Henri Poincaré
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Jules Henri Poincaré (UK: /ˈpwæ̃kɑːreɪ/, US: /ˌpwæ̃kɑːˈreɪ/; French: [ɑ̃ʁi pwɛ̃kaʁe] ⓘ;[1][2][3] 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The Last Universalist",[4] since he excelled in all fields of the discipline as it existed during his lifetime. Due to his scientific success, influence and his discoveries, he has been deemed "the philosopher par excellence of modern science."[5]
As a mathematician and physicist, he made many original fundamental contributions to pure and applied mathematics, mathematical physics, and celestial mechanics.[6] 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 also considered to be one of the founders of the field of topology.
Poincaré made clear the importance of paying attention to the invariance of laws of physics under different transformations, 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 Hendrik Lorentz in 1905. Thus he obtained perfect invariance of all of Maxwell's equations, an important step in the formulation of the theory of special relativity. In 1905, Poincaré first proposed gravitational waves (ondes gravifiques) emanating from a body and propagating at the speed of light as being required by the Lorentz transformations.[7] In 1912, he wrote an influential paper which provided a mathematical argument for quantum mechanics.[8][9]
The Poincaré group used in physics and mathematics was named after him.
Early in the 20th century he formulated the Poincaré conjecture that became over time one of the famous unsolved problems in mathematics until it was solved in 2002–2003 by Grigori Perelman.
Life
Poincaré was born on 29 April 1854 in Cité Ducale neighborhood,
Education
During his childhood he was seriously ill for a time with diphtheria and received special instruction from his mother, Eugénie Launois (1830–1897).
In 1862, Henri entered the Lycée in
During the
Poincaré entered the
As a graduate of the École des Mines, he joined the
At the same time, Poincaré was preparing for his
First scientific achievements
After receiving his degree, Poincaré began teaching as junior
There, in Caen, he met his future wife, Louise Poulain d'Andecy (1857–1934), granddaughter of Isidore Geoffroy Saint-Hilaire and great-granddaughter of Étienne Geoffroy Saint-Hilaire and on 20 April 1881, they married.[16] Together they had four children: Jeanne (born 1887), Yvonne (born 1889), Henriette (born 1891), and Léon (born 1893).
Poincaré immediately established himself among the greatest mathematicians of Europe, attracting the attention of many prominent mathematicians. In 1881 Poincaré was invited to take a teaching position at the Faculty of Sciences of the
In 1881–1882, Poincaré created a new branch of mathematics: qualitative theory of differential equations. He showed how it is possible to derive the most important information about the behavior of a family of solutions without having to solve the equation (since this may not always be possible). He successfully used this approach to problems in celestial mechanics and mathematical physics.
Career
He never fully abandoned his career in the mining administration to mathematics. He worked at the
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).[17] Eventually, he held the chairs of Physical and Experimental Mechanics, Mathematical Physics and Theory of Probability,[18] and Celestial Mechanics and Astronomy.
In 1887, at the young age of 32, Poincaré was elected to the
In 1887, he won
In 1893, Poincaré joined the French Bureau des Longitudes, which engaged him in the synchronisation of time around the world. In 1897 Poincaré backed an unsuccessful proposal for the decimalisation of circular measure, and hence time and longitude.[19] It was this post which led him to consider the question of establishing international time zones and the synchronisation of time between bodies in relative motion. (See work on relativity section below.)
In 1904, he intervened in the trials of Alfred Dreyfus, attacking the spurious scientific claims regarding evidence brought against Dreyfus.
Poincaré was the President of the Société Astronomique de France (SAF), the French astronomical society, from 1901 to 1903.[20]
Students
Poincaré had two notable doctoral students at the University of Paris, Louis Bachelier (1900) and Dimitrie Pompeiu (1905).[21]
Death
In 1912, Poincaré underwent surgery for a
A former French Minister of Education,
Work
Summary
Poincaré made many contributions to different fields of pure and applied mathematics such as:
He was also a populariser of mathematics and physics and wrote several books for the lay public.
Among the specific topics he contributed to are the following:
- algebraic topology (a field that Poincaré virtually invented)
- the theory of analytic functions of several complex variables
- the theory of abelian functions
- algebraic geometry
- the Poincaré conjecture, proven in 2003 by Grigori Perelman.
- Poincaré recurrence theorem
- hyperbolic geometry
- number theory
- the three-body problem
- the theory of diophantine equations
- electromagnetism
- the special theory of relativity
- the fundamental group
- In the field of Poincaré sphere and the Poincaré map.
- Poincaré on "everybody's belief" in the Normal Law of Errors (see normal distribution for an account of that "law")
- Published an influential paper providing a novel mathematical argument in support of quantum mechanics.[8][23]
Three-body problem
The problem of finding the general solution to the motion of more than two orbiting bodies in the
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 be considered to be prizeworthy. The prize was finally awarded to Poincaré, even though he did not solve the original problem. One of the judges, the distinguished Karl Weierstrass, said, "This work cannot indeed be considered as furnishing the complete solution of the question proposed, but that it is nevertheless of such importance that its publication will inaugurate a new era in the history of celestial mechanics." (The first version of his contribution even contained a serious error; for details see the article by Diacu[24] and the book by Barrow-Green[25]). The version finally printed[26] contained many important ideas which led to the theory of chaos. The problem as stated originally was finally solved by Karl F. Sundman for n = 3 in 1912 and was generalised to the case of n > 3 bodies by Qiudong Wang in the 1990s. The series solutions have very slow convergence. It would take millions of terms to determine the motion of the particles for even very short intervals of time, so they are unusable in numerical work.[24]
Work on relativity
Local time
Poincaré's work at the Bureau des Longitudes on establishing international time zones led him to consider how clocks at rest on the Earth, which would be moving at different speeds relative to absolute space (or the "luminiferous aether"), could be synchronised. At the same time Dutch theorist Hendrik Lorentz was developing Maxwell's theory into a theory of the motion of charged particles ("electrons" or "ions"), and their interaction with radiation. In 1895 Lorentz had introduced an auxiliary quantity (without physical interpretation) called "local time" [27] and introduced the hypothesis of
Principle of relativity and Lorentz transformations
In 1881 Poincaré described
In 1892 Poincaré developed a
He discussed the "principle of relative motion" in two papers in 1900[30][35] and named it the principle of relativity in 1904, according to which no physical experiment can discriminate between a state of uniform motion and a state of rest.[36] In 1905 Poincaré wrote to Lorentz 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.[37] In a second letter to Lorentz, 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 he gave what is now known as the relativistic velocity-addition law.[38] 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 he wrote:[39]
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:
and showed that the arbitrary function must be unity for all (Lorentz had set 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 is invariant. He noted that a Lorentz transformation is merely a rotation in four-dimensional space about the origin by introducing as a fourth imaginary coordinate, and he used an early form of four-vectors.[40] Poincaré expressed a lack of interest in a four-dimensional reformulation of his new mechanics in 1907, because in his opinion the translation of physics into the language of four-dimensional geometry would entail too much effort for limited profit.[41] So it was Hermann Minkowski who worked out the consequences of this notion in 1907.[citation needed]
Mass–energy relation
Like
However, Poincaré's resolution led to a
Poincaré himself came back to this topic in his St. Louis lecture (1904).[36] He rejected[42] the possibility that energy carries mass and criticized his own solution to compensate the above-mentioned problems:
The apparatus will recoil as if it were a cannon and the projected energy a ball, and that contradicts the principle of Newton, since our present projectile has no mass; it is not matter, it is energy. [..] Shall we say that the space which separates the oscillator from the receiver and which the disturbance must traverse in passing from one to the other, is not empty, but is filled not only with ether, but with air, or even in inter-planetary space with some subtile, yet ponderable fluid; that this matter receives the shock, as does the receiver, at the moment the energy reaches it, and recoils, when the disturbance leaves it? That would save Newton's principle, but it is not true. If the energy during its propagation remained always attached to some material substratum, this matter would carry the light along with it and Fizeau has shown, at least for the air, that there is nothing of the kind. Michelson and Morley have since confirmed this. We might also suppose that the motions of matter proper were exactly compensated by those of the ether; but that would lead us to the same considerations as those made a moment ago. The principle, if thus interpreted, could explain anything, since whatever the visible motions we could imagine hypothetical motions to compensate them. But if it can explain anything, it will allow us to foretell nothing; it will not allow us to choose between the various possible hypotheses, since it explains everything in advance. It therefore becomes useless.
In the above quote he refers to the Hertz assumption of total aether entrainment that was falsified by the Fizeau experiment but that experiment does indeed show that that light is partially "carried along" with a substance. Finally in 1908[43] he revisits the problem and ends with abandoning the principle of reaction altogether in favor of supporting a solution based in the inertia of aether itself.
But we have seen above that Fizeau's experiment does not permit of our retaining the theory of Hertz; it is necessary therefore to adopt the theory of Lorentz, and consequently to renounce the principle of reaction.
He also 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 Marie Curie.
It was Albert Einstein's concept of mass–energy equivalence (1905) that a body losing energy as radiation or heat was losing mass of amount m = E/c2 that resolved[44] Poincaré's paradox, without using any compensating mechanism within the ether.[45] The Hertzian oscillator loses mass in the emission process, and momentum is conserved in any frame. However, concerning Poincaré's solution of the Center of Gravity problem, Einstein noted that Poincaré's formulation and his own from 1906 were mathematically equivalent.[46]
Gravitational waves
In 1905 Poincaré first proposed
It has become important to examine this hypothesis more closely and in particular to ask in what ways it would require us to modify the laws of gravitation. That is what I have tried to determine; at first I was led to assume that the propagation of gravitation is not instantaneous, but happens with the speed of light.[47][39]
Poincaré and Einstein
Einstein's first paper on relativity was published three months after Poincaré's short paper,[39] but before Poincaré's longer version.[40] Einstein relied on the principle of relativity to derive the Lorentz transformations and used a similar clock synchronisation procedure (Einstein synchronisation) to the one that Poincaré (1900) had described, but Einstein's paper was remarkable in that it contained no references at all. Poincaré never acknowledged Einstein's work on special relativity. However, Einstein expressed sympathy with Poincaré's outlook obliquely in a letter to Hans Vaihinger on 3 May 1919, when Einstein considered Vaihinger's general outlook to be close to his own and Poincaré's to be close to Vaihinger's.[48] In public, Einstein acknowledged Poincaré posthumously in the text of a lecture in 1921 titled "Geometrie und Erfahrung (Geometry and Experience)" in connection with non-Euclidean geometry, but not in connection with special relativity. A few years before his death, 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 ....".[49]
Assessments on Poincaré and relativity
Poincaré's work in the development of special relativity is well recognised,[44] though most historians stress that despite many similarities with Einstein's work, the two had very different research agendas and interpretations of the work.[50] Poincaré developed a similar physical interpretation of local time and noticed the connection to signal velocity, but contrary to Einstein he continued to use the ether-concept in his papers and argued that clocks at rest in the ether show the "true" time, and moving clocks show the local time. So Poincaré tried to keep the relativity principle in accordance with classical concepts, while Einstein developed a mathematically equivalent kinematics based on the new physical concepts of the relativity of space and time.[51][52][53][54][55]
While this is the view of most historians, a minority go much further, such as E. T. Whittaker, who held that Poincaré and Lorentz were the true discoverers of relativity.[56]
Algebra and number theory
Poincaré introduced
Topology
The subject is clearly defined by Felix Klein in his "Erlangen Program" (1872): the geometry invariants of arbitrary continuous transformation, a kind of geometry. The term "topology" was introduced, as suggested by Johann Benedict Listing, instead of previously used "Analysis situs". Some important concepts were introduced by Enrico Betti and Bernhard Riemann. But the foundation of this science, for a space of any dimension, was created by Poincaré. His first article on this topic appeared in 1894.[58]
His research in geometry led to the abstract topological definition of homotopy and homology. He also first introduced the basic concepts and invariants of combinatorial topology, such as Betti numbers and the fundamental group. Poincaré proved a formula relating the number of edges, vertices and faces of n-dimensional polyhedron (the Euler–Poincaré theorem) and gave the first precise formulation of the intuitive notion of dimension.[59]
Astronomy and celestial mechanics
Poincaré published two now classical monographs, "New Methods of Celestial Mechanics" (1892–1899) and "Lectures on Celestial Mechanics" (1905–1910). In them, he successfully applied the results of their research to the problem of the motion of three bodies and studied in detail the behavior of solutions (frequency, stability, asymptotic, and so on). They introduced the small parameter method, fixed points, integral invariants, variational equations, the convergence of the asymptotic expansions. Generalizing a theory of Bruns (1887), Poincaré showed that the three-body problem is not integrable. In other words, the general solution of the three-body problem can not be expressed in terms of
These monographs include an idea of Poincaré, which later became the basis for mathematical "chaos theory" (see, in particular, the Poincaré recurrence theorem) and the general theory of dynamical systems. Poincaré authored important works on astronomy for the equilibrium figures of a gravitating rotating fluid. He introduced the important concept of bifurcation points and proved the existence of equilibrium figures such as the non-ellipsoids, including ring-shaped and pear-shaped figures, and their stability. For this discovery, Poincaré received the Gold Medal of the Royal Astronomical Society (1900).[61]
Differential equations and mathematical physics
After defending his doctoral thesis on the study of singular points of the system of
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Saddle
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Focus
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Center
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Node
Character
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
Toulouse's characterisation
Poincaré's mental organisation was interesting not only to Poincaré himself but also to Édouard Toulouse, a psychologist of the Psychology Laboratory of the School of Higher Studies in Paris. Toulouse wrote a book entitled Henri Poincaré (1910).[65][66] 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 nearsighted.
- 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 the lecturer wrote on the blackboard.
These abilities were offset to some extent 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 started from basic principles each time (O'Connor et al., 2002).
His method of thinking is well summarised 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 (accustomed to neglecting details and to looking only at mountain tops, he went from one peak to another with surprising rapidity, and the facts he discovered, clustering around their center, were instantly and automatically pigeonholed in his memory).
— Belliver (1956)
Publications
- Leçons sur la théorie mathématique de la lumière (in French). Paris: Carrè. 1889.
- Solutions periodiques, non-existence des integrales uniformes, solutions asymptotiques (in French). Vol. 1. Paris: Gauthier-Villars. 1892.
- Methodes de mm. Newcomb, Gylden, Lindstedt et Bohlin (in French). Vol. 2. Paris: Gauthier-Villars. 1893.
- Oscillations électriques (in French). Paris: Carrè. 1894.
- Invariants integraux, solutions periodiques du deuxieme genre, solutions doublement asymptotiques (in French). Vol. 3. Paris: Gauthier-Villars. 1899.
- Valeur de la science (in French). Paris: Flammarion. 1900.
- Electricité et optique (in French). Paris: Carrè & Naud. 1901.
- Science et l'hypothèse (in French). Paris: Flammarion. 1902.
- Thermodynamique (in French). Paris: Gauthier-Villars. 1908.
- Dernières pensées (in French). Paris: Flammarion. 1913.
- Science et méthode. London: Nelson and Sons. 1914.
Honours
Awards
- Oscar II, King of Sweden's mathematical competition (1887)
- Foreign member of the Royal Netherlands Academy of Arts and Sciences (1897)[67]
- American Philosophical Society (1899)
- Gold Medal of the Royal Astronomical Society of London (1900)
- Bolyai Prize (1905)
- Matteucci Medal (1905)
- French Academy of Sciences (1906)
- Académie française(1909)
- Bruce Medal (1911)
Named after him
- Institut Henri Poincaré (mathematics and theoretical physics centre)
- Poincaré Prize(Mathematical Physics International Prize)
- Annales Henri Poincaré (Scientific Journal)
- Poincaré Seminar (nicknamed "Bourbaphy")
- The crater Poincaré on the Moon
- 2021 Poincaré
- List of things named after Henri Poincaré
Henri Poincaré did not receive the
The fact that renowned theoretical physicists like Poincaré, Boltzmann or Gibbs were not awarded the Nobel Prize is seen as evidence that the Nobel committee had more regard for experimentation than theory.[71][72] In Poincaré's case, several of those who nominated him pointed out that the greatest problem was to name a specific discovery, invention, or technique.[68]
Philosophy
Poincaré had
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
].However, Poincaré did not share
Free will
Poincaré's famous lectures before the Société de Psychologie in Paris (published as Science and Hypothesis, The Value of Science, and Science and Method) were cited by Jacques Hadamard as the source for the idea that creativity and invention consist of two mental stages, first random combinations of possible solutions to a problem, followed by a critical evaluation.[76]
Although he most often spoke of a
It is certain that the combinations which present themselves to the mind in a kind of sudden illumination after a somewhat prolonged period of unconscious work are generally useful and fruitful combinations... all the combinations are formed as a result of the automatic action of the subliminal ego, but those only which are interesting find their way into the field of consciousness... A few only are harmonious, and consequently at once useful and beautiful, and they will be capable of affecting the geometrician's special sensibility I have been speaking of; which, once aroused, will direct our attention upon them, and will thus give them the opportunity of becoming conscious... In the subliminal ego, on the contrary, there reigns what I would call liberty, if one could give this name to the mere absence of discipline and to disorder born of chance.[77]
Poincaré's two stages—random combinations followed by selection—became the basis for Daniel Dennett's two-stage model of free will.[78]
Bibliography
Poincaré's writings in English translation
Popular writings on the philosophy of science:
- Poincaré, Henri (1902–1908), The Foundations of Science, New York: Science Press; reprinted in 1921; this book includes the English translations of Science and Hypothesis (1902), The Value of Science (1905), Science and Method (1908).
- 1905. "Science and Hypothesis", The Walter Scott Publishing Co.
- 1906. "The End of Matter", Athenæum
- 1913. "The New Mechanics", The Monist, Vol. XXIII.
- 1913. "The Relativity of Space", The Monist, Vol. XXIII.
- 1913. Last Essays., New York: Dover reprint, 1963
- 1956. Chance. In James R. Newman, ed., The World of Mathematics (4 Vols).
- 1958. The Value of Science, New York: Dover.
- 1895. Analysis Situs (PDF), archived (PDF) from the original on 27 March 2012. The first systematic study of topology.
- 1890. Poincaré, Henri (2017). The three-body problem and the equations of dynamics: Poincaré's foundational work on dynamical systems theory. Translated by Popp, Bruce D. Cham, Switzerland: Springer International Publishing. ISBN 978-3-319-52898-4.
- 1892–99. New Methods of Celestial Mechanics, 3 vols. English trans., 1967. ISBN 1-56396-117-2.
- 1905. "The Capture Hypothesis of J. J. See", The Monist, Vol. XV.
- 1905–10. Lessons of Celestial Mechanics.
On the philosophy of mathematics:
- Ewald, William B., ed., 1996. From Kant to Hilbert: A Source Book in the Foundations of Mathematics, 2 vols. Oxford Univ. Press. Contains the following works by Poincaré:
- 1894, "On the Nature of Mathematical Reasoning", 972–81.
- 1898, "On the Foundations of Geometry", 982–1011.
- 1900, "Intuition and Logic in Mathematics", 1012–20.
- 1905–06, "Mathematics and Logic, I–III", 1021–70.
- 1910, "On Transfinite Numbers", 1071–74.
- 1905. "The Principles of Mathematical Physics", The Monist, Vol. XV.
- 1910. "The Future of Mathematics", The Monist, Vol. XX.
- 1910. "Mathematical Creation", The Monist, Vol. XX.
Other:
- 1904. Maxwell's Theory and Wireless Telegraphy, New York, McGraw Publishing Company.
- 1905. "The New Logics", The Monist, Vol. XV.
- 1905. "The Latest Efforts of the Logisticians", The Monist, Vol. XV.
Exhaustive bibliography of English translations:
- 1892–2017. Henri Poincaré Papers, archived from the original on 1 August 2020.
See also
Concepts
- Poincaré–Andronov–Hopf bifurcation
- Poincaré complex – an abstraction of the singular chain complex of a closed, orientable manifold
- Poincaré duality
- Poincaré disk model
- Poincaré expansion
- Poincaré gauge
- Poincaré group
- Poincaré half-plane model
- Poincaré homology sphere
- Poincaré inequality
- Poincaré lemma
- Poincaré map
- Poincaré residue
- Poincaré series (modular form)
- Poincaré space
- Poincaré metric
- Poincaré plot
- Poincaré polynomial
- Poincaré series
- Poincaré sphere
- Poincaré–Einstein synchronisation
- Poincaré–Lelong equation
- Poincaré–Lindstedt method
- Poincaré–Lindstedt perturbation theory
- Poincaré–Steklov operator
- Euler–Poincaré characteristic
- Neumann–Poincaré operator
- Reflecting Function
Theorems
Here is a list of theorems proved by Poincaré:
- Poincaré's recurrence theorem: certain systems will, after a sufficiently long but finite time, return to a state very close to the initial state.
- Poincaré–Bendixson theorem: a statement about the long-term behaviour of orbits of continuous dynamical systems on the plane, cylinder, or two-sphere.
- Poincaré–Hopf theorem: a generalization of the hairy-ball theorem, which states that there is no smooth vector field on a sphere having no sources or sinks.
- Poincaré–Lefschetz duality theorem: a version of Poincaré duality in geometric topology, applying to a manifold with boundary
- Poincaré separation theorem: gives the upper and lower bounds of eigenvalues of a real symmetric matrix B'AB that can be considered as the orthogonal projection of a larger real symmetric matrix A onto a linear subspace spanned by the columns of B.
- Poincaré–Birkhoff theorem: every area-preserving, orientation-preserving homeomorphism of an annulus that rotates the two boundaries in opposite directions has at least two fixed points.
- Poincaré–Birkhoff–Witt theorem: an explicit description of the universal enveloping algebra of a Lie algebra.
- Poincaré–Bjerknes circulation theorem: theorem about a conservation of quantity for the rotating frame.
- Poincaré conjecture (now a theorem): Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere.
- Poincaré–Miranda theorem: a generalization of the intermediate value theorem to n dimensions.
Other
- French epistemology
- History of special relativity
- List of things named after Henri Poincaré
- Institut Henri Poincaré, Paris
- Brouwer fixed-point theorem
- Relativity priority dispute
- Epistemic structural realism[79]
References
Footnotes
- ^ "Poincaré". Oxford English Dictionary (Online ed.). Oxford University Press. (Subscription or participating institution membership required.)
- ^ "Poincaré pronunciation: How to pronounce Poincaré in French". forvo.com.
- ^ "How To Pronounce Henri Poincaré". pronouncekiwi.com.
- ISBN 978-981-4556-61-3.
- ^ Moulton, Forest Ray; Jeffries, Justus J. (1945). The Autobiography of Science. Doubleday & Company. p. 509.
- ^ Hadamard, Jacques (July 1922). "The early scientific work of Henri Poincaré". The Rice Institute Pamphlet. 9 (3): 111–183.
- ISSN 2218-1997.
- ^ S2CID 120934561
- ^ Prentis, Jeffrey J. (1 April 1995). "Poincaré's proof of the quantum discontinuity of nature". pubs.aip.org. Retrieved 22 October 2023.
- ^ Belliver, 1956
- ^ Sagaret, 1911
- ^ The Internet Encyclopedia of Philosophy Archived 2 February 2004 at the Wayback Machine Jules Henri Poincaré article by Mauro Murzi – Retrieved November 2006.
- ^ O'Connor et al., 2002
- ^ Carl, 1968
- ^ F. Verhulst
- S2CID 190028919.
- ^ Sageret, 1911
- ISBN 9783034808347.
- ^ see Galison 2003
- ^ "Bulletin de la Société astronomique de France, 1911, vol. 25, pp. 581–586". 1911.
- ^ Mathematics Genealogy Project Archived 5 October 2007 at the Wayback Machine North Dakota State University. Retrieved April 2008.
- ^ "Lorentz, Poincaré et Einstein". Archived from the original on 27 November 2004.
- ^ S2CID 119728316
- OCLC 34357985.
- OCLC 987302273.
- ^ Lorentz, Hendrik A. (1895), , Leiden: E.J. Brill
- ^ Poincaré, Henri (1898), , Revue de Métaphysique et de Morale, 6: 1–13
- ^ a b c Poincaré, Henri (1900), English translation , Archives Néerlandaises des Sciences Exactes et Naturelles, 5: 252–278. See also the
- ^ Poincaré, H. (1881). "Sur les applications de la géométrie non-euclidienne à la théorie des formes quadratiques" (PDF). Association Française Pour l'Avancement des Sciences. 10: 132–138. Archived from the original (PDF) on 1 August 2020.
- S2CID 124088818.
- ^ Poincaré, H. (1892). "Chapitre XII: Polarisation rotatoire". Théorie mathématique de la lumière II. Paris: Georges Carré.
- .
- ^ Poincaré, H. (1900), "Les relations entre la physique expérimentale et la physique mathématique", Revue Générale des Sciences Pures et Appliquées, 11: 1163–1175. Reprinted in "Science and Hypothesis", Ch. 9–10.
- ^ a b Poincaré, Henri (1913),
{{citation}}
: CS1 maint: postscript (link) available in online chapter from 1913 book , The Foundations of Science (The Value of Science), New York: Science Press, pp. 297–320; article translated from 1904 original - ^ Poincaré, H. (2007), "38.3, Poincaré to H. A. Lorentz, May 1905", in Walter, S. A. (ed.), La correspondance entre Henri Poincaré et les physiciens, chimistes, et ingénieurs, Basel: Birkhäuser, pp. 255–257
- ^ Poincaré, H. (2007), "38.4, Poincaré to H. A. Lorentz, May 1905", in Walter, S. A. (ed.), La correspondance entre Henri Poincaré et les physiciens, chimistes, et ingénieurs, Basel: Birkhäuser, pp. 257–258
- ^ a b c [1] (PDF) Membres de l'Académie des sciences depuis sa création : Henri Poincare. Sur la dynamique de l' electron. Note de H. Poincaré. C.R. T.140 (1905) 1504–1508.
- ^ S2CID 120211823(Wikisource translation)
- ^ Walter (2007), Secondary sources on relativity
- ^ Miller 1981, Secondary sources on relativity
- ^ Poincaré, Henri (1908–1913). . The foundations of science (Science and Method). New York: Science Press. pp. 486–522.
- ^ a b Darrigol 2005, Secondary sources on relativity
- doi:10.1002/andp.19053231314. See also English translation.
- S2CID 120361282, archived from the original(PDF) on 18 March 2006
- ^ "Il importait d'examiner cette hypothèse de plus près et en particulier de rechercher quelles modifications elle nous obligerait à apporter aux lois de la gravitation. C'est ce que j'ai cherché à déterminer; j'ai été d'abord conduit à supposer que la propagation de la gravitation n'est pas instantanée, mais se fait avec la vitesse de la lumière."
- S2CID 170178963.
- ^ Darrigol 2004, Secondary sources on relativity
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Sources
- ISBN 0-671-62818-6.
- Belliver, André, 1956. Henri Poincaré ou la vocation souveraine. Paris: Gallimard.
- Bernstein, Peter L, 1996. "Against the Gods: A Remarkable Story of Risk". (p. 199–200). John Wiley & Sons.
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- Folina, Janet, 1992. Poincaré and the Philosophy of Mathematics. Macmillan, New York.
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Further reading
Secondary sources to work on relativity
- Cuvaj, Camillo (1969), "Henri Poincaré's Mathematical Contributions to Relativity and the Poincaré Stresses", American Journal of Physics, 36 (12): 1102–1113,
- Darrigol, O. (1995), "Henri Poincaré's criticism of Fin De Siècle electrodynamics", Studies in History and Philosophy of Science, 26 (1): 1–44,
- Darrigol, O. (2000), Electrodynamics from Ampére to Einstein, Oxford: Clarendon Press, ISBN 978-0-19-850594-5
- Darrigol, O. (2004), "The Mystery of the Einstein–Poincaré Connection", Isis, 95 (4): 614–626, S2CID 26997100
- Darrigol, O. (2005), "The Genesis of the theory of relativity" (PDF), Séminaire Poincaré, 1: 1–22, ISBN 978-3-7643-7435-8, archived(PDF) from the original on 28 February 2008
- Galison, P. (2003), Einstein's Clocks, Poincaré's Maps: Empires of Time, New York: W.W. Norton, ISBN 978-0-393-32604-8
- Giannetto, E. (1998), "The Rise of Special Relativity: Henri Poincaré's Works Before Einstein", Atti del XVIII Congresso di Storia della Fisica e dell'astronomia: 171–207
- ISBN 978-0-08-025790-7
- Goldberg, S. (1967), "Henri Poincaré and Einstein's Theory of Relativity", American Journal of Physics, 35 (10): 934–944,
- Goldberg, S. (1970), "Poincaré's silence and Einstein's relativity", British Journal for the History of Science, 5: 73–84, S2CID 123766991
- Holton, G. (1988) [1973], "Poincaré and Relativity", ISBN 978-0-674-87747-4
- Katzir, S. (2005), "Poincaré's Relativistic Physics: Its Origins and Nature", Phys. Perspect., 7 (3): 268–292, S2CID 14751280
- Keswani, G.H., Kilmister, C.W. (1983), "Intimations of Relativity: Relativity Before Einstein", Br. J. Philos. Sci., 34 (4): 343–354, S2CID 65257414, archived from the original on 26 March 2009)
{{citation}}
: CS1 maint: multiple names: authors list (link - Keswani, G.H. (1965), "Origin and Concept of Relativity, Part I", Br. J. Philos. Sci., 15 (60): 286–306, S2CID 229320737
- Keswani, G.H. (1965), "Origin and Concept of Relativity, Part II", Br. J. Philos. Sci., 16 (61): 19–32, S2CID 229320603
- Keswani, G.H. (1966), "Origin and Concept of Relativity, Part III", Br. J. Philos. Sci., 16 (64): 273–294, S2CID 122596290
- Kragh, H. (1999), Quantum Generations: A History of Physics in the Twentieth Century, Princeton University Press, ISBN 978-0-691-09552-3
- Langevin, P. (1913), "L'œuvre d'Henri Poincaré: le physicien", Revue de Métaphysique et de Morale, 21: 703
- Macrossan, M. N. (1986), "A Note on Relativity Before Einstein", Br. J. Philos. Sci., 37 (2): 232–234, S2CID 121973100, archived from the originalon 29 October 2013, retrieved 27 March 2007
- Miller, A.I. (1973), "A study of Henri Poincaré's "Sur la Dynamique de l'Electron", Arch. Hist. Exact Sci., 10 (3–5): 207–328, S2CID 189790975
- Miller, A.I. (1981), Albert Einstein's special theory of relativity. Emergence (1905) and early interpretation (1905–1911), Reading: Addison–Wesley, ISBN 978-0-201-04679-3
- Miller, A.I. (1996), "Why did Poincaré not formulate special relativity in 1905?", in Jean-Louis Greffe; Gerhard Heinzmann; Kuno Lorenz (eds.), Henri Poincaré : science et philosophie, Berlin, pp. 69–100
{{citation}}
: CS1 maint: location missing publisher (link) - Popp, B.D. (2020), Henri Poincaré: Electrons to Special Relativity, Cham: Springer Nature, ISBN 978-3-030-48038-7
- Schwartz, H. M. (1971), "Poincaré's Rendiconti Paper on Relativity. Part I", American Journal of Physics, 39 (7): 1287–1294,
- Schwartz, H. M. (1972), "Poincaré's Rendiconti Paper on Relativity. Part II", American Journal of Physics, 40 (6): 862–872,
- Schwartz, H. M. (1972), "Poincaré's Rendiconti Paper on Relativity. Part III", American Journal of Physics, 40 (9): 1282–1287,
- Scribner, C. (1964), "Henri Poincaré and the principle of relativity", American Journal of Physics, 32 (9): 672–678,
- Walter, S. (2005), "Henri Poincaré and the theory of relativity", in Renn, J. (ed.), Albert Einstein, Chief Engineer of the Universe: 100 Authors for Einstein, Berlin: Wiley-VCH, pp. 162–165
- Walter, S. (2007), "Breaking in the 4-vectors: the four-dimensional movement in gravitation, 1905–1910", in Renn, J. (ed.), The Genesis of General Relativity, vol. 3, Berlin: Springer, pp. 193–252
- Whittaker, E.T. (1953), "The Relativity Theory of Poincaré and Lorentz", A History of the Theories of Aether and Electricity: The Modern Theories 1900–1926, London: Nelson
- Zahar, E. (2001), Poincaré's Philosophy: From Conventionalism to Phenomenology, Chicago: Open Court Pub Co, ISBN 978-0-8126-9435-2
Non-mainstream sources
- Leveugle, J. (2004), La Relativité et Einstein, Planck, Hilbert—Histoire véridique de la Théorie de la Relativitén, Pars: L'Harmattan
- Logunov, A.A. (2004), Henri Poincaré and relativity theory, ISBN 978-5-02-033964-4
External links
- Works by Henri Poincaré at Project Gutenberg
- Works by or about Henri Poincaré at Internet Archive
- Works by Henri Poincaré at LibriVox (public domain audiobooks)
- Henri Poincaré's Bibliography
- Internet Encyclopedia of Philosophy: "Henri Poincaré Archived 2 February 2004 at the Wayback Machine"—by Mauro Murzi.
- Internet Encyclopedia of Philosophy: "Poincaré’s Philosophy of Mathematics"—by Janet Folina.
- Henri Poincaré at the Mathematics Genealogy Project
- Henri Poincaré on Information Philosopher
- O'Connor, John J.; Robertson, Edmund F., "Henri Poincaré", MacTutor History of Mathematics Archive, University of St Andrews
- A timeline of Poincaré's life University of Nantes (in French).
- Henri Poincaré Papers University of Nantes (in French).
- Bruce Medal page
- Collins, Graham P., "Henri Poincaré, His Conjecture, Copacabana and Higher Dimensions," Scientific American, 9 June 2004.
- BBC in Our Time, "Discussion of the Poincaré conjecture," 2 November 2006, hosted by Melvynn Bragg.
- Poincare Contemplates Copernicus at MathPages
- High Anxieties – The Mathematics of Chaos (2008) BBC documentary directed by David Malone looking at the influence of Poincaré's discoveries on 20th Century mathematics.