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第33行： − 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,<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. − − 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。 − − − − 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". − − 在托姆一生的最后二十年中，他的主要著作涉及的是哲学和认识论，他对亚里士多德的科学著作进行了重新评估。1992年，他是18位向剑桥大学致信的抗议者之一，抗议计划授予雅克·德里达名誉博士学位。 − − − − 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". − − − 第108行：
第85行： − − {{commons category}} − − * {{MacTutor Biography|id=Thom}} − − * {{MathGenealogyProject|93398}} − − − 第126行：
第94行： − − − {{Fields medalists}} − − {{John von Neumann Lecturers}} − − {{Authority control}} − − − − Category:1923 births − − Category:2002 deaths − − − − Category:People from Montbéliard − − − − Category:20th-century French mathematicians − − − − Category:École Normale Supérieure alumni − − Category:École Normale Supérieure alumni − − − Category:Recipients of the National Order of Scientific Merit (Brazil) − − − − Category:Fields Medalists − − − − Category:Brouwer Medalists − − − − Category:French semioticians − − − − Category:Members of the French Academy of Sciences − − − − Category:Institute for Advanced Study visiting scholars − − − − Category:Theoretical biologists − − − − Category:Topologists − − − − Category:Lycée Saint-Louis alumni − − − − Category:University of Strasbourg faculty − − − − <small>This page was moved from [[wikipedia:en:René Thom]]. Its edit history can be viewed at [[托姆/edithistory]]</small></noinclude> −
无编辑摘要
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。
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。
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。
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，<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>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]] 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。<ref name="New Kind of Science" />
在托姆一生的最后二十年中，他的主要著作涉及的是哲学和认识论，他对亚里士多德的科学著作进行了重新评估。1992年，他是18位向剑桥大学致信的抗议者之一，抗议计划授予[[雅克·德里达]]名誉博士学位。<ref>{{cite web|url=http://ontology.buffalo.edu/smith/derridaletter.htm|title=Derrida Letter, The Cambridge Affair, 1992}}</ref>
除了对代数拓扑的贡献之外，托姆还通过通有性质来研究可微映射。在他的最后几年里，他将注意力转移到以“'''<font color="#ff8000"> Semiophysics</font>'''”的形式将有关结构地形的思想应用于思维，语言和含义的问题中去。
除了对代数拓扑的贡献之外，托姆还通过通有性质来研究可微映射。在他的最后几年里，他将注意力转移到以“'''<font color="#ff8000"> Semiophysics</font>'''”的形式将有关结构地形的思想应用于思维，语言和含义的问题中去。
== Bibliography 参考书目 ==
== 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 }}
== External links 相关链接 ==
== External links 相关链接 ==
* [https://www.washingtonpost.com/wp-dyn/articles/A64970-2002Nov16.html Washington Post Online edition] (free registration)
* [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]
* [https://web.archive.org/web/20110720170236/http://www.pedagopsy.eu/meeting_rene_thom.htm Meeting René THOM]
* O'Connor, John J.; Robertson, Edmund F., "勒内·托姆", MacTutor History of Mathematics archive, University of St Andrews.
* O'Connor, John J.; Robertson, Edmund F., "勒内·托姆", MacTutor History of Mathematics archive, University of St Andrews.
* 遇见勒内·托姆
* 遇见勒内·托姆
类别: 1923出生
类别: 1923出生
{{DEFAULTSORT:Thom, Rene}}
{{DEFAULTSORT:Thom, Rene}}
分类: 2002年死亡人数
分类: 2002年死亡人数
[[Category:1923 births]]
[[Category:1923 births]]
类别: 蒙贝利亚尔人
类别: 蒙贝利亚尔人
[[Category:2002 deaths]]
[[Category:2002 deaths]]
范畴: 20世纪法国数学家
范畴: 20世纪法国数学家
[[Category:People from Montbéliard]]
[[Category:People from Montbéliard]]
[[Category:20th-century French mathematicians]]
[[Category:20th-century French mathematicians]]
类别: 国家科学成就勋章获得者(巴西)
类别: 国家科学成就勋章获得者(巴西)
[[Category:École Normale Supérieure alumni]]
[[Category:École Normale Supérieure alumni]]
类别: 菲尔兹奖获得者
类别: 菲尔兹奖获得者
[[Category:Recipients of the National Order of Scientific Merit (Brazil)]]
[[Category:Recipients of the National Order of Scientific Merit (Brazil)]]
组别: Brouwer Medalists
组别: Brouwer Medalists
[[Category:Fields Medalists]]
[[Category:Fields Medalists]]
分类: 法国符号学家
分类: 法国符号学家
[[Category:Brouwer Medalists]]
[[Category:Brouwer Medalists]]
类别: 法国科学院成员
类别: 法国科学院成员
[[Category:French semioticians]]
[[Category:French semioticians]]
类别: 高级研究所访问学者
类别: 高级研究所访问学者
[[Category:Members of the French Academy of Sciences]]
[[Category:Members of the French Academy of Sciences]]
类别: 理论生物学家
类别: 理论生物学家
[[Category:Institute for Advanced Study visiting scholars]]
[[Category:Institute for Advanced Study visiting scholars]]
类别: 拓扑学家
类别: 拓扑学家
[[Category:Theoretical biologists]]
[[Category:Theoretical biologists]]
类别: 圣路易公立中学校友
类别: 圣路易公立中学校友
[[Category:Topologists]]
[[Category:Topologists]]
类别: 斯特拉斯堡大学
类别: 斯特拉斯堡大学
<noinclude>
<noinclude>