更改

{{short description|French mathematician}}

{{short description|French mathematician}}

{{Infobox scientist

{{Infobox scientist

|name=René Thom

|name=René Thom

|image=René Thom.jpeg

|image=René Thom.jpeg

|caption=René Thom in [[Nice]], 1970

|caption=René Thom in [[Nice]], 1970

|birth_date = {{birth date|1923|9|2|df=y}}

|birth_date = {{birth date|1923|9|2|df=y}}

|birth_place= [[Montbéliard]], France

|birth_place= [[Montbéliard]], France

|death_date = {{death date and age|2002|10|25|1923|9|2|df=y}}

|death_date = {{death date and age|2002|10|25|1923|9|2|df=y}}

|death_place=[[Bures-sur-Yvette]], France

|death_place=[[Bures-sur-Yvette]], France

|nationality      = French

|nationality      = French

|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]]

|alma_mater=[[École Normale Supérieure]], [[University of Paris]]

|alma_mater=[[École Normale Supérieure]], [[University of Paris]]

|doctoral_advisor= [[Henri Cartan]]

|doctoral_advisor= [[Henri Cartan]]

|doctoral_students=[[David Trotman]]

|doctoral_students=[[David Trotman]]

|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

|field = [[Mathematics]]

|field = [[Mathematics]]

|prizes=[[Fields Medal]] in 1958

|prizes=[[Fields Medal]] in 1958

|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>[[Thom space|Pontryagin–Thom construction]]<br>[[Thom–Porteous formula]]

}}

}}

'''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''' ({{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 (; 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。

'''勒内·托姆René Frédéric Thom'''（法语：[ʁənetɔm]；1923年9月2日至2002年10月25日）是法国数学家。他以拓扑学家著称，特别是在研究所谓的'''<font color="#ff8000"> 奇点理论Singularity theory</font>'''领域。在广大学术界以及教育程度高的大众眼中，他作为'''<font color="#ff8000"> 突变理论Catastrophe theory</font>'''的创始人而举世闻名，后来该理论由埃里克·克里斯托弗·塞曼Erik Christopher Zeeman深入研究。1958年，他获得了菲尔兹奖。

==Biography==

== Biography 个人简介==

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 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。

勒内·托姆出生于杜省的蒙贝利亚。他曾就读于巴黎的圣路易中学LycéeSaint-Louis和巴黎高等师范学校École Normale Supérieure，并于1951年在巴黎大学获得博士学位。在亨利·嘉当Henri Cartan的指导下，他完成了他的论文“ Espaces fibrés en sphères et carrés de Steenrod”（球形纤维丛和斯廷罗德平方）。1958年，勒内·托姆因他提出的配边理论基础，在爱丁堡国际数学家大会上获得菲尔兹奖。该理论其实曾在他早期的论文中提出过。

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.

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。

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，他转而进入伊维特河畔布尔斯Bures-sur-Yvette的高等科学研究院工作。后来于1970年获得了布劳维尔奖章，于1974年获得了巴黎科学奖，且于1976年成为巴黎科学院的成员。

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, 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&ndash;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.

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&ndash;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。

勒内·托姆1968年至1972年间发展的突变理论利用了他先前在微分拓扑上的工作成果，进而发展了生物形式的通用理论。尽管后来因此而广为公众所知，但他的学术成就主要还是涉及在拓扑上的数学研究。在1950年代初，托姆就开始研究诸如'''<font color="#ff8000"> 托姆空间Thom spaces</font>'''，'''<font color="#ff8000"> 特征类Characteristic classes</font>'''，'''<font color="#ff8000"> 托姆配边理论Cobordism theory</font>'''和'''<font color="#ff8000"> 托姆横截性定理定理Thom transversality theorem</font>'''。另一个例子是'''<font color="#ff8000"> 托姆猜想Thom conjecture</font>'''，后已使用'''<font color="#ff8000"> 规范理论Gauge theory</font>'''研究了其形式。从1950年代中期开始，他开始研究奇点理论，其包含了突变理论，在1960年至1969年之间的一系列较深入（当时并不明确）的论文中，他提出了'''<font color="#ff8000"> 分层集合论stratified sets</font>'''和'''<font color="#ff8000"> 分层映射理论stratified maps</font>'''，证明了描述'''<font color="#ff8000"> 惠特尼分层集合的局部圆锥结构 local conical structure of Whitney stratified sets</font>'''的基本'''<font color="#ff8000"> 分层同质化定理stratified isotopy theorem</font>'''，现称为'''<font color="#ff8000"> 托姆 - 马瑟同质化定理Thom–Mather isotopy theorem</font>'''。他在分层集上所做的大部分工作都是为了理解拓扑稳定图的概念而开发的，并最终证明了两个平滑流形之间的拓扑稳定映射集是一个密集集的结果。托姆于1960年在波恩大学发表的关于微分映射图稳定性的演讲，后来由Harold Levine详细记载，并在1969-70年于利物浦大学举行的为期一年的奇点研讨会论文集中发表，该研讨会由C.T.C. Wall编辑。约翰·马瑟John Mather于1970年根据托姆在过去十年中提出的思想，完成了拓扑稳定映射密度的证明。克里斯托弗·吉布森Christopher Gibson，克劳斯·维特穆勒Klaus Wirthmüller，安德鲁·迪·普莱西斯Andrew du Plessis和爱德华·洛伊吉恩加Eduard Looijenga于1976年发表了更详尽的论述。尽管汤姆的生物学著作（后来由克里斯托弗·塞曼Christopher Zeeman继续）的大众化版本获得了公众的普遍认可，但由于其数学的不可及性，这项研究仍在努力吸引自然科学家的注意。

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".

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".

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".

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==

 

== Bibliography 参考书目 ==

* {{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=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 }}

* ''Structural Stability and Morphogenesis'', W. A. Benjamin, (1972),  {{isbn|0-201-40685-3}}.

* ''Structural Stability and Morphogenesis'', W. A. Benjamin, (1972),  {{isbn|0-201-40685-3}}.

*"[[List of important publications in mathematics#Quelques propriétés globales des variétés differentiables|Quelques propriétés globales des variétés differentiables]]"

*"[[List of important publications in mathematics#Quelques propriétés globales des variétés differentiables|Quelques propriétés globales des variétés differentiables]]"

* [https://web.archive.org/web/20110720170236/http://www.pedagopsy.eu/meeting_rene_thom.htm Meeting René THOM]

* [https://web.archive.org/web/20110720170236/http://www.pedagopsy.eu/meeting_rene_thom.htm Meeting René THOM]

{{Fields medalists}}

{{Fields medalists}}