=René| url=http://archive.numdam.org/article/ASENS_1952_3_69__109_0.pdf | title=Espaces fibrés en sphères et carrés de Steenrod | journal= [[Annales Scientifiques de l'École Normale Supérieure]] |series=Série 3 | volume=69 | year=1952 | pages=109–182| doi=10.24033/asens.998 }}
* {{citation|mr=0061823| title=Quelques propriétés globales des variétés différentiables|journal= [[Commentarii Mathematici Helvetici]] |volume= 28|year= 1954|pages= 17–86 |url=http://www.digizeitschriften.de/dms/img/?PID=GDZPPN002056259| doi=10.1007/BF02566923 | author=Thom, René}}
* "[https://projecteuclid.org/euclid.bams/1183530285 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}}
* ''Structural Stability and Morphogenesis'', W. A. Benjamin, (1972), {{isbn|0-201-40685-3}}.
==See also==
*"[[List of important publications in mathematics#Quelques propriétés globales des variétés differentiables|Quelques propriétés globales des variétés differentiables]]"
==References==
<references />
*{{cite book |title=Logos et Théorie des Catastrophes: à partir de l'oeuvre de René Thom |editor-first=Jean |editor-last=Petitot |series=Colloque de Cerisy-la-Salle 1982 |publisher=Patiño |location=Geneva |year=1996 |isbn=978-2-88213-010-5 }}
*{{cite book |first=David |last=Aubin |chapterurl=https://webusers.imj-prg.fr/~david.aubin/publis/2004a.pdf |chapter=Forms of Explanations in the Catastrophe Theory of René Thom: Topology, Morphogenesis, and Structuralism |title=Growing Explanations: Historical Perspective on the Sciences of Complexity |editor-first=M. N. |editor-last=Wise |location=Durham |publisher=Duke University Press |year=2004 |pages=95–130 |isbn= }}
*{{cite book |first=Brian J. |last=Reilly |chapter=René Thom |title=The Columbia History of Twentieth-Century French Thought |editor-first=Lawrence D. |editor-last=Kritzman |location=New York |publisher=Columbia University Press |year=2006 |isbn=978-0-231-10791-4 |pages=[https://archive.org/details/columbiahistoryo2006unse/page/663 663–666] |url=https://archive.org/details/columbiahistoryo2006unse/page/663 }}
*{{cite news |first=Martin |last=Weil |title=French Mathematician René Thom Dies |newspaper=[[Washington Post]] |date=November 17, 2002 |page=C10 }}
*{{cite news |first=Athanase |last=Papadopoulos |title=René Thom: Portrait Mathématique et philosophique |publisher=CNRS Editions, Paris |year=2018 |isbn=978-2-271-11827-1}}
==External links==
{{commons category}}
* {{MacTutor Biography|id=Thom}}
* {{MathGenealogyProject|93398}}
* [https://www.washingtonpost.com/wp-dyn/articles/A64970-2002Nov16.html Washington Post Online edition] (free registration)
* [https://web.archive.org/web/20110720170236/http://www.pedagopsy.eu/meeting_rene_thom.htm Meeting René THOM]
{{Fields medalists}}
{{John von Neumann Lecturers}}
{{Authority control}}
Category:1923 births
类别: 1923出生
{{DEFAULTSORT:Thom, Rene}}
Category:2002 deaths
分类: 2002年死亡人数
[[Category:1923 births]]
Category:People from Montbéliard
类别: 蒙贝利亚尔人
[[Category:2002 deaths]]
Category:20th-century French mathematicians
范畴: 20世纪法国数学家
[[Category:People from Montbéliard]]
Category:École Normale Supérieure alumni
Category:École Normale Supérieure alumni
[[Category:20th-century French mathematicians]]
Category:Recipients of the National Order of Scientific Merit (Brazil)
类别: 国家科学成就勋章获得者(巴西)
[[Category:École Normale Supérieure alumni]]
Category:Fields Medalists
类别: 菲尔兹奖获得者
[[Category:Recipients of the National Order of Scientific Merit (Brazil)]]
Category:Brouwer Medalists
组别: Brouwer Medalists
[[Category:Fields Medalists]]
Category:French semioticians
分类: 法国符号学家
[[Category:Brouwer Medalists]]
Category:Members of the French Academy of Sciences
类别: 法国科学院成员
[[Category:French semioticians]]
Category:Institute for Advanced Study visiting scholars
类别: 高级研究所访问学者
[[Category:Members of the French Academy of Sciences]]
Category:Theoretical biologists
类别: 理论生物学家
[[Category:Institute for Advanced Study visiting scholars]]
Category:Topologists
类别: 拓扑学家
[[Category:Theoretical biologists]]
Category:Lycée Saint-Louis alumni
类别: 圣路易公立中学校友
[[Category:Topologists]]
Category:University of Strasbourg faculty
类别: 斯特拉斯堡大学
<noinclude>
<small>This page was moved from [[wikipedia:en:René Thom]]. Its edit history can be viewed at [[托姆/edithistory]]</small></noinclude>
[[Category:待整理页面]]
{{short description|French mathematician}}
{{Infobox scientist
{{Infobox scientist
{信息盒科学家
|name=René Thom
|name=René Thom
|name=René Thom
|image=René Thom.jpeg
|image=René Thom.jpeg
|image=René Thom.jpeg
|caption=René Thom in [[Nice]], 1970
|caption=René Thom in Nice, 1970
1970年摄于尼斯
|birth_date = {{birth date|1923|9|2|df=y}}
|birth_date =
出生日期
|birth_place= [[Montbéliard]], France
|birth_place= Montbéliard, France
出生地: 法国蒙贝利亚德
|death_date = {{death date and age|2002|10|25|1923|9|2|df=y}}
|death_date =
死亡日期
|death_place=[[Bures-sur-Yvette]], France
|death_place=Bures-sur-Yvette, France
死亡地点: 伊维特河畔比尔，法国
|nationality = French
|nationality = French
| 国籍: 法国
|workplaces = [[University of Strasbourg]]<br>[[Université Joseph Fourier]]<br>[[Institut des Hautes Études Scientifiques]]
|workplaces = University of Strasbourg<br>Université Joseph Fourier<br>Institut des Hautes Études Scientifiques
约瑟夫傅立叶大学斯特拉斯堡大学法国高等科学研究所
|alma_mater=[[École Normale Supérieure]], [[University of Paris]]
|alma_mater=École Normale Supérieure, University of Paris
|alma_mater=École Normale Supérieure, University of Paris
|doctoral_advisor= [[Henri Cartan]]
|doctoral_advisor= Henri Cartan
博士生导师: Henri Cartan
|doctoral_students=[[David Trotman]]
|doctoral_students=David Trotman
博士生: David Trotman
|thesis_title = Espaces fibrés en sphères et carrés de Steenrod
|thesis_title = Espaces fibrés en sphères et carrés de Steenrod
|thesis_title = Espaces fibrés en sphères et carrés de Steenrod
|thesis_year = 1951
|thesis_year = 1951
论文年份 = 1951
|field = [[Mathematics]]
|field = Mathematics
| field = 数学
|prizes=[[Fields Medal]] in 1958
|prizes=Fields Medal in 1958
1958年菲尔兹奖
|known_for=[[Dold–Thom theorem]]<br>[[Thom isomorphism]]<br>[[Thom space|Pontryagin–Thom construction]]<br>[[Thom–Porteous formula]]
|known_for=Dold–Thom theorem<br>Thom isomorphism<br>Pontryagin–Thom construction<br>Thom–Porteous formula
托姆同构庞特里亚金结构托姆-波特罗公式
}}
}}
}}
'''René Frédéric Thom''' ({{IPA-fr|ʁəne tɔm|lang}}; 2 September 1923 – 25 October 2002) was a French [[mathematician]]. 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]]). He received the [[Fields Medal]] in 1958.
René Frédéric Thom (; 2 September 1923 – 25 October 2002) was a French mathematician. 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). He received the Fields Medal in 1958.
René Frédéric Thom (; 1923年9月2日至2002年10月25日)是一位法国数学家。他作为一个拓扑学家而闻名于世，并开始研究后来被称为奇点理论的一些方面; 他在更广泛的学术界和受过教育的公众中因后一个方面而闻名于世，那就是他作为灾难理论创始人的工作(后来由 Erik Christopher Zeeman 发展)。他于1958年获得菲尔兹奖。
==Biography==
René Thom was born in [[Montbéliard]], [[Doubs]]. He was educated 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, titled ''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 the [[International Congress of Mathematicians]] in [[Edinburgh]] in 1958, were already present in his thesis.
René Thom was born in Montbéliard, Doubs. He was educated 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, titled 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 the International Congress of Mathematicians in Edinburgh in 1958, were already present in his thesis.
René Thom 出生于杜城的蒙贝利亚尔。他在圣路易公立中学和高等师范学校接受教育，都在巴黎。他于1951年在巴黎大学获得博士学位。他的论文名为 Espaces fibres en sphères et carrés de Steenrod (球束和 Steenrod 方块) ，是在亨利 · 卡尔坦的指导下写成的。1958年，他在爱丁堡的国际数学家大会获得了菲尔兹奖，其合作主义理论的基础已经出现在他的论文中。
After a fellowship in the [[United States]], he went on to teach at the Universities of [[Université Joseph Fourier|Grenoble]] (1953–1954) and [[University of Strasbourg|Strasbourg]] (1954–1963), where he was appointed Professor in 1957. In 1964, he moved to the [[Institut des Hautes Études Scientifiques]], in [[Bures-sur-Yvette]]. He was awarded the [[Brouwer Medal]] in 1970, the [[Grand Prix Scientifique de la Ville de Paris]] in 1974, and became a Member of the [[Académie des Sciences]] of Paris in 1976.
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 Professor in 1957. In 1964, he moved to the Institut des Hautes Études Scientifiques, in Bures-sur-Yvette. He was awarded the Brouwer Medal in 1970, the Grand Prix Scientifique de la Ville de Paris in 1974, and became a Member of the Académie des Sciences of Paris in 1976.
在美国获得奖学金后，他继续在格勒诺布尔大学(1953-1954)和斯特拉斯堡大学(1954-1963)任教，并于1957年被任命为教授。1964年，他搬到了法国高等科学研究所伊维特河畔比尔。他于1970年获得布鲁沃奖章，1974年获得 Grand Prix Scientifique de la Ville de Paris 奖章，并于1976年成为巴黎法国科学院委员会成员。
While René Thom is most known to the public for his development of [[catastrophe theory]] between 1968 and 1972, in which he uses his earlier work on [[differential topology]] to develop a general theory of biological form,<ref name="New Kind of Science">{{cite book|last=Wolfram|first=Stephen|title=A New Kind of Science|publisher=Wolfram Media, Inc.|year=2002|page=[https://www.wolframscience.com/nks/notes-8-6--history-of-theories-of-biological-form/ 1003]|isbn=1-57955-008-8|url=https://www.wolframscience.com/nks/}}</ref> his academic achievements concern mostly his mathematical work on topology. 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 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 (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]]. While Thom found general recognition among the general public for the popularized version of his work on biology (later developed by [[Christopher Zeeman]]), this work struggled to gain traction among natural scientists due to the inaccessibility of its mathematics.<ref name="New Kind of Science" />
While René Thom is most known to the public for his development of catastrophe theory between 1968 and 1972, in which he uses his earlier work on differential topology to develop a general theory of biological form, 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. 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. While Thom found general recognition among the general public for the popularized version of his work on biology (later developed by Christopher Zeeman), this work struggled to gain traction among natural scientists due to the inaccessibility of its mathematics.
在1968年到1972年间，rené Thom 因发展了灾难理论而为公众所熟知，在这个理论中，他利用他早期的微分拓扑理论发展了一个生物形态的通用理论，他的学术成就主要是关于拓扑学的数学工作。在20世纪50年代早期，它涉及到现在所谓的 Thom 空间、特征类、协边理论和 Thom 横截性定理。这一系列工作的另一个例子是汤姆猜想，其版本已被用规范理论研究。从20世纪50年代中期开始，他进入了奇点理论，突变理论只是其中的一个方面，在1960年到1969年间，他发表了一系列深入的论文，发展了分层集合和分层映射理论，证明了描述惠特尼分层集合的局部锥形结构的基本分层同位定理，现在被称为---- 马瑟同位定理。他关于分层集的大部分工作都是为了理解拓扑稳定映射的概念，并最终证明两个光滑流形之间的拓扑稳定映射集是一个稠密集。的关于可微映射稳定性的演讲，于1960年在波恩大学上发表，由 Harold Levine 撰写，并于1969-1970年间在利物浦大学关于奇点的长达一年的研讨会上发表，由 C.T.c. Wall 编辑。1970年，John Mather 完成了拓扑稳定映射密度的证明，该证明基于 Thom 在过去十年中发展的思想。1976年，Klaus Wirthmüller，Andrew du Plessis 和 Eduard Looijenga 发表了一份详细的克里斯·吉布森。虽然 Thom 发现他的生物学工作(后来由 Christopher Zeeman 开发)的普及版本得到了公众的普遍认可，但由于数学难以获得，这项工作难以在自然科学家中获得吸引力。
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 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".
除了 Thom 对代数拓扑的贡献之外，他还通过研究通用性质来研究可微映射。在他生命的最后几年，他把注意力转向努力将他关于结构地形学的思想以“半物理学”的形式应用到思想、语言和意义的问题上。
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".
==Bibliography==
* {{citation|mr=0054960| last=Thom| first=René| url=http://archive.numdam.org/article/ASENS_1952_3_69__109_0.pdf | title=Espaces fibrés en sphères et carrés de Steenrod | journal= [[Annales Scientifiques de l'École Normale Supérieure]] |series=Série 3 | volume=69 | year=1952 | pages=109–182| doi=10.24033/asens.998 }}
* {{citation|mr=0061823| title=Quelques propriétés globales des variétés différentiables|journal= [[Commentarii Mathematici Helvetici]] |volume= 28|year= 1954|pages= 17–86 |url=http://www.digizeitschriften.de/dms/img/?PID=GDZPPN002056259| doi=10.1007/BF02566923 | author=Thom, René}}
* "[https://projecteuclid.org/euclid.bams/1183530285 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}}
* ''Structural Stability and Morphogenesis'', W. A. Benjamin, (1972), {{isbn|0-201-40685-3}}.
==See also==
*"[[List of important publications in mathematics#Quelques propriétés globales des variétés differentiables|Quelques propriétés globales des variétés differentiables]]"
==References==
<references />
*{{cite book |title=Logos et Théorie des Catastrophes: à partir de l'oeuvre de René Thom |editor-first=Jean |editor-last=Petitot |series=Colloque de Cerisy-la-Salle 1982 |publisher=Patiño |location=Geneva |year=1996 |isbn=978-2-88213-010-5 }}
*{{cite book |first=David |last=Aubin |chapterurl=https://webusers.imj-prg.fr/~david.aubin/publis/2004a.pdf |chapter=Forms of Explanations in the Catastrophe Theory of René Thom: Topology, Morphogenesis, and Structuralism |title=Growing Explanations: Historical Perspective on the Sciences of Complexity |editor-first=M. N. |editor-last=Wise |location=Durham |publisher=Duke University Press |year=2004 |pages=95–130 |isbn= }}
*{{cite book |first=Brian J. |last=Reilly |chapter=René Thom |title=The Columbia History of Twentieth-Century French Thought |editor-first=Lawrence D. |editor-last=Kritzman |location=New York |publisher=Columbia University Press |year=2006 |isbn=978-0-231-10791-4 |pages=[https://archive.org/details/columbiahistoryo2006unse/page/663 663–666] |url=https://archive.org/details/columbiahistoryo2006unse/page/663 }}
*{{cite news |first=Martin |last=Weil |title=French Mathematician René Thom Dies |newspaper=[[Washington Post]] |date=November 17, 2002 |page=C10 }}
*{{cite news |first=Athanase |last=Papadopoulos |title=René Thom: Portrait Mathématique et philosophique |publisher=CNRS Editions, Paris |year=2018 |isbn=978-2-271-11827-1}}
==External links==
{{commons category}}
* {{MacTutor Biography|id=Thom}}
* {{MathGenealogyProject|93398}}
* [https://www.washingtonpost.com/wp-dyn/articles/A64970-2002Nov16.html Washington Post Online edition] (free registration)
* [https://web.archive.org/web/20110720170236/http://www.pedagopsy.eu/meeting_rene_thom.htm Meeting René THOM]
{{Fields medalists}}
{{John von Neumann Lecturers}}
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<small>This page was moved from [[wikipedia:en:René Thom]]. Its edit history can be viewed at [[托姆/edithistory]]</small></noinclude>
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