Jules Henri Poincare. Henri Poincare - French mathematician, mechanic, physicist

Henri Poincare

French mathematician, mechanic, physicist, astronomer and philosopher

short biography

Jules Henri Poincare(French Jules Henri Poincaré; April 29, 1854, Nancy, France - July 17, 1912, Paris, France) - French mathematician, mechanic, physicist, astronomer and philosopher. Head of the Paris Academy of Sciences (1906), member of the French Academy (1908) and more than 30 academies of the world, including a foreign corresponding member of the St. Petersburg Academy of Sciences (1895).

Historians rank Henri Poincaré as the greatest mathematicians of all time. He is considered, along with Hilbert, the last universal mathematician, a scientist capable of covering all the mathematical results of his time. He is the author of over 500 articles and books. "It would not be an exaggeration to say that there was no area of contemporary mathematics, 'pure' or 'applied', that he did not enrich with remarkable methods and results."

Among his biggest achievements:

Creation of topology.
Qualitative theory differential equations.
Theory of automorphic functions.
Development of new, extremely effective methods celestial mechanics.
Creation of the mathematical foundations of the theory of relativity, as well as the generalization of the principle of relativity to all physical phenomena.
Visual model of Lobachevsky's geometry.

Early years and training (1854-1879)

Henri Poincare was born on April 29, 1854 in Nancy (Lorraine, France). His father, Leon Poincaré (1828-1892), was a professor of medicine at the Medical School (since 1878 at the University of Nancy). Henri's mother, Eugenie Lanois ( Eugenie Launois), all free time devoted to the upbringing of children - the son of Henri and the youngest daughter of Alina.

Among Poincare's relatives there are other celebrities: cousin Raymond became President of France (from 1913 to 1920), another cousin, famous physicist Lucien Poincaré was Inspector General of Public Education of France, and from 1917 to 1920 - Rector of the University of Paris.

From childhood, Henri had a reputation as an absent-minded person, which he retained for the rest of his life. As a child, he suffered from diphtheria, which was complicated by temporary paralysis of the legs and soft palate. The illness dragged on for several months, during which he could neither walk nor speak. During this time, his auditory perception developed very strongly and, in particular, appeared unusual ability- color perception of sounds, which remained with him until the end of his life.

Good home preparation allowed Henri at the age of eight and a half to enter immediately into the second year of study at the Lyceum. There he was noted as a diligent and inquisitive student with broad erudition. At this stage, his interest in mathematics was moderate - after a while he moved to the department of literature, where he perfectly mastered Latin, German and English; this later helped Poincaré to communicate actively with his colleagues. August 5, 1871 Poincaré received a bachelor's degree in literature with a mark of "good". A few days later, Henri expressed a desire to participate in the exams for the Bachelor of Science (natural) degree, which he managed to pass, but only with a "satisfactory" grade, because he absent-mindedly answered the wrong question in a written exam in mathematics.

In subsequent years, Poincaré's mathematical talents became more and more obvious. In October 1873, he became a student at the prestigious Paris Polytechnic School, where he won first place in the entrance exams. His tutor in mathematics was Charles Hermite. AT next year Poincaré published in the Annals of Mathematics his first scientific work in differential geometry.

Based on the results of a two-year study (1875), Poincaré was admitted to the Mining School, the most authoritative specialized higher educational institution at that time. There, a few years later (1879), under the guidance of Hermite, he defended his doctoral dissertation, about which Gaston Darboux, who was a member of the commission, said: “From the first glance it became clear to me that the work goes beyond the ordinary and more than deserves to be accepted. It contained quite enough results to provide material for many good dissertations.

First scientific achievements (1879-1882)

Having received degree, Poincare began teaching at the University of Caen in Normandy (December 1879). At the same time, he published his first serious articles - they are devoted to the class of automorphic functions introduced by him.

There, in Cana, he met his future wife, Louise Poulain d'Andecy ( Louise Poulain d'Andecy). On April 20, 1881, their wedding took place. They had a son and three daughters.

In 1879

Originality, breadth and high scientific level Poincaré's work immediately placed him among the greatest mathematicians in Europe and attracted the attention of other prominent mathematicians. In 1881, Poincaré was invited to take up a teaching position at the Faculty of Sciences at the University of Paris and accepted the invitation. In parallel, from 1883 to 1897, he taught mathematical analysis at the Higher Polytechnic School.

In 1881-1882, Poincaré created a new branch of mathematics - the qualitative theory of differential equations. He showed how it is possible, without solving equations (since this is not always possible), to obtain practically important information about the behavior of a family of solutions. He applied this approach with great success to solving problems of celestial mechanics and mathematical physics.

Leader of French mathematicians (1882-1899)

A decade after the completion of the study of automorphic functions (1885-1895), Poincaré devoted himself to solving several the most difficult tasks astronomy and mathematical physics. He investigated the stability of the figures of the planets formed in the liquid (molten) phase, and found, in addition to ellipsoidal, several other possible figures of equilibrium.

In 1889

In 1885, King Oscar II of Sweden organized math competition and offered participants a choice of four topics. The first one was the most difficult: to calculate the motion of the gravitating bodies of the solar system. Poincaré showed that this problem (the so-called three-body problem) does not have a complete mathematical solution. However, Poincaré soon suggested effective methods its approximate solution. In 1889, Poincaré received the prize of the Swedish competition (together with his friend and future biographer Paul Appel, who was investigating a different topic). One of the two judges, Mittag-Leffler, wrote of Poincaré's work: "The prized memoir will prove to be among the most significant mathematical discoveries of the century." The second judge, Weierstrass, declared that after Poincaré's work "a new era in the history of celestial mechanics will begin." For this success, the French government awarded Poincare the Order of the Legion of Honor.

In the autumn of 1886, 32-year-old Poincaré headed the department of mathematical physics and probability theory at the University of Paris. A symbol of Poincare's recognition as the leading French mathematician was his election as president of the French Mathematical Society (1886) and a member of the Paris Academy of Sciences (1887).

In 1887, Poincaré generalized Cauchy's theorem to the case of several complex variables and laid the foundation for the theory of residues in a multidimensional complex space.

In 1889, the fundamental "Course of Mathematical Physics" by Poincare was published in 10 volumes, and in 1892-1893 - two volumes of the monograph "New Methods of Celestial Mechanics" (the third volume was published in 1899).

Since 1893, Poincaré has been a member of the prestigious Bureau of Longitudes (in 1899 he was elected its president). Since 1896, he moved to the university chair of celestial mechanics, which he held until the end of his life. In the same period, while continuing his work on astronomy, he simultaneously realized the long-thought-out plan of creating quality geometry, or topology: since 1894, he began publishing articles on the construction of a new, exceptionally promising science.

Last years

In August 1900, Poincaré led the logic section of the First World Philosophical Congress, held in Paris. There he made a keynote speech "On the Principles of Mechanics", where he outlined his conventionalist philosophy: the principles of science are temporary conditional agreements adapted to experience, but having no direct analogues in reality. He subsequently substantiated this platform in detail in the books Science and Hypothesis (1902), The Value of Science (1905) and Science and Method (1908). In them, he also described his vision of the essence of mathematical creativity, in which leading role intuition plays, and logic is assigned the role of a strict justification of intuitive insights. The clear style and depth of thought provided these books with considerable popularity, they were immediately translated into many languages. At the same time, the Second International Congress of Mathematicians was held in Paris, where Poincaré was elected chairman (all congresses were timed to coincide with the World Exhibition of 1900).

In 1903, Poincaré was included in a group of 3 experts who examined the evidence in the Dreyfus case. On the basis of a unanimously accepted expert opinion, the court of cassation found Dreyfus not guilty.

The main area of interest of Poincaré in the 20th century was physics (especially electromagnetism) and the philosophy of science. Poincare shows a deep understanding of electromagnetic theory, his insightful remarks are highly valued and considered by Lorentz and other leading physicists. From 1890, Poincaré published a series of papers on Maxwell's theory, and in 1902 he began to read a course of lectures on electromagnetism and radio communications. In his articles of 1904-1905, Poincaré was far ahead of Lorentz in understanding the situation, in fact creating mathematical foundations theory of relativity (the physical foundation of this theory was developed by Einstein in 1905).

In 1906, Poincaré was elected president of the Paris Academy of Sciences. In 1908, he fell seriously ill and was unable to read his report "The Future of Mathematics" at the Fourth Mathematical Congress. The first operation ended successfully, but after 4 years Poincaré's condition worsened again. He died in Paris after an operation for an embolism on July 17, 1912 at the age of 58. He was buried in the family vault at the Montparnasse cemetery.

Probably, Poincare had a premonition of his unexpected death, since in the last article he described a problem he had not solved (“Poincaré's last theorem”), which he had never done before. A few months later, this theorem was proved by George Birkhoff. Later, with the assistance of Birkhoff, the Poincaré Institute for Theoretical Physics was established in France.

Contribution to science

Poincaré's mathematical activity was of an interdisciplinary nature, thanks to which, in the thirty-odd years of his intense creative activity he left fundamental works in almost all areas of mathematics. Poincaré's works, published by the Paris Academy of Sciences in 1916-1956, comprise 11 volumes. These are works on the topology he created, automorphic functions, the theory of differential equations, multidimensional complex analysis, integral equations, non-Euclidean geometry, probability theory, number theory, celestial mechanics, physics, philosophy of mathematics and philosophy of science.

In all the various fields of his work, Poincaré obtained important and profound results. Although his scientific legacy includes many major works on "pure mathematics" ( general algebra, algebraic geometry, number theory, etc.), nevertheless, the works, the results of which have direct applied application. This is especially noticeable in his works of the last 15-20 years. However, Poincaré's discoveries tended to have general character and later successfully applied in other fields of science.

Poincaré's creative method was based on the creation of an intuitive model of the problem posed: he always first completely solved the problems in his head, and then wrote down the solution. Poincaré had a phenomenal memory and could quote books read and conversations word for word (Henri Poincaré's memory, intuition and imagination even became the subject of real psychological research). Also, he never worked on a single task. for a long time, believing that the subconscious has already received the task and continues to work, even when he thinks about other things. Poincare described his creative method in detail in the report "Mathematical Creativity" (Paris Psychological Society, 1908).

Paul Painlevé assessed the significance of Poincaré for science as follows:

He comprehended everything, deepened everything. Possessing an unusually inventive mind, he knew no limits to his inspiration, tirelessly paving new paths, and in the abstract world of mathematics, he repeatedly discovered unknown areas. Everywhere that the human mind penetrated, no matter how difficult and thorny its path was - whether it was the problems of wireless telegraphy, X-rays or the origin of the Earth - Henri Poincaré walked alongside ... Together with the great French mathematician, the only person whose mind could embrace everything that is created by the mind of other people, to penetrate into the very essence of everything that human thought has comprehended today, and to see something new in it.

Automorphic functions

During the 19th century, practically all prominent European mathematicians participated in the development of the theory of elliptic functions, which proved to be extremely useful in solving differential equations. Nevertheless, these functions did not fully justify the hopes placed on them, and many mathematicians began to think about whether it was possible to extend the class of elliptic functions so that the new functions could also be applied to those equations where elliptic functions are useless.

Poincaré first found this idea in an article by Lazar Fuchs, the most prominent specialist in those years on linear differential equations (1880). Over the course of several years, Poincaré developed Fuchs's idea far, creating the theory of a new class of functions, which he, with Poincaré's usual indifference to questions of priority, proposed to call fuchsian functions(fr. les fonctions fuchsiennes) - although he had every reason to give his name to this class. The case ended with the fact that Felix Klein proposed the name "automorphic functions", which was fixed in science. Poincaré deduced the expansion of these functions into series, proved the addition theorem and the theorem on the possibility of uniformization of algebraic curves (that is, their representation through automorphic functions; this is Hilbert's 22nd problem, solved by Poincaré in 1907). These discoveries "may rightly be considered the pinnacle of the entire development of the theory analytic functions complex variable in the 19th century.

In developing the theory of automorphic functions, Poincaré discovered their connection with Lobachevsky's geometry, which allowed him to present many questions of the theory of these functions in terms of geometric language. He published visual model geometry of Lobachevsky, with the help of which he illustrated the material on the theory of functions.

After the work of Poincaré, elliptic functions turned from a priority direction of science into a limited special case of a more powerful general theory. Automorphic functions discovered by Poincare allow solving any linear differential equation with algebraic coefficients and find wide application in many areas of the exact sciences.

Differential Equations and Mathematical Physics

After defending his doctoral dissertation devoted to the study of singular points of a system of differential equations, Poincaré wrote a series of memoirs under common name"On curves defined by differential equations" (1881-1882 for equations of the 1st order, supplemented in 1885-1886 for equations of the 2nd order). In these articles, he built a new branch of mathematics, which was called the "qualitative theory of differential equations." Poincaré showed that even if a differential equation cannot be solved in terms of known functions, nevertheless, from the very form of the equation one can obtain extensive information about the properties and behavior of the family of its solutions. In particular, Poincare studied the nature of the course of integral curves on a plane, gave a classification of singular points (saddle, focus, center, node), introduced the concepts of a limit cycle and cycle index, and proved that the number of limit cycles is always finite, except for a few special cases. Poincaré also developed a general theory of integral invariants and solutions of equations in variations. For equations in finite differences, he created a new direction - the asymptotic analysis of solutions. He applied all these achievements to research practical tasks mathematical physics and celestial mechanics, and the methods used became the basis of his topological work.

Singular points of integral curves

Saddle

Focus

Center

Knot

Poincare also dealt a lot with partial differential equations, mainly in the study of problems of mathematical physics. He significantly supplemented the methods of mathematical physics, in particular, made a significant contribution to the theory of potential, the theory of heat conduction, studied the vibrations of three-dimensional bodies, and a number of problems in the theory of electromagnetism. He also owns works on the justification of the Dirichlet principle, for which he developed in the article "On Partial Differential Equations" the so-called. balayage method (fr. méthode de balayage).

Algebra and number theory

Already in his first works, Poincaré successfully applied the group-theoretic approach, which became for him the most important tool in many further research- from topology to the theory of relativity. Poincaré was the first to introduce group theory into physics; in particular, he was the first to study the group of Lorentz transformations. He also made major contributions to the theory of discrete groups and their representations.

AT early period creativity Poincaré explored cubic ternary and quaternary forms.

Topology

The subject of topology was clearly defined by Felix Klein in his Erlangen Program (1872): it is the geometry of invariants of arbitrary continuous transformations, a kind of high quality geometry. The term "topology" itself (instead of the previously used Analysis situs) was suggested earlier by Johann Benedict Listing. Some important concepts were introduced by Enrico Betti and Bernhard Riemann. However, the foundation of this science, and developed in sufficient detail for a space of any number of dimensions, was created by Poincaré. His first article on the subject appeared in 1894, it aroused general interest, and Poincaré published five additions to this pioneering work between 1899 and 1902. The last of these additions contained the famous Poincaré conjecture.

Research in geometry led Poincaré to an abstract topological definition of homotopy and homology. He also for the first time introduced the basic concepts and invariants of combinatorial topology, such as Betti numbers, the fundamental group, proved a formula relating the number of edges, vertices and faces of an n-dimensional polyhedron (the Euler-Poincaré formula), gave the first exact formulation of the intuitive concept of dimension.

Multivariate complex analysis

Poincaré generalized Cauchy's theorem to the case of several complex variables, founded the theory of residues for the multidimensional case, laid the foundation for the study of biholomorphic mappings of domains in a complex space.

Astronomy and Celestial Mechanics

Poincaré published two classic monographs: New Methods of Celestial Mechanics (1892-1899) and Lectures on Celestial Mechanics (1905-1910). In them, he successfully applied the results of his research to the problem of movement of three bodies, having studied in detail the behavior of the solution (periodicity, stability, asymptotic behavior, etc.). He introduced methods of a small parameter (Poincaré's theorem on the expansion of integrals with respect to a small parameter), fixed points, integral invariants, equations in variations, and the convergence of asymptotic expansions is studied. Generalizing the Bruns theorem (1887), Poincaré proved that the three-body problem is not integrable in principle. In other words, common decision three-body problems cannot be expressed in terms of algebraic or single-valued transcendental functions of coordinates and velocities of bodies. His work in this area is considered the greatest achievement in celestial mechanics since Newton.

These works of Poincare contain ideas that later became the basis for the mathematical "chaos theory" and the general theory of dynamical systems.

Poincare wrote important for astronomy works on the figures of equilibrium of a gravitating rotating fluid. He introduced the important concept of bifurcation points, proved the existence of equilibrium figures other than the ellipsoid, including ring-shaped and pear-shaped figures, and studied their stability. For this discovery, Poincaré received a gold medal from the Royal Astronomical Society of London (1900).

Physics and other works

As a member of the Bureau of Longitudes, Poincaré participated in the measurement work of this institution and published several meaningful works on problems of geodesy, gravimetry and the theory of tides.

From the end of the 1880s until the end of his life, Poincaré devoted much effort to Maxwell's electromagnetic theory and its version supplemented by Lorentz. He actively corresponded with Heinrich Hertz and Lorenz, often prompting them with the right ideas. In particular, Poincaré wrote out the Lorentz transformations in modern form, while Lorentz suggested their approximate version somewhat earlier. Nevertheless, it was Poincaré who named these transformations after Lorentz. For Poincaré's contribution to the development of the theory of relativity, see below.

It was on the initiative of Poincaré that the young Antoine Henri Becquerel began to study the connection between phosphorescence and X-rays (1896), and during these experiments the radioactivity of uranium compounds was discovered. Poincaré was the first to derive the law of attenuation of radio waves.

In the last two years of his life Poincaré was keenly interested in quantum theory. In a detailed article "On the Theory of Quanta" (1911), he proved that it was impossible to obtain Planck's radiation law without the hypothesis of quanta, thereby burying all hopes of somehow preserving the classical theory.

Scientific terms associated with the name Poincaré

Poincare conjecture
Poincaré group
Poincaré duality
Poincaré-Cartan integral
Poincaré's lemma
Poincaré metric
Poincaré model of Lobachevsky space
Poincaré-Dulac normal form
Poincaré mapping
Poincaré's last theorem
Poincaré sphere
Cauchy-Poincaré theorem
Poincaré-Bendixon theorem
Poincaré - Birkhoff - Witt theorem
Poincaré-Volterra theorem
Poincaré's vector field theorem
Poincaré recurrence theorem
Poincaré's theorem on the classification of homeomorphisms of the circle
Poincaré's theorem on the expansion of integrals with respect to a small parameter
Poincaré's theorem on the rate of growth of an entire function

and many others.

The role of Poincare in the creation of the theory of relativity

Poincare's work in the field of relativistic dynamics

Poincaré's name is directly related to the success of the theory of relativity. He actively participated in the development of Lorentz's theory. In this theory, it was assumed that there is a fixed ether, and the speed of light relative to the ether does not depend on the speed of the source. When switching to a moving frame of reference, Lorentz transformations are performed instead of Galilean ones (Lorentz considered these transformations to be a real change in the size of bodies). It was Poincaré who gave the correct mathematical formulation of these transformations (Lorentz himself offered only their first-order approximation) and showed that they form a group of transformations.

Back in 1898, long before Einstein, Poincaré in his work “Measurement of Time” formulated the general (not only for mechanics) principle of relativity, and then even introduced a four-dimensional space-time, the theory of which was later developed by Hermann Minkowski. Nevertheless, Poincaré continued to use the concept of the ether, although he was of the opinion that it could never be discovered - see Poincaré's paper at the Physics Congress, 1900. In the same report, Poincaré was the first to express the idea that the simultaneity of events is not absolute, but is a conditional agreement ("convention"). It was also suggested that the speed of light is limited.

Influenced by Poincaré's criticism, Lorentz proposed in 1904 new version of his theory. In it, he suggested that high speeds Newtonian mechanics needs to be corrected. In 1905, Poincaré developed these ideas far in his article "On the Dynamics of the Electron". The preliminary version of the article appeared on June 5, 1905 in Comptes Rendus, expanded was completed in July 1905, published in January 1906, for some reason in a little-known Italian mathematical journal.

In this final article, the general principle of relativity is again and clearly formulated for all physical phenomena (in particular, electromagnetic, mechanical and also gravitational), with Lorentz transformations as the only possible coordinate transformations that preserve the same record of physical equations for all reference systems. Poincaré found an expression for the four-dimensional interval as an invariant of the Lorentz transformations: r 2 + (i c t) 2 , a four-dimensional formulation of the principle least effect. In this article, he also offered the first draft of a relativistic theory of gravity; in his model, gravitation propagated in the ether at the speed of light, and the theory itself was non-trivial enough to remove the lower limit obtained by Laplace on the speed of propagation of the gravitational field. preliminary short message came out before Einstein's work was published in the journal, the last, large article also came to publishers before Einstein's, but by the time it was published, Einstein's first article on the theory of relativity had already been published.

Poincaré and Einstein: similarities and differences

Einstein, in his early work on relativity, used essentially the same mathematical model as Poincaré: the Lorentz transformations, relativistic formula addition of velocities, etc. However, unlike Poincaré, Einstein made a decisive conclusion: it is absurd to use the concept of ether only to prove the impossibility of its observation. He completely abolished both the concept of ether, which Poincaré continued to use, and the concepts of absolute motion and absolute time based on the ether hypothesis. It was this theory that, at the suggestion of Max Planck, was called theory of relativity(Poincaré preferred to talk about subjectivity or conventions, see below).

All the new effects that Lorentz and Poincaré considered to be the dynamical properties of the ether in Einstein's theory of relativity follow from objective properties space and time, that is, transferred by Einstein from dynamics to kinematics. This is the main difference between the approaches of Poincaré and Einstein, disguised by their outward similarity. mathematical models: they differently understood the deep physical(and not just mathematical) essence of these models. The transfer to kinematics allowed Einstein to create a holistic and universal theory of space and time, as well as to solve previously intractable problems within its framework - for example, confusing question about different types mass, the dependence of mass on energy, the ratio of local and "absolute" time, etc. Now this theory is called the "special theory of relativity" (SRT). Another significant difference between the positions of Poincaré and Einstein was that the Lorentz contraction of length, the growth of inertia with speed, and other relativistic conclusions were understood by Poincaré as absolute effects, while Einstein as relative, having no physical consequences in their own reference frame. What was real to Einstein physical time in a moving frame of reference, Poincaré called time "apparent", "apparent" (fr. temps apparent) and clearly distinguished it from "true time" (fr. le temps vrai).

Possibly, the insufficiently deep analysis of the physical essence of SRT in the works of Poincaré was the reason why physicists did not pay the attention they deserved to these works; accordingly, the wide resonance of Einstein's first article was caused by a clear and deep analysis of the foundations of the studied physical picture. In the subsequent discussion of relativity, Poincaré's name was not mentioned (even in France); when in 1910 Poincaré was nominated for Nobel Prize, in the list of his merits nothing was said about the theory of relativity.

Rationale new mechanics was also different. In Einstein's articles of 1905, the principle of relativity from the very beginning is not affirmed as a conclusion from dynamic considerations and experiments, but is put at the heart of physics as a kinematic axiom (also for all phenomena without exception). From this axiom and from the constancy of the speed of light, the mathematical apparatus of Lorentz-Poincaré is obtained automatically. The rejection of the ether made it possible to emphasize that the “resting” and “moving” coordinate systems are completely equal in rights, and when passing to a moving coordinate system, the same effects are already found in the resting one.

Einstein, according to his later confession, at the time of the beginning of work on the theory of relativity was not familiar with either the latest publications of Poincaré (probably only with his work of 1900, in any case, not with the works of 1904), nor with the last article of Lorentz (1904 year).

"The Silence of Poincaré"

Shortly after the appearance of Einstein's work on the theory of relativity (1905), Poincaré stopped publishing on this topic. In no work of the last seven years of his life did he mention either the name of Einstein or the theory of relativity (except for one case when he referred to Einstein's theory of the photoelectric effect). Poincare still continued to discuss the properties of the ether and mentioned absolute motion relative to the ether.

The meeting and conversation of two great scientists took place only once - in 1911 at the First Solvay Congress. In a letter to his Zurich friend Dr. Zangger dated November 16, 1911, Einstein wrote ruefully:

Poincare [in relation to the relativistic theory] rejected everything completely and showed, for all his subtlety of thought, a poor understanding of the situation.

original text(German)
Poincaré war (gegen die Relativitätstheorie) einfach allgemein ablehnend, zeigte bei allem Scharfsinn wenig Verständnis für die Situation.
- A. Pais. Subtle is the Lord. Oxford University Press, Oxford 1982, p. 170.

(the insert in brackets is probably Pais's).

Despite the rejection of the theory of relativity, Poincare personally treated Einstein with great respect. Einstein's characteristic, which was given by Poincaré at the end of 1911, has been preserved. The characteristic was requested by the administration of the Zurich Higher Polytechnic School in connection with the invitation of Einstein to the post of professor at the school.

Mr. Einstein is one of the most original minds I have known; despite his youth, he already took a very honorable place among the most prominent scientists of his time. Most of all, he admires the ease with which he adapts to new concepts and is able to extract all the consequences from them.
He does not hold on to classical principles and, when confronted with a physical problem, is ready to consider all possibilities. Thanks to this, his mind anticipates new phenomena, which in time can be experimentally verified. I do not mean to say that all these predictions will stand the test of experience the day it becomes possible; on the contrary, since he seeks in all directions, it is to be expected that most of the paths he enters will turn out to be dead ends; but at the same time, one must hope that one of the directions indicated by him will turn out to be correct, and this is enough. That is exactly what should be done. The role of mathematical physics is to ask questions correctly; only experience can solve them.
The future will show more definitely what the significance of Mr. Einstein is, and the university that manages to bind the young master to itself will derive much honor from this.

In April 1909, at the invitation of Hilbert, Poincaré came to Göttingen and gave a number of lectures there, including on the principle of relativity. Poincaré never once mentioned in these lectures not only Einstein, but also Minkowski, Goettingen. Many hypotheses have been put forward about the reasons for the "silence of Poincaré". Some historians of science have suggested that Poincaré's resentment against German school physicists, who underestimated his merits in the creation of the relativistic theory. Others consider this explanation implausible, since Poincare was never seen in his life taking offense over priority disputes, and Einstein's theory was preferred not only in Germany, but also in Great Britain and even in France itself (for example, Langevin). Even Lorentz, whose theory Poincaré sought to develop, after 1905 preferred to speak of "Einstein's principle of relativity." The following hypothesis was also put forward: Kaufman's experiments conducted during these years cast doubt on the principle of relativity and the formula for the dependence of inertia on speed, so it is possible that Poincaré decided to simply wait with the conclusions until these issues were clarified.

In Göttingen, Poincaré made an important prediction: relativistic corrections to the theory of gravitation should explain the secular shift of Mercury's perihelion. The prediction soon came true (1915) when Einstein completed the development of the general theory of relativity.

Poincare's position is somewhat clarified by his lecture "Space and Time", which he delivered in May 1912 at the University of London. Poincare considers the principle of relativity and the new laws of mechanics to be primary in the restructuring of physics. The properties of space and time, according to Poincaré, must be derived from these principles or established conventionally. Einstein did the opposite - he derived dynamics from new properties of space and time. Poincare still considers the transition of physicists to a new mathematical formulation of the principle of relativity (Lorentz transformations instead of Galilean ones) a matter of agreement:

What will be our attitude towards these new [relativistic] ideas? Will they force us to change our conclusions? Not at all; we accepted the well-known conditional agreement because it seemed convenient to us ... Now some physicists want to accept a new conditional agreement. This does not mean that they were forced to do so; they find this new arrangement more convenient, that's all. And those who do not adhere to their opinion and are unwilling to give up their old habits can rightly keep the old agreement. Between us, I think they will continue to do so for a long time to come.

From these words one can understand why Poincaré not only did not complete his path to the theory of relativity, but even refused to accept the already created theory. This can also be seen from a comparison of the approaches of Poincaré and Einstein. What Einstein understands as relative but objective, Poincaré understands as purely subjective, conventional (conventional). The difference between the positions of Poincaré and Einstein and its possible philosophical roots have been studied in detail by historians of science.

The founder of quantum mechanics, Louis de Broglie, the first winner of the Poincaré medal (1929), blames his positivist views for everything:

A little more, and Henri Poincare, and not Albert Einstein, would have been the first to build the theory of relativity in all its generality, thereby giving French science the honor of this discovery ... However, Poincaré did not take the decisive step, and gave Einstein the honor to see all the consequences of the principle of relativity and, in particular, through a deep analysis of the measurements of length and time, to find out the true physical nature connection established by the principle of relativity between space and time.
Why didn't Poincare reach the end in his conclusions?... Poincaré, as a scientist, was first of all a pure mathematician... Poincaré took a somewhat skeptical position in relation to physical theories, believing that in general there are infinitely many logically equivalent points of view and pictures of reality, from which the scientist, guided solely by considerations of convenience, chooses one. Probably, such nominalism sometimes prevented him from recognizing the fact that among logically possible theories there are those that are closer to physical reality, in any case, better agree with the intuition of the physicist, and thus can help him more ... The philosophical inclination of his mind to " nominalistic convenience" prevented Poincaré from understanding the significance of the idea of relativity in all its grandiosity.

The French historian of science Jean Ulmo came to the same conclusions ( Jean Ullmo): Poincaré was unable to find physical interpretation theory of relativity, "because he held to a false philosophy - a philosophy of prescription, convention, arbitrary representation into which phenomena can always be squeezed, at a stretch at the very least."

Estimation of Poincaré's contribution to special relativity

Poincaré's contribution to the creation special theory relativity (SRT) is estimated differently by contemporary physicists and later historians of science. Their opinions range from dismissing this contribution to claiming that Poincaré's understanding was no less complete and profound than that of other founders, including Einstein. However, the vast majority of historians adhere to a fairly balanced point of view, assigning both (and also Lorentz and Planck and Minkowski, who later joined the development of the theory) a significant role in the successful development of relativistic ideas.

PS Kudryavtsev, in his course on the history of physics, highly appreciates the role of Poincaré. He quotes the words of D. D. Ivanenko and V. K. Frederiks that “From a formal point of view, Poincare’s article contains not only Einstein’s work parallel to it, but in some of its parts and much later - almost three years - Minkowski's article, and in part even surpasses the last one. Einstein's contribution, according to P. S. Kudryavtsev, was that it was he who managed to create an integral theory of maximum generality and clarify its physical essence.

A. A. Tyapkin in the afterword to the collection "The Principle of Relativity" writes:

So, which of the scientists should we consider the creators of SRT?... Of course, the Lorentz transformations discovered before Einstein include the entire content of SRT. But Einstein's contribution to their explanation, to the construction of a coherent physical theory and in the interpretation of the main consequences of this theory is so essential and fundamental that Einstein is rightfully considered the creator of SRT. However, the high evaluation of Einstein's work does not give any reason to consider him the only creator of SRT and neglect the contribution of other scientists.

Einstein himself in 1953, in a welcoming letter to the organizing committee of the conference dedicated to the 50th anniversary of the theory of relativity (held in 1955), wrote: “I hope that the merits of G. A. Lorentz and A. Poincaré will be duly noted.”

Wikipedia has articles about other people with this surname, see Poincaré.

Henri Poincare
Henri Poincare

Date of Birth:	April 29, 1854 (((padleft:1854\|4\|0))-((padleft:4\|2\|0))-((padleft:29\|2\|0)))
Place of Birth:	Nancy, France
Date of death:	July 17, 1912 (((padleft:1912\|4\|0))-((padleft:7\|2\|0))-((padleft:17\|2\|0))) (58 years old)
A place of death:	Paris, France
Country:	France
Scientific area:	mathematics, mechanics, physics, philosophy
Place of work:	mining school, University of Paris, Polytechnic School
Academic title:	corresponding member of SPbAN
Alma mater:	Lyceum Nancy, Polytechnic School, mining school
Scientific adviser:	Charles Hermite
Known as:	one of the creators of topology and the theory of relativity
Awards and prizes
Signature:
Citations on Wikiquote.
Artworks in Wikisource
Henri Poincare at Wikimedia Commons

Jules Henri Poincare(fr. Jules Henri Poincare; April 29, 1854, Nancy, France - July 17, 1912, Paris, France) - French mathematician, mechanic, physicist, astronomer and philosopher. Head of the Paris Academy of Sciences (1906), member of the French Academy (1908) and more than 30 academies of the world, including a foreign corresponding member of the St. Petersburg Academy of Sciences (1895).

Historians rank Henri Poincare among the greatest mathematicians of all time. He is considered, along with Hilbert, the last universal mathematician, a scientist capable of covering all the mathematical results of his time. He is the author of over 500 articles and books. "It would not be an exaggeration to say that there was no area of contemporary mathematics, 'pure' or 'applied', that he did not enrich with remarkable methods and results."

Among his biggest achievements:

Creation of topology.
Qualitative theory of differential equations.
Theory of automorphic functions.
Development of new, extremely effective methods of celestial mechanics.
Creation of the mathematical foundations of the theory of relativity, as well as the generalization of the principle of relativity to all physical phenomena.
Visual model of Lobachevsky's geometry.

Biography

Early years and training (1854-1879)

Henri Poincare was born on April 29, 1854 in Nancy (Lorraine, France). His father, Léon Poincaré (1828-1892), was a professor of medicine at the University of Nancy. Henri's mother, Eugenie Lanois ( Eugenie Launois), devoted all her free time to raising children - her son Henri and her youngest daughter Alina.

There are other celebrities among Poincaré's relatives: cousin Raymond became President of France (from 1913 to 1920), another cousin, the famous physicist Lucien Poincaré ( English), was the inspector general of public education in France, and from 1917 to 1920 - the rector of the University of Paris.

From childhood, Henri had a reputation as an absent-minded person, which he retained for the rest of his life. As a child, he suffered from diphtheria, which was complicated by temporary paralysis of the legs and soft palate. The illness dragged on for several months, during which he could neither walk nor speak. During this time, his auditory perception developed very strongly and, in particular, an unusual ability appeared - the color perception of sounds, which remained with him until the end of his life.

Good home preparation allowed Henri at the age of eight and a half to enter immediately into the second year of study at the Lyceum. There he was noted as a diligent and inquisitive student with broad erudition. At this stage, his interest in mathematics is moderate - after a while he moves to the department of literature. August 5, 1871 Poincaré received a bachelor's degree in literature with a mark of "good". A few days later, Henri expressed a desire to participate in the exams for the Bachelor of Science (natural) degree, which he managed to pass, but only with a "satisfactory" grade, because he absent-mindedly answered the wrong question in a written exam in mathematics.

Polytechnic school, old building on the street. Descartes (now Ministry of Higher Education)

In subsequent years, Poincaré's mathematical talents became more and more obvious. In October 1873, he became a student at the prestigious Paris Polytechnic School, where he won first place in the entrance exams. His tutor in mathematics was Charles Hermite. The following year, Poincaré published his first scientific work on differential geometry in the Annals of Mathematics.

First scientific achievements (1879-1882)

Having received a degree, Poincaré began teaching at the University of Caen in Normandy (December 1879). At the same time, he published his first serious articles - they are devoted to the class of automorphic functions introduced by him.

There, in Cana, he met his future wife, Louise Poulain d'Andecy ( Louise Poulain d'Andecy). On April 20, 1881, their wedding took place. They had a son and three daughters.

The originality, breadth and high scientific level of Poincaré's work immediately placed him among the greatest mathematicians in Europe and attracted the attention of other prominent mathematicians. In 1881, Poincaré was invited to take up a teaching position at the Faculty of Sciences at the University of Paris and accepted the invitation. In parallel, from 1883 to 1897, he taught mathematical analysis at the Higher Polytechnic School.

Leader of French mathematicians (1882-1899)

A decade after the completion of the study of automorphic functions (1885-1895), Poincaré devoted himself to solving several of the most difficult problems of astronomy and mathematical physics. He investigated the stability of the figures of the planets formed in the liquid (molten) phase, and found, in addition to ellipsoidal, several other possible figures of equilibrium.

In 1885, King Oscar II of Sweden organized a mathematical competition and offered participants a choice of four topics. The first one was the most difficult: to calculate the motion of the gravitating bodies of the solar system. Poincaré showed that this problem (the so-called three-body problem) does not have a complete mathematical solution. Nevertheless, Poincaré soon proposed efficient methods for its approximate solution. In 1889, Poincare (together with Paul Appel, who studied the fourth theme), received the prize of the Swedish competition. One of the two judges, Mittag-Leffler, wrote of Poincaré's work: "The prized memoir will prove to be among the most significant mathematical discoveries of the century." The second judge, Weierstrass, declared that after Poincaré's work "a new era in the history of celestial mechanics will begin." For this success, the French government awarded Poincare the Order of the Legion of Honor.

In 1887, Poincaré generalized Cauchy's theorem to the case of several complex variables and laid the foundation for the theory of residues in a multidimensional complex space.

Last years

One of recent photos. Poincaré and Marie Sklodowska-Curie at the Solvay Congress (1911)

In August 1900, Poincaré led the logic section of the First World Philosophical Congress, held in Paris. There he made a keynote speech "On the Principles of Mechanics", where he outlined his conventionalist philosophy: the principles of science are temporary conditional agreements adapted to experience, but having no direct analogues in reality. He subsequently substantiated this platform in detail in the books Science and Hypothesis (1902), The Value of Science (1905) and Science and Method (1908). In them, he also described his vision of the essence of mathematical creativity, in which intuition plays the main role, and logic is assigned the role of substantiating intuitive insights. The clear style and depth of thought provided these books with considerable popularity, they were immediately translated into many languages. At the same time, the Second International Congress of Mathematicians was held in Paris, where Poincare was elected chairman (all congresses were timed to coincide with the World Exhibition of 1900).

Poincaré's grave in Montparnasse

The main area of interest of Poincaré in the 20th century was physics (especially electromagnetism) and the philosophy of science. Poincare shows a deep understanding of electromagnetic theory, his insightful remarks are highly valued and considered by Lorentz and other leading physicists. From 1890, Poincaré published a series of papers on Maxwell's theory, and in 1902 he began to read a course of lectures on electromagnetism and radio communications. In his papers of 1904-1905, Poincaré is far ahead of Lorentz in understanding the situation, having actually created the mathematical foundations of the theory of relativity (the physical foundation of this theory was developed by Einstein in 1905).

Contribution to science

Bust of A. Poincaré at the Polytechnic School

Poincaré's mathematical activity was of an interdisciplinary nature, thanks to which, over the thirty-odd years of his intense creative activity, he left fundamental works in almost all areas of mathematics. Poincaré's works, published by the Paris Academy of Sciences in 1916-1956, comprise 11 volumes. These are works on the topology he created, automorphic functions, the theory of differential equations, multidimensional complex analysis, integral equations, non-Euclidean geometry, probability theory, number theory, celestial mechanics, physics, philosophy of mathematics and philosophy of science.

In all the various fields of his work, Poincaré obtained important and profound results. Although his scientific heritage contains many major works on "pure mathematics" (general algebra, algebraic geometry, number theory, etc.), the works, the results of which have direct applied application, still predominate. This is especially noticeable in his works of the last 15-20 years. Nevertheless, Poincare's discoveries, as a rule, were of a general nature and were later successfully applied in other areas of science.

Poincaré's creative method was based on the creation of an intuitive model of the problem posed: he always first completely solved the problems in his head, and then wrote down the solution. Poincaré had a phenomenal memory and could quote books read and conversations word for word (Henri Poincaré's memory, intuition and imagination even became the subject of real psychological research). In addition, he never worked on one task for a long time, believing that the subconscious has already received the task and continues to work even when he is thinking about other things. Poincare described his creative method in detail in the report "Mathematical Creativity" (Paris Psychological Society, 1908).

Paul Painlevé assessed the significance of Poincaré for science as follows:

He comprehended everything, deepened everything. Possessing an unusually inventive mind, he knew no limits to his inspiration, tirelessly paving new paths, and in the abstract world of mathematics, he repeatedly discovered unknown areas. Everywhere that the human mind penetrated, no matter how difficult and thorny its path was - whether it was the problems of wireless telegraphy, X-rays or the origin of the Earth - Henri Poincaré walked alongside ... Together with the great French mathematician, the only person whose mind could embrace everything that is created by the mind of other people, to penetrate into the very essence of everything that human thought has comprehended today, and to see something new in it.

Automorphic functions

Poincaré first found this idea in an article by Lazar Fuchs, the most prominent specialist in those years on linear differential equations (1880). Over the course of several years, Poincaré developed Fuchs's idea far, creating the theory of a new class of functions, which he, with Poincaré's usual indifference to questions of priority, proposed to call fuchsian functions(fr. Les Fuchsiennes Fuchsiennes) - although he had every reason to give this class its own name. The case ended with the fact that Felix Klein proposed the name "automorphic functions", which was fixed in science. Poincaré deduced the expansion of these functions into series, proved the addition theorem and the theorem on the possibility of uniformization of algebraic curves (that is, their representation through automorphic functions; this is Hilbert's 22nd problem, solved by Poincaré in 1907). These discoveries "may rightly be considered the pinnacle of the entire development of the theory of analytic functions of a complex variable in the 19th century."

In developing the theory of automorphic functions, Poincaré discovered their connection with Lobachevsky's geometry, which allowed him to present many questions of the theory of these functions in geometric language. He published a visual model of Lobachevsky's geometry, with the help of which he illustrated material on the theory of functions.

After the work of Poincaré, elliptic functions turned from a priority direction of science into a limited special case of a more powerful general theory. The automorphic functions discovered by Poincare allow solving any linear differential equation with algebraic coefficients and are widely used in many areas of the exact sciences.

Differential Equations and Mathematical Physics

After defending his doctoral dissertation on the study of singular points of a system of differential equations, Poincaré wrote a series of memoirs under the general title "On Curves Defined by Differential Equations" (1881-1882 - for equations of the 1st order, supplemented in 1885-1886 for equations 2- th order). In these articles, he built a new branch of mathematics, which was called the "qualitative theory of differential equations." Poincaré showed that even if a differential equation cannot be solved in terms of known functions, nevertheless, from the very form of the equation, one can obtain extensive information about the properties and behavior of the family of its solutions. In particular, Poincare studied the nature of the course of integral curves on a plane, gave a classification of singular points (saddle, focus, center, node), introduced the concepts of a limit cycle and cycle index, and proved that the number of limit cycles is always finite, except for a few special cases. Poincaré also developed a general theory of integral invariants and solutions of equations in variations. For equations in finite differences, he created a new direction - the asymptotic analysis of solutions. He applied all these achievements to the study of practical problems of mathematical physics and celestial mechanics, and the methods used became the basis of his topological work.

Algebra and number theory

Already in his first works, Poincare successfully applied the group-theoretical approach, which became the most important tool for him in many further studies - from topology to the theory of relativity. Poincaré was the first to introduce group theory into physics; in particular, he was the first to study the group of Lorentz transformations. He also made major contributions to the theory of discrete groups and their representations.

In the early period of Poincare's work, he studied cubic ternary and quaternary forms.

Topology

Multivariate complex analysis

Astronomy and Celestial Mechanics

Poincaré published two classic monographs: New Methods of Celestial Mechanics (1892-1899) and Lectures on Celestial Mechanics (1905-1910). In them, he successfully applied the results of his research to the problem of the motion of three bodies, studying in detail the behavior of the solution (periodicity, stability, asymptotic behavior, etc.). He introduced the methods of a small parameter (Poincaré's theorem on the expansion of integrals with respect to a small parameter), fixed points, integral invariants, equations in variations, and investigated the convergence of asymptotic expansions. Generalizing the Bruns theorem (1887), Poincaré proved that the three-body problem is not integrable in principle. In other words, the general solution of the three-body problem cannot be expressed in terms of algebraic or single-valued transcendental functions of coordinates and velocities of bodies. His work in this area is considered the greatest achievement in celestial mechanics since Newton.

These works by Poincaré contain ideas that later became the basis for the mathematical "chaos theory" (see, in particular, the Poincaré recurrence theorem) and the general theory of dynamical systems.

Physics and other works

From the end of the 1880s until the end of his life, Poincaré devoted much effort to Maxwell's electromagnetic theory and its version supplemented by Lorentz. He actively corresponded with Heinrich Hertz and Lorenz, often prompting them with the right ideas. In particular, Poincaré wrote out the Lorentz transformations in their modern form, while Lorentz proposed their approximate version somewhat earlier. Nevertheless, it was Poincaré who named these transformations after Lorentz. For Poincaré's contribution to the development of the theory of relativity, see below.

Scientific terms associated with the name Poincaré

Poincare conjecture
Poincaré group
Poincaré duality
Poincaré-Cartan integral
Poincaré's lemma
Poincaré metric
Poincaré model of Lobachevsky space
Poincaré-Dulac normal form
Poincaré mapping
Poincaré's last theorem
Poincaré sphere
Cauchy-Poincaré theorem
Poincaré-Bendixon theorem
Poincaré - Birkhoff - Witt theorem
Poincaré-Volterra theorem
Poincaré's vector field theorem
Poincaré recurrence theorem
Poincaré's theorem on the classification of homeomorphisms of the circle
Poincaré's theorem on the expansion of integrals with respect to a small parameter
Poincaré's theorem on the rate of growth of an entire function

and many others.

The role of Poincare in the creation of the theory of relativity

Poincare's work in the field of relativistic dynamics

Hendrik Anton Lorenz

Under the influence of Poincaré's criticism, Lorentz proposed a new version of his theory in 1904. In it, he suggested that at high speeds, Newtonian mechanics needs to be corrected. In 1905, Poincaré developed these ideas far in his article "On the Dynamics of the Electron". The preliminary version of the article appeared on June 5, 1905 in Comptes Rendus, expanded was completed in July 1905, published in January 1906, for some reason in a little-known Italian mathematical journal.

In this final article, the general principle of relativity is again and clearly formulated for all physical phenomena (in particular, electromagnetic, mechanical and also gravitational), with Lorentz transformations as the only possible coordinate transformations that preserve the same record of physical equations for all reference systems. Poincaré found an expression for the four-dimensional interval as an invariant of the Lorentz transformations: , a four-dimensional formulation of the principle of least action. In this article, he also offered the first draft of a relativistic theory of gravity; in his model, gravitation propagated in the ether at the speed of light, and the theory itself was non-trivial enough to remove the lower limit obtained by Laplace on the speed of propagation of the gravitational field. A preliminary short report was published before Einstein's work was published in the journal, the last, large article also came to publishers before Einstein's, but by the time it was published, Einstein's first article on the theory of relativity had already been published.

Poincaré and Einstein: similarities and differences

Albert Einstein (1911)

Einstein in his first works on the theory of relativity used essentially the same mathematical model as Poincaré: Lorentz transformations, the relativistic formula for adding velocities, etc. to prove the impossibility of his observation. He completely abolished both the concept of ether, which Poincaré continued to use, and the concepts of absolute motion and absolute time based on the ether hypothesis. It was this theory that, at the suggestion of Max Planck, was called theory of relativity(Poincaré preferred to talk about subjectivity or conventions, see below).

All the new effects that Lorentz and Poincaré considered to be the dynamic properties of the ether, in Einstein's theory of relativity, follow from the objective properties of space and time, that is, they were transferred by Einstein from dynamics to kinematics. This is the main difference between the approaches of Poincaré and Einstein, masked by the external similarity of their mathematical models: they understood the deep physical(and not just mathematical) essence of these models. The transfer to kinematics allowed Einstein to create a holistic and universal theory of space and time, as well as to solve previously intractable problems within its framework - for example, the confusing question of different types of mass, the dependence of mass on energy, the relationship between local and "absolute" time, etc. Now this theory is called the "special theory of relativity" (SRT). Another significant difference between the positions of Poincaré and Einstein was that the Lorentz contraction of length, the growth of inertia with speed, and other relativistic conclusions were understood by Poincaré as absolute effects, while Einstein as relative, having no physical consequences in their own reference frame. What for Einstein was real physical time in a moving frame of reference, Poincaré called time “apparent”, “visible” (fr. temps apparent) and clearly distinguished it from "true time" (fr. le temps vrai).

Possibly, the insufficiently deep analysis of the physical essence of SRT in the works of Poincaré was the reason why physicists did not pay the attention they deserved to these works; accordingly, the wide resonance of Einstein's first article was caused by a clear and deep analysis of the foundations of the studied physical picture. In the subsequent discussion of relativity, Poincaré's name was not mentioned (even in France); when Poincaré was nominated for the Nobel Prize in 1910, the list of his achievements did not mention the theory of relativity.

The justification for the new mechanics also varied. In Einstein's articles of 1905, the principle of relativity from the very beginning is not affirmed as a conclusion from dynamic considerations and experiments, but is put at the heart of physics as a kinematic axiom (also for all phenomena without exception). From this axiom and from the constancy of the speed of light, the mathematical apparatus of Lorentz-Poincaré is obtained automatically. The rejection of the ether made it possible to emphasize that the “resting” and “moving” coordinate systems are completely equal in rights, and when passing to a moving coordinate system, the same effects are already found in the resting one.

"The Silence of Poincaré"

1st Solvay Congress. Seated far right: Poincaré. Standing second from right: Einstein.

(insert in square brackets probably belongs to Pais).

Mr. Einstein is one of the most original minds I have known; despite his youth, he already took a very honorable place among the most prominent scientists of his time. Most of all, he admires the ease with which he adapts to new concepts and is able to extract all the consequences from them.

He does not hold on to classical principles and, when confronted with a physical problem, is ready to consider all possibilities. Thanks to this, his mind anticipates new phenomena, which in time can be experimentally verified. I do not mean to say that all these predictions will stand the test of experience the day it becomes possible; on the contrary, since he seeks in all directions, it is to be expected that most of the paths he enters will turn out to be dead ends; but at the same time, one must hope that one of the directions indicated by him will turn out to be correct, and this is enough. That is exactly what should be done. The role of mathematical physics is to ask questions correctly; only experience can solve them.

The future will show more definitely what the significance of Mr. Einstein is, and the university that manages to bind the young master to itself will derive much honor from this.

In April 1909, at the invitation of Hilbert, Poincaré came to Göttingen and gave a number of lectures there, including on the principle of relativity. Poincaré never once mentioned in these lectures not only Einstein, but also Minkowski, Goettingen. Many hypotheses have been put forward about the reasons for the "silence of Poincaré". Some historians of science have suggested that Poincaré's resentment against the German school of physicists, which underestimated his contribution to the creation of the relativistic theory, is to blame. Others consider this explanation implausible, since Poincare was never seen in his life taking offense over priority disputes, and Einstein's theory was preferred not only in Germany, but also in Great Britain and even in France itself (for example, Langevin). Even Lorentz, whose theory Poincaré sought to develop, after 1905 preferred to speak of "Einstein's principle of relativity." The following hypothesis was also put forward: Kaufman's experiments conducted during these years cast doubt on the principle of relativity and the formula for the dependence of inertia on speed, so it is possible that Poincaré decided to simply wait with the conclusions until these issues were clarified.

What will be our attitude towards these new [relativistic] ideas? Will they force us to change our conclusions? Not at all; we accepted the well-known conditional agreement because it seemed convenient to us ... Now some physicists want to accept a new conditional agreement. This does not mean that they were forced to do so; they find this new arrangement more convenient, that's all. And those who do not adhere to their opinion and are unwilling to give up their old habits can rightly keep the old agreement. Between us, I think they will continue to do so for a long time to come.

The founder of quantum mechanics, Louis de Broglie, the first winner of the Poincaré medal (1929), blames his positivist views for everything:

A little more, and Henri Poincaré, and not Albert Einstein, would have been the first to build the theory of relativity in all its generality, thereby giving French science the honor of this discovery ... However, Poincaré did not take the decisive step, and gave Einstein the honor to see all the consequences of the principle of relativity and, in particular, through a deep analysis of the measurements of length and time, to find out the true physical nature of the connection established by the principle of relativity between space and time.

Why didn't Poincare reach the end in his conclusions?... Poincaré, as a scientist, was first of all a pure mathematician... Poincaré took a somewhat skeptical position in relation to physical theories, believing that in general there are infinitely many logically equivalent points of view and pictures of reality, from which the scientist, guided solely by considerations of convenience, chooses one. Probably, such nominalism sometimes prevented him from recognizing the fact that among logically possible theories there are those that are closer to physical reality, in any case, better agree with the intuition of the physicist, and thus can help him more ... The philosophical inclination of his mind to " nominalistic convenience" prevented Poincaré from understanding the significance of the idea of relativity in all its grandiosity.

The French historian of science Jean Ulmo came to the same conclusions ( Jean Ullmo): Poincare was unable to find a physical interpretation of the theory of relativity "because he adhered to a false philosophy - a philosophy of recipe, convention, arbitrary representation, into which phenomena can always be squeezed, at the very least, with a stretch."

Estimation of Poincaré's contribution to special relativity

Poincaré's contribution to the creation of the special theory of relativity (SRT) is estimated differently by contemporary physicists and later historians of science. Their opinions range from dismissing this contribution to claiming that Poincaré's understanding was no less complete and profound than that of other founders, including Einstein. However, the vast majority of historians adhere to a fairly balanced point of view, assigning both (and also Lorentz and Planck and Minkowski, who later joined the development of the theory) a significant role in the successful development of relativistic ideas.

A. A. Tyapkin in the afterword to the collection "The Principle of Relativity" writes:

So, which of the scientists should we consider the creators of SRT?... Of course, the Lorentz transformations discovered before Einstein include the entire content of SRT. But Einstein's contribution to their explanation, to the construction of an integral physical theory and to the interpretation of the main consequences of this theory is so significant and fundamental that Einstein is rightfully considered the creator of SRT. However, the high evaluation of Einstein's work does not give any reason to consider him the only creator of SRT and neglect the contribution of other scientists.

The outstanding French scientist Henri Poincaré was a man ahead of his time. He owns the authorship of 11 volumes of the most serious research, which affected almost all mathematical fields. In his work, the scientist outlined the theoretical foundations that are still used in scientific research. Today we will consider the biography of the French mathematician and briefly get acquainted with his achievements.

Childhood

Henri Poincaré was born on April 29, 1854 in France, in the small town of Cite Ducal near Nancy. His father, Leon Poincaré, was a physician and lecturer in the Faculty of Medicine. Mother, Eugenie Lanois, was a housewife, and devoted a lot of time to children. Henri had a sister, Alina. From early childhood, the boy suffered from absent-mindedness. Throughout his life, Henri, this problem accompanied him. However, when he matured, it became clear that absent-mindedness is evidence of his amazing ability dive into own thoughts, reflect and analyze.

In early childhood, Poincaré contracted diphtheria. Due to the complication that the disease gave, he could not even walk or speak for several months. In that difficult period he taught himself to turn more attention to sounds. Over the years, this feature resulted in the fact that the sounds of the future scientist began to be associated with certain colors. For many people, this ability is observed in childhood, but goes to maturity. Poincaré kept it for the rest of his life.

home education

Gradually, the boy recovered, began to talk and walk, but physical weakness did not leave him. Due to his illness, he became timid and shy. He received his first education at home thanks to A. Ginzelin, the most educated person at that time. Whatever science they were engaged in, Henri rarely took notes and perfectly calculated in his mind. He didn't have to be forced to homework and loaded with redundant information. Ginzelin's classes with Henri looked like a conversation between an adult and a child about everything in the world. These classes contributed to the further development of Poincaré's auditory memory. The sickly timid boy quickly became an educated and erudite guy with an individual way of thinking. By the way, Henri's dislike for writing remained for life.

School

The boy was so developed that he was taken immediately to the second grade of the Lyceum in Nancy. At that time, classes were counted from 10th to 1st, so, to put it more correctly, Henri entered the 9th grade. The teachers of the Lyceum were very proud of him. He easily coped with any math problems and wrote interesting essays. Despite the fact that the mathematics teacher noted great potential in Poincare, as a schoolboy, he was more inclined to humanitarian subjects. Ultimately, Henri moved to the humanitarian department.

In June 1870, military confrontations between France and Prussia began, which brought the French a lot of grief and disappointment. During these times, Father Henri was in charge of medicine in the city. His son helped him in his work with wounded soldiers. He served as an assistant in the dispensary and personal secretary to Léon Poincaré.

The events of that terrible war developed very rapidly and caused a true shock in a sixteen-year-old boy. The future scientist reflected his experiences in the dissertation “How can a nation rise?”, Written after graduation from the gymnasium.

Higher education

In 1871, Henri Poincaré passed the entrance examination for a bachelor's degree in literature with a mark of "good". He had the opportunity to enter Faculty of Philology, but in three months the young man takes exams for the faculty natural sciences. He almost failed the math exam because of his absent-mindedness. Henri was late for it, and, confused, began to tell material that did not relate to the question posed to him. The guy’s failure was treated with understanding, as they knew that he was capable of more. Henri was admitted to the oral exam, in which he showed himself in all its glory. As a result, Poincaré received a bachelor's degree in natural sciences. While studying in the class of elementary mathematics, he additionally studied literature and more than once won first places in mathematical competitions.

Polytechnic and mining schools

In the autumn of 1873, Henri became a student at the Polytechnic School. At first he was one of best students, but soon lost their positions. The reason for this was several subjects that the young scientist simply could not take seriously. Among them were drawing, drawing, and also military art. Thus, Poincaré did not finish school with the best results. Later he entered the Mining School, which at that time was considered very prestigious. educational institution. Here Henri was engaged in crystallographic research.

In 1879, the young scientist defended his doctoral dissertation at the Mining School, which pleased Professor G. Darboux of the Sorbonne. The latter claimed that in one work Poincare was able to place as many materials and ideas as would be enough for several good dissertations.

In April 1879, Poincare began working as an engineer in the mines. When an explosion occurred in one of the mines, as a result of which people died, Henri was not afraid to go down to the site of the explosion in order to investigate the causes and extent of the tragedy. After defending his dissertation, the scientist began to teach mathematical analysis in Cana.

Family life

Despite his boundless love for science, Poincaré also found time for his family. In 1881, he married Louise Paulin d "Andesy. The wedding was quite magnificent and took place in Paris. In 1887, the long-awaited first-born, a girl named Jeanne, was born. Two years later, his wife gave birth to a second girl, Yvonne, and a year later - the third, Henrietta.Two years after the birth of their third daughter, the Poincare couple had a son, who was named Lyon.

The family life of the French mathematician was filled with love and peace. The "gigantic work of thought", which the scientist did on his creative path, he owes much to his wife. She always maintained a favorable atmosphere in the family.

Mathematical merit

A series of notes on Fuchsian functions written by Poincaré for the French journal Compres Rendus attracted the attention of eminent mathematicians (mainly Weierstrass and Kovalevskaya) and aroused genuine interest in the scientific community. The notes were followed by five more interesting works on the same topic.

Having eventually discovered automorphic functions, the mathematician received a teaching position at the University of Paris. Having moved to the French capital, twenty-seven-year-old Poincaré takes care of his family, teaching activities, and collaborates closely with young mathematicians, Émile Picard and Paul Appel. Professor Ermit becomes the mentor of the trio of newly minted scientists.

Soon a work by Henri Poincaré was published in Paris entitled "On Curves Defined by Differential Equations", which consists of four parts. Previously this method remained in the scientific community without attention. The scientist in this treatise lays down the theory of stability of differential equations with respect to small parameters and initial conditions. In 1886, the hero of our conversation heads the department of mathematical physics and probability theory. And at 33, he enters the ranks of the French Academy of Sciences.

The scientist's research led him to topology. He introduced such concepts as the Betti number and the fundamental group into science, proved the Euler-Poincare formula and formulated the general concept of dimension. The French mathematician made a lot of discoveries in differential geometry, algebraic topology, probability theory and many other areas of mathematics. The scientist discovered a connection between the conformal Euclidean model and the problems of the theory of functions of a complex variable. This became one of the first serious applications of Lobachevsky's geometry. Because of this, the conformally Euclidean model is often referred to as the "Poincaré model - Lobachevsky space". In addition, Poincaré is the author of works on the justification of the Dirichlet principle.

From an early age, Poincaré was interested in the stars and the laws by which celestial bodies move. In 1889, his treatise "The luminaries will never cross the prescribed boundaries" was published. The work received an award for international competition. A little later, the scientist wrote a three-volume work "New methods of celestial mechanics." In addition, he published many significant works on the topic of stability of motion and equilibrium figures of a rotating gravitating fluid. The scientist also created the method of integral invariants and much more. Since 1896, celestial mechanics entered his life even more closely: Poincaré became head of the department of celestial mechanics at the Sorbonne University.

Physics

The influence of the French scientist on physics was also enormous. Despite the fact that Poincare and Einstein enjoy varying degrees of popularity, Poincaré, long before Einstein, revealed in his articles the foundations of such a concept as the theory of relativity. The main of these articles was the work "Measurement of time". At the same time, the scientist really liked working with students. He taught a fairly voluminous course in physics, which was later published in the form of a twelve-volume book. In his work, he touched on everything topical issues and offered his own approach to their solution. The physicist and mathematician Poincare anticipated many of the conclusions of other scientists who lived later.

In 1902, Henri Poincare published a work on science, called "Science and Hypothesis". It caused a huge resonance in the scientific community. Two years later, giving a lecture in America, Poincaré makes a splash. In an article entitled "Notes of the Academy of Sciences", published in 1905, he proves the invariance of Maxwell's equations under Lorentz transformations. M. Born believed that the theory of relativity is not the merit of any particular scientist. It is the result of the collective work of brilliant minds from all over the world. Poincaré Henri certainly belongs to them.

"The Poincaré Hypothesis"

The French mathematician and physicist put forward a lot of ideas during his career. interesting hypotheses. One of them was simply called the Poincaré Hypothesis. She argued that any three-dimensional, simply connected, compact manifold is infinitely homeomorphic to a three-dimensional sphere. The American scientist Marcus Du Sotoy of Oxford considered this hypothesis to be a central problem in both mathematics and physics. He called it an attempt to understand what forms the universe can take. Ultimately, the hypothesis of the French scientist was included in the list of "Seven Millennium Challenges". For each of these tasks, the Clay Institute put forward a reward of 1 million US dollars.

For a long time, the Poincaré hypothesis, formulated in 1904, did not receive much attention. The first interest in resolving it was shown by Henry Whitehead. The scientist even announced his proof, but it turned out to be wrong. Since then, many have tried to prove the hypothesis, especially in the 60s of the last century. Great amount evidence has been refuted.

In 2004, the Russian scientist Grigory Perelman nevertheless proved the Poincare conjecture. For this he was awarded the international award "Fields Medal". In 2010, the Clay Institute awarded the Russian scientist the promised award, but Perelman refused it.

The American mathematician Hamilton also worked on the proof, but did not finish the job. In 2011, Perelman insisted that the Clay Institute award be given to Hamilton, since it was he who created the mathematical theory, which Perelman partly used in his proof.

Awards and titles

The merits of Henri Poincare, whose biography has become the topic of our conversation today, have been appreciated more than once. He has received the following awards:

Poisele (in 1885).
King of Sweden (in 1889).
Jean Reynaud (Paris Academy of Sciences, 1896).
Boya (Hungarian Academy of Sciences, 1905).

The scientist was also awarded medals from the Astronomical Society of London, London royal society and many others. The scientific societies of Britain, France and Russia considered it an honor to have Poincaré in their ranks.

On July 17, 1912, the great scientist passed away. At that time he was only 58 years old. Poincaré was buried in the Montparnasse cemetery, in the family crypt. An asteroid, one of the lunar craters, the Paris Mathematical Institute, a Parisian street and many mathematical terms were named after him.

Conclusion

Today we got acquainted with the life and work of an outstanding French scientist. Thanks to the craving for knowledge, which was laid down by Poincaré since childhood, he not only defeated serious illnesses, but was also able to achieve phenomenal success in science. This fact alone deserves respect.

Jules-Henri Poincaré is a brilliant scientist, whose wide profile of activity he outlined huge contribution in many mathematics and mechanics. This man became the founder of qualitative methods of topology and theory, he created the basis of the theory of stability of motion. "Science and Hypothesis" by Henri Poincaré is a work that has become a classic, studied by all students of technical universities.

Science

Poincaré's papers, long before Einstein's works, contained formulations of the main provisions of the theory of relativity. For example, the principle of relativity, the relativity of the concept of simultaneity, clock synchronization by means of light signals, Lorentz transformations, the immutability of the constancy of Maxwell's equations, and many others.

Henri Poincaré developed the small parameter method and applied it to the problems of celestial mechanics, he also independently investigated the classical task of three tel. Even in philosophy, he managed to create a completely new direction, called conventionalism.

Childhood

The great scientist was born in the Lorraine city of Nancy in France on April 29, 1854. His father, Leon Poincaré, was at that time still very young, but already a well-known practitioner in the city and its environs, and besides, he did a lot of laboratory research and lectured at the medical faculty of the university. His mother - Evgenia - raised children. The daughter did not cause as much anxiety as little Jules-Henri Poincare: his absent-mindedness eventually became legendary.

Mother was unaware that this defect speaks of an innate quality to surrender to deep inner thoughts and be completely distracted from reality. In addition, after diphtheria, Henri Poincaré acquired a new quality - to associate vowel sounds with certain colors. Occasionally children (especially those who are naturally mute) have this quality. Henri Poincaré retained this ability throughout his life.

Home schooling

A real erudite and a man of broad education, a born teacher, Alfons Ginzelin, studied with the baby. In addition to the rules of grammar, history, geography and biology, the boy quickly mastered all four arithmetic operations and began to count easily in the mind. The teacher didn’t leave any assignments for him, they didn’t write anything down, so the already magnificent auditory memory the child became aggravated and strengthened. By the way, he did not like the graphic fixation of his discoveries, he felt persistent neglect of the letter. This went down the drain.

Lyceum

The teachers at the Nancy Lyceum were glad that such an inquisitive and diligent student like Henri Poincaré. He got such a good home training that began to study immediately in the second grade. He wrote compositions beautifully, arithmetic was also easy for him, but he did not yet feel much love for it.

Only a few years later, an excited teacher came to Poincare's mother Henri and predicted a great mathematical future for her son. But, despite this, the boy continued his studies at the department of literature, studying Latin and ancient classics. Humanities education the great scientist turned out to be more than complete by the age of sixteen. At the same time, events of great importance took place in the life of not only France, but throughout Europe: Franco-Prussian War and

University

Twice becoming a bachelor (literature and science), Poincaré Henri began to study elementary mathematics - now truly selflessly. And geometry, and algebra, and mathematical analysis - all this super-serious scientific literature was like a treat for him, he literally savored every line of the works of Roucher, Bertrand, Chall, Duhamel. He learned elementary mathematics in this way within a year.

Polytechnic School

In order to work in the state apparatus or in the army in a good technical position, Poincaré Henri became a student at the Polytechnic School, where, undoubtedly, he was a leader among the first students in almost all subjects. He did not excel in drawing, drafting and military affairs.

His drawings, for example, were neither parallel nor converging where they should have been, nor even just straight lines. But in physics, chemistry and mathematics, he turned out to be so strong that there were no equals to him. After graduating from the Polytechnic School, the future great scientist continued his studies at Gornaya, where he already took up real scientific research in earnest.

mining school

The ideas that he searched for and found a way out of his thoughts during his studies at the School of Mines will be the foundation of his doctoral dissertation in a few years. Everything that did not concern mathematics had already ceased to be interesting to him, with the exception of mineralogy alone. And not even mineralogy itself, but its section concerning crystallography. Because everything that Henri Poincaré knew about science by that time, curled around the theory of groups, where the kinematics of a rigid body plus crystallography is one of the main points of application of this branch of mathematics, at that time practically abstract. This is how the dissertation was written. She received many accolades from professors and scientists. The defense of the dissertation gave the right to teach at universities, which the great scientist took advantage of, having worked for some time on distribution in the mines of Vesoul. In 1979, Henri Poincaré arrived at the University of Cannes to teach calculus.

Decisive 1881

In 1881 the most authoritative Science Magazine France published an article by Poincaré on Fuchsian functions, which became a breakthrough in mathematical science. Over the next two years, more than twenty-five articles appeared. European mathematicians began to closely follow every step of the new mathematical luminary.

Five more articles are devoted to Fuchsian functions, each of which was a real scientific discovery. Despite an extremely deep immersion in mathematics, in 1881 Jules-Henri Poincaré managed to fall in love, get married and move with his family from Normandy to Paris to start teaching at the university.

Paris

At the capital's university, young scientists conducted four major studies on differential equations, integral curves with their singular points and limit cycles, which constituted a new branch of mathematics as a science. Twenty-seven-year-old Henri Poincaré, whose selected works have already been included in textbooks, did not rest on his laurels, since no one has yet studied the qualitative methods of the theory of differential equations. This radically new layer of mathematical science required further study: methods of a small parameter with the theory of integral invariants and the theory of stable differential equations with respect to small parameters and initial conditions.

Already in 1886, Henri Poincaré became the head of the Department of Mathematical Physics and Probability Theory, and in 1887 he was elected a member of the French Academy of Sciences. Discoveries followed discoveries: the theory of automorphic functions, combinatorial topology, differential geometry, algebraic topology, probability theory, and many other areas of knowledge ceased to be a secret with seven seals for Henri Poincaré.

Physicist

Three-dimensional oscillations of mathematical physics with the formula of the theory of wave propagation (diffraction), problems of heat conduction, theory of potentials, justification - this is not all that was investigated, resolved and proved by a brilliant scientist in a very short period of time. As a child, he gazed fascinated into the depths of the starry night, and now the adult Poincaré knew for sure that heavenly bodies they give not only the light that people can see with carnal vision, but also another, refined, clarifying mind. "Science and Hypothesis" by Henri Poincaré is a work that sheds light on much concerning the human perception of scientific phenomena.

In 1889 he receives international award for work on "celestial mechanics", the physics of three bodies, where the motto was a line from an ancient poem in Latin: Nunquam praescriptos transibunt sidera fines - "The luminaries will never cross the prescribed boundaries." Further study of this area resulted in a three-volume treatise "New Methods of Celestial Mechanics", which became a classic of scientific research not only in astronomy and mechanics, but also in quantum mechanics, and in static physics. As a result, Professor Henri Poincaré was invited to the Sorbonne to head the department of celestial mechanics there, and accepted this offer. Ten years of studying probability theory and mathematical physics in Paris flew by like one day.

Zenith

The work of Henri Poincaré "Science and Hypothesis" was published in 1902 and caused a tangible resonance in scientific circles, since the scientist wrote, first of all, about perception, that there is no absolute in anything - neither in space nor in time, people feel exclusively relative movements, even time is felt by them in different ways. Only facts of a mechanical order are indicated, and without non-Euclidean geometry it is impossible to consider them as scientific.

During his life, Poincaré received all kinds of titles, awards and prizes, the Paris Mathematical Institute was named after him and big crater on the back (dark) side of the moon.

Poincaré phenomenon

Hiking was the only kind of physical exercise that Poincaré did willingly and systematically. According to the testimony of people who knew him closely, he could walk up to 15 kilometers. However, he most likely considered even this kind of physical education as constituent part his mental activity. Walking was essential active work his brain. On this occasion, one can recall the words of one of the characters of Emile Ogier, who said: "Legs are the wheels of thought." A significant part of his theoretical research Poincare carried out "on the go."

His nephew P. Butroux writes in his memoirs: “He indulges in his thoughts on the street, heading to the Sorbonne, attending meetings of various learned societies, during habitual long walks after breakfast. He is meditating in his hallway, in the meeting room of the Institute, walking back and forth with small steps with a concentrated look, jingling a bunch of keys. He thinks at the table, in the family circle, in the living room, often breaking off the conversation in the middle and leaving his interlocutor to follow the leap that his thought has made. All the work accompanying the discovery, the uncle does in his mind, often without even having to check his calculations or write down evidence on paper. The invariable bunch of keys, which Poincaré mechanically fiddles with his fingers during his thoughts, has already become famous. F. Masson in his report called it "obstetric forceps for ideas."

And in his office, Poincaré prefers not to sit at the table, but to measure the room with steps from wall to wall, slightly hunched over, putting his large head forward. In such moments of the highest intensity of thought, when in the lightning of vague insights visions of his future discoveries are born before him, and the colossal inner tension is ready to break out every minute with the long-awaited result, he does not belong either to himself or to anyone else. Ordinary life with all its conventions and institutions recedes into the background. It sometimes comes to violations of the norms of generally accepted human communication that are unusual for his nature.

A well-known Finnish mathematician traveled a long way to Paris to consult with a famous French scientist on an issue of interest to him. scientific question. When Poincaré was informed of the arrival of a guest, he did not even leave his office, but continued to pace back and forth with concentration. This went on for about three hours. All this time the visitor sat in the next room, separated from Poincaré only by a light curtain, and listened to the sound of his restless steps. Finally, the curtains parted, and the head of the famous master poked into the room. But instead of a greeting or a proper apology, the guest heard an annoyed one: “You are disturbing me very much!” - and Poincaré disappeared again. The Finnish mathematician left for his homeland without meeting the one for whom he undertook his journey.

None of those who knew Poincare closely would have regarded this act as a manifestation of rudeness or hostility on his part. At the height of his creative process, Poincaré preferred to remain in inner solitude, alone with the elusive truth. In these moments, he should be free from any worries and obligations. Only his spirit, completely liberated from all earthly hardships, could soar to such heights where the imagination of no mortal could reach. The consciousness that a visitor was waiting for him behind the curtain put pressure on his psyche, knocked him out of the right frame of mind. Even conversations and noise did not interfere with Poincare's work, since they did not encroach on his inner life, they were an alien element to his creative process. But the idea that they were waiting for him, which had settled in his brain, haunted him, disturbed him and distracted him from the main thing on which he was supposed to focus.

This case makes it possible to understand at the cost of what an incredible internal stress he got surprising intuitive insights. It's on its own amazing phenomenon becomes doubly surprising if we remember that his brain, with the tirelessness of a trouble-free machine, worked without fatigue and rest. Poincare could repeat after Balzac: "My life consists of one monotonous labor, which is diversified by labor itself." But the famous French mathematician Émile Borel best described the incessancy of his mental activity: “It can be said, although such a paradoxical statement risks being poorly understood, that his brain worked too continuously to ever have the rest necessary for reflection.”

It seems simply incredible that such a severe incessant work did not completely exhaust the intellectual forces of the scientist. True, in later photographs one can see the external traces of many years of enormous nervous tension, imprinted on his appearance. But how many famous scientists could not withstand the enormous mental load and left the creative path for a while or forever! Suffice it to recall the unfortunate case of F. Klein. At the age of 46, D. Gilbert experienced a similar creative breakdown, who, as his biographers write, left his health and natural optimism due to a complete decline in strength. S. Kovalevskaya, according to her daughter, was so exhausted by the work presented for the Borden Prize that she even had to be treated. Another contemporary of Poincaré, the German physicist and chemist W. Ostwald, as a result of intensive scientific activity, suffered a severe nervous breakdown and at one time wanted to completely "leave the stage." It is known that M. Faraday, having completed his electrochemical research, was on the verge of insanity for four years, and never completely recovered. And G. Davy after exhausting work, culminating in the discovery alkali metals suffered a severe nervous illness. There are so many such examples in science that such phenomena began to be considered almost inevitable and typical for any creative person.

But Poincaré's intellect, like the miraculous Phoenix bird, after each sizzling creative outburst, is reborn anew for the next act of creation. And each time it seems that a huge reserve of still untouched forces has woken up in him, capable of withstanding any tension of thought. Why such an inexhaustible creative energy in a short, round-shouldered person who eschews any kind of strengthening physical exercises? This can only be explained by the exceptionally high natural endowment of his intellect. Such unusualness could not but excite. The Poincare phenomenon has attracted the attention of physicians, psychologists and physiologists during the lifetime of the great creator. Since 1897, Dr. Toulouse has been observing him. He undertook medical and psychological examinations of a number of eminent figures science and art, including the chemist M. Berthelot, the composer Saint-Saens, the sculptor Rodin, the writers A. Daudet, E. Goncourt, E. Zola, the poet S. Mallarmé. His publications caused lengthy and lively discussions, as they directly related to the then widely discussed question: is genius a norm or a pathology? In 1910, Toulouse published a book dedicated to Poincaré.

An interesting comparison made by the author creative characters writer E. Zola and scientist A. Poincare. Zola belonged to the type strong-willed people. He forced himself to regular daily work, regardless of his mood and condition. Poincaré, on the other hand, could not force himself to work if he did not have an inner inclination to do so. However, as we know, it worked almost continuously. About five hundred articles and books were written by him throughout his life. creative life. More than one job per month. This speaks for itself. And we must also take into account not only the time of immediate creation, but also the inevitable preparatory work: thinking about a new problem and entering into it. But there is no contradiction between Toulouse's conclusions and these facts. Poincaré really worked without forcing himself, only internal needs. But this need to create lived in him all the time, like a wonderful inexhaustible source, a continuously acting creative stimulus.

Poincare not only allows himself to be observed, but he himself peers intently, delves into, listens to his creative process. This propensity for introspection and self-observation was reflected in his famous report made in 1908 in Paris at a meeting of the Psychological Society. "Mathematical creativity" - this is the name of this work. In it, the author, as it were, bifurcates: he acts both as a researcher and as an object of research. Poincaré does not adhere to the opinion widely held in scientific circles that only the results of research with their evidence belong to science, and the ways of approaching the truth remain outside of it. It is the "process of mathematical thought" that he analyzes in his report. He is especially interested in sudden intuitive insights, when, as if with a flash of lightning, a direct perception of the truth comes to the scientist. A happy thought dawns on the creator, as a rule, not at the time when he is working on a problem, but after, having not found a solution, he temporarily postpones the task, forgets about it. An idea is born either thanks to an insignificant hint, or without any visible external push, testifying to subconscious work which takes place in the brain independently of the will and consciousness. These observations of Poincaré are in complete agreement with those reported earlier by Helmholtz and Gauss. The French scientist illustrates his conclusions with examples from the early stage of his scientific activity, when he worked on Fuchsian functions. These examples have now become textbooks and have already been cited many times in the literature on scientific creativity.

Like Helmholtz, Poincaré notes that “these sudden inspirations come only after a few days of conscious effort, which seemed absolutely fruitless when one assumes that nothing good has been done and when it seems that a completely wrong path has been chosen. These efforts, however, are not as futile as is thought; they set the machine of the unconscious in motion, without them it would not have come into operation and would not have produced anything. A leap of the imagination only crowns long and persistent reflections on the problem. After Helmholtz and Poincaré, the need for preliminary intensive work, even if not bringing direct results, was recognized by psychologists who studied the conditions for making intuitive discoveries.

"The 'I-subconscious' is by no means inferior to the 'I-conscious'," concludes Poincaré, "it is not purely automatic, it is able to judge sensibly, it has a sense of proportion and sensitivity, it knows how to choose and guess. What can I say, it knows how to guess better than my mind, because it succeeds where the mind cannot.” Does it not follow from this that the unconscious is higher than consciousness? This was the conclusion reached by Émile Boutroux, who spoke at a meeting of the Psychological Society two months earlier. The unconscious, to which he refers religious feeling, is, in his opinion, the source of the most subtle, true knowledge. The facts just reported to Poincaré also seem to confirm Boutroux's idealistic views. But Poincaré is categorical in his rejection of this point of view, which is alien to him: "I assert that I cannot agree with this."

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Portal for the student. Self-training

short biography

Early years and training (1854-1879)

First scientific achievements (1879-1882)

Leader of French mathematicians (1882-1899)

Last years

Contribution to science

Automorphic functions

Differential Equations and Mathematical Physics

Singular points of integral curves

Algebra and number theory

Topology

Multivariate complex analysis

Astronomy and Celestial Mechanics

Physics and other works

Scientific terms associated with the name Poincaré

The role of Poincare in the creation of the theory of relativity

Poincare's work in the field of relativistic dynamics

Poincaré and Einstein: similarities and differences

"The Silence of Poincaré"

Estimation of Poincaré's contribution to special relativity

Biography

Early years and training (1854-1879)

First scientific achievements (1879-1882)

Leader of French mathematicians (1882-1899)

Last years

Contribution to science

Automorphic functions

Differential Equations and Mathematical Physics

Algebra and number theory

Topology

Multivariate complex analysis

Astronomy and Celestial Mechanics

Physics and other works

Scientific terms associated with the name Poincaré

The role of Poincare in the creation of the theory of relativity

Poincare's work in the field of relativistic dynamics

Poincaré and Einstein: similarities and differences

"The Silence of Poincaré"

Estimation of Poincaré's contribution to special relativity

Childhood

home education

School

Higher education

Polytechnic and mining schools

Family life

Mathematical merit

Physics

"The Poincaré Hypothesis"

Awards and titles

Conclusion

Science

Childhood

Home schooling

Lyceum

University

Polytechnic School

mining school

Decisive 1881

Paris

Physicist

Zenith

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