Poincaré, Henri

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{{Infobox_Scientist
 
{{Infobox_Scientist
 
| name = Henri Poincaré
 
| name = Henri Poincaré
| image = Poincare jh.jpg
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| image = JH Poincare.jpg
 
| image_width = 230px
 
| image_width = 230px
 
| caption = <small> Henri Poincaré, photograph from the frontispiece of the 1913 edition of "Last Thoughts" </small>
 
| caption = <small> Henri Poincaré, photograph from the frontispiece of the 1913 edition of "Last Thoughts" </small>
 
| birth_date = April 29, 1854
 
| birth_date = April 29, 1854
| birth_place = [[Nancy]], [[France]]
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| birth_place = [[Nancy]], [[France]]
 
| death_date = July 17, 1912
 
| death_date = July 17, 1912
 
| death_place = [[Paris]], [[France]]
 
| death_place = [[Paris]], [[France]]
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'''Jules Henri Poincaré''' (April 29, 1854 &ndash; July 17, 1912) ([[IPA chart for English|IPA]]: [{{IPA|pwɛ̃kaˈʀe}}]<ref> [http://www.bartleby.com/61/wavs/3/P0400300.wav] Poincaré pronunciation example at Bartleby.com </ref>) was one of [[France]]'s greatest [[mathematician]]s and theoretical [[physicist]]s, and a [[philosophy of science|philosopher of science]]. Poincaré is often described as a [[polymath]], and in mathematics as 'The Last Universalist', since he excelled in all fields of the discipline as it existed during his lifetime.
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'''Jules Henri Poincaré''' (April 29, 1854 &ndash; July 17, 1912), generally known as '''Henri Poincaré''', was one of [[France]]'s greatest [[mathematician]]s and theoretical [[physicist]]s, and a [[philosophy of science|philosopher of science]]. He is often described as a [[polymath]] and as 'The Last Universalist' in mathematics, because he excelled in all fields of the discipline as it existed during his lifetime. He is known for his early formulation of the theory of relativity and for formulating the [[Poincaré conjecture]], one of the most famous problems in mathematics. He also laid the groundwork for [[chaos theory]] in the process of attempting to solve the important problem of the motion of three or more bodies acting under mutual gravitation. In addition, he is considered one of the founders of the field of [[topology]].
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==Biography==
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=== Early life and education ===
  
As a mathematician and physicist, he made many original fundamental contributions to [[Pure mathematics|pure]] and [[applied mathematics]], [[mathematical physics]], and [[celestial mechanics]]. He was responsible for formulating the [[Poincaré conjecture]], one of the most famous problems in mathematics. In his research on the [[three-body problem]], Poincaré became the first person to discover a chaotic deterministic system which laid the foundations of modern [[chaos theory]]. He is considered to be one of the founders of the field of [[topology]].
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Poincaré was born on April 29, 1854, into an influential family in the Cité Ducale neighborhood of [[Nancy]], France. His father, Leon Poincaré (1828-1892), was a professor of medicine at the [[University of Nancy]] (Sagaret, 1911). His younger sister, Aline, married the spiritual philosopher [[Emile Boutroux]]. Another notable member of Jules' family was his cousin [[Raymond Poincaré]], who became the President of France (from 1913 to 1920) and a fellow member of the [[Académie Française]].<ref name="IEP">Mauro Murzi, [http://www.utm.edu/research/iep/p/poincare.htm Jules Henri Poincaré.] ''The Internet Encyclopedia of Philosophy''. Retrieved November 12, 2007.</ref>
  
Poincaré introduced the modern [[principle of relativity]] and was the first to present the [[Lorentz transformations]] in their modern symmetrical form. Poincaré discovered the remaining relativistic velocity transformations and recorded them in a letter to Lorentz in 1905. Thus he obtained perfect invariance of all of [[Maxwell's equations]], the final step in the formulation of the theory of [[special relativity]].  
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During his childhood, he was seriously ill for a time with [[diphtheria]] and lost his voice for the better part of a year. He received special instructions from his mother, Eugénie Launois (1830-1897) and excelled in written composition.
  
The [[Poincaré group]] used in physics and mathematics was named after him.
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In 1862, Henri entered the Lycée in Nancy, now renamed the Lycée Henri Poincaré in his honor. He spent eleven years at the Lycée and during this time proved to be one of the top students in every topic he studied. 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"<ref>J. John O'Connor et al.,  2002. "Jules Henri Poincaré". University of St. Andrews, Scotland. Retrieved November 13, 2007. </ref> However, poor eyesight and a tendency toward absentmindedness may have contributed to these difficulties. He graduated from the Lycée in 1871 with a Bachelor's degree in letters and sciences.
  
== Life ==
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During the [[Franco-Prussian War]] of 1870, he served alongside his father in the Ambulance Corps, tending to the wounded and learning German.
Poincaré was born on April 29, 1854 in Cité Ducale neighborhood, [[Nancy]], France into an influential family (Belliver, 1956). His father Leon Poincaré (1828-1892) was a professor of medicine at the [[University of Nancy]] (Sagaret, 1911). His adored younger sister Aline married the spiritual philosopher [[Emile Boutroux]]. Another notable member of Jules' family was his cousin, Raymond, who would become the President of France, 1913 to 1920, and a fellow member of the [[Académie française]].<ref name="IEP">  [http://www.utm.edu/research/iep/p/poincare.htm The Internet Encyclopedia of Philosophy] Jules Henri Poincaré article by Mauro Murzi - accessed November 2006. </ref>
 
  
===Education===
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Poincaré entered the [[École Polytechnique]] in 1873. There he studied mathematics as a student of [[Charles Hermite]], continuing to excel and publishing his first paper (''Démonstration nouvelle des propriétés de l'indicatrice d'une surface'') in 1874. He graduated in 1875 and went on to the [[École des Mines]], continuing to study mathematics in addition to the mining engineering syllabus, and received the degree of ordinary engineer in March of 1879.
During his childhood he was seriously ill for a time with [[diphtheria]] and received special instruction from his gifted mother, Eugénie Launois (1830-1897).
 
  
In 1862 Henri entered the Lycée in Nancy (now renamed the Lycée Henri Poincaré in his honour, along with the University of 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" (O'Connor et al., 2002). However, poor eyesight and a tendency towards absentmindedness may explain these difficulties (Carl, 1968). He graduated from the Lycée in 1871 with a Bachelor's degree in letters and sciences.
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===Mining career===
  
During the [[Franco-Prussian War]] of 1870 he served alongside his father in the Ambulance Corps.
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As a graduate of the École des Mines, Poincaré joined the [[Corps des Mines]] as an inspector for the [[Vesoul]] region in northeast France. He was on the scene of a mining disaster at [[Magny]] in August 1879, in which 18 miners died. He carried out the official investigation into the accident in a characteristically thorough and humane way. Because he rushed into the mine after the accident, he was at first listed among the dead in the accident. In spite of his other activities, Poincare stayed loyal to his mining career, which in later life led to important government appointments.
  
Poincaré entered the [[École Polytechnique]] in 1873. There he studied mathematics as a student of [[Charles Hermite]], continuing to excel and publishing his first paper (''Démonstration nouvelle des propriétés de l'indicatrice d'une surface'') in 1874. He graduated in 1875 or 1876. He went on to study at the [[École des Mines]], continuing to study mathematics in addition to the mining engineering syllabus and received the degree of ordinary engineer in March 1879.
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=== Doctoral work ===
  
As a graduate of the École des Mines he joined the [[Corps des Mines]] as an inspector for the [[Vesoul]] region in northeast France. He was on the scene of a mining disaster at [[Magny]] in August 1879 in which 18 miners died. He carried out the official investigation into the accident in a characteristically thorough and humane way.
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While undertaking his professional responsibilities, Poincaré prepared for his doctorate in mathematics under the supervision of Hermite. His doctoral thesis was in the field of [[differential equations]]. Poincaré devised a new way of studying the properties of these expressions. He not only faced the question of determining the solution of such equations, but also was the first person to study their general geometric properties. He realized that they could be used to model the behavior of multiple bodies in free motion within the [[Solar System]]. Poincaré was awarded his doctorate from the University of Paris in 1879.
  
At the same time, Poincaré was preparing for his doctorate in sciences in mathematics under the supervision of [[Charles Hermite]]. His doctoral thesis was in the field of [[differential equations]]. 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.
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[[Image:Young Poincare.jpg|left|150px|thumb|The young Henri Poincaré.]]
  
[[Image:Young Poincare.jpg|left|200px|thumb|The young Henri Poincaré]]
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===Start of career in mathematics===
  
===Career===
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Soon after graduation, he was offered a post as junior lecturer in mathematics at [[Caen University]], but 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.
Soon after, he was offered a post as junior lecturer in mathematics at [[Caen University]], but 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.  
 
  
Beginning in 1881 and for the rest of his career, he taught at the [[University of Paris]] (the [[Sorbonne]]). He was initially appointed as the ''maître de conférences d'analyse'' (associate professor of analysis) (Sageret, 1911). Eventually, he held the chairs of Physical and Experimental Mechanics, Mathematical Physics and Theory of Probability, and Celestial Mechanics and Astronomy.  
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Beginning in 1881 and for the rest of his career, he taught at the [[University of Paris]] (the [[Sorbonne]]). He was initially appointed as associate professor of analysis (Sageret, 1911). Eventually, he held the chairs of Physical and Experimental Mechanics, Mathematical Physics and Theory of Probability, and Celestial Mechanics and Astronomy.  
  
 
Also in that same year, Poincaré married Miss Poulain d'Andecy. Together they had four children: Jeanne (born 1887), Yvonne (born 1889), Henriette (born 1891), and Léon (born 1893).
 
Also in that same year, Poincaré married Miss Poulain d'Andecy. Together they had four children: Jeanne (born 1887), Yvonne (born 1889), Henriette (born 1891), and Léon (born 1893).
  
In 1887, at the young age of 32, Poincaré was elected to the [[French Academy of Sciences]]. He became its president in 1906, and was elected to the [[Académie française]] in 1909.
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In 1887, at the age of 32, Poincaré was elected to the [[French Academy of Sciences]]. He became its president in 1906 and was elected to the [[Académie Française]] in 1909.
  
In 1887 he won [[Oscar II of Sweden|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 [[#The three-body problem]] section below)
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=== Gravitation, chaos, and the three-body problem ===
  
In 1893 Poincaré joined the French [[Bureau des Longitudes]], which engaged him in the synchronization of time around the world. In 1897 Poincaré backed an unsuccessful proposal for the decimalization of circular measure, and hence time and [[longitude]] (see Galison 2003). It was this post which led him to consider the question of establishing international time zones and the synchronization of time between bodies in relative motion. (See [[#Work on Relativity]] section below)
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In 1887, Poincaré won the [[Oscar II of Sweden|Oscar II, King of Sweden]]'s mathematical competition for a resolution of the [[three-body problem]] concerning the free motion of multiple orbiting bodies. Although he did not solve this problem, the insights he offered were striking and original enough for him to merit the prize.
  
In 1899, and again more successfully in 1904, he intervened in the trials of [[Alfred Dreyfus]]. He attacked the spurious scientific claims of some of the evidence brought against Dreyfus, who was a Jewish officer in the French army charged with treason by anti-Semitic colleagues.
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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]]'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 nineteenth century. Indeed in 1887, in honor of his 60th birthday, King Oscar II, advised by [[Gösta Mittag-Leffler]], established a prize for anyone who could find the solution to the problem. The announcement was quite specific:
  
In 1912 Poincaré underwent surgery for a [[prostate]] problem and subsequently died from an [[embolism]] on July 17, 1912, in Paris. He was aged 58. He is buried in the Poincaré family vault in the [[Cimetière du Montparnasse|Cemetery of Montparnasse]], Paris.
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{{cquote|Given a system of arbitrarily many mass points that attract each [[inverse-square law|according to Newton's law]], under the assumption that no two points ever collide, try to find a representation of the coordinates of each point as a series in a variable that is some known function of time and for all of whose values the series [[uniform convergence|converges uniformly]].}}
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In case the problem could not be solved, any other important contribution to classical mechanics would then considered worthy of the prize. Based on this stipulation, Poincaré's contribution was found to merit the prize. 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."
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The first version of Poincaré's paper contained a serious error. When he realized this, he used his own money to purchase copies of the work that contained the error to take them out of circulation. The version finally printed contained many important ideas that led to the [[chaos theory|theory of chaos]]. The problem as stated originally was finally solved by [[Karl Sundman]] for ''n''&nbsp;=&nbsp;3 in 1912, and it was generalized to the case of ''n''&nbsp;>&nbsp;3 bodies by [[Qiudong Wang]] in the 1990s.
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===Time and the theory of relativity===
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In 1893, Poincaré joined the French [[Bureau des Longitudes]], which engaged him in the synchronization of time around the world. In 1897, Poincaré backed an unsuccessful proposal for the decimalization of circular measure, and hence time and [[longitude]] (Galison 2003). This post led him to consider the question of establishing international time zones and the synchronization of time between bodies in relative motion.
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[[Image:Curie and Poincare 1911 Solvay.jpg|thumb|200px|right|[[Marie Curie]] and Poincaré talk at the 1911 [[Solvay Conference]].]]
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Poincaré's work at the Bureau des Longitudes on establishing international time zones, led him to consider how to synchronize clocks at rest on the Earth—clocks that would be moving at different speeds relative to absolute space (or the "luminiferous aether"). At the same time, [[Netherlands|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. What Lorentz realized is that, to make his equations applicable to a translation of uniform velocity, he had to introduce a different time variable for each reference frame. He called this "local time," given by the following equation:
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:<math>t^\prime = t-vx^\prime/c^2,\; \mathrm{where}\; x^\prime = x - vt</math> 
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where the primed variables refer to a reference frame in uniform motion relative to that of the unprimed variables. Lorentz was using it to explain the "failure" of the [[Michelson-Morley experiment]]—an experiment that failed to detect motion relative to the aether, the hypothetical medium that was thought to be the carrier of electromagnetic waves.
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In ''The Measure of Time'' (Poincaré 1898), Poincaré discussed the difficulty of establishing simultaneity at a distance and concluded it can be established by convention. He also discussed the "postulate of the speed of light," and formulated the [[principle of relativity]], according to which no mechanical or electromagnetic experiment can discriminate between a state of uniform motion and a state of rest. In 1900, Poincaré discussed Lorentz's concept of local time and remarked that it arose when moving clocks are synchronized by exchanging light signals assumed to travel with the same speed in both directions in a moving frame.<ref>Michael N. Macrossan, 1986-01-01, A Note on Relativity Before Einstein. ''British Journal for the Philosophy of Science'' 37 : 232-234. ''The University of Queensland, Australia''. </ref>
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Thereafter, Poincaré was a constant interpreter (and sometimes friendly critic) of Lorentz's theory. As a philosopher, Poincaré was interested in the "deeper meaning" of the theory. Thus he interpreted Lorentz's theory in terms of the [[principle of relativity]], and in so doing, he came up with many insights that are now associated with the theory of [[special relativity]].
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===Relationship between mass and energy===
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In his paper of 1900, Poincaré discussed the recoil of a physical object when it emits a burst of radiation in one direction, as predicted by Maxwell-Lorentz electrodynamics. He remarked that the stream of radiation appeared to act like a "fictitious fluid" with a mass per unit volume of ''e/c''<sup>2</sup>, where ''e'' is the energy density; in other words, the equivalent mass of the radiation is <math>m = E/c^2</math>.
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Poincaré considered the recoil of the emitter to be an unresolved feature of Maxwell-Lorentz theory, which he discussed again in "Science and Hypothesis" (1902) and "[[The Value of Science]]" (1905). In the latter he said the recoil "is contrary to the principle of Newton since our projectile here has no mass, it is not matter, it is energy," and discussed two other unexplained effects: (1) non-conservation of mass implied by Lorentz's variable mass <math>\gamma m</math>, Abraham's theory of variable mass and [[Walter Kaufmann (physicist)|Kaufmann]]'s experiments on the mass of fast moving electrons and (2) the non-conservation of energy in the radium experiments of [[Madame Curie]].
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It was Einstein's insight that a body losing energy as radiation or heat was losing mass of amount <math>m = E/c^2</math>, and the corresponding [[mass-energy equivalence|mass-energy conservation law]], ''E''&nbsp;=&nbsp;''mc''², that resolved these problems.<ref>H.E. Ives (1952) wrote that Einstein's derivation was a tautology due to Einstein's use of approximations, and credited [[Max Planck|Planck]] (1907) with the first correct derivation of <math>E = mc^2</math> in Einstein's meaning. In response J. Riseman and I. G. Young (1953) defended Einstein's derivation and physical insight, and Ives (1953) replied.</ref>
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===Correcting Lorentz===
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In 1905, Poincaré wrote to Lorentz<ref> [http://www.univ-nancy2.fr/poincare/chp/text/lorentz3.xml Poincaré à Lorentz.] Poincaré's letter to Lorentz. (In French). Retrieved November 12, 2007.</ref> about Lorentz's paper of 1904, which Poincaré described as a "paper of supreme importance." In this letter, he pointed out an error Lorentz had made when he had applied his transformation to one of Maxwell's equations, that for charge-occupied space, and also questioned the time dilation factor given by Lorentz. In a second letter to Lorentz,<ref> [http://web.archive.org/web/20050224225216/http://www.univ-nancy2.fr/poincare/chp/text/lorentz4.html Poincaré à Lorentz.] Poincaré's letter to Lorentz. (In French). Retrieved November 12, 2007.</ref> Poincaré explained a mathematical property of the transformations that Lorentz had not noticed, and gave his own reason why Lorentz's time dilation factor was indeed correct: Lorentz’s factor was necessary to make the Lorentz transformation from what mathematicians call a ''group.'' In the letter, he also gave Lorentz what is now known as the relativistic velocity-addition law, which is necessary to demonstrate invariance.
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Poincaré later delivered a paper at the meeting of the Academy of Sciences in Paris on June 5, 1905, in which these issues were addressed. In the published version of that short paper,<ref> [http://www.soso.ch/wissen/hist/SRT/P-1905-1.pdf Sur la Dynamique de l'Électron.] Retrieved November 12, 2007.</ref> he wrote:
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<div style="background:white">
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{{cquote|1=The essential point, established by Lorentz, is that the equations of the electromagnetic field are not altered by a certain transformation (which I will call by the name of Lorentz) of the form{{rf|2|LT1904}}:
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::<math>x^\prime = k\ell\left(x + \varepsilon t\right),</math><math>t^\prime = k\ell\left(t + \varepsilon x\right),</math><math>y^\prime = \ell y,</math> <math>z^\prime = \ell z,</math><math> k = 1/\sqrt{1-\varepsilon^2}.</math>}}
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</div>
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He then wrote that in order for the Lorentz transformations to form a ''group'' and satisfy the principle of relativity, the arbitrary function <math>\ell\left(\varepsilon\right)</math> must be unity for all <math>\varepsilon</math> (Lorentz had set <math>\ell = 1</math> by a different argument). Poincaré's discovery of the velocity transformations, allowed him to obtain perfect invariance, the final step in the  discovery of his theory of relativity.
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In an enlarged version of the paper that did not appear until 1906,<ref>[http://www.soso.ch/wissen/hist/SRT/P-1905.pdf Sur la Dynamique de l'Électron.] Retrieved November 12, 2007.</ref> he published his group property proof, incorporating the velocity addition law that he had previously written to Lorentz. The paper contains many other deductions from, and applications of, the transformations. For example, Poincaré (1906) pointed out that the combination <math>x^2+ y^2+ z^2- c^2t^2</math> is [[invariant]], and he introduced the 4-vector notation for which [[Hermann Minkowski]] became known.
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===Einstein and Poincaré===
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[[Albert Einstein]]'s first paper on [[relativity]] in 1905 derived the Lorentz transformation and presented them in the same form as had Poincaré. It was published three months after Poincaré's short paper but before Poincaré's longer version appeared in 1906. Although Einstein relied on the [[principle of relativity]] and used the same clock synchronization procedure that Poincaré (1900) had described, his paper was remarkable in that it had no references at all.
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Poincaré never acknowledged Einstein's work on relativity, but Einstein acknowledged Poincaré's somewhat belatedly in the text of a [[lecture]] in 1921 titled ''Geometrie und Erfahrung.'' Later, Einstein referred to Poincaré as one of the pioneers of relativity, saying that "Lorentz had already recognized that the transformation named after him is essential for the analysis of Maxwell's equations, and Poincaré deepened this insight still further …"
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Einstein formulated a ''general theory of relativity,'' which gave an expanded explanation of systems accelerating with respect to one another. The theory relating reference frames in uniform motion with respect to one another then became known as the ''special theory of relativity.''
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=== Father of relativity: Lorentz, Poincaré or Einstein? ===
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Poincaré's work in the development of Special Relativity is well recognized<ref>Olivier Darrigol, The Mystery of the Einstein-Poincaré Connection. ''Isis'' 95(4) (2004): 614-428.
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</ref>. Most historians, however, stress that despite many similarities with Einstein's work, the two had very different research agendas and interpretations of the work<ref>Peter Louis Galison. 2003. ''Einstein's Clocks, Poincaré's Maps: Empires of Time.'' (New York, NY: W.W. Norton)</ref><ref>Kragh 1999</ref>. A minority go much further, such as the historian of science Sir Edmund Whittaker, who held that Poincaré and Lorentz were the true discoverers of Relativity<ref>E.T. Whittaker. ''A History of the Theories of Aether and Electricity: Vol 2: The Modern Theories 1900-1926.'' Chapter II: The Relativity Theory of Poincaré and Lorentz. (London, UK: Nelson, 1953)</ref>.
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Poincaré consistently credited Lorentz's achievements, ranking his own contributions as minor. Thus, he wrote (Poincaré 1905):
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{{cquote| Lorentz has tried to modify his hypothesis so as to make it in accord with the hypothesis of complete impossibility of measuring absolute motion. ''He has succeeded in doing so'' in his article [Lorentz 1904]. The importance of the problem has made me take up the question again; the results that I have obtained agreement on ''all important points'' with those of Lorentz; ''I have been led only to modify or complete them on some points of detail''. The essential point, established by Lorentz, is that the equations of the electromagnetic field are not altered by a certain transformation. [emphases added].}}
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In an address in 1909 on "The New Mechanics," Poincaré discussed the demolition of Newton's mechanics brought about by [[Max Abraham]] and Lorentz, without mentioning Einstein. In one of his last essays entitled "The Quantum Theory" (1913), when referring to the [[Solvay Conference]], Poincaré again described special relativity as the "mechanics of Lorentz":
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{{cquote| … at every moment [the twenty physicists from different countries] could be heard talking of the new mechanics which they contrasted with the old mechanics. Now what was the old mechanics? Was it that of Newton, the one which still reigned uncontested at the close of the nineteenth century? No, it was ''the mechanics of Lorentz, the one dealing with the principle of relativity''; the one which, hardly five years ago, seemed to be the height of boldness … the mechanics of Lorentz endures … no body in motion will ever be able to exceed the speed of light … the mass of a body is not constant … no experiment will ever be able [to detect] motion either in relation to absolute space or even in relation to the aether. [emphasis added]}}
  
The French Minister of Education, [[Claude Allegre]], has recently (2004) proposed that Poincaré be reburied in the [[Panthéon, Paris|Panthéon]] in Paris, which is reserved for French citizens only of the highest honor.<ref>http://www.lexpress.fr/idees/tribunes/dossier/allegre/dossier.asp?ida=430274</ref>
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On the other hand, in a memoir written as a tribute to Poincaré after his death, Lorentz readily admitted the mistake he had made and credited Poincaré's achievements:
  
== Work ==
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{{cquote|For certain of the physical magnitudes which enter in the formulae I have not indicated the transformation which suits best. This has been done by Poincaré, and later by Einstein and Minkowski. My formulae were encumbered by certain terms which should have been made to disappear. […] ''I have not established the principle of relativity as rigorously and universally true''. Poincaré, on the other hand, has obtained a perfect invariance of the electro-magnetic equations, and he has formulated 'the postulate of relativity', terms which he was the first to employ. [emphasis added]}}
Poincaré made many contributions to different fields of applied mathematics such as: [[celestial mechanics]], [[fluid mechanics]], [[optics]], [[electricity]], [[telegraphy]], [[capillarity]], [[elasticity]], [[thermodynamics]], [[potential theory]], [[Quantum mechanics|quantum theory]], [[theory of relativity]] and [[physical cosmology]].
 
  
He was also a popularizer of mathematics and physics and wrote several books for the lay public.
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In summary, Poincaré regarded the mechanics as developed by Lorentz in order to obey the principle of relativity as the essence of the theory, while Lorentz stressed that perfect invariance was first obtained by Poincaré. The modern view is inclined to say that the group property and the invariance are the essential points.
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===Later life===
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In 1899, and again more successfully in 1904, he intervened in the trials of [[Alfred Dreyfus]]. He attacked the spurious scientific claims of some of the evidence brought against Dreyfus, who was a Jewish officer in the French army charged with treason by anti-Semitic colleagues. Some of these arguments involved probability, and Poincare noted that they were improperly applied to the evidence.
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In 1912, Poincaré underwent surgery for a [[prostate]] problem and subsequently died from an [[embolism]] on July 17, 1912, aged 58. He is buried in the Poincaré family vault in the [[Cimetière du Montparnasse|Cemetery of Montparnasse]], Paris.
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In 2004, [[Claude Allegre]], the French Minister of Education, proposed that Poincaré be reburied in the [[Panthéon, Paris|Pantheon]] in Paris, which is reserved for French citizens deserving of the highest honor.<ref>[http://www.lexpress.fr/idees/tribunes/dossier/allegre/dossier.asp?ida=430274 Lorentz, Poincaré et Einstein.] ''lexpress.fr''. (In French.) Retrieved November 12, 2007.</ref>
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== Significant contributions ==
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Poincaré made many contributions to different fields of physics and applied mathematics, such as [[celestial mechanics]], [[fluid mechanics]], [[optics]], [[electricity]], [[telegraphy]], [[capillarity]], [[elasticity]], [[thermodynamics]], [[potential theory]], [[Quantum mechanics|quantum theory]], [[theory of relativity]] and [[physical cosmology]]. He was also a popularizer of mathematics and physics and wrote several books for the lay public.
  
 
Among the specific topics he contributed to are the following:   
 
Among the specific topics he contributed to are the following:   
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*In an 1894 paper, he introduced the concept of the [[fundamental group]].
 
*In an 1894 paper, he introduced the concept of 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 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 sphere]] and the [[Poincaré map]].
*Poincaré on "everybody's belief" in the [http://en.wikiquote.org/wiki/Henri_Poincaré ''Normal Law of Errors''] (see [[normal distribution]] for an account of that "law")
+
*Poincaré on "everybody's belief" in the [http://en.wikiquote.org/wiki/Henri_Poincaré ''Normal Law of Errors''],
  
===The three-body problem===
+
== Character traits ==
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 nineteenth century. Indeed in 1887, in honor 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:
 
  
{{cquote|Given a system of arbitrarily many mass points that attract each [[inverse-square law|according to Newton's law]], under the assumption that no two points ever collide, try to find a representation of the coordinates of each point as a series in a variable that is some known function of time and for all of whose values the series [[uniform convergence|converges uniformly]].}}
+
Poincaré's work habits have been compared to a bee flying from flower to flower. Poincaré was interested in the way his mind worked; he studied his habits and gave a talk about his observations in 1908 at the Institute of General Psychology in Paris. He linked his way of thinking to how he made several discoveries.
  
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.
+
The mathematician Darboux claimed he was ''un intuitif'' (intuitive), arguing that this is demonstrated by the fact that he worked so often by visual representation. He did not care about being rigorous and disliked logic. He believed that logic was not a way to invent but a way to structure ideas and that logic limits ideas.
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). The version finally printed contained many important ideas which lead 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.
 
  
===Work on relativity===
+
===Toulouse's characterization ===
  
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 synchronized. At the same time [[Netherlands|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. He had introduced the concept of local time
+
Poincaré's mental organization interested not only Poincaré himself but also Toulouse, a psychologist of the Psychology Laboratory of the School of Higher Studies in Paris. Toulouse wrote a book entitled ''Henri Poincaré'' (1910). In it, he discussed Poincaré's regular schedule:
  
:<math>t^\prime = t-vx^\prime/c^2,\; \mathrm{where}\; x^\prime = x - vt</math> 
+
* He worked during the same times each day in short periods of time. He undertook mathematical research for four hours a day, between 10 a.m. and noon then again from 5 p.m. to 7 p.m.. He would read articles in journals later in the evening.
  
and was using it to explain the failure of optical and electrical experiments to detect motion relative to the aether (see [[Michelson-Morley experiment]]). Poincaré (1900) discussed Lorentz's "wonderful invention" of local time and remarked that it arose when moving clocks are synchronized by exchanging light signals assumed to travel with the same speed in both directions in a moving frame.<ref>http://eprint.uq.edu.au/archive/00002307/</ref> In "The Measure of Time" (Poincaré 1898), he discussed the difficulty of establishing simultaneity at a distance and concluded it can be established by convention. He also discussed the "postulate of the speed of light," and formulated the [[principle of relativity]], according to which no mechanical or electromagnetic experiment can discriminate between a state of uniform motion and a state of rest.  
+
* His normal work habit was to solve a problem completely in his head, then commit the completed problem to paper.  
  
Thereafter, 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 in terms of the [[principle of relativity]] and in so doing he came up with many insights that are now associated with special relativity.  
+
* He was ambidextrous and nearsighted.  
  
[[Image:Curie and Poincare 1911 Solvay.jpg|thumb|200px|right|[[Marie Curie]] and Poincaré talk at the 1911 [[Solvay Conference]].]]
+
* His ability to visualize what he heard proved particularly useful when he attended lectures since his eyesight was so poor that he could not see properly what his lecturers were writing on the blackboard.
  
In the paper of 1900 Poincaré discussed the recoil of a physical object when it emits a burst of radiation in one direction, as predicted by Maxwell-Lorentz electrodynamics. He remarked that the stream of radiation appeared to act like a "fictitious fluid" with a mass per unit volume of ''e/c''<sup>2</sup>, where ''e'' is the energy density; in other words, the equivalent mass of the radiation is <math>m = E/c^2</math>. Poincaré considered the recoil of the emitter to be an unresolved feature of Maxwell-Lorentz theory, which he discussed again in "Science and Hypothesis" (1902) and "[[The Value of Science]]" (1905). In the latter he said the recoil "is contrary to the principle of Newton since our projectile here has no mass, it is not matter, it is energy," and discussed two other unexplained effects: (1) non-conservation of mass implied by Lorentz's variable mass <math>\gamma m</math>, Abraham's theory of variable mass and [[Walter Kaufmann (physicist)|Kaufmann]]'s experiments on the mass of fast moving electrons and (2) the non-conservation of energy in the radium experiments of [[Madame Curie]]. It was Einstein's insight that a body losing energy as radiation or heat was losing mass of amount <math>m = E/c^2</math>, and the corresponding [[mass-energy equivalence|mass-energy conservation law]], ''E''&nbsp;=&nbsp;''mc''², that resolved these problems.<ref>H.E. Ives (1952) wrote that Einstein's derivation was a tautology due to Einstein's use of approximations, and credited [[Max Planck|Planck]] (1907) with the first correct derivation of <math>E = mc^2</math> in Einstein's meaning. In response J. Riseman and I. G. Young (1953) defended Einstein's derivation and physical insight, and Ives (1953) replied.</ref>
+
However, these abilities were somewhat balanced by his shortcomings:
  
In 1905 Poincaré wrote to Lorentz<ref>http://web.archive.org/web/20050224225212/http://www.univ-nancy2.fr/poincare/chp/text/lorentz3.xml</ref> about Lorentz's paper of 1904, which Poincaré described as a "paper of supreme importance." In this letter he pointed out an error Lorentz had made when he had applied his transformation to one of Maxwell's equations, that for charge-occupied space, and also questioned the time dilation factor given by Lorentz. In a second letter to Lorentz,<ref>http://web.archive.org/web/20050224225216/http://www.univ-nancy2.fr/poincare/chp/text/lorentz4.html</ref> Poincaré gave his own reason why Lorentz's time dilation factor was indeed correct after all: it was necessary to make the Lorentz transformation form a group and gave what is now known as the relativistic velocity-addition law. Poincaré later delivered a paper at the meeting of the Academy of Sciences in Paris on 5 June 1905 in which these issues were addressed. In the published version of that short paper,<ref>[http://www.soso.ch/wissen/hist/SRT/P-1905-1.pdf Sur la Dynamique de l'Électron.] Retrieved July 19, 2007.</ref> he wrote:
+
* He was physically clumsy and artistically inept.  
<div style="background:white">
 
{{cquote|1=The essential point, established by Lorentz, is that the equations of the electromagnetic field are not altered by a certain transformation (which I will call by the name of Lorentz) of the form<ref>Lorentz (1904) had written <math>x^\prime = k\ell x^{\prime\prime},</math> <math>t^{\prime} = \ell t/k - k\ell wx^{\prime\prime}/c^2,</math> <math>k^2 = c^2/\left(c^2-w^2\right)</math>. Later in the paper he deduced that <math>\ell = 1.</math>  Lorentz's <math> x^{\prime\prime}</math> was, in Poincaré's notation, equal to <math>x - wt.</math> Eliminating <math>x^{\prime\prime}</math> and putting <math>\varepsilon = -w/c</math> yields the Lorentz transformations as Poincaré wrote them.</ref>:
 
::<math>x^\prime = k\ell\left(x + \varepsilon t\right),~</math><math>t^\prime = k\ell\left(t + \varepsilon x\right),~</math><math>y^\prime = \ell y,~</math> <math>z^\prime = \ell z,~</math><math>k = 1/\sqrt{1-\varepsilon^2}.</math>}}
 
</div>
 
and showed that the arbitrary function <math>\ell\left(\varepsilon\right)</math> must be unity for all <math>\varepsilon</math> (Lorentz had set <math>\ell = 1</math> by a different argument) to make the transformations form a group. In an enlarged version of the paper that appeared in 1906 Poincaré pointed out that the combination <math>x^2+ y^2+ z^2- c^2t^2</math> is [[invariant]], and he introduced the 4-vector notation for which [[Hermann Minkowski]] became known.
 
  
Einstein's first paper on relativity was published three months after Poincaré's short paper, but before Poincaré's longer version.<ref>[http://www.soso.ch/wissen/hist/SRT/P-1905.pdf Sur la Dynamique de l'Électron.] Retrieved July 19, 2007.</ref> It relied on the principle of relativity to derive the Lorentz transformations and used the same clock synchronization procedure that Poincaré (1900) had described, but was remarkable in that it contained no references at all. Poincaré never acknowledged Einstein's work on Special Relativity, but Einstein acknowledged Poincaré's in the text of a [[lecture]] in 1921 called ''Geometrie und Erfahrung''. Later Einstein commented on Poincaré as being one of the pioneers of relativity, saying "Lorentz had already recognized that the transformation named after him is essential for the analysis of Maxwell's equations, and Poincaré deepened this insight still further ..."
+
* He was always in a rush and disliked going back for changes or corrections.  
  
Poincaré's work in the development of Special Relativity is well recognized (''e.g.'' Darrigol 2004), though most historians stress that despite many similarities with Einstein's work, the two had very different research agendas and interpretations of the work (see Galison 2003 and Kragh 1999). A minority go much further, such as the historian of science Sir Edmund Whittaker, who held that Poincaré and Lorentz were the true discoverers of Relativity (Whittaker 1953). Poincaré consistently credited Lorentz's achievements, ranking his own contributions as minor. Thus, he wrote:
+
* He never spent a long time on a problem since he believed that the subconscious would continue working on the problem while he consciously worked on another problem.  
"Lorentz has tried to modify his hypothesis so as to make it in accord with the hypothesis of complete impossibility of measuring absolute motion. ''He has succeeded in doing so'' in his article [Lorentz 1904]. The importance of the problem has made me take up the question again; the results that I have obtained agreement on ''all important points'' with those of Lorentz; ''I have been led only to modify or complete them on some points of detail''." (Poincaré 1905) [emphasis added].
 
In an address in 1909 on "The New Mechanics," Poincaré discussed the demolition of Newton's mechanics brought about by [[Max Abraham]] and Lorentz, without mentioning Einstein. In one of his last essays entitled "The Quantum Theory" (1913), when referring to the [[Solvay Conference]], Poincaré again described special relativity as the "mechanics of Lorentz":
 
  
{{cquote| ... at every moment [the twenty physicists from different countries] could be heard talking of the new mechanics which they contrasted with the old mechanics. Now what was the old mechanics? Was it that of Newton, the one which still reigned uncontested at the close of the nineteenth century? No, it was ''the mechanics of Lorentz, the one dealing with the principle of relativity''; the one which, hardly five years ago, seemed to be the height of boldness ... the mechanics of Lorentz endures ... no body in motion will ever be able to exceed the speed of light ... the mass of a body is not constant ... no experiment will ever be able [to detect] motion either in relation to absolute space or even in relation to the aether. [emphasis added]}}
+
In addition, Toulouse stated that most mathematicians worked from principles already established while Poincaré was the type that started from basic principle each time.<ref>J. John O'Connor et al., 2002, [http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Poincare.html "Jules Henri Poincaré"]. ''University of St. Andrews, Scotland''. Retrieved November 13, 2007.</ref> 
  
On the other hand, in a memoir written as a tribute to Poincaré after his death, Lorentz readily admitted the mistake he had made and credited Poincaré's achievements:
+
His method of thinking is well summarized as:
  
{{cquote|For certain of the physical magnitudes which enter in the formulae I have not indicated the transformation which suits best. This has been done by Poincaré, and later by Einstein and Minkowski. My formulae were encumbered by certain terms which should have been made to disappear. [...] ''I have not established the principle of relativity as rigorously and universally true''. Poincaré, on the other hand, has obtained a perfect invariance of the electromagnetic equations, and he has formulated 'the postulate of relativity', terms which he was the first to employ. [emphasis added]}}
+
''Habitué à négliger les détails et à ne regarder que les cimes, il passait de l'une à l'autre avec une promptitude surprenante et les faits qu'il découvrait se groupant d'eux-mêmes autour de leur centre étaient instantanément et automatiquement classés dans sa mémoire.'' (He neglected details and jumped from idea to idea, the facts gathered from each idea would then come together and solve the problem.)<ref>André Belliver. 1956. ''Henri Poincaré ou la vocation souveraine.'' (Paris, FR: Gallimard)</ref>
  
In summary, Poincaré regarded the mechanics as developed by Lorentz in order to obey the principle of relativity as the essence of the theory, while Lorentz stressed that perfect invariance was first obtained by Poincaré. The modern view is inclined to say that the group property and the invariance are the essential points.
+
===Shortcomings===
  
== Character ==
+
While a brilliant researcher, Poincaré's abilities to critique work in his field were limited, evidenced in what are considered Poincaré's decision-failures. For example, Poincaré was resistant to contributions from mathematicians like [[Georg Cantor]] and underestimated mathematical work that was highly relevant to fields such as economics and finance. In 1900 Poincaré misvalued [[Louis Bachelier]]'s thesis "The Theory of Speculation," saying: "M. Bachelier has evidenced an original and precise mind [but] the subject is somewhat remote from those our other candidates are in the habit of treating."<ref>Bernstein, 1996, 199-200</ref> However, Bachelier's work explained what was then the French government's pricing options on French Bonds and anticipated many of the pricing theories in financial markets used even today.
Poincaré's work habits have been compared to a bee flying from flower to flower. Poincaré was interested in the way his mind worked; he studied his habits and gave a talk about his observations in 1908 at the Institute of General Psychology in Paris. He linked his way of thinking to how he made several discoveries.  
 
  
The mathematician Darboux claimed he was ''un intuitif'' (intuitive), arguing that this is demonstrated by the fact that he worked so often by visual representation. He did not care about being rigorous and disliked logic. He believed that logic was not a way to invent but a way to structure ideas and that logic limits ideas.
+
== Philosophy ==
  
===Toulouse' characterization ===
+
Poincaré had the opposite philosophical views of [[Bertrand Russell]] and [[Gottlob Frege]], who believed that mathematics was a branch of [[logic]]. Poincaré strongly disagreed, claiming that [[intuition (knowledge)|intuition]] was the life of mathematics. Poincaré gives an interesting point of view in his book ''Science and Hypothesis'':
Poincaré's mental organization was not only interesting to Poincaré himself but also to Toulouse, a psychologist of the Psychology Laboratory of the School of Higher Studies in Paris. Toulouse wrote a book entitled ''Henri Poincaré'' (1910). In it, he discussed Poincaré's regular schedule:
 
  
* He worked during the same times each day in short periods of time.  He undertook mathematical research for four hours a day, between 10 a.m. and noon then again from 5 p.m. to 7 p.m.. He would read articles in journals later in the evening.
+
:''For a superficial observer, scientific truth is beyond the possibility of doubt; the logic of science is infallible, and if the scientists are sometimes mistaken, this is only from their mistaking its rule.''
  
* His normal work habit was to solve a problem completely in his head, then commit the completed problem to paper.
+
Poincaré believed that [[arithmetic]] is a [[Analytic/synthetic distinction|synthetic]] science. He argued that [[Peano's axioms]] cannot be proven non-circularly with the principle of induction (Murzi, 1998), therefore concluding that arithmetic is ''[[A priori and a posteriori (philosophy)|a priori]]'' synthetic and not analytic. Poincaré then went on to say that mathematics cannot be deduced from logic since it is not analytic. His views were the same as those of [[Kant]] (Kolak, 2001). However Poincaré did not share Kantian views in all branches of philosophy and mathematics. For example, in geometry, Poincaré believed that the structure of [[Non-Euclidean geometry|non-Euclidean space]] can be known analytically.
  
* He was ambidextrous and nearsighted.  
+
Selected quotations of Poincaré are given below.<ref>[http://en.wikiquote.org/wiki/Henri_Poincar%C3%A9 Henri Poincaré.] ''Wikiquote''. Retrieved November 12, 2007.</ref>
 +
 
 +
=== "Normal Law of Errors" ===
  
* His ability to visualise what he heard proved particularly useful when he attended lectures since his eyesight was so poor that he could not see properly what his lecturers were writing on the blackboard.  
+
* Everybody firmly believes in it because the mathematicians imagine it is a fact of observation, and observers that it is a theory of mathematics.<ref>On the "Normal Law of Errors" in the Introduction to his book ''Thermodynamique'' (1892); as told by J.H. Gaddum in ''Nature'' 156 (1945): 463-466.</ref>
  
However, these abilities were somewhat balanced by his shortcomings:
+
=== Quotes from ''La Science et l'Hypothèse (Of Science and Hypotheses)'' (1901) ===
  
* He was physically clumsy and artistically inept.  
+
* To doubt everything or to believe everything are two equally convenient solutions; both dispense with the necessity of reflection.
  
* He was always in a rush and disliked going back for changes or corrections.  
+
* Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.
  
* He never spent a long time on a problem since he believed that the subconscious would continue working on the problem while he consciously worked on another problem.  
+
* Sociology is the science with the greatest number of methods and the least results.
  
In addition, Toulouse stated that most mathematicians worked from principles already established while Poincaré was the type that started from basic principle each time. (O'Connor et al., 2002)  
+
=== Quotes from ''Valeur de la Science (The Value of Science)'' (1904) ===
  
His method of thinking is well summarized as:
+
* It is not nature which imposes [time and space] upon us, it is we who impose them upon nature because we find them convenient.
  
''Habitué à négliger les détails et à ne regarder que les cimes, il passait de l'une à l'autre avec une promptitude surprenante et les faits qu'il découvrait se groupant d'eux-mêmes autour de leur centre étaient instantanément et automatiquement classés dans sa mémoire.'' (He neglected details and jumped from idea to idea, the facts gathered from each idea would then come together and solve the problem.) (Belliver, 1956)
+
* If all the parts of the universe are interchained in a certain measure, any one phenomenon will not be the effect of a single cause, but the resultant of causes infinitely numerous.
  
===Shortcomings===
+
* Does the harmony the human intelligence thinks it discovers in nature exist outside of this intelligence?  No, beyond doubt, a reality completely independent of the mind which conceives it, sees or feels it, is an impossibility.
  
While a brilliant researcher, Poincaré's abilities to critique work in his field were limited, evidenced in what are considered Poincaré's decision-failures. For example, Poincaré was resistant to contributions from mathematicians like [[Georg Cantor]] and underestimated mathematical work that was highly relevant to fields such as economics and finance. In 1900 Poincaré misvalued [[Louis Bachelier]]'s thesis "The Theory of Speculation," saying: "M. Bachelier has evidenced an original and precise mind [but] the subject is somewhat remote from those our other candidates are in the habit of treating." (Bernstein, 1996, p.199-200) However, Bachelier's work explained what was then the French government's pricing options on French Bonds and anticipated many of the pricing theories in financial markets used even today. As such, Poincaré's life interests and work can be interpreted as following what was the popular, socially demanded research at the time, rather than what is [[ontological]]ly true. {{Fact|date=May 2007}}
+
* The advance of science is not comparable to the changes of a city, where old edifices are pitilessly torn down to give place to new, but to the continuous evolution of zoologic types which develop ceaselessly and end by becoming unrecognizable to the common sight, but where an expert eye finds always traces of the prior work of the past centuries.
  
 
== Honors ==
 
== Honors ==
 +
 
'''Awards'''
 
'''Awards'''
 
* Oscar II, King of Sweden's mathematical competition (1887)
 
* Oscar II, King of Sweden's mathematical competition (1887)
* [[American Philosophical Society]] 1899
+
* [[American Philosophical Society]] (1899)
 
*[[Gold Medal of the Royal Astronomical Society]] of London (1900)
 
*[[Gold Medal of the Royal Astronomical Society]] of London (1900)
* [[Matteucci Medal]] 1905
+
* [[Matteucci Medal]] (1905)
*[[French Academy of Sciences]] 1906  
+
*[[French Academy of Sciences]] (1906)
*[[Académie Française]] 1909
+
*[[Académie Française]] (1909)
 
*[[Bruce Medal]] (1911)
 
*[[Bruce Medal]] (1911)
  
 
'''Named after him'''
 
'''Named after him'''
 +
* The [[Poincaré group]] used in physics and mathematics was named after him.
 
*[[Poincaré Prize]] (Mathematical Physics International Prize)
 
*[[Poincaré Prize]] (Mathematical Physics International Prize)
 
*[[Annales Henri Poincaré]] (Scientific Journal)
 
*[[Annales Henri Poincaré]] (Scientific Journal)
Line 188: Line 254:
  
 
He published two major works that placed celestial mechanics on a rigorous mathematical basis:
 
He published two major works that placed celestial mechanics on a rigorous mathematical basis:
* ''New Methods of Celestial Mechanics'' ISBN 1563961172 (3 vols., 1892-99; Eng. trans., 1967)
+
* ''New Methods of Celestial Mechanics'' ISBN 1563961172 (3 vols., 1892-1899; English trans., 1967)
* ''Lessons of Celestial Mechanics''. (1905-10).
+
* ''Lessons of Celestial Mechanics.'' (1905-1910).
  
 
In popular writings he helped establish the fundamental popular definitions and perceptions of science by these writings:
 
In popular writings he helped establish the fundamental popular definitions and perceptions of science by these writings:
Line 197: Line 263:
 
*''Science and Method'', 1908.
 
*''Science and Method'', 1908.
  
* ''Dernières pensées'' (Eng., "Last Thoughts"); Edition Ernest Flammarion, Paris, 1913.
+
* ''Dernières pensées'' (Eng., "Last Thoughts"); Edition Ernest Flammarion, Paris, 1913.
 
 
== Philosophy ==
 
Poincaré had the opposite philosophical views of [[Bertrand Russell]] and [[Gottlob Frege]], who believed that mathematics was a branch of [[logic]]. Poincaré strongly disagreed, claiming that [[intuition (knowledge)|intuition]] was the life of mathematics. Poincaré gives an interesting point of view in his book ''Science and Hypothesis'':
 
 
 
:''For a superficial observer, scientific truth is beyond the possibility of doubt; the logic of science is infallible, and if the scientists are sometimes mistaken, this is only from their mistaking its rule.''
 
 
 
Poincaré believed that [[arithmetic]] is a [[Analytic/synthetic distinction|synthetic]] science.    He argued that [[Peano's axioms]] cannot be proven non-circularly with the principle of induction (Murzi, 1998), therefore concluding that arithmetic is ''[[A priori and a posteriori (philosophy)|a priori]]'' synthetic and not analytic. Poincaré then went on to say that mathematics cannot be deduced from logic since it is not analytic. His views were the same as those of [[Kant]] (Kolak, 2001). However Poincaré did not share Kantian views in all branches of philosophy and mathematics. For example, in geometry, Poincaré believed that the structure of [[Non-Euclidean geometry|non-Euclidean space]] can be known analytically.
 
  
 
== See also ==
 
== See also ==
  
*[[Poincaré symmetry]]
+
* [[Capillarity]]
*[[Poincaré–Hopf theorem]]
+
* [[Celestial mechanics]]
*[[Poincaré metric]]
+
* [[Elasticity]]
*[[Poincaré duality]]
+
* [[Electricity]]
*[[Poincaré group]]
+
* [[Fluid mechanics]]
*[[Poincaré map]]
+
* [[Optics]]
*[[History of special relativity]]
+
* [[Quantum mechanics]]
*[[Relativity priority disputes]]
+
* [[Special relativity]]
 +
* [[Telegraphy]]
 +
* [[Thermodynamics]]
  
 
== Notes ==
 
== Notes ==
Line 225: Line 286:
 
===General references===
 
===General references===
  
* [[Eric Temple Bell|Bell, Eric Temple]], 1986. ''Men of Mathematics'' (reissue edition). Touchstone Books. ISBN 0671628186.
+
* Bell, Eric Temple. 1986. ''Men of Mathematics'' (reissue edition). New York, NY: Simon & Schuster. ISBN 0671628186.
* Belliver, André, 1956. ''Henri Poincaré ou la vocation souveraine''. Paris: Gallimard.
+
* Belliver, André. 1956. ''Henri Poincaré ou la vocation souveraine.'' Paris, FR: Gallimard.
*Bernstein, Peter L, 1996. "Against the Gods: A Remarkable Story of Risk." (p. 199-200). John Wiley & Sons.
+
*Bernstein, Peter L. 1996. ''Against the Gods: A Remarkable Story of Risk.'' New York, NY: John Wiley & Sons. ISBN 0471121045.
* Boyer, B. Carl, 1968. ''A History of Mathematics: Henri Poincaré'', John Wiley & Sons.
+
* Boyer, B. Carl. 1968. ''A History of Mathematics: Henri Poincaré.'' New York, NY: John Wiley & Sons.
* Olivier Darrigol (2004): "The Mystery of the Einstein-Poincaré Connection." Isis: Vol.95, Issue 4; pg. 614, 14 pgs
+
* Darrigol, Olivier. 2004. The Mystery of the Einstein-Poincaré Connection. ''Isis''. 95(4):614-628.
* Ewald, William B., ed., 1996. ''From Kant to Hilbert: A Source Book in the Foundations of Mathematics'', 2 vols. Oxford Uni. Press. Contains among others:
+
* Ewald, William B. ed., 1996. ''From Kant to Hilbert: A Source Book in the Foundations of Mathematics.'' 2 vols. Oxford, UK: Oxford University Press. ISBN 0198532717.
* [[Ivor Grattan-Guinness|Grattan-Guinness, Ivor]], 2000. ''The Search for Mathematical Roots 1870-1940. Princeton Uni. Press.
+
* Grattan-Guinness, Ivor. 2000. ''The Search for Mathematical Roots 1870-1940.'' Princeton, NJ: Princeton University Press. ISBN 0691058571.
* Gray, Jeremy, 1986. ''Linear differential equations and group theory from Riemann to Poincaré'', Birkhauser
+
* Gray, Jeremy. 2000. ''Linear differential equations and group theory from Riemann to Poincaré.'' Boston, MA: Birkhauser. ISBN 0817638377.
* Kolak, Daniel, 2001. ''Lovers of Wisdom'', 2nd ed. Wadsworth.
+
* Kolak, Daniel. 2001. ''Lovers of Wisdom'', 2nd ed. Belmont, CA: Wadsworth. ISBN 0534541461.
* Murzi, 1998. [http://www.iep.utm.edu/p/poincare.htm "Henri Poincaré"].
+
* Murzi. 1998. [http://www.iep.utm.edu/p/poincare.htm "Henri Poincaré"]. Retrieved November 13, 2007.
* O'Connor, J. John, and Robertson, F. Edmund, 2002, [http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Poincare.html "Jules Henri Poincaré"]. University of St. Andrews, Scotland.
+
* O'Connor, J. John, and F. Edmund Robertson. 2002. [http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Poincare.html "Jules Henri Poincaré"]. University of St. Andrews, Scotland. Retrieved November 13, 2007.
* [[Ivars Peterson|Peterson, Ivars]], 1995. ''Newton's Clock: Chaos in the Solar System'' (reissue edition). W H Freeman & Co. ISBN 0716727242.
+
* Peterson, Ivars. 1995. ''Newton's Clock: Chaos in the Solar System.'' (reissue edition). New York, NY: W H Freeman & Co. ISBN 0716727242.
*Poincaré, Henri. 1894. "On the nature of mathematical reasoning," 972-81.
+
* Poincaré, Henri. 1894. On the nature of mathematical reasoning. 972-981.
*________. 1898. "On the foundations of geometry," 982-1011.
+
* Poincaré, Henri. 1898. On the foundations of geometry. 982-1011.
*________. 1900. "Intuition and Logic in mathematics," 1012-20.
+
* Poincaré, Henri. 1900. Intuition and Logic in mathematics. 1012-1020.
*________. 1905-06. "Mathematics and Logic, I-III," 1021-70.
+
* Poincaré, Henri. 1905-06. Mathematics and Logic, I-III. 1021-1070.
*________. 1910. "On transfinite numbers," 1071-74.
+
* Poincaré, Henri. 1910. On transfinite numbers. 1071-1074.
* Sageret, Jules, 1911. ''Henri Poincaré''. Paris: Mercure de France.
+
* Sageret, Jules. 1911. ''Henri Poincaré.'' Paris, FR: Mercure de France.
* Toulouse, E.,1910. ''Henri Poincaré''. - (Source biography in French)
+
* Toulouse, E. 1910. ''Henri Poincaré.'' (Source biography in French)
  
 
=== References to work on relativity ===
 
=== References to work on relativity ===
* Einstein, A. (1905) "Zur Elektrodynamik Bewegter Körper," ''Annalen der Physik'', '''17''', 891. [http://www.fourmilab.ch/etexts/einstein/specrel/www/ English translation]
+
* Einstein, A. 1905. [http://www.fourmilab.ch/etexts/einstein/specrel/www/ Zur Elektrodynamik Bewegter Körper (English Translation)]. ''Annalen der Physik'' 17:891. Retrieved November 13, 2007.
* Einstein, A. (1915) "Erklärung der Periheldrehung des Merkur aus der allgemainen Relativitätstheorie," ''Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin'', 799-801
+
* Einstein, A. 1915. Erklärung der Periheldrehung des Merkur aus der allgemainen Relativitätstheorie. ''Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin.'' 799-801.
* Einstein, A. (1916) "Die Grundlage der allgemeinen Relativitätstheorie," ''Annalen der Physik'', 49
+
* Einstein, A. 1916. Die Grundlage der allgemeinen Relativitätstheorie. ''Annalen der Physik'' 49.
* Giannetto, Enrico (1998) [http://www.brera.unimi.it/old/Atti-Como-98/Giannetto.pdf "The Rise of Special Relativity: Henri Poincaré's Works Before Einstein"], ''Atti del XVIII congresso di storia della fisica e dell'astronomia
+
* Giannetto, Enrico. 1998. The Rise of Special Relativity: Henri Poincaré's Works Before Einstein. ''Atti del XVIII congresso di storia della fisica e dell'astronomia.''
* [[Peter Galison|Galison, Peter Louis]] (2003) ''Einstein's Clocks, Poincaré's Maps: Empires of Time''. New York: W.W. Norton. ISBN 0393020010
+
* Galison, Peter Louis. 2003. ''Einstein's Clocks, Poincaré's Maps: Empires of Time.'' New York, NY: W.W. Norton. ISBN 0393020010.
* Hasenöhrl, F. (1907) ''Wien Sitz.'' '''CXVI''' 2a, p.1391
+
* Hasenöhrl, F. 1907. Wien Sitz. ''CXVI'' 2a:1391
* Ives, H. E. (1952) "Derivation of the Mass-Energy Relationship," ''J. Optical Society America'', '''42''', pp. 540-543.
+
* Ives, H. E. 1952. Derivation of the Mass-Energy Relationship. ''J. Optical Society America'' 42:540-543.
* Ives, H. E. (1953) "Note on 'Mass-Energy Relationship'," ''J. Optical Society America'', '''43''', 619.
+
* Ives, H. E. 1953. Note on 'Mass-Energy Relationship' ''J. Optical Society America'' 43:619.
* Keswani, G. H. (1965-6) "Origin and Concept of Relativity, Parts I, II, III," ''Brit. J. Phil. Sci.'', v'''15-17'''.
+
* Keswani, G. H. 1965-6. Origin and Concept of Relativity, Parts I, II, III. ''Brit. J. Phil. Sci.'' 15-17.
* Kragh, Helge. (1999) ''Quantum Generations: A History of Physics in the Twentieth Century.'' Princeton, N.J. : Princeton University Press.  
+
* Kragh, Helge. 1999. ''Quantum Generations: A History of Physics in the Twentieth Century.'' Princeton, NJ: Princeton University Press. ISBN 0691012067.
* Langevin, P. (1905) "Sur l'origine des radiations et l'inertie électromagnétique," ''Journal de Physique Théorique et Appliquée'', '''4''', pp.165-183.
+
* Langevin, P. 1905. Sur l'origine des radiations et l'inertie électromagnétique. ''Journal de Physique Théorique et Appliquée'' 4:165-183.
* Langevin, P. (1914) "Le Physicien" in ''Henri Poincaré Librairie'' (Felix Alcan 1914) pp. 115-202.  
+
* Langevin, P. 1914. "Le Physicien" in ''Henri Poincaré Librairie.'' Felix Alcan, 1914.  
* Lewis, G. N. (1908) ''Philosophical Magazine'', '''XVI''', 705
+
* Lewis, G. N. 1908. ''Philosophical Magazine'' XVI:705
* Logunov, A, (2005) [http://uk.arxiv.org/abs/physics/0408077 Book "Henri Poincaré and Relativity Theory",] [http://www.maik.rssi.ru/eng/book/index.html Nauka, Moscow, ISBN 5-02-033964-4]
+
* Logunov, A. 2005. ''[http://uk.arxiv.org/abs/physics/0408077 Henri Poincaré and Relativity Theory].'' Moscow, RU: Nauka. ISBN 5020339644. Retrieved November 13, 2007.
* Lorentz, H. A. (1899) "Simplified Theory of Electrical and Optical Phenomena in Moving Systems," ''Proc. Acad. Science Amsterdam'', '''I''', 427-43.  
+
* Lorentz, H. A. 1899. Simplified Theory of Electrical and Optical Phenomena in Moving Systems. ''Proc. Acad. Science Amsterdam'' I: 427-443.  
* Lorentz, H. A. (1904) "Electromagnetic Phenomena in a System Moving with Any Velocity Less Than That of Light," ''Proc. Acad. Science Amsterdam'', '''IV''', 669-78.  
+
* Lorentz, H.A. 1904. Electromagnetic Phenomena in a System Moving with Any Velocity Less Than That of Light. ''Proc. Acad. Science Amsterdam'' IV:669-78.  
* Lorentz, H. A. (1911) ''Amsterdam Versl.'' '''XX''', 87
+
* Lorentz, H.A. 1911. ''Amsterdam Versl.'' XX:87.
* Lorentz, H.A. (1921) 1914 manuscripts "Deux memoires de Henri Poincaré," ''Acta Mathematica 38'', p.293.
+
* Lorentz, H.A. 1921. 1914 manuscripts. Deux memoires de Henri Poincaré. ''Acta Mathematica 38'' 293.
* Macrossan, M. N. (1986) [http://espace.library.uq.edu.au/view.php?pid=UQ:9560 "A Note on Relativity Before Einstein"], ''Brit. J. Phil. Sci''., '''37''', pp.232-34.
+
* Macrossan, M.N. 1986. [http://espace.library.uq.edu.au/view.php?pid=UQ:9560 A Note on Relativity Before Einstein]. ''Brit. J. Phil. Sci''. 37:232-34. Retrieved November 13, 2007.
* Planck, M. (1907) ''Berlin Sitz.'', 542
+
* Planck, M. 1907. ''Berlin Sitz.'' 542.
* Planck, M. (1908) ''Verh. d. Deutsch. Phys. Ges.'' '''X''', p218, and ''Phys. ZS'', '''IX''', 828
+
* Planck, M. 1908. ''Verh. d. Deutsch. Phys. Ges.'' X:218, and ''Phys. ZS''. IX:828
* Poincaré, H. (1897) [http://www.marxists.org/reference/subject/philosophy/works/fr/poincare.htm "The Relativity of Space"], article in English translation
+
* Poincaré, H. 1897. [http://www.marxists.org/reference/subject/philosophy/works/fr/poincare.htm The Relativity of Space]. Article in English translation. Retrieved November 13, 2007.
* Poincaré, H. (1898) "La mesure du Temps," reprinted in [http://fr.wikisource.org/wiki/La_Valeur_de_la_Science_-_CHAPITRE_II_:_LA_MESURE_DU_TEMPS. "La valeur de la science"], Ernest Flammarion, Paris.
+
* Poincaré, H. 1898. La mesure du Temps. reprinted in "La valeur de la science." Ernest Flammarion, Paris. Retrieved November 13, 2007.
* Poincaré, H. (1900) "La Theorie de Lorentz et la Principe de Reaction," ''Archives Neerlandaises'', '''V''', 252-78.  
+
* Poincaré, H. 1900. La Theorie de Lorentz et la Principe de Reaction. ''Archives Neerlandaises''. V:252-78.  
* Poincaré, H. (1905) [http://fr.wikisource.org/wiki/La_Valeur_de_la_Science "La valeur de la Science"]
+
* Poincaré, H. 1905. [http://fr.wikisource.org/wiki/La_Valeur_de_la_Science La valeur de la Science]. Wikisource. Retrieved November 13, 2007.
* Poincaré, H. (1904) "L'état actuel et l'avenir de la physique mathématique," ''Bulletin des sciences mathématiques 28(1904)'', 302-324 (Congress of Arts and Science, St. Louis, September 24, 1904)
+
* Poincaré, H. 1904. L'état actuel et l'avenir de la physique mathématique. ''Bulletin des sciences mathématiques 28(1904)'', 302-324 (Congress of Arts and Science, St. Louis, September 24, 1904)
* Poincaré, H. (1905) [http://www.soso.ch/wissen/hist/SRT/P-1905-1.pdf "Sur la dynamique de l'electron"], ''Comptes Rendues'', '''140''', 1504-8.
+
* Poincaré, H. 1905. [http://www.soso.ch/wissen/hist/SRT/P-1905-1.pdf Sur la dynamique de l'electron]. ''Comptes Rendues''. 140:1504-8. Retrieved November 13, 2007.
* Poincaré, H. (1906) [http://www.soso.ch/wissen/hist/SRT/P-1905.pdf "Sur la dynamique de l'electron"], Rendiconti del Circolo matematico di Palermo, t.21, 129-176.  
+
* Poincaré, H. 1906. [http://www.soso.ch/wissen/hist/SRT/P-1905.pdf Sur la dynamique de l'electron]. ''Rendiconti del Circolo matematico di Palermo''. 21:129-176. Retrieved November 13, 2007.
* Poincaré, H. (1913) ''Mathematics and Science: Last Essays'', Dover 1963 (translated from ''Dernières Pensées'' posthumously published by Ernest Flammarion, 1913)
+
* Poincaré, H. 1913. ''Mathematics and Science: Last Essays''. New York, NY: Dover 1963. (translated from ''Dernières Pensées'' posthumously published by Ernest Flammarion, 1913)
* Riseman, J. and I. G. Young (1953) "Mass-Energy Relationship," ''J. Optical Society America'', '''43''', 618.
+
* Riseman, J. and I.G. Young. 1953. Mass-Energy Relationship. ''J. Optical Society America'' 43:618.
* Whittaker, E. T (1953) ''A History of the Theories of Aether and Electricity: Vol 2 The Modern Theories 1900-1926. Chapter II: The Relativity Theory of Poincaré and Lorentz'', Nelson, London.
+
* Whittaker, E.T. 1953. ''A History of the Theories of Aether and Electricity: Vol 2 The Modern Theories 1900-1926. Chapter II: The Relativity Theory of Poincaré and Lorentz.'' London, UK: Nelson.
  
 
==External links==
 
==External links==
 +
All links retrieved December 15, 2017.
 +
*{{gutenberg author| id=Henri+Poincaré | name=Henri Poincaré}}.
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* {{MathGenealogy |id=34227}}.
 +
* {{MacTutor Biography|id=Poincare}}.
 +
*[http://www-history.mcs.st-andrews.ac.uk/Biographies/Poincare.html Jules Henri Poincaré].
 +
*[http://www.iep.utm.edu/poincare/ Jules Henri Poincaré (1854—1912)] - Internet Encyclopedia of Philosophy
 +
*[http://phys-astro.sonoma.edu/brucemedalists/Poincare/index.html Bruce Medal page].
  
*{{gutenberg author| id=Henri+Poincaré | name=Henri Poincaré}}
 
* {{MathGenealogy |id=34227}}
 
* {{MacTutor Biography|id=Poincare}}
 
*[http://www-history.mcs.st-andrews.ac.uk/Biographies/Poincare.html Jules Henri Poincaré]
 
*[http://spartan.ac.brocku.ca/~lward/Poincare/Poincare_1905_toc.html Science and Hypothesis (complete text online - in English)]
 
*[http://www.utm.edu/research/iep/p/poincare.htm A review of Poincaré's life and mathematical achievements] - from the University of Tennessee at Martin, USA.
 
*[http://www.univ-nancy2.fr/ACERHP/documents/kronowww.html A timeline of Poincaré's life] University of Nancy (in French).
 
*[http://phys-astro.sonoma.edu/brucemedalists/Poincare/index.html Bruce Medal page]
 
*[http://www.sciam.com/print_version.cfm?articleID=0003848D-1C61-10C7-9C6183414B7F0000 Henri Poincaré, His Conjecture, Copacabana and Higher Dimensions]
 
*[http://www.bbc.co.uk/radio4/history/inourtime/inourtime.shtml BBC In Our Time — discussion of the Poincaré conjecture, November 2, 2006, hosted by Melvynn Bragg] [http://web.archive.org/web/*/http://www.bbc.co.uk/radio4/history/inourtime/inourtime.shtml See Internet Archive]
 
  
 
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|SHORT DESCRIPTION= [[Mathematician]] and [[physicist]]
 
|DATE OF BIRTH= April 29, 1854
 
|PLACE OF BIRTH= [[Nancy]],  [[France]]
 
|DATE OF DEATH= July 17, 1912
 
|PLACE OF DEATH= [[Paris]], [[France]]
 
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Revision as of 15:21, 25 January 2023

Henri Poincaré

File:JH Poincare.jpg
Henri Poincaré, photograph from the frontispiece of the 1913 edition of "Last Thoughts"
Born

April 29, 1854
Nancy, France

Died July 17, 1912

Paris, France

Residence Flag of France.svg France
Nationality Flag of France.svg French
Field Mathematician and physicist
Institutions Corps des Mines
Caen University
La Sorbonne
Bureau des Longitudes
Alma mater Lycée Nancy
École Polytechnique
École des Mines
Academic advisor  Charles Hermite
Notable students  Louis Bachelier
Known for Poincaré conjecture
Three-body problem
Topology
Special relativity
Notable prizes Matteucci Medal (1905)

Jules Henri Poincaré (April 29, 1854 – July 17, 1912), generally known as Henri Poincaré, was one of France's greatest mathematicians and theoretical physicists, and a philosopher of science. He is often described as a polymath and as 'The Last Universalist' in mathematics, because he excelled in all fields of the discipline as it existed during his lifetime. He is known for his early formulation of the theory of relativity and for formulating the Poincaré conjecture, one of the most famous problems in mathematics. He also laid the groundwork for chaos theory in the process of attempting to solve the important problem of the motion of three or more bodies acting under mutual gravitation. In addition, he is considered one of the founders of the field of topology.

Biography

Early life and education

Poincaré was born on April 29, 1854, into an influential family in the Cité Ducale neighborhood of Nancy, France. His father, Leon Poincaré (1828-1892), was a professor of medicine at the University of Nancy (Sagaret, 1911). His younger sister, Aline, married the spiritual philosopher Emile Boutroux. Another notable member of Jules' family was his cousin Raymond Poincaré, who became the President of France (from 1913 to 1920) and a fellow member of the Académie Française.[1]

During his childhood, he was seriously ill for a time with diphtheria and lost his voice for the better part of a year. He received special instructions from his mother, Eugénie Launois (1830-1897) and excelled in written composition.

In 1862, Henri entered the Lycée in Nancy, now renamed the Lycée Henri Poincaré in his honor. He spent eleven years at the Lycée and during this time proved to be one of the top students in every topic he studied. 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"[2] However, poor eyesight and a tendency toward absentmindedness may have contributed to these difficulties. He graduated from the Lycée in 1871 with a Bachelor's degree in letters and sciences.

During the Franco-Prussian War of 1870, he served alongside his father in the Ambulance Corps, tending to the wounded and learning German.

Poincaré entered the École Polytechnique in 1873. There he studied mathematics as a student of Charles Hermite, continuing to excel and publishing his first paper (Démonstration nouvelle des propriétés de l'indicatrice d'une surface) in 1874. He graduated in 1875 and went on to the École des Mines, continuing to study mathematics in addition to the mining engineering syllabus, and received the degree of ordinary engineer in March of 1879.

Mining career

As a graduate of the École des Mines, Poincaré joined the Corps des Mines as an inspector for the Vesoul region in northeast France. He was on the scene of a mining disaster at Magny in August 1879, in which 18 miners died. He carried out the official investigation into the accident in a characteristically thorough and humane way. Because he rushed into the mine after the accident, he was at first listed among the dead in the accident. In spite of his other activities, Poincare stayed loyal to his mining career, which in later life led to important government appointments.

Doctoral work

While undertaking his professional responsibilities, Poincaré prepared for his doctorate in mathematics under the supervision of Hermite. His doctoral thesis was in the field of differential equations. Poincaré devised a new way of studying the properties of these expressions. He not only faced the question of determining the solution of such equations, but also was the first person to study their general geometric properties. He realized that they could be used to model the behavior of multiple bodies in free motion within the Solar System. Poincaré was awarded his doctorate from the University of Paris in 1879.

The young Henri Poincaré.

Start of career in mathematics

Soon after graduation, he was offered a post as junior lecturer in mathematics at Caen University, but 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.

Beginning in 1881 and for the rest of his career, he taught at the University of Paris (the Sorbonne). He was initially appointed as associate professor of analysis (Sageret, 1911). Eventually, he held the chairs of Physical and Experimental Mechanics, Mathematical Physics and Theory of Probability, and Celestial Mechanics and Astronomy.

Also in that same year, Poincaré married Miss Poulain d'Andecy. Together they had four children: Jeanne (born 1887), Yvonne (born 1889), Henriette (born 1891), and Léon (born 1893).

In 1887, at the age of 32, Poincaré was elected to the French Academy of Sciences. He became its president in 1906 and was elected to the Académie Française in 1909.

Gravitation, chaos, and the three-body problem

In 1887, Poincaré won the Oscar II, King of Sweden's mathematical competition for a resolution of the three-body problem concerning the free motion of multiple orbiting bodies. Although he did not solve this problem, the insights he offered were striking and original enough for him to merit the prize.

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'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 nineteenth century. Indeed in 1887, in honor of his 60th birthday, King Oscar II, advised by Gösta Mittag-Leffler, established a prize for anyone who could find the solution to the problem. The announcement was quite specific:

Given a system of arbitrarily many mass points that attract each according to Newton's law, under the assumption that no two points ever collide, try to find a representation of the coordinates of each point as a series in a variable that is some known function of time and for all of whose values the series converges uniformly.

In case the problem could not be solved, any other important contribution to classical mechanics would then considered worthy of the prize. Based on this stipulation, Poincaré's contribution was found to merit the prize. 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 Poincaré's paper contained a serious error. When he realized this, he used his own money to purchase copies of the work that contained the error to take them out of circulation. The version finally printed contained many important ideas that led to the theory of chaos. The problem as stated originally was finally solved by Karl Sundman for n = 3 in 1912, and it was generalized to the case of n > 3 bodies by Qiudong Wang in the 1990s.

Time and the theory of relativity

In 1893, Poincaré joined the French Bureau des Longitudes, which engaged him in the synchronization of time around the world. In 1897, Poincaré backed an unsuccessful proposal for the decimalization of circular measure, and hence time and longitude (Galison 2003). This post led him to consider the question of establishing international time zones and the synchronization of time between bodies in relative motion.

Marie Curie and Poincaré talk at the 1911 Solvay Conference.

Poincaré's work at the Bureau des Longitudes on establishing international time zones, led him to consider how to synchronize clocks at rest on the Earth—clocks that would be moving at different speeds relative to absolute space (or the "luminiferous aether"). 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. What Lorentz realized is that, to make his equations applicable to a translation of uniform velocity, he had to introduce a different time variable for each reference frame. He called this "local time," given by the following equation:

where the primed variables refer to a reference frame in uniform motion relative to that of the unprimed variables. Lorentz was using it to explain the "failure" of the Michelson-Morley experiment—an experiment that failed to detect motion relative to the aether, the hypothetical medium that was thought to be the carrier of electromagnetic waves.

In The Measure of Time (Poincaré 1898), Poincaré discussed the difficulty of establishing simultaneity at a distance and concluded it can be established by convention. He also discussed the "postulate of the speed of light," and formulated the principle of relativity, according to which no mechanical or electromagnetic experiment can discriminate between a state of uniform motion and a state of rest. In 1900, Poincaré discussed Lorentz's concept of local time and remarked that it arose when moving clocks are synchronized by exchanging light signals assumed to travel with the same speed in both directions in a moving frame.[3]

Thereafter, Poincaré was a constant interpreter (and sometimes friendly critic) of Lorentz's theory. As a philosopher, Poincaré was interested in the "deeper meaning" of the theory. Thus he interpreted Lorentz's theory in terms of the principle of relativity, and in so doing, he came up with many insights that are now associated with the theory of special relativity.

Relationship between mass and energy

In his paper of 1900, Poincaré discussed the recoil of a physical object when it emits a burst of radiation in one direction, as predicted by Maxwell-Lorentz electrodynamics. He remarked that the stream of radiation appeared to act like a "fictitious fluid" with a mass per unit volume of e/c2, where e is the energy density; in other words, the equivalent mass of the radiation is .

Poincaré considered the recoil of the emitter to be an unresolved feature of Maxwell-Lorentz theory, which he discussed again in "Science and Hypothesis" (1902) and "The Value of Science" (1905). In the latter he said the recoil "is contrary to the principle of Newton since our projectile here has no mass, it is not matter, it is energy," and discussed two other unexplained effects: (1) non-conservation of mass implied by Lorentz's variable mass , Abraham's theory of variable mass and Kaufmann's experiments on the mass of fast moving electrons and (2) the non-conservation of energy in the radium experiments of Madame Curie.

It was Einstein's insight that a body losing energy as radiation or heat was losing mass of amount , and the corresponding mass-energy conservation law, E = mc², that resolved these problems.[4]

Correcting Lorentz

In 1905, Poincaré wrote to Lorentz[5] about Lorentz's paper of 1904, which Poincaré described as a "paper of supreme importance." In this letter, he pointed out an error Lorentz had made when he had applied his transformation to one of Maxwell's equations, that for charge-occupied space, and also questioned the time dilation factor given by Lorentz. In a second letter to Lorentz,[6] Poincaré explained a mathematical property of the transformations that Lorentz had not noticed, and gave his own reason why Lorentz's time dilation factor was indeed correct: Lorentz’s factor was necessary to make the Lorentz transformation from what mathematicians call a group. In the letter, he also gave Lorentz what is now known as the relativistic velocity-addition law, which is necessary to demonstrate invariance.

Poincaré later delivered a paper at the meeting of the Academy of Sciences in Paris on June 5, 1905, in which these issues were addressed. In the published version of that short paper,[7] he wrote:

The essential point, established by Lorentz, is that the equations of the electromagnetic field are not altered by a certain transformation (which I will call by the name of Lorentz) of the form2:

He then wrote that in order for the Lorentz transformations to form a group and satisfy the principle of relativity, the arbitrary function must be unity for all (Lorentz had set by a different argument). Poincaré's discovery of the velocity transformations, allowed him to obtain perfect invariance, the final step in the discovery of his theory of relativity.

In an enlarged version of the paper that did not appear until 1906,[8] he published his group property proof, incorporating the velocity addition law that he had previously written to Lorentz. The paper contains many other deductions from, and applications of, the transformations. For example, Poincaré (1906) pointed out that the combination is invariant, and he introduced the 4-vector notation for which Hermann Minkowski became known.

Einstein and Poincaré

Albert Einstein's first paper on relativity in 1905 derived the Lorentz transformation and presented them in the same form as had Poincaré. It was published three months after Poincaré's short paper but before Poincaré's longer version appeared in 1906. Although Einstein relied on the principle of relativity and used the same clock synchronization procedure that Poincaré (1900) had described, his paper was remarkable in that it had no references at all.

Poincaré never acknowledged Einstein's work on relativity, but Einstein acknowledged Poincaré's somewhat belatedly in the text of a lecture in 1921 titled Geometrie und Erfahrung. Later, Einstein referred to Poincaré as one of the pioneers of relativity, saying that "Lorentz had already recognized that the transformation named after him is essential for the analysis of Maxwell's equations, and Poincaré deepened this insight still further …"

Einstein formulated a general theory of relativity, which gave an expanded explanation of systems accelerating with respect to one another. The theory relating reference frames in uniform motion with respect to one another then became known as the special theory of relativity.

Father of relativity: Lorentz, Poincaré or Einstein?

Poincaré's work in the development of Special Relativity is well recognized[9]. Most historians, however, stress that despite many similarities with Einstein's work, the two had very different research agendas and interpretations of the work[10][11]. A minority go much further, such as the historian of science Sir Edmund Whittaker, who held that Poincaré and Lorentz were the true discoverers of Relativity[12].

Poincaré consistently credited Lorentz's achievements, ranking his own contributions as minor. Thus, he wrote (Poincaré 1905):

Lorentz has tried to modify his hypothesis so as to make it in accord with the hypothesis of complete impossibility of measuring absolute motion. He has succeeded in doing so in his article [Lorentz 1904]. The importance of the problem has made me take up the question again; the results that I have obtained agreement on all important points with those of Lorentz; I have been led only to modify or complete them on some points of detail. The essential point, established by Lorentz, is that the equations of the electromagnetic field are not altered by a certain transformation. [emphases added].

In an address in 1909 on "The New Mechanics," Poincaré discussed the demolition of Newton's mechanics brought about by Max Abraham and Lorentz, without mentioning Einstein. In one of his last essays entitled "The Quantum Theory" (1913), when referring to the Solvay Conference, Poincaré again described special relativity as the "mechanics of Lorentz":

… at every moment [the twenty physicists from different countries] could be heard talking of the new mechanics which they contrasted with the old mechanics. Now what was the old mechanics? Was it that of Newton, the one which still reigned uncontested at the close of the nineteenth century? No, it was the mechanics of Lorentz, the one dealing with the principle of relativity; the one which, hardly five years ago, seemed to be the height of boldness … the mechanics of Lorentz endures … no body in motion will ever be able to exceed the speed of light … the mass of a body is not constant … no experiment will ever be able [to detect] motion either in relation to absolute space or even in relation to the aether. [emphasis added]

On the other hand, in a memoir written as a tribute to Poincaré after his death, Lorentz readily admitted the mistake he had made and credited Poincaré's achievements:

For certain of the physical magnitudes which enter in the formulae I have not indicated the transformation which suits best. This has been done by Poincaré, and later by Einstein and Minkowski. My formulae were encumbered by certain terms which should have been made to disappear. […] I have not established the principle of relativity as rigorously and universally true. Poincaré, on the other hand, has obtained a perfect invariance of the electro-magnetic equations, and he has formulated 'the postulate of relativity', terms which he was the first to employ. [emphasis added]

In summary, Poincaré regarded the mechanics as developed by Lorentz in order to obey the principle of relativity as the essence of the theory, while Lorentz stressed that perfect invariance was first obtained by Poincaré. The modern view is inclined to say that the group property and the invariance are the essential points.

Later life

In 1899, and again more successfully in 1904, he intervened in the trials of Alfred Dreyfus. He attacked the spurious scientific claims of some of the evidence brought against Dreyfus, who was a Jewish officer in the French army charged with treason by anti-Semitic colleagues. Some of these arguments involved probability, and Poincare noted that they were improperly applied to the evidence.

In 1912, Poincaré underwent surgery for a prostate problem and subsequently died from an embolism on July 17, 1912, aged 58. He is buried in the Poincaré family vault in the Cemetery of Montparnasse, Paris.

In 2004, Claude Allegre, the French Minister of Education, proposed that Poincaré be reburied in the Pantheon in Paris, which is reserved for French citizens deserving of the highest honor.[13]

Significant contributions

Poincaré made many contributions to different fields of physics 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. He was also a popularizer of mathematics and physics and wrote several books for the lay public.

Among the specific topics he contributed to are the following:

  • algebraic topology
  • the theory of analytic functions of several complex variables
  • the theory of abelian functions
  • algebraic geometry
  • Poincaré was responsible for formulating one of the most famous problems in mathematics. Known as the Poincaré conjecture, it is a problem in topology.
  • Poincaré recurrence theorem
  • Hyperbolic geometry
  • number theory
  • the three-body problem
  • the theory of diophantine equations
  • the theory of electromagnetism
  • the special theory of relativity
  • In an 1894 paper, he introduced the concept of 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 sphere and the Poincaré map.
  • Poincaré on "everybody's belief" in the Normal Law of Errors,

Character traits

Poincaré's work habits have been compared to a bee flying from flower to flower. Poincaré was interested in the way his mind worked; he studied his habits and gave a talk about his observations in 1908 at the Institute of General Psychology in Paris. He linked his way of thinking to how he made several discoveries.

The mathematician Darboux claimed he was un intuitif (intuitive), arguing that this is demonstrated by the fact that he worked so often by visual representation. He did not care about being rigorous and disliked logic. He believed that logic was not a way to invent but a way to structure ideas and that logic limits ideas.

Toulouse's characterization

Poincaré's mental organization interested not only Poincaré himself but also Toulouse, a psychologist of the Psychology Laboratory of the School of Higher Studies in Paris. Toulouse wrote a book entitled Henri Poincaré (1910). In it, he discussed Poincaré's regular schedule:

  • He worked during the same times each day in short periods of time. He undertook mathematical research for four hours a day, between 10 a.m. and noon then again from 5 p.m. to 7 p.m.. He would read articles in journals later in the evening.
  • His normal work habit was to solve a problem completely in his head, then commit the completed problem to paper.
  • He was ambidextrous and nearsighted.
  • His ability to visualize what he heard proved particularly useful when he attended lectures since his eyesight was so poor that he could not see properly what his lecturers were writing on the blackboard.

However, these abilities were somewhat balanced by his shortcomings:

  • He was physically clumsy and artistically inept.
  • He was always in a rush and disliked going back for changes or corrections.
  • He never spent a long time on a problem since he believed that the subconscious would continue working on the problem while he consciously worked on another problem.

In addition, Toulouse stated that most mathematicians worked from principles already established while Poincaré was the type that started from basic principle each time.[14]

His method of thinking is well summarized as:

Habitué à négliger les détails et à ne regarder que les cimes, il passait de l'une à l'autre avec une promptitude surprenante et les faits qu'il découvrait se groupant d'eux-mêmes autour de leur centre étaient instantanément et automatiquement classés dans sa mémoire. (He neglected details and jumped from idea to idea, the facts gathered from each idea would then come together and solve the problem.)[15]

Shortcomings

While a brilliant researcher, Poincaré's abilities to critique work in his field were limited, evidenced in what are considered Poincaré's decision-failures. For example, Poincaré was resistant to contributions from mathematicians like Georg Cantor and underestimated mathematical work that was highly relevant to fields such as economics and finance. In 1900 Poincaré misvalued Louis Bachelier's thesis "The Theory of Speculation," saying: "M. Bachelier has evidenced an original and precise mind [but] the subject is somewhat remote from those our other candidates are in the habit of treating."[16] However, Bachelier's work explained what was then the French government's pricing options on French Bonds and anticipated many of the pricing theories in financial markets used even today.

Philosophy

Poincaré had the opposite philosophical views of Bertrand Russell and Gottlob Frege, who believed that mathematics was a branch of logic. Poincaré strongly disagreed, claiming that intuition was the life of mathematics. Poincaré gives an interesting point of view in his book Science and Hypothesis:

For a superficial observer, scientific truth is beyond the possibility of doubt; the logic of science is infallible, and if the scientists are sometimes mistaken, this is only from their mistaking its rule.

Poincaré believed that arithmetic is a synthetic science. He argued that Peano's axioms cannot be proven non-circularly with the principle of induction (Murzi, 1998), therefore concluding that arithmetic is a priori synthetic and not analytic. Poincaré then went on to say that mathematics cannot be deduced from logic since it is not analytic. His views were the same as those of Kant (Kolak, 2001). However Poincaré did not share Kantian views in all branches of philosophy and mathematics. For example, in geometry, Poincaré believed that the structure of non-Euclidean space can be known analytically.

Selected quotations of Poincaré are given below.[17]

"Normal Law of Errors"

  • Everybody firmly believes in it because the mathematicians imagine it is a fact of observation, and observers that it is a theory of mathematics.[18]

Quotes from La Science et l'Hypothèse (Of Science and Hypotheses) (1901)

  • To doubt everything or to believe everything are two equally convenient solutions; both dispense with the necessity of reflection.
  • Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.
  • Sociology is the science with the greatest number of methods and the least results.

Quotes from Valeur de la Science (The Value of Science) (1904)

  • It is not nature which imposes [time and space] upon us, it is we who impose them upon nature because we find them convenient.
  • If all the parts of the universe are interchained in a certain measure, any one phenomenon will not be the effect of a single cause, but the resultant of causes infinitely numerous.
  • Does the harmony the human intelligence thinks it discovers in nature exist outside of this intelligence? No, beyond doubt, a reality completely independent of the mind which conceives it, sees or feels it, is an impossibility.
  • The advance of science is not comparable to the changes of a city, where old edifices are pitilessly torn down to give place to new, but to the continuous evolution of zoologic types which develop ceaselessly and end by becoming unrecognizable to the common sight, but where an expert eye finds always traces of the prior work of the past centuries.

Honors

Awards

  • Oscar II, King of Sweden's mathematical competition (1887)
  • American Philosophical Society (1899)
  • Gold Medal of the Royal Astronomical Society of London (1900)
  • Matteucci Medal (1905)
  • French Academy of Sciences (1906)
  • Académie Française (1909)
  • Bruce Medal (1911)

Named after him

  • The Poincaré group used in physics and mathematics was named after him.
  • Poincaré Prize (Mathematical Physics International Prize)
  • Annales Henri Poincaré (Scientific Journal)
  • Poincaré Seminar (nicknamed "Bourbaphy")
  • Poincaré crater (on the Moon)
  • Asteroid 2021 Poincaré

Publications

Poincaré's major contribution to algebraic topology was Analysis situs (1895), which was the first real systematic look at topology.

He published two major works that placed celestial mechanics on a rigorous mathematical basis:

  • New Methods of Celestial Mechanics ISBN 1563961172 (3 vols., 1892-1899; English trans., 1967)
  • Lessons of Celestial Mechanics. (1905-1910).

In popular writings he helped establish the fundamental popular definitions and perceptions of science by these writings:

  • Dernières pensées (Eng., "Last Thoughts"); Edition Ernest Flammarion, Paris, 1913.

See also

Notes

  1. Mauro Murzi, Jules Henri Poincaré. The Internet Encyclopedia of Philosophy. Retrieved November 12, 2007.
  2. J. John O'Connor et al., 2002. "Jules Henri Poincaré". University of St. Andrews, Scotland. Retrieved November 13, 2007.
  3. Michael N. Macrossan, 1986-01-01, A Note on Relativity Before Einstein. British Journal for the Philosophy of Science 37 : 232-234. The University of Queensland, Australia.
  4. H.E. Ives (1952) wrote that Einstein's derivation was a tautology due to Einstein's use of approximations, and credited Planck (1907) with the first correct derivation of in Einstein's meaning. In response J. Riseman and I. G. Young (1953) defended Einstein's derivation and physical insight, and Ives (1953) replied.
  5. Poincaré à Lorentz. Poincaré's letter to Lorentz. (In French). Retrieved November 12, 2007.
  6. Poincaré à Lorentz. Poincaré's letter to Lorentz. (In French). Retrieved November 12, 2007.
  7. Sur la Dynamique de l'Électron. Retrieved November 12, 2007.
  8. Sur la Dynamique de l'Électron. Retrieved November 12, 2007.
  9. Olivier Darrigol, The Mystery of the Einstein-Poincaré Connection. Isis 95(4) (2004): 614-428.
  10. Peter Louis Galison. 2003. Einstein's Clocks, Poincaré's Maps: Empires of Time. (New York, NY: W.W. Norton)
  11. Kragh 1999
  12. E.T. Whittaker. A History of the Theories of Aether and Electricity: Vol 2: The Modern Theories 1900-1926. Chapter II: The Relativity Theory of Poincaré and Lorentz. (London, UK: Nelson, 1953)
  13. Lorentz, Poincaré et Einstein. lexpress.fr. (In French.) Retrieved November 12, 2007.
  14. J. John O'Connor et al., 2002, "Jules Henri Poincaré". University of St. Andrews, Scotland. Retrieved November 13, 2007.
  15. André Belliver. 1956. Henri Poincaré ou la vocation souveraine. (Paris, FR: Gallimard)
  16. Bernstein, 1996, 199-200
  17. Henri Poincaré. Wikiquote. Retrieved November 12, 2007.
  18. On the "Normal Law of Errors" in the Introduction to his book Thermodynamique (1892); as told by J.H. Gaddum in Nature 156 (1945): 463-466.

References
ISBN links support NWE through referral fees

This article incorporates material from Jules Henri Poincaré on PlanetMath, which is licensed under the GFDL.

General references

  • Bell, Eric Temple. 1986. Men of Mathematics (reissue edition). New York, NY: Simon & Schuster. ISBN 0671628186.
  • Belliver, André. 1956. Henri Poincaré ou la vocation souveraine. Paris, FR: Gallimard.
  • Bernstein, Peter L. 1996. Against the Gods: A Remarkable Story of Risk. New York, NY: John Wiley & Sons. ISBN 0471121045.
  • Boyer, B. Carl. 1968. A History of Mathematics: Henri Poincaré. New York, NY: John Wiley & Sons.
  • Darrigol, Olivier. 2004. The Mystery of the Einstein-Poincaré Connection. Isis. 95(4):614-628.
  • Ewald, William B. ed., 1996. From Kant to Hilbert: A Source Book in the Foundations of Mathematics. 2 vols. Oxford, UK: Oxford University Press. ISBN 0198532717.
  • Grattan-Guinness, Ivor. 2000. The Search for Mathematical Roots 1870-1940. Princeton, NJ: Princeton University Press. ISBN 0691058571.
  • Gray, Jeremy. 2000. Linear differential equations and group theory from Riemann to Poincaré. Boston, MA: Birkhauser. ISBN 0817638377.
  • Kolak, Daniel. 2001. Lovers of Wisdom, 2nd ed. Belmont, CA: Wadsworth. ISBN 0534541461.
  • Murzi. 1998. "Henri Poincaré". Retrieved November 13, 2007.
  • O'Connor, J. John, and F. Edmund Robertson. 2002. "Jules Henri Poincaré". University of St. Andrews, Scotland. Retrieved November 13, 2007.
  • Peterson, Ivars. 1995. Newton's Clock: Chaos in the Solar System. (reissue edition). New York, NY: W H Freeman & Co. ISBN 0716727242.
  • Poincaré, Henri. 1894. On the nature of mathematical reasoning. 972-981.
  • Poincaré, Henri. 1898. On the foundations of geometry. 982-1011.
  • Poincaré, Henri. 1900. Intuition and Logic in mathematics. 1012-1020.
  • Poincaré, Henri. 1905-06. Mathematics and Logic, I-III. 1021-1070.
  • Poincaré, Henri. 1910. On transfinite numbers. 1071-1074.
  • Sageret, Jules. 1911. Henri Poincaré. Paris, FR: Mercure de France.
  • Toulouse, E. 1910. Henri Poincaré. (Source biography in French)

References to work on relativity

  • Einstein, A. 1905. Zur Elektrodynamik Bewegter Körper (English Translation). Annalen der Physik 17:891. Retrieved November 13, 2007.
  • Einstein, A. 1915. Erklärung der Periheldrehung des Merkur aus der allgemainen Relativitätstheorie. Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin. 799-801.
  • Einstein, A. 1916. Die Grundlage der allgemeinen Relativitätstheorie. Annalen der Physik 49.
  • Giannetto, Enrico. 1998. The Rise of Special Relativity: Henri Poincaré's Works Before Einstein. Atti del XVIII congresso di storia della fisica e dell'astronomia.
  • Galison, Peter Louis. 2003. Einstein's Clocks, Poincaré's Maps: Empires of Time. New York, NY: W.W. Norton. ISBN 0393020010.
  • Hasenöhrl, F. 1907. Wien Sitz. CXVI 2a:1391
  • Ives, H. E. 1952. Derivation of the Mass-Energy Relationship. J. Optical Society America 42:540-543.
  • Ives, H. E. 1953. Note on 'Mass-Energy Relationship' J. Optical Society America 43:619.
  • Keswani, G. H. 1965-6. Origin and Concept of Relativity, Parts I, II, III. Brit. J. Phil. Sci. 15-17.
  • Kragh, Helge. 1999. Quantum Generations: A History of Physics in the Twentieth Century. Princeton, NJ: Princeton University Press. ISBN 0691012067.
  • Langevin, P. 1905. Sur l'origine des radiations et l'inertie électromagnétique. Journal de Physique Théorique et Appliquée 4:165-183.
  • Langevin, P. 1914. "Le Physicien" in Henri Poincaré Librairie. Felix Alcan, 1914.
  • Lewis, G. N. 1908. Philosophical Magazine XVI:705
  • Logunov, A. 2005. Henri Poincaré and Relativity Theory. Moscow, RU: Nauka. ISBN 5020339644. Retrieved November 13, 2007.
  • Lorentz, H. A. 1899. Simplified Theory of Electrical and Optical Phenomena in Moving Systems. Proc. Acad. Science Amsterdam I: 427-443.
  • Lorentz, H.A. 1904. Electromagnetic Phenomena in a System Moving with Any Velocity Less Than That of Light. Proc. Acad. Science Amsterdam IV:669-78.
  • Lorentz, H.A. 1911. Amsterdam Versl. XX:87.
  • Lorentz, H.A. 1921. 1914 manuscripts. Deux memoires de Henri Poincaré. Acta Mathematica 38 293.
  • Macrossan, M.N. 1986. A Note on Relativity Before Einstein. Brit. J. Phil. Sci. 37:232-34. Retrieved November 13, 2007.
  • Planck, M. 1907. Berlin Sitz. 542.
  • Planck, M. 1908. Verh. d. Deutsch. Phys. Ges. X:218, and Phys. ZS. IX:828
  • Poincaré, H. 1897. The Relativity of Space. Article in English translation. Retrieved November 13, 2007.
  • Poincaré, H. 1898. La mesure du Temps. reprinted in "La valeur de la science." Ernest Flammarion, Paris. Retrieved November 13, 2007.
  • Poincaré, H. 1900. La Theorie de Lorentz et la Principe de Reaction. Archives Neerlandaises. V:252-78.
  • Poincaré, H. 1905. La valeur de la Science. Wikisource. Retrieved November 13, 2007.
  • Poincaré, H. 1904. L'état actuel et l'avenir de la physique mathématique. Bulletin des sciences mathématiques 28(1904), 302-324 (Congress of Arts and Science, St. Louis, September 24, 1904)
  • Poincaré, H. 1905. Sur la dynamique de l'electron. Comptes Rendues. 140:1504-8. Retrieved November 13, 2007.
  • Poincaré, H. 1906. Sur la dynamique de l'electron. Rendiconti del Circolo matematico di Palermo. 21:129-176. Retrieved November 13, 2007.
  • Poincaré, H. 1913. Mathematics and Science: Last Essays. New York, NY: Dover 1963. (translated from Dernières Pensées posthumously published by Ernest Flammarion, 1913)
  • Riseman, J. and I.G. Young. 1953. Mass-Energy Relationship. J. Optical Society America 43:618.
  • Whittaker, E.T. 1953. A History of the Theories of Aether and Electricity: Vol 2 The Modern Theories 1900-1926. Chapter II: The Relativity Theory of Poincaré and Lorentz. London, UK: Nelson.

External links

All links retrieved December 15, 2017.


Preceded by:
Sully Prudhomme
Seat 24
Académie française
1908-1912

Succeeded by:
Alfred Capus

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