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[[File:Henri Poincaré maison natale Nancy plaque.jpg|thumb|right|200px| Plaque on the birthplace of Henri Poincaré at house number 117 on the Grande Rue in the city of Nancy]]

[[File:Henri Poincaré maison natale Nancy plaque.jpg|thumb|right|200px| Plaque on the birthplace of Henri Poincaré at house number 117 on the Grande Rue in the city of Nancy]]

  Plaque on the birthplace of Henri Poincaré at house number 117 on the Grande Rue in the city of Nancy

  Plaque on the birthplace of Henri Poincaré at house number 117 on the Grande Rue in the city of Nancy

位于南希市大街117号的昂利 · 庞加莱出生地牌匾

位于南希市格兰德大街117号昂利 · 庞加莱出生地的牌匾

During his childhood he was seriously ill for a time with diphtheria and received special instruction from his mother, Eugénie Launois (1830–1897).

During his childhood he was seriously ill for a time with diphtheria and received special instruction from his mother, Eugénie Launois (1830–1897).

在童年时期，他曾一度患有严重的白喉病，并接受了他母亲欧热尼 · 劳诺伊斯(Eugénie Launois，1830-1897)的特别指导。

在童年时期，他曾一度患有严重的白喉病，受到他母亲欧热尼 · 劳诺伊斯(Eugénie Launois，1830-1897)的特别照顾。

In 1862, Henri entered the Lycée in Nancy (now renamed the  in his honour, along with Henri Poincaré University, also in Nancy). He spent eleven years at the Lycée and during this time he proved to be one of the top students in every topic he studied. He excelled in written composition. His mathematics teacher described him as a "monster of mathematics" and he won first prizes in the concours général, a competition between the top pupils from all the Lycées across France. His poorest subjects were music and physical education, where he was described as "average at best". However, poor eyesight and a tendency towards absentmindedness may explain these difficulties. He graduated from the Lycée in 1871 with a bachelor's degree in letters and sciences.

In 1862, Henri entered the Lycée in Nancy (now renamed the  in his honour, along with Henri Poincaré University, also in Nancy). He spent eleven years at the Lycée and during this time he proved to be one of the top students in every topic he studied. He excelled in written composition. His mathematics teacher described him as a "monster of mathematics" and he won first prizes in the concours général, a competition between the top pupils from all the Lycées across France. His poorest subjects were music and physical education, where he was described as "average at best". However, poor eyesight and a tendency towards absentmindedness may explain these difficulties. He graduated from the Lycée in 1871 with a bachelor's degree in letters and sciences.

1862年，亨利进入南希的 Lycée (为了纪念他，现在与同样位于南希的亨利 · 庞加莱大学一起重新命名为南希大学)。他在 Lycée 学习了11年，在此期间，他证明自己在所学的每一个领域都是最优秀的学生之一。他的作文写得很好。他的数学老师形容他是一个“数学怪兽” ，他在总决赛中获得了一等奖，总决赛是法国所有中学的优秀学生之间的比赛。他最差的科目是音乐和体育，在那里他被描述为“最好的平均水平”。然而，视力差和心不在焉的倾向也许可以解释这些困难。他于1871年毕业于 Lycée，获得文理学学士学位。

1862年，亨利进入南希市的高中 (为了纪念他，现在与同样位于南希的亨利 · 庞加莱大学一起重新命名)。他在 高中学习了11年，在此期间，他证明自己在所学的每一个领域都是最优秀的学生之一。他的作文写得很好。他的数学老师形容他是一个“数学怪兽” ，他在总决赛中获得了一等奖，总决赛是法国所有中学的优秀学生之间的比赛。他最差的科目是音乐和体育，在那里他被描述为“最好的平均水平”。然而，视力差和心不在焉的倾向也许可以解释这些困难。他于1871年毕业于 Lycée，获得文理学学士学位。

At the same time, Poincaré was preparing for his Doctorate in Science in mathematics under the supervision of Charles Hermite. His doctoral thesis was in the field of differential equations. It was named Sur les propriétés des fonctions définies par les équations aux différences partielles. Poincaré devised a new way of studying the properties of these equations. He not only faced the question of determining the integral of such equations, but also was the first person to study their general geometric properties. He realised that they could be used to model the behaviour of multiple bodies in free motion within the solar system. Poincaré graduated from the University of Paris in 1879.

At the same time, Poincaré was preparing for his Doctorate in Science in mathematics under the supervision of Charles Hermite. His doctoral thesis was in the field of differential equations. It was named Sur les propriétés des fonctions définies par les équations aux différences partielles. Poincaré devised a new way of studying the properties of these equations. He not only faced the question of determining the integral of such equations, but also was the first person to study their general geometric properties. He realised that they could be used to model the behaviour of multiple bodies in free motion within the solar system. Poincaré graduated from the University of Paris in 1879.

与此同时，庞加莱在查尔斯 · 埃尔米特的指导下正在准备他的数学博士学位。他的博士论文是在微分方程领域。It was named Sur les propriétés des fonctions définies par les équations aux différences partielles.庞加莱设计了一种研究这些方程性质的新方法。他不仅面临着确定这些方程的积分的问题，而且是第一个研究它们的一般几何性质的人。他意识到，这些物质可以用来模拟太阳系内自由运动的多个物体的行为。庞加莱1879年毕业于巴黎大学。

与此同时，庞加莱在查尔斯 · 埃尔米特的指导下正在准备他的数学博士学位。他的博士论文是在微分方程领域，《关于部分差公式定义的函数属性》。庞加莱设计了一种研究这些方程性质的新方法。他不仅面临着确定这些方程的积分的问题，而且是第一个研究它们的一般几何性质的人。他意识到，它们可以用来模拟太阳系内自由运动的多个星体的行为。庞加莱1879年毕业于巴黎大学。

===First scientific achievements===

===First scientific achievements最初科学成就===

After receiving his degree, Poincaré began teaching as junior lecturer in mathematics at the [[Caen University|University of Caen]] in Normandy (in December 1879). At the same time he published his first major article concerning the treatment of a class of [[automorphic function]]s.

After receiving his degree, Poincaré began teaching as junior lecturer in mathematics at the [[Caen University|University of Caen]] in Normandy (in December 1879). At the same time he published his first major article concerning the treatment of a class of [[automorphic function]]s.

After receiving his degree, Poincaré began teaching as junior lecturer in mathematics at the University of Caen in Normandy (in December 1879). At the same time he published his first major article concerning the treatment of a class of automorphic functions.

After receiving his degree, Poincaré began teaching as junior lecturer in mathematics at the University of Caen in Normandy (in December 1879). At the same time he published his first major article concerning the treatment of a class of automorphic functions.

获得学位后，庞加莱开始在诺曼底的卡昂大学担任数学初级讲师(1879年12月)。与此同时，他发表了第一篇关于一类自守函数的处理的重要文章。

获得学位后，庞加莱开始在诺曼底的卡昂大学担任数学初级讲师(1879年12月)。与此同时，他发表了第一篇重要文章，关于一类<font color="#ff8000"> 自守函数Automorphic functions</font>的处理。

Poincaré immediately established himself among the greatest mathematicians of Europe, attracting the attention of many prominent mathematicians. In 1881 Poincaré was invited to take a teaching position at the Faculty of Sciences of the University of Paris; he accepted the invitation. During the years of 1883 to 1897, he taught mathematical analysis in École Polytechnique.

Poincaré immediately established himself among the greatest mathematicians of Europe, attracting the attention of many prominent mathematicians. In 1881 Poincaré was invited to take a teaching position at the Faculty of Sciences of the University of Paris; he accepted the invitation. During the years of 1883 to 1897, he taught mathematical analysis in École Polytechnique.

In 1881–1882, Poincaré created a new branch of mathematics: qualitative theory of differential equations. He showed how it is possible to derive the most important information about the behavior of a family of solutions without having to solve the equation (since this may not always be possible). He successfully used this approach to problems in celestial mechanics and mathematical physics.

In 1881–1882, Poincaré created a new branch of mathematics: qualitative theory of differential equations. He showed how it is possible to derive the most important information about the behavior of a family of solutions without having to solve the equation (since this may not always be possible). He successfully used this approach to problems in celestial mechanics and mathematical physics.

1881-1882年，庞加莱创立了一个新的数学分支: 微分方程定性理论。他展示了如何不用解方程就可以得到关于一组解的行为的最重要的信息(因为这可能并不总是可能的)。他成功地用这种方法解决了天体力学和数学物理的问题。

1881-1882年，庞加莱创立了一个新的数学分支: <font color="#ff8000"> 微分方程定性理论Qualitative theory of differential equations</font>。他展示了如何不用解方程就可以得到关于一组解的行为的最重要的信息(因为这可能并不总是可能的)。他成功地用这种方法解决了天体力学和数学物理的问题。

===Career===

===Career职业生涯===

He never fully abandoned his mining career to mathematics. He worked at the [[Ministry of Public Services]] as an engineer in charge of northern railway development from 1881 to 1885. He eventually became chief engineer of the Corps de Mines in 1893 and inspector general in 1910.

He never fully abandoned his mining career to mathematics. He worked at the [[Ministry of Public Services]] as an engineer in charge of northern railway development from 1881 to 1885. He eventually became chief engineer of the Corps de Mines in 1893 and inspector general in 1910.

He never fully abandoned his mining career to mathematics. He worked at the Ministry of Public Services as an engineer in charge of northern railway development from 1881 to 1885. He eventually became chief engineer of the Corps de Mines in 1893 and inspector general in 1910.

He never fully abandoned his mining career to mathematics. He worked at the Ministry of Public Services as an engineer in charge of northern railway development from 1881 to 1885. He eventually became chief engineer of the Corps de Mines in 1893 and inspector general in 1910.

In 1887, he won Oscar II, King of Sweden's mathematical competition for a resolution of the three-body problem concerning the free motion of multiple orbiting bodies. (See three-body problem section below.)

In 1887, he won Oscar II, King of Sweden's mathematical competition for a resolution of the three-body problem concerning the free motion of multiple orbiting bodies. (See three-body problem section below.)

在1887年，他赢得了奥斯卡二世，瑞典国王的数学竞赛，以获得关于多轨道天体自由运动的三体。(见下面的三体问题。)

在1887年，他以解决有关多个轨道物体自由运动的三体问题，赢得了奥斯卡二世，瑞典国王的数学竞赛。(见下面的三体问题。)

The Poincaré family grave at the [[Cimetière du Montparnasse]]

The Poincaré family grave at the [[Cimetière du Montparnasse]]

庞加莱家族在[蒙帕纳斯公墓]的坟墓

庞加莱家族在[蒙帕纳斯公墓]]的坟墓

In 1893, Poincaré joined the French [[Bureau des Longitudes]], which engaged him in the [[Clock synchronization|synchronisation of time]] around the world. In 1897 Poincaré backed an unsuccessful proposal for the [[Decimal degrees|decimalisation of circular measure]], and hence time and [[longitude]].<ref>see Galison 2003</ref> It was this post which led him to consider the question of establishing international time zones and the synchronisation of time between bodies in relative motion. (See [[#Work on relativity|work on relativity]] section below.)

In 1893, Poincaré joined the French [[Bureau des Longitudes]], which engaged him in the [[Clock synchronization|synchronisation of time]] around the world. In 1897 Poincaré backed an unsuccessful proposal for the [[Decimal degrees|decimalisation of circular measure]], and hence time and [[longitude]].<ref>see Galison 2003</ref> It was this post which led him to consider the question of establishing international time zones and the synchronisation of time between bodies in relative motion. (See [[#Work on relativity|work on relativity]] section below.)

====Students====

====Students学生====

Poincaré had two notable doctoral students at the University of Paris, [[Louis Bachelier]] (1900) and [[Dimitrie Pompeiu]] (1905).<ref>[http://www.genealogy.ams.org/id.php?id=34227 Mathematics Genealogy Project] {{Webarchive|url=https://web.archive.org/web/20071005011853/http://www.genealogy.ams.org/id.php?id=34227 |date=5 October 2007 }} North Dakota State University. Retrieved April 2008.</ref>

Poincaré had two notable doctoral students at the University of Paris, [[Louis Bachelier]] (1900) and [[Dimitrie Pompeiu]] (1905).<ref>[http://www.genealogy.ams.org/id.php?id=34227 Mathematics Genealogy Project] {{Webarchive|url=https://web.archive.org/web/20071005011853/http://www.genealogy.ams.org/id.php?id=34227 |date=5 October 2007 }} North Dakota State University. Retrieved April 2008.</ref>

=== Death ===

=== Death死亡 ===

==Work==

==Work成就==

===Summary===

===Summary综述===

Poincaré made many contributions to different fields of pure and applied mathematics such as: [[celestial mechanics]], [[fluid mechanics]], [[optics]], electricity, [[telegraphy]], [[capillarity]], [[Elasticity (physics)|elasticity]], [[thermodynamics]], [[potential theory]], [[Quantum mechanics|quantum theory]], [[theory of relativity]] and [[physical cosmology]].

Poincaré made many contributions to different fields of pure and applied mathematics such as: [[celestial mechanics]], [[fluid mechanics]], [[optics]], electricity, [[telegraphy]], [[capillarity]], [[Elasticity (physics)|elasticity]], [[thermodynamics]], [[potential theory]], [[Quantum mechanics|quantum theory]], [[theory of relativity]] and [[physical cosmology]].

Poincaré made many contributions to different fields of pure and applied mathematics such as: celestial mechanics, fluid mechanics, optics, electricity, telegraphy, capillarity, elasticity, thermodynamics, potential theory, quantum theory, theory of relativity and physical cosmology.

Poincaré made many contributions to different fields of pure and applied mathematics such as: celestial mechanics, fluid mechanics, optics, electricity, telegraphy, capillarity, elasticity, thermodynamics, potential theory, quantum theory, theory of relativity and physical cosmology.

在纯数学和应用数学的不同领域做出了很多贡献，例如: 天体力学、流体力学、光学、电学、电报学、毛细现象、弹性力学、热力学、势论、量子理论、相对论和物理宇宙学。

庞加莱在纯数学和应用数学的不同领域做出了很多贡献，例如: 天体力学、流体力学、光学、电学、电报学、毛细现象、弹性力学、热力学、势论、量子理论、相对论和物理宇宙学。

*[[algebraic topology]]

*[[algebraic topology]]

 

*[[several complex variables|the theory of analytic functions of several complex variables]]

*[[several complex variables|the theory of analytic functions of several complex variables]]

 

*[[abelian variety|the theory of abelian functions]]

*[[abelian variety|the theory of abelian functions]]

 

*[[algebraic geometry]]

*[[algebraic geometry]]

 

*the [[Poincaré conjecture]], proven in 2003 by [[Grigori Perelman]].

*the [[Poincaré conjecture]], proven in 2003 by [[Grigori Perelman]].

 

*[[Poincaré recurrence theorem]]

*[[Poincaré recurrence theorem]]

 

*[[hyperbolic geometry]]

*[[hyperbolic geometry]]

 

*[[number theory]]

*[[number theory]]

 

*the [[three-body problem]]

*the [[three-body problem]]

 

*[[diophantine equation|the theory of diophantine equations]]

*[[diophantine equation|the theory of diophantine equations]]

 

*[[electromagnetism]]

*[[electromagnetism]]

 

*[[Special relativity|the special theory of relativity]]

*[[Special relativity|the special theory of relativity]]

 

*the [[fundamental group]]

*the [[fundamental group]]

 

*In the field of [[differential equations]] Poincaré has given many results that are critical for the qualitative theory of differential equations, for example the [[Poincaré homology sphere|Poincaré sphere]] and the [[Poincaré map]].

*In the field of [[differential equations]] Poincaré has given many results that are critical for the qualitative theory of differential equations, for example the [[Poincaré homology sphere|Poincaré sphere]] and the [[Poincaré map]].

 

*Poincaré on "everybody's belief" in the [[q:Henri Poincaré|''Normal Law of Errors'']] (see [[normal distribution]] for an account of that "law")

*Poincaré on "everybody's belief" in the [[q:Henri Poincaré|''Normal Law of Errors'']] (see [[normal distribution]] for an account of that "law")

 

*Published an influential paper providing a novel mathematical argument in support of [[quantum mechanics]].<ref name=McCormmach>{{Citation | last = McCormmach | first = Russell | title = Henri Poincaré and the Quantum Theory | journal = Isis | volume = 58 | issue = 1 | pages = 37–55 | date =Spring 1967 | doi =10.1086/350182| s2cid = 120934561 }}</ref><ref name=Irons>{{Citation | last = Irons | first = F. E. | title = Poincaré's 1911–12 proof of quantum discontinuity interpreted as applying to atoms | journal = American Journal of Physics | volume = 69 | issue = 8 | pages = 879–884 | date = August 2001 | doi =10.1119/1.1356056 |bibcode = 2001AmJPh..69..879I }}</ref>

*Published an influential paper providing a novel mathematical argument in support of [[quantum mechanics]].<ref name=McCormmach>{{Citation | last = McCormmach | first = Russell | title = Henri Poincaré and the Quantum Theory | journal = Isis | volume = 58 | issue = 1 | pages = 37–55 | date =Spring 1967 | doi =10.1086/350182| s2cid = 120934561 }}</ref><ref name=Irons>{{Citation | last = Irons | first = F. E. | title = Poincaré's 1911–12 proof of quantum discontinuity interpreted as applying to atoms | journal = American Journal of Physics | volume = 69 | issue = 8 | pages = 879–884 | date = August 2001 | doi =10.1119/1.1356056 |bibcode = 2001AmJPh..69..879I }}</ref>

 

===Three-body problem三体问题===

===Three-body problem===

The problem of finding the general solution to the motion of more than two orbiting bodies in the solar system had eluded mathematicians since [[Isaac Newton|Newton's]] time. This was known originally as the three-body problem and later the [[n-body problem|''n''-body problem]], where ''n'' is any number of more than two orbiting bodies. The ''n''-body solution was considered very important and challenging at the close of the 19th century. Indeed, in 1887, in honour of his 60th birthday, [[Oscar II of Sweden|Oscar II, King of Sweden]], advised by [[Gösta Mittag-Leffler]], established a prize for anyone who could find the solution to the problem. The announcement was quite specific:

The problem of finding the general solution to the motion of more than two orbiting bodies in the solar system had eluded mathematicians since [[Isaac Newton|Newton's]] time. This was known originally as the three-body problem and later the [[n-body problem|''n''-body problem]], where ''n'' is any number of more than two orbiting bodies. The ''n''-body solution was considered very important and challenging at the close of the 19th century. Indeed, in 1887, in honour of his 60th birthday, [[Oscar II of Sweden|Oscar II, King of Sweden]], advised by [[Gösta Mittag-Leffler]], established a prize for anyone who could find the solution to the problem. The announcement was quite specific:

The problem of finding the general solution to the motion of more than two orbiting bodies in the solar system had eluded mathematicians since Newton's time. This was known originally as the three-body problem and later the n-body problem, where n is any number of more than two orbiting bodies. The n-body solution was considered very important and challenging at the close of the 19th century. Indeed, in 1887, in honour of his 60th birthday, Oscar II, King of Sweden, advised by Gösta Mittag-Leffler, established a prize for anyone who could find the solution to the problem. The announcement was quite specific:

The problem of finding the general solution to the motion of more than two orbiting bodies in the solar system had eluded mathematicians since Newton's time. This was known originally as the three-body problem and later the n-body problem, where n is any number of more than two orbiting bodies. The n-body solution was considered very important and challenging at the close of the 19th century. Indeed, in 1887, in honour of his 60th birthday, Oscar II, King of Sweden, advised by Gösta Mittag-Leffler, established a prize for anyone who could find the solution to the problem. The announcement was quite specific:

自从牛顿时代以来，数学家们就一直没有解决太阳系中两个以上轨道天体运动的一般解的问题。这个问题最初被称为三体问题，后来又被称为 n 体问题，其中 n 是任意数量的两个以上的轨道天体。在19世纪末，n 体解被认为是非常重要和具有挑战性的。事实上，在1887年，为了庆祝他的60岁生日，瑞典国王奥斯卡二世在哥斯塔·米塔-列夫勒的建议下，设立了一个奖项，奖励任何能够找到解决问题的方法的人。声明非常具体:

自从牛顿时代以来，数学家们就一直没有解决太阳系中两个以上轨道天体运动的一般解的问题。这个问题最初被称为<font color="#ff8000"> 三体问题Three-body problem</font>，后来又被称为 <font color="#ff8000"> n 体问题n-body problem</font>，其中 n 是任意数量的两个以上的轨道天体。在19世纪末，n 体解被认为是非常重要和具有挑战性的。事实上，在1887年，为了庆祝他的60岁生日，瑞典国王奥斯卡二世在哥斯塔·米塔-列夫勒的建议下，设立了一个奖项，奖励任何能够找到解决问题的方法的人。声明非常具体:

In case the problem could not be solved, any other important contribution to classical mechanics would then be considered to be prizeworthy. The prize was finally awarded to Poincaré, even though he did not solve the original problem. One of the judges, the distinguished Karl Weierstrass, said, "This work cannot indeed be considered as furnishing the complete solution of the question proposed, but that it is nevertheless of such importance that its publication will inaugurate a new era in the history of celestial mechanics." (The first version of his contribution even contained a serious error; for details see the article by Diacu and the book by Barrow-Green). The version finally printed contained many important ideas which led to the theory of chaos. The problem as stated originally was finally solved by Karl F. Sundman for n&nbsp;=&nbsp;3 in 1912 and was generalised to the case of n&nbsp;>&nbsp;3 bodies by Qiudong Wang in the 1990s.

In case the problem could not be solved, any other important contribution to classical mechanics would then be considered to be prizeworthy. The prize was finally awarded to Poincaré, even though he did not solve the original problem. One of the judges, the distinguished Karl Weierstrass, said, "This work cannot indeed be considered as furnishing the complete solution of the question proposed, but that it is nevertheless of such importance that its publication will inaugurate a new era in the history of celestial mechanics." (The first version of his contribution even contained a serious error; for details see the article by Diacu and the book by Barrow-Green). The version finally printed contained many important ideas which led to the theory of chaos. The problem as stated originally was finally solved by Karl F. Sundman for n&nbsp;=&nbsp;3 in 1912 and was generalised to the case of n&nbsp;>&nbsp;3 bodies by Qiudong Wang in the 1990s.

如果这个问题无法解决，任何其他对经典力学的重要贡献都会被认为是值得的。尽管 Poincaré 没有解决最初的问题，但他最终获得了诺贝尔和平奖。其中一位评委，尊敬的卡尔·魏尔斯特拉斯，说，“这项工作确实不能被认为是提供了提议的问题的完整解决方案，但它是如此重要，它的出版将开创一个新的时代，在天体力学的历史。”(他的贡献的第一个版本甚至包含了一个严重的错误; 详情见 Diacu 的文章和 Barrow-Green 的书)。最后印刷出来的版本包含了许多重要的思想，这些思想导致了混沌理论的产生。1912年，Karl f. Sundman 最终解决了 n = 3的问题，1990年代，王将其推广到 n > 3具尸体的情况。

如果这个问题无法解决，那么对经典力学的任何其他重要贡献都将被认为是值得获奖。虽然庞加莱没有解决最初的问题，但最终还是把奖颁给了他。其中一位评委，著名的卡尔·魏尔斯特拉斯说：“这项工作确实不能被视为提供了所提出问题的完整解决方案，但它的出版将开创天体力学史上的一个新纪元。”(他贡献的第一个版本甚至包含了一个严重的错误; 详情见 Diacu 的文章和 Barrow-Green 的书)。最终印刷的版本包含了许多导致混沌理论的重要思想。最初所述的问题最终由Karl F.Sundman在1912年解决了n&nbsp;=&nbsp;3的情况，并在1990年代将其推广到王秋东的n&nbsp;>&nbsp;3体的案例中。

| last=Diacu|first= Florin | year=1996 | title=The solution of the ''n''-body Problem | journal=The Mathematical Intelligencer | volume =18 | pages =66–70 | doi=10.1007/BF03024313

| last=Diacu|first= Florin | year=1996 | title=The solution of the ''n''-body Problem | journal=The Mathematical Intelligencer | volume =18 | pages =66–70 | doi=10.1007/BF03024313

| issue=3|s2cid= 119728316 }}</ref> and the book by [[June Barrow-Green|Barrow-Green]]<ref>{{Cite book|title=Poincaré and the three body problem|title-link= Poincaré and the Three-Body Problem |last=Barrow-Green|first=June|publisher=[[American Mathematical Society]]|year=1997|isbn=978-0821803677|location=Providence, RI|series=History of Mathematics|volume=11|pages=|oclc=34357985}}</ref>). The version finally printed<ref>{{Cite book|title=The three-body problem and the equations of dynamics: Poincaré's foundational work on dynamical systems theory|last=Poincaré|first=J. Henri|publisher=Springer International Publishing|others=Popp, Bruce D. (Translator)|year=2017|isbn=9783319528984|location=Cham, Switzerland|pages=|oclc=987302273}}</ref> contained many important ideas which led to the [[chaos theory|theory of chaos]]. The problem as stated originally was finally solved by [[Karl F. Sundman]] for ''n''&nbsp;=&nbsp;3 in 1912 and was generalised to the case of ''n''&nbsp;>&nbsp;3 bodies by [[Qiudong Wang]] in the 1990s.

| issue=3|s2cid= 119728316 }}</ref> and the book by [[June Barrow-Green|Barrow-Green]]<ref>{{Cite book|title=Poincaré and the three body problem|title-link= Poincaré and the Three-Body Problem |last=Barrow-Green|first=June|publisher=[[American Mathematical Society]]|year=1997|isbn=978-0821803677|location=Providence, RI|series=History of Mathematics|volume=11|pages=|oclc=34357985}}</ref>). The version finally printed<ref>{{Cite book|title=The three-body problem and the equations of dynamics: Poincaré's foundational work on dynamical systems theory|last=Poincaré|first=J. Henri|publisher=Springer International Publishing|others=Popp, Bruce D. (Translator)|year=2017|isbn=9783319528984|location=Cham, Switzerland|pages=|oclc=987302273}}</ref> contained many important ideas which led to the [[chaos theory|theory of chaos]]. The problem as stated originally was finally solved by [[Karl F. Sundman]] for ''n''&nbsp;=&nbsp;3 in 1912 and was generalised to the case of ''n''&nbsp;>&nbsp;3 bodies by [[Qiudong Wang]] in the 1990s.

[玛丽 · 居里和庞加莱在1911年索尔维会议大会上的演讲]

[玛丽 · 居里和庞加莱在1911年索尔维会议大会上的演讲]

===Work on relativity===

===Work on relativity相对论研究===

[[Image:Curie and Poincare 1911 Solvay.jpg|thumb|right|[[Marie Curie]] and Poincaré talk at the 1911 [[Solvay Conference]]]]

[[Image:Curie and Poincare 1911 Solvay.jpg|thumb|right|[[Marie Curie]] and Poincaré talk at the 1911 [[Solvay Conference]]]]

 

{{main|Lorentz ether theory|History of special relativity}}

{{main|Lorentz ether theory|History of special relativity}}

 

Poincaré's work at the Bureau des Longitudes on establishing international time zones led him to consider how clocks at rest on the Earth, which would be moving at different speeds relative to absolute space (or the "luminiferous aether"), could be synchronised. At the same time Dutch theorist Hendrik Lorentz was developing Maxwell's theory into a theory of the motion of charged particles ("electrons" or "ions"), and their interaction with radiation. In 1895 Lorentz had introduced an auxiliary quantity (without physical interpretation) called "local time" <math>t^\prime = t-v x/c^2 \,</math>

Poincaré's work at the Bureau des Longitudes on establishing international time zones led him to consider how clocks at rest on the Earth, which would be moving at different speeds relative to absolute space (or the "luminiferous aether"), could be synchronised. At the same time Dutch theorist Hendrik Lorentz was developing Maxwell's theory into a theory of the motion of charged particles ("electrons" or "ions"), and their interaction with radiation. In 1895 Lorentz had introduced an auxiliary quantity (without physical interpretation) called "local time" <math>t^\prime = t-v x/c^2 \,</math>

庞加莱在法国经度管理局关于建立国际时区的工作使他思考如何使地球上静止的时钟以不同的速度相对于绝对空间(或称为“以太时间”)进行同步。与此同时，荷兰理论家亨德里克 · 洛伦兹正在将麦克斯韦理论发展成一个关于带电粒子(“电子”或“离子”)运动及其与辐射相互作用的理论。1895年，洛伦兹引入了一个辅助量(没有物理解释) ，叫做“本地时间” t ^ prime = t-v x/c ^ 2

庞加莱在法国经度管理局关于建立国际时区的工作使他思考如何使地球上静止的时钟以不同的速度相对于绝对空间(或称为“以太时间”)进行同步。与此同时，荷兰理论家亨德里克 · 洛伦兹正在将麦克斯韦理论发展成一个关于带电粒子(“电子”或“离子”)运动及其与辐射相互作用的理论。1895年，洛伦兹引入了一个辅助量(没有物理解释) ，叫做“本地时间” <math>t^\prime = t-v x/c^2 \,</math>

====Local time====

====Local time当下时间====

and introduced the hypothesis of length contraction to explain the failure of optical and electrical experiments to detect motion relative to the aether (see Michelson–Morley experiment).

and introduced the hypothesis of length contraction to explain the failure of optical and electrical experiments to detect motion relative to the aether (see Michelson–Morley experiment).

Poincaré was a constant interpreter (and sometimes friendly critic) of Lorentz's theory. Poincaré as a philosopher was interested in the "deeper meaning". Thus he interpreted Lorentz's theory and in so doing he came up with many insights that are now associated with special relativity. In The Measure of Time (1898), Poincaré said, "

Poincaré was a constant interpreter (and sometimes friendly critic) of Lorentz's theory. Poincaré as a philosopher was interested in the "deeper meaning". Thus he interpreted Lorentz's theory and in so doing he came up with many insights that are now associated with special relativity. In The Measure of Time (1898), Poincaré said, "

庞加莱是洛伦兹理论的不断解释者(有时也是友好的批评者)。作为一个哲学家，庞加莱对“更深层的意义”很感兴趣。因此，他解释了 Lorentz 的理论，并由此提出了许多现在与狭义相对论有关的见解。在《时间的度量》(1898)中，庞加莱说:

庞加莱是洛伦兹理论的不断解释者(有时也是友好的批评者)。作为一个哲学家，庞加莱对“更深层的意义”很感兴趣。因此，他解释了 洛伦茨的理论，并由此提出了许多现在与狭义相对论有关的见解。在《时间的度量》(1898)中，庞加莱说:

|url=https://books.google.com/books?id=amLqckyrvUwC}}, [https://books.google.com/books?id=amLqckyrvUwC&pg=PA37 Section A5a, p 37]</ref>

|url=https://books.google.com/books?id=amLqckyrvUwC}}, [https://books.google.com/books?id=amLqckyrvUwC&pg=PA37 Section A5a, p 37]</ref>

A little reflection is sufficient to understand that all these affirmations have by themselves no meaning. They can have one only as the result of a convention." He also argued that scientists have to set the constancy of the speed of light as a postulate to give physical theories the simplest form.

A little reflection is sufficient to understand that all these affirmations have by themselves no meaning. They can have one only as the result of a convention." He also argued that scientists have to set the constancy of the speed of light as a postulate to give physical theories the simplest form.

and introduced the hypothesis of [[length contraction]] to explain the failure of optical and electrical experiments to detect motion relative to the aether (see [[Michelson–Morley experiment]]).<ref>{{Citation

and introduced the hypothesis of [[length contraction]] to explain the failure of optical and electrical experiments to detect motion relative to the aether (see [[Michelson–Morley experiment]]).<ref>{{Citation