Henri Poincaré

Henri Poincaré (April 29th 1854 with Nancy, France - July 17th 1912 with Paris) is a Mathématicien, Physicien and Philosophe French. Genious theorist, his contributions with many fields of mathematics and physics radically modified these two sciences. Among those, let us quote its work in Optique, Relativité, on the Problème of the three bodies, in differential Calculus and Théorie of chaos.

Biography

Great-grandson of Etienne Geoffroy Saint-Hilaire, he is the cousin of the politician and president of the French Republic Raymond Poincaré, and of Lucien Poincaré, director of Secondary education to the Ministry for the State education and the Art schools.

Brilliance raises, it obtains the baccalaureat arts and science in 1871, between first with the Polytechnic school in 1873, then with the École des Mines in October 1875; he is bachelor of science on August 2nd, 1876. Appointed mining engineer of 3rd class in March 1879 in Vesoul, it obtains on August 1st, 1879 the science doctorate mathematics with the Faculty of Science of Paris and becomes part-time lecturer of analysis to the Faculty of Science of Caen on December 1st, 1879.

Two years later, it obtains its first outstanding results in mathematics (on the representation of the Courbe S and on the differential equations linear with algebraic coefficients), and quickly, it is interested in the application of its mathematical knowledge in Physique and more particularly in Mécanique.

It goes back to Paris in 1881 as university lecturer of analysis to the Faculty of Science of Paris. It is named repeater of analysis at the Polytechnic school on November 6th, 1883, charges that it occupies until its resignation in March 1897. Named with the pulpit of physical and experimental mechanics on March 16th, 1885, it leaves this one for the pulpit of Mathematical physics and probability theory in August 1886, succeeding Gabriel Lippmann.

He is elected member of the Academy of Science in 1887. He becomes member of the Bureau of longitudes in 1893 and is named chief engineer of the mines. In November 1896, it obtains the mathematical pulpit of Astronomie and celestial mechanics , succeeding Felix Tisserand.

It is, in 1901, the first prize winner of the Médaille Sylvester of the Royal Society. He was president of the mathematical Société of France in 1886 and 1900 and chair French company of physics in 1902.

October 1st, 1904, Poincaré is named professor of general astronomy without treatment the Polytechnic school in order to avoid the removal of this pulpit.

Poincaré and relativity

In 1902, Poincaré publishes Science and the assumption . Even if this book is more one work of epistemology that of physics, it invites not to regard as too real many artefacts of the physics of its time: absolute time, absolute space, the existence of the ether. This book thus contains the tracks of the restricted Relativité, and it is known that Albert Einstein studied it closely.

In 1905, Poincaré poses the equations of the Transformations of Lorentz, and presents them to the Academy of Science of Paris on June 5th, 1905. These transformations check the Invariance of Lorentz, completing the work of Hendrik Antoon Lorentz itself (Lorentz was corresponding of Poincaré). These transformations are those which apply in restricted relativity, and one employs still today the equations such as wrote Poincaré. But to explain the physical origin of these transformations, Poincaré has recourse has physical contractions of space and time, preserving in references an ether and an absolute time. It is Einstein which gets busy to show that one finds the same transformations while leaving the principle of relativity simply, eliminating the concepts of reference frames or clock absolute, and making differences in length of the effects of the prospect in a space time in four dimensions, and not of the real contractions.

Poincaré also proposed certain ideas on gravity, which were confirmed by the General relativity, in particular the propagation of the gravitation to speed of light and indicated the possibility of existence of the gravitational waves which it called “gravific waves”. The new law was invariant by the transformations of Lorentz. Its weakness was too much to seek the analogy with the laws of electromagnetism. Paul Langevin note that Poincaré found several possible solutions which present all this common character that the gravitation is propagated with the Speed of light, of the body attracting with the attracted body, and that the new law makes it possible to better represent the movements of the Astre S still than the ordinary law since it still attenuates the divergences existing between this one and the facts, in the movement of the perihelion of Mercury, for example.

If the physicists of the time were perfectly with the current of work of Poincaré, the general public then almost forgot it, whereas the name of Einstein is almost known today of all. Recently, some voices sought has to point out the role of Poincaré, but others went further, seeking to make of Poincaré the author of the theory of relativity. This Controverse on the paternity of relativity is all the more delicate as the political conflicts are interfered with the questions with reading with the articles physics.

Mathematics

Poincaré is the founder of the algebraic Topologie. Its principal mathematical work had as an aim the algebraic Géométrie, of the particular types of functions - the functions known as “automorphes” (he discovers the functions fuschiennes and kleinéennes), the differential equations… The concept of Continuité is central in its work, as much by its theoretical repercussions that for the topological problems which it involves.

Bases of mathematics

As from 1905 and during the six last years of its life, Poincaré takes an active part in the debates on the bases which crossed at the time the mathematical community. It forever tried to contribute to it on the technical plan, but some of its ideas had an undeniable influence. One of its contradictors, Bertrand Russell will write in 1914 “It is not possible to be always right in philosophy; but the opinions of Poincaré, right or false, are always the expression of a powerful and original thought, been useful by completely exceptional scientific knowledge”. Inter alia, because of its refusal to accept the infinite current one, i.e. the possibility of regarding the infinite one as a completed entity and not simply as a process which can be prolonged arbitrarily a long time, Poincaré is regarded per many intuitionalist S as a precursor. Poincaré however never called into question third-excluded and nothing indicates that it could have adhered to a as radical recasting mathematics as that which Brouwer will propose.

The position of Poincaré evolved/moved. During one previous time, it was interested in work of Georg Cantor, whose work on the construction of realities and the set theory rests in an essential way on infinite current, at the point to supervise the translation in French of part of the articles of this last (in 1871,1883…), and to use its results in its report on the kleinéens groups (1884). It is also interested in work of David Hilbert on axiomatization: it makes in 1902 a neat and very laudatory recension of the Fondements of the geometry (1899).

In 1905 and 1906, Poincaré reacts, in a rather polemical way to a series of articles of Louis Couturat on the “principles of mathematics” in the re-examined of metaphysics and morals , articles which gave off an account of the Principles Mathematics of Bertrand Russell (1903). Russell will finish by to intervene itself in debate supports on intuitionalism of [[Kant] which stipulates, inter alia, that time and space to us are given like synthetic objects a priori .] Poincaré as opposed to what one often says forever divided what one calls in a vague way Kantian intuitionalism. When it evokes the intuition (the value of science, CH 1), this term means " image" or " modèle". Its design of the experiment does not have great a deal to see with that of Kant: neither space, nor time is " forms a priori " because the experiment is only the occasion from which space represented is put in relation to space like amorphous continuum: " The experiment thus played one part, it was used as occasion. But this role was not less very important; and I believed necessary to emphasize it. This role would have been useless if there was a " form a priori " imposing itself on our sensitivity and which would be space with three dimensions." (The value of science, CH. 4, § 6). When Poincaré evokes the idea of convenience, it is closer to the empirists than idealists: the idea of truth does not have great any more a deal to see with the idea of synthetic judgment a priori because one " choisit" his principles or axioms just like one chooses the facts in sciences of nature. The principle of recurrence seems to have of another goal only to show it not relevance of the logicism which makes deduction the central spring of the mathematical demonstration. For him, it is precisely the case of the principle of Récurrence, which it also names “principle of induction”, in what it is opposed to deduction, and that it refuses to regard as the fruit of a purely analytical judgment, like is for him the logical reasoning. This opposes it to Russell (and through him to Gottlob Frege, that Poincaré ignores), which wants to reduce mathematics to logic, that also opposes it to those which it calls the cantoriens like Ernst Zermelo and from which it distinguishes Hilbert partly. The latter it reproaches the use of infinite current, through their way “of passing from the general to the private individual”, for example the fact of supposing the existence of infinite units to define the whole of the natural entireties, whereas for him, the natural entireties are first. He refuses what he calls, the not-predicative definitions (see Paradoxe of Richard) which to define a unit E calls upon “the notion of the unit E itself” (typically the current definition in axiomatic Théorie of the units of NR , the whole of the entireties natural, like intersection of the units containing 0 and closed by successor, is not-predicative within the meaning of Poincaré, since NR belongs to the latter). Objections of Poincaré, by the reactions which they required, one played a considerable part in the birth of the Logique mathematics and the Set theory, even if its ideas had finally relatively little success. They influence all the same notably the intuitionalism of Brouwer and its successors (who remains very marginal in the mathematicians), and experienced developments in Théorie of the demonstration as from the years 1960.

The problem of the three bodies

Poincaré is also the inventor of the strange Attracteur, which gives information on the solutions of the Problème of the three bodies, while at the same time he is impossible to clarify these solutions: it found that three bodies obeying the universal Gravitation of Newton have, under certain conditions, a trajectory which strongly depends on the initial Condition. Thus, one will be able to never determine with exactitude the destiny of these bodies, because the least disturbance in its measurements would irremediably involve a strong difference in trajectory.

These calculations are at the origin of the Théorie of chaos.

Conjecture of Poincaré

Philosopher and man of letters

He is also the last to have double specificity to include/understand the whole of mathematics of his time and to be at the same time a philosophical thinker . One regards it as one of the large last erudite universal, because of his research in transverse fields (Physique, Optique, Astronomie…), and of its scientific attitude founded on an esthetics of science and number, to bring closer to that of the former Greeks.

Poincaré has work all its career lasting with the Vulgarisation of its results and great work of science, attitude which will be taken again by later physicists, like Albert Einstein or Stephen Hawking.

With Science and the assumption , Poincaré interests the artistic world, in particular the Cubistes, and gives keys of not-Euclidean comprehension to the geometries.

In a more anecdotic way, one can note that Poincaré would have written a novel of youth.

Legendary school results

In a more anecdotic way, it holds to now the record of the average of the notes obtained with the entrance examination to the Polytechnic school. It entered major, and second left there.

Concerning its admission with the Polytechnic school, he would have been the only student to have been allowed there whereas he had obtained one zero with a test of drawing (Lavis), which constitutes an eliminatory note normally. What would have leant in its favor would be the fact that it obtained the maximum note, that is to say 20/20, with all the other tests. The Entrance Board would have been divided between the fact of depriving of an element as brilliance as him, and the application of the rule of the zero eliminating heat. This distorsion with the payment remains single in the history of École.Il thus exists a legend according to which a point would have been withdrawn in physics and réattribué in drawing is: 1/20 in drawing, 20 /20 with the three tests of mathematics and 19 in physics.

Honors

Prize winner of the open Competition.
Gold medal of Royal Astronomical Society (1900)
Member of the French Academy (1908)
Medal Bruce (1911)

For the whole of its work, Poincaré was had a presentiment of twelve times at the Nobel Prize of physics. The Université Henri Poincaré is named in its honor.

Principal publications

Science and the assumption (Flammarion - 1902)
the Value of Science (Flammarion - 1905)
Science and method (Flammarion - 1908)
Erudite and writers (Flammarion - 1910)
mathematical Theory of the light (Square - 1892 and 1899)
Thermodynamic (Square - 1892)
Theory of elasticity (Square and Naud- 1892)
Theory of the swirls (Square and Naud- 1893)
Capillarity (Square and Naud- 1893)
analytical Theory of the propagation of heat (Square and Naud- 1895)
Probability theory (Square and Naud- 1896)
Electricity and optical (Square and Naud- 1901)
new methods of celestial mechanics (Gauthier-Villars 1893)
Last Thoughts (1913) Flammarion, republished by Flammarion, supplemented other articles in appendix starting from the second edition of 1926.
Course of the Faculty of Science of Paris - Course of Mathematical physics - Thermodynamics per H. Poincaré, Member of the Institute - Drafting of J. Cableway, Aggregate of the University Paris Gauthier-Villars 1908 - Reprinting 1995 of the Editions Jacques Gabay.

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