Geological history shows us that life is only a fleeting episode between two eternities of death, and that in this episode the past and future duration of conscious thought is no more than a moment. Thought is just a flash of light in the middle long night. But this flash is everything.

Henri Poincare

Jules Henri Poincare (April 29, 1854 - July 17, 1912) - the great French scientist who contributed huge contribution in many branches of mathematics, physics and mechanics. Founder qualitative methods theory of differential equations and topology. Created the foundations of the theory of stability of motion. In his articles before Einstein's work, the main provisions of the special theory of relativity were formulated, such as the conditionality of the concept of simultaneity, the principle of relativity, the constancy of the speed of light, clock synchronization by light signals, Lorentz transformations, and the invariance of Maxwell's equations. Developed and applied the small parameter method to problems celestial mechanics, carried out a classical study of the three-body problem. In philosophy, he created a new direction, called conventionalism.

Henri Poincare was born in the French city of Nancy. His 26-year-old father, Leon Poincare successfully combines the duties of a medical practitioner with laboratory research and lectures at the Faculty of Medicine. Madame Poincare, Eugenie Lanois, spent the whole day in trouble. Her whole life was devoted exclusively to the upbringing of children - the son of Henri and the daughter of Alina. The unusual distraction of little Henri surprises and worries the relatives. He will never get rid of this shortcoming, and in time whole legends will be told about the absent-mindedness of the famous Poincaré. No one has yet realized that Henri's absent-mindedness indicates innate ability almost completely distracted from the surrounding reality, going deep into your inner world.

As a child, he suffered from diphtheria, which was complicated by temporary paralysis of the legs and soft palate. The paralysis of the legs receded more quickly, but months passed, and Henri was still speechless. He became especially attentive to sound side life flowing very close, behind the doors of the room. The rumor became the only link between him and the rest of the house. Henri became a receptacle for unspoken sounds. Many years later, psychologists, examining a brilliant scientist, will note an infrequent feature in him - a colorful perception of sounds. Each vowel is associated in Poincaré with some color. Usually this ability, if it exists, is most pronounced in childhood. Henri Poincaré kept it until the end of his life.

Fortunately, the worst fears did not come true: Henri gained the ability to speak. But the physical weakness did not go away for a very long time. Everyone noticed that after the illness, Henri had changed a lot, not only externally, but also internally. He became timid, soft and shy. Henri, weakened by illness, is homeschooled by Alphonse Ginzelin, a longtime friend of the Poincaré family - a well-educated and erudite person, a born teacher. Lesson after lesson Henri went through a kind of training course. They did not bypass their attention to biology, geography, history, grammar rules, four steps of arithmetic. The teacher, not without surprise, was convinced that Henri did a good job of counting in his mind. But no matter what they did, Henri rarely had to pick up a pen or pencil. They did not ask him for written assignments, they did not load him with routine. To an outside observer, it might seem that the teacher is simply talking with his student about all sorts of things. Naturally gorgeous auditory memory Henri became even stronger and sharper from these exercises. The experience of assimilation of knowledge almost without fixing on paper, with a minimum of written work, having fallen on "fertile" soil, grew into a deeply peculiar, sharply individual manner. For the rest of his life he will remain, if not disgust, then at least disdain for writing, for the process graphic pinning their knowledge. All subsequent years of study could not correct this trait of his.

Good home preparation allowed Henri to enter the ninth grade of the Lyceum for eight and a half years (classes are counted in reverse order- from the tenth, primary, to the first, the oldest class). The teachers of the Nancy Lyceum were pleased with the diligent and inquisitive student. The essay in French, which he wrote at the end of the ninth grade, was called by the lyceum professor "a small masterpiece" for its style and inspirational and emotional presentation. Mathematics, or rather arithmetic, did not touch his soul, although he coped with the material presented without much difficulty. But one day, when Henri was in the fourth grade, one of the Lyceum teachers came to Poincaré's house. Very excited, he told the hostess who met him: "Madame, your son will be a mathematician!" And since the face of Madame Puncaré did not reflect either delight or surprise, the new-born prophet hastened to add: "I mean, he will be a great mathematician!"

Despite encouraging and unequivocal successes in mathematics, he moves to the department of literature. Apparently, this was the desire of his parents, who believed that their son must certainly receive full liberal education. Henri intensively studies Latin, studies ancient and new classics.

On August 5, 1871, the lyceum student Poincare successfully passed the exams for a bachelor of literature with a mark of "good". His Latin composition surpassed even that of French and deserved the highest rating. The ranks of French philologists could be replenished with a very talented, outstanding thinker if Henri chose Faculty of Philology university. But these hopes of some teachers of the lyceum were not destined to come true. A few days later, Henri expressed his desire to participate in the examinations for the degree of Bachelor of Science.

The exam took place on November 7, 1871. Poincaré passed it, but only with a "satisfactory" rating. let him down paperwork in mathematics, which Henri simply failed. The story of this incident is as follows: being late for the exam, very excited and unsettled, Henri did not understand the task well. It was required to derive a formula for the sum geometric progression. But Poincaré digressed from the topic and began to present a completely different question. As a result, the work he wrote deserved only an unsatisfactory rating. According to the formal rules, Henri had to drop out of the examination in this case. But the fame of his unusual mathematical abilities even reached the walls of the university, where the bachelor's examinations took place. University professors regarded his failure as unfortunate misunderstanding and turned a blind eye to some violation of formal canons for the sake of the triumph of justice. They did not have to regret it when they attended oral exam. Henri answered confidently and brilliantly, demonstrating Fluency material. He was awarded a Bachelor of Science degree.

After receiving a Bachelor of Science degree, Henri enters the elementary mathematics class. Only now does he truly fully and selflessly surrender to his future calling. Not content with recommended textbooks, he studies more serious mathematical literature.

In October 1873, Henri became a student at the Polytechnic School, which recruited and prepared applicants for the highest technical positions in state apparatus and in the army. After entrance exams Poincaré comes out on top of the list of the best school students but then gradually loses it. This was due to such subjects as military affairs, drafting and drawing. As in the Lyceum, Henri shows no signs of artistic talent. Even in mathematics classes, if he draws straight lines on the board that converge at one point, then they turn out to be neither straight nor converging.

Poincaré's mentor in mathematics was Charles Hermite. AT next year Poincaré published in the Annals of Mathematics his first scientific work in differential geometry.

According to the results of two years of study, in 1875, Poincaré was admitted to the School of Mines, the most authoritative specialized higher educational institution at that time. There, a few years later, under the guidance of Hermite, he defended his doctoral dissertation, about which Gaston Darboux, thirty-six years old French mathematician, professor at the Sorbonne and normal school who was on the committee said:

From the first glance, it became clear to me that the work is beyond the ordinary and more than deserves to be accepted. It contained enough results to provide material for many good dissertations.

Since April 1879, a graduate of the Mining School, Henri Poincaré, was assigned to Vesoul as a simple third-class mine engineer. His duties include supervision, control and inspection of coal mines. In addition, he is in the service of the control and operation of railways.

In the early morning of September 1, 1879, before dawn, there was an explosion of firedamp and the fate of about two dozen miners who remained underground is unknown. Fulfilling his duty, Poincaré descends, together with the rescue and search group, into the gaping mouth of the mine towards complete obscurity. In the ensuing turmoil, the administration even announced the death of the engineer Poincaré while investigating the circumstances of the accident. Fortunately, this was a mistake. He safely rose to the surface of the earth, finding out the size and causes of the catastrophe.

The dissertation gave Henri Poincaré the right to teach at higher educational institutions. And he was not slow to take advantage of it.

On December 1, 1879, he leaves for Caen, where he was appointed lecturer in the course of mathematical analysis at the Faculty of Sciences. After leaving Vesoul, he would never return to mining engineering, but would still be in his department, receiving promotions from time to time.

In Canet, Poincaré met his future wife, Louise Poulain d'Andecy. On April 20, 1881, their wedding took place. They had a son and three daughters.

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 he accepted the invitation. In parallel, from 1883 to 1897, he taught mathematical analysis in the Higher Polytechnic School.

In 1881-1882 Poincaré created new section 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 on the behavior of a family of solutions. He applied this approach with great success to solving problems of celestial mechanics and mathematical physics.

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 the usual Poincaré indifference to questions of priority, proposed to call Fuchsian functions - although he had every reason to give this class his 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 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 works of Poincaré, elliptic functions turned from a priority direction of science into a limited one. special case 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.

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 balance.

When Poincare was still a child, the majestic spectacle of the starry night captivated his infantile mind. He would later write in one of his articles:

The stars send us not only visible and tangible light that affects our carnal vision; they also emit a different, more subtle light that clarifies our mind.

Probably it was this refined "light" of comprehended truth that Poincaré saw with his inner vision, when his interest turned to the laws of motion. celestial bodies.

In January 1889, eleven works were submitted to an international competition announced by King Oscar II. The jury of the competition recognized two of them as the best. One work belonged to Paul Appel and was called "On integrals of functions with factors and on their application to the expansion of Abelian functions in trigonometric series". Another work had as its motto a line from a Latin poem: "Nunquam praescriptos transibunt sidera fines" - "The luminaries will never cross the prescribed boundaries." It was a memoir by Henri Poincare, which was an extensive study of the three-body problem. Both works were awarded the prize on the equal grounds. Friends shared glory and honors.

One of the two judges, Mittag-Leffler, wrote of Poincaré's work:

The award-winning memoir will be among the most significant mathematical discoveries century.

The second judge, Weierstrass, stated that after Poincaré's work

will begin new era in the history of celestial mechanics.

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 Poincaré's recognition as France's leading mathematician was his election as president of the French Mathematical Society in 1886 and as a member of the Paris Academy of Sciences the following year.

In 1889 Poincaré's fundamental "Course of Mathematical Physics" was published in 10 volumes.

Like Euler, Poincare for short term rethought and updated the mathematical apparatus of celestial mechanics that had evolved over two centuries, using the latest achievements in mathematics. In the three-volume treatise "New Methods of Celestial Mechanics" (1892-1899), Poincaré studied periodic and asymptotic solutions of differential equations, proved the asymptotic nature of some series that are solutions of partial differential equations, introduced the methods of a small parameter, the method of fixed points. He also owns important for celestial mechanics works on the stability of motion and on the equilibrium figures of a gravitating rotating fluid. The method of "integral invariants" used by Poincaré has become a classic tool theoretical research not only in mechanics and astronomy, but also in static physics and quantum mechanics. Henri Poincaré's contribution to celestial mechanics was so significant that he was approved unanimously for the vacant position of head of the department of celestial mechanics at the Sorbonne. Leaving the Department of Mathematical Physics and Probability Theory, which he led for ten years, since the autumn of 1896, Professor Poincaré has already been teaching courses in some traditional sections of celestial mechanics.

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 high-quality geometry, or topology: from 1894, he began publishing articles on the construction of a new, exceptionally promising science.

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 qualitative geometry. The term "topology" itself was proposed by Johann Benedict Listing even earlier. Some important concepts 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.

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 Poincaré was elected chairman.

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 communication. 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).

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.

It was on the initiative of Poincaré that the young Antoine Henri Becquerel began to study the connection between phosphorescence and X-rays in 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.

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 at the Fourth Mathematical Congress himself. The first operation ended successfully, but after 4 years Poincaré's condition worsened again.

Henri Poincaré died in Paris after an embolism operation on July 17, 1912, at the age of 58. He was buried in the family vault at the Montparnasse cemetery.

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. Among his biggest achievements:

• topology creation
• qualitative theory of differential equations
• theory of automorphic functions
• development of new, extremely efficient methods of celestial mechanics
• creation of the mathematical foundations of the theory of relativity
• visual model of Lobachevsky's geometry.

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", still the works, the results of which have direct applied application. This is especially noticeable in his works of the last 15-20 years. Nevertheless, Poincaré'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 he had read and conversations he had read word for word. Also, he never worked on a single task. long time, believing that the subconscious has already received the task and continues to work, even when he thinks about other things. Mine creative method Poincare described in detail in the report "Mathematical creativity" (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 has penetrated human mind, no matter how difficult and thorny his path was - whether it be the problems of wireless telegraphy, x-ray radiation or the origin of the Earth - Henri Poincaré walked alongside ... Together with the great French mathematician, the only person left us whose mind could encompass everything that was created by the mind of other people, penetrate into the very essence of everything that human thought has comprehended today, and see something in it new.

Henri Poincare was a member of 22 Academies and an honorary doctor of 8 universities.

Awards and titles received by Poincaré:

• 1885: Poncelet Prize, Paris Academy of Sciences
• 1886: Elected President of the French Mathematical Society
• 1887: Elected member of the Paris Academy of Sciences
• 1889: Award for victory in math competition King Oscar II of Sweden
• 1889: Order of the Legion of Honor
• 1893: Elected member of the Bureau of Longitudes (this is the historical name of the Paris Institute of Celestial Mechanics)
• 1894: Elected a Foreign Fellow of the Royal Society of London
• 1895: elected a foreign corresponding member of the St. Petersburg Academy of Sciences
• 1896: Jean Reynaud Prize, Paris Academy of Sciences
• 1896: Elected President of the French Astronomical Society
• 1899: American Philosophical Society Prize
• 1900: Gold Medal of the Royal Astronomical Society, London
• 1901: Sylvester medal, Royal Society, London
• 1903: Golden medal fund named after N.I. Lobachevsky (Physical and Mathematical Society of Kazan), as a reviewer of David Hilbert
• 1905: Janos and Farkas Bolyai Prize, Hungarian Academy of Sciences
• 1905: Matteucci medal, Italian Scientific Society
• 1906: Elected President of the Paris Academy of Sciences
• 1908: elected member French Academy
• 1909: gold medal, French Association for the Promotion of Science
• 1911: Katherine Bruce Medal, Pacific Astronomical Society
• 1912: elected director of the French Academy

Named after Poincaré:

• crater on reverse side Moon.
• asteroid
• International Poincare Prize for work in mathematical physics
• Institute of Mathematics and Theoretical Physics in Paris
• university in Nancy.
• street in paris

The following mathematical objects bear the Poincaré name:

• Poincare conjecture
• Poincaré group
• Poincaré duality
• Poincaré's lemma
• Poincaré metric
• Poincaré model of Lobachevsky space
• Poincaré-Dulac normal form
• Poincaré mapping
• Poincaré's last theorem
• Poincaré sphere
• Poincare-Bendixon theorem
• Poincaré-Volterra theorem
• Poincaré's vector field theorem
• Poincare recurrence theorem
• Poincaré's theorem on the rate of growth of an entire function
• Poincaré's theorem on the classification of circle homeomorphisms
• Poincaré - Birkhoff - Witt theorem
• Poincaré-Hopf theorem
• Poincaré complex
• Poincare deduction
• Poincaré inequalities
• Poincaré - Einstein synchronization
• Poincaré-Lelon equation
• modular Poincaré form
• Poincaré metrics
• Poincaré spaces
• operator Poincaré - Steklova
• Poincaré symmetry, etc.

Based on materials from Wikipedia, the site eqworld.ipmnet.ru and the book "The Line of Great Mathematicians" (Warsaw, ed. Nasha Ksengarnya, 1970).

In each of his works, Poincare managed to achieve significant results. The main application of his achievements is applied. With his general, the works of Henri Poincaré later served the development of science, have been used and are still being used in many scientific fields.

Childhood

Henri Poincaré was born on 04/29/1854 in the small French town of Cite Ducal near Nancy in the family of a doctor and teacher of the medical faculty Leon Poincaré and Eugenie Lanois, who was engaged exclusively in household chores and children. There were two children: Henri and Alina. From a very early age, little Henri suffers from severe absent-mindedness. She will accompany him all his life. At that time, no one realizes that this shortcoming is evidence of his talent to immerse himself in his thoughts, analyze, and reflect.

boy in early age contracted diphtheria. The disease gave a complication, and for several months the child could not walk or talk. Henri began to pay more attention to sounds, and over the years this resulted in the fact that he began to associate sounds with a certain color. Many children have this ability, but by maturity it disappears. She stayed with Poincaré for the rest of her life.

Over time, the boy recovered, began to walk and talk, but was physically very weak. The disease also changed him internally: he became shy and timid. A. Ginzelin, the most educated person at that time, studied with him at home. It is interesting that no matter what science they studied, Henri rarely wrote anything, he counted perfectly in his mind, he was not forced to do homework and not loaded with unnecessary information. All lessons could seem only a conversation between an adult and a child about everything in the world. However, such activities contributed to the improvement of the already good auditory memory. The soil turned out to be "fertile", and a brilliant scientist with his own individual manner grew out of a sickly timid little boy. By the way, Jules Henri's dislike for any writing will remain until the end of his life.

Henri mastered the knowledge at home school so well that he immediately entered the 9th grade. He was just over 8 years old. Lyceum classes at that time were considered from 10 to 1. The first was similar to our eleventh, graduation. The teachers of the Lyceum in Nancy were proud of him. He wrote excellent essays and presentations, without difficulty he did all the mathematical tasks. However, at that time mathematics did not occupy him much. The teacher of mathematics prophesied a great future for him, but Poincaré is more engaged in literature and moves to the humanitarian department.

On June 19, 1870, the war between France and Prussia began, which brought disappointment and grief to the French. During this period, Henri actively helps his father, who is at the head of the entire city's medicine for working with wounded soldiers. The guy performs the duties of an assistant in the outpatient clinic and personal secretary.

Events are developing rapidly. The capture of the city by the Germans, then the proclamation of the Commune, the flight of the top of Thiers and the May "bloody week" shocked the sixteen-year-old boy. Dissertation "How can a nation rise?" at the end of the gymnasium, it reflected all his experiences and thoughts about the Motherland.

08/05/1871 exam for a bachelor of literature at the university passed with a mark "good". It would seem that the Faculty of Philology is ahead of him, but Poincaré on 11/07/1871 takes exams for a bachelor's degree natural sciences. Mathematics was almost failed all by the same legendary absent-mindedness. Jules Henri was late for the exam, became confused and began to tell something completely different, material that did not concern exam question. The failure was treated with understanding, as they knew about the outstanding abilities of Henri. He was admitted to the oral examination, where he showed himself in all his splendor. A bachelor's degree in natural sciences was obtained.

Studying in the class of elementary mathematics, Poincaré studies additional literature and repeatedly wins general mathematical competitions.

Studying at the Polytechnic and Mining Schools

Since the autumn of 1873, Poincaré has been a student at the Polytechnic School. First topping the list of the best, later on he loses leadership positions due to some subjects that he does not take seriously. These are drawing, drafting and military art. Graduates from high school in second place. Then he enters the Mining School, which was considered at that time a very prestigious educational institution. There he is engaged in scientific research in the field of crystallography.

In 1879, at the School of Mines, under the guidance of Ermit, he defended his doctoral dissertation, which was approved by Professor G. Darboux of the Sorbonne. The professor believed that in one work Poincaré worked out the material and put forward ideas for several dissertations.

Since April 1879, Poincaré has been working as a mine engineer. After one of the explosions in the mine, when people died, he descends to the site of the explosion and finds out why the tragedy occurred and what its dimensions are. After defending his dissertation, teaching activities. He works in Cana on a mat. analysis at the Faculty of Sciences.

Family life

The boundless love for mathematics does not obscure from him another, no less important - love for a woman. 04/20/1881 Henri Poincare and Louise Paulin d "Andesy are legally married. A magnificent wedding took place in Paris. At first there were no children for a long time, then in 1887 a long-awaited girl was born, who was named Jeanne, two years later Yvonne was born, then - Henriette.God sends the Poincare couple another son.Leon was born two years after Henrietta.

The family life of a mathematician was full of peace and love. In many ways, due to the fact that Madame Poincaré maintained a favorable atmosphere around her husband and in the family, he managed to carry out such a "gigantic work of thought."

Achievement in Mathematics

The appearance of a whole series of notes in the journal "Compres Rendus" (France) about Fuchsian functions attracts the attention of venerable mathematicians, Weierstrass, S. Kovalevskaya, and arouse genuine interest in the scientific world. This is followed by five more interesting works on the same subject.

After his discovery of automorphic functions, the mathematician receives a teaching position at the University of Paris. Having moved there, the twenty-seven-year-old scientist takes care of his family, teaches and actively collaborates with newly arrived young mathematicians Paul Appel and Emile Picard. Their mentor is Professor Sh. Hermit.

In Paris, the work of Poincaré is published from 4 hours “On curves defined by differential equations” (1882-1886). Before the scientist, this method was ignored. He laid the foundations for the theory of stability of differential equations with respect to initial conditions and small parameters. In 1886 J. A. Poincaré became head of the Department of Mathematical Physics and Probability Theory, and when he turned 33, became a member of the French Academy of Sciences.

All his research led the researcher to topology. He is credited with introducing such concepts as the Betti numbers, the fundamental group, he proved the Euler-Poincaré formula and gave the formulation general concept dimensions. He made many discoveries in algebraic topology, in differential geometry, in probability theory, and more. etc. Wrote works on the substantiation of the Dirichlet principle.

Advances in celestial mechanics

From childhood, Poincaré was fascinated by the stars and became interested in the laws by which celestial bodies move. His work "The luminaries will never cross the prescribed boundaries" in 1889 received an award for international competition. The treatise "New Methods of Celestial Mechanics" was written (in 3 volumes). Significant works on the stability of motion and on the equilibrium figures of a gravitating rotating fluid have been published, the method of "integral invariants" has been introduced, and many others. etc. Since 1896, Poincaré has been the head of the department of celestial mechanics at the Sorbonne University.

Achievements in physics

Poincaré's influence on the development of physics is enormous. Long before Einstein, in 1897 - 1905, in his articles, in particular in the work "Measurement of Time", he revealed some provisions of the special theory of relativity. In addition, he was very interested in working with students. A very voluminous course of lectures on physics was read, which was later embodied in a twelve-volume edition. All the most relevant in science was touched upon and its own approach to the solution was given. Many of the conclusions of other scientists Poincaré anticipated much earlier.

1902 - "Science and Hypothesis" is published, which stirred up many scientists. 1904 - Poincaré gives a lecture in the USA (St. Louis), where he makes a splash. In his article "Notes of the Academy of Sciences" (1905), he proved the invariance of Maxwell's equations with respect to Lorentz transformations. According to M. Born, the theory of relativity is not the merit of one scientist, but the result of the collective work of brilliant scientists, each of whom contributed to it. A. Poincaré undoubtedly belongs to them.

Poincare - Hamilton - Perelman

French scientists have put forward many interesting hypotheses. One of them is called the Poincaré hypothesis. In its original form, it states that any simply connected compact 3-manifold without boundary is homeomorphic to a 3-sphere. According to the American scientist Marcus Du Sotay (Oxford), the Poincare hypothesis is "the central problem of mathematics and physics, an attempt to understand what shape the Universe can be ...". The hypothesis was included in the gold list of the Seven Millennium Challenges, for the solution of each of them the Clay Institute put forward a reward of 1 million US dollars.

Formed in 1904, for a long time did not attract special attention. Interest in it aroused Henry Whitehead (England), announcing his proof. It turned out to be incorrect. Since then, many have tried to do this, especially in the 60s of the last century. There was a great deal of evidence, which in the end turned out to be erroneous.

Our compatriot Perelman managed to prove the Poincaré conjecture. The Russian published his work in 2004, he was awarded international award Fields Medal, and in 2010 Mathematical Institute Clay awarded Grigory Perelman a $1 million prize for proving this Millennium Problem. Perelman refused all awards.

The American mathematician Hamilton also worked on the proof, without completing his work to the end, he ceases to be interested in it. In 2011, at the urging of Grigory Perelman, R. Hamilton received a $1,000,000 award for creating mathematical theory, partly used by G. Perelman.

Awards and titles

The merits of Poincaré were appreciated. He is the owner of a number of awards: Poisele (1885), King Oscar II of Sweden (1889), Jean Reino of the Paris Academy of Sciences (1896), Boya of the Hungarian Academy of Sciences (1905). Awarded with medals: Royal Astronomical Society of London (1900), them. J. Sylvester of the Royal Society of London (1901) and others. Many scientific French, British and Russian societies and the academies considered it an honor to be a member of their ranks.

The great scientist died in Paris on July 17, 1912, he was only 58 years old. Poincare was buried in the family crypt at the Montparnasse cemetery. One of the lunar craters and an asteroid, the Paris Mathematical Institute, a street in Paris and whole line mathematical terms and tasks.

(1854-1912) French mathematician

Jules Henri Poincaré was born on April 29, 1854 in Nancy, administrative center Department of Meurthe and Moselle, in the family of the doctor Leon Poincaré. Mother, Evgenia Lanois, devoted her whole life to raising her son Henri and daughter Alina, who was two years younger than Henri.

His first teacher, Alfons Ginzelin, who lived next door, worked as an inspector of the lower grades of the Lyceum. He had an original pedagogy: he talked about everything - about history and mathematics, paleontology and grammar, and Henri listened and memorized. Probably, from that time on, he began to disdain records, fixing knowledge on paper.

Henri was in his ninth year when he was sent to the Nancy Lyceum. During the interview, he showed such good "home" knowledge that he was immediately assigned to the ninth grade. Henri studied very well, was the first student in the class. In the fourth grade, teachers say that he will be a great mathematician, but his family insists on liberal education. The young man graduates from the lyceum and takes exams for a bachelor of literature, and two months later for a bachelor of science. In the additional class of the lyceum, he studies in the class of elementary mathematics, prepares for exams in high school, mathematics has already completely captured him, and he wins the competition in elementary mathematics, becomes the best young mathematician France.

In 1873, 19-year-old Henri Poincare entered the Ecole Polytechnique, one of the most prestigious educational institutions in France. His authority among his peers is undeniable, and in one of the conflicts between students and a professor of mathematics, Henri puts the latter on both shoulder blades, proving that the professor erroneously formulated the exam question.

After the Polytechnic School, Jules Henri Poincare goes to study at the School of Mines. There he is fond of crystallography, which is connected with the theory of groups, which he will later be passionate about. Poincaré graduates from the School of Mines and becomes a mining engineer at the Vehaul mine. There he almost got into an accident: firedamp exploded and 16 miners died.

The defense of his dissertation opens the way for him to the university, and he leaves the mine, saying goodbye to the profession of a mining engineer. His path lies from east to west, to the city of Caen, one of the most learned cities in France. Lectures by Henri Poincare at the university do not arouse enthusiasm among students. The subject of his thoughts is differential equations. Poincaré works a lot in this direction, discovers the new kind functions, and his name becomes known among European mathematicians so much that he was immediately invited to the University of Paris to the Faculty of Sciences.

If mathematics won the mind and intellect of Henri Poincaré, then the charming Paulin d'Andesy captivated his heart. On April 20, 1881, their wedding took place in Paris. The Poincare couple now lives in Paris, in the Latin Quarter.

In October 1881, the young scientist was invited to teach at the university. There, Charles Hermite, famous all over Europe, takes to all mathematical meetings three young teachers of mathematics at the Sorbonne - Picard, Appel and Poincaré. Charles Hermite introduces them into the light of mathematics.

The fame of Jules Henri Poincare is growing, he writes articles in the most various areas mathematics. He is compared to the great Cauchy. Now mathematicians who come to Paris want to meet Henri Poincaré and discuss mathematical problems with him.

In 1886 he became a professor at the Sorbonne, received the chair of mathematical physics and probability theory, and a year later was elected to the Academy of Sciences.

In 1889, Henri Poincaré and Paul Appel, two friends, received the Swedish King Oscar II for solving the three-body problem. The merit in holding this competition belonged to the famous Swedish mathematician Mittag-Leffler and the international journal Acta mathematica founded by him. The University of Paris offers Poincaré the chair of celestial mechanics after the death of F. Tisserand, the author of a four-volume treatise on celestial mechanics. Henri Poincaré's attention is focused on a new science, the science of the 20th century - topology.

The famous mathematician could not but be concerned about the general problems of science. Everything he said is relevant to this day. Until now, there are disputes in the scientific world about what is more important - applied Science or fundamental.

At first, Henri and Paulin did not have children for a long time. Then, in 1887, Jeanne was born, two years later - Yvonne, two years later - Henrietta, and two years later - the son of Leon. The life of the family flowed quietly and calmly. The intense work of Poincaré would have been simply unthinkable without a strict regime. Pauline "surrounded her husband with a family atmosphere, deeply calm and quiet, which alone allows him to do a gigantic work of thought," Appel, his friend, wrote in his memoirs.

A new age has come. On August 6, 1900, the second International Congress of Mathematicians began to work in Paris at the Palais des Congrès, Henri Poincare was elected its chairman, and physicists elected him vice-president of the International Physical Congress. The famous French mathematician and theoretical physicist is a true leader of world science. Among those to whom the theory of relativity owes its appearance, along with the great Einstein, they also name Henri Poincaré.

His work in many areas of mathematics and in theoretical physics naturally led him to the general philosophical problems science, his thoughts are set forth in the books "Science and Hypothesis", "Science and Method", "The Value of Science". The works of Henri Poincaré caused a storm in scientific circles. There were many opponents of his views. Science for him is not a granite pantheon, but an eternally living and changing organism, when new theories are born. Today they are new, tomorrow they are obsolete. In a theory that dies, a grain of truth remains.

The scientific discoveries of Jules Henri Poincare in mathematics and physics are many years ahead of science, and in completely different directions.

He often travels to international congresses, speaks, writes a lot (about 500 works), and he writes quickly, almost never corrects what is written. He is reproached that his proofs are not rigorous enough, they cite great mathematicians as an example German school who were characterized by pedantry.

In 1908, in Rome, at the IV International Mathematical Congress, Poincaré's report "The Future of Mathematics" was presented, which was read by another famous French mathematician - Gaston Darboux. And Poincare himself was in the hospital. It seemed that the disease receded for a while, but the doctors insisted on an operation. It was successful, but on July 17, the scientist felt unwell and died 15 minutes later from blockage of blood vessels. I could not believe that the living, impetuous Henri Poincaré, this volcano of ideas and problems, the luminary of world science, was no more. He was only 58 years old.

Henri Poincaré is a brilliant French scientist of a wide profile who made a great contribution to many branches of mathematics, physics and mechanics. Founder of qualitative methods in the theory of differential equations and topology. Created the foundations of the theory of stability of motion. In his articles, before the works of A. Einstein, the main provisions of the special theory of relativity were formulated, such as the conditionality of the concept of simultaneity, the principle of relativity, the constancy of the speed of light, clock synchronization by light signals, Lorentz transformations, the invariance of Maxwell's equations, etc. Developed and applied the small parameter method to the problems of celestial mechanics, conducted a classical study of the three-body problem. In philosophy, he created a new direction, called conventionalism.

Childhood and homeschooling

Henri Poincaré was born on April 29, 1854 in Nancy (Lorraine, France). His 26-year-old father, Leon Poincare successfully combines the duties of a medical practitioner with laboratory research and lectures at the Faculty of Medicine. Madame Poincare, Eugenie Lanois, spent the whole day in trouble. Her whole life was devoted exclusively to the upbringing of children - the son of Henri and the daughter of Alina. The unusual distraction of little Henri surprises and worries the relatives. He will never get rid of this shortcoming, and in time whole legends will be told about the absent-mindedness of the famous Poincaré. No one is yet aware that Henri's absent-mindedness indicates an innate ability to be almost completely distracted from the surrounding reality, deeply withdrawing into his inner world.

Having fallen ill with diphtheria, for several months Henri turned into a weak prisoner, bedridden, with a seal of silence on his lips - the disease was complicated by paralysis of the legs and soft palate. Forces very slowly returned to the body exhausted by the disease. The paralysis of the legs receded more quickly, but months passed, and Henri was still speechless. He became especially attentive to the sound side of life flowing very close by, behind the doors of the room. The rumor became the only link between him and the rest of the house. Henri became a receptacle for unspoken sounds. Many years later, psychologists, examining a brilliant scientist, will note an infrequent feature in him - a colorful perception of sounds. Each vowel is associated in Poincaré with some color. Usually this ability, if it exists, is most pronounced in childhood. Henri Poincaré kept it until the end of his life.

Fortunately, the worst fears did not come true: Henri gained the ability to speak. But the physical weakness did not go away for a very long time. Everyone noticed that after the illness, Henri had changed a lot, not only externally, but also internally. He became timid, soft and shy. Henri, weakened by illness, is homeschooled by Alphonse Ginzelin, a longtime friend of the Poincare family - a well-educated and erudite person, a born teacher. Lesson after lesson Henri went through a kind of training course. They did not bypass their attention to biology, geography, history, grammar rules, four steps of arithmetic. The teacher, not without surprise, was convinced that Henri did a good job of counting in his mind. But no matter what they did, Henri rarely had to pick up a pen or pencil. They did not ask him for written assignments, they did not load him with routine. To an outside observer, it might seem that the teacher is simply talking with his student about all sorts of things. By nature, Henri's excellent auditory memory was further strengthened and sharpened by these exercises. The experience of assimilation of knowledge almost without fixing on paper, with a minimum of written work, having fallen on "fertile" soil, grew into a deeply peculiar, sharply individual manner. For the rest of his life, he will remain, if not disgust, then at least disdain for writing, for the process of graphic consolidation of his knowledge. All subsequent years of study could not correct this trait of his.

Lyceum education. War between France and Prussia. Blood Week. Exams

Good home preparation allowed Henri to enter the ninth grade of the lyceum for eight and a half years (the counting of classes is carried out in the reverse order - from the tenth, primary, to the first, the oldest grade). The teachers of the Nancy Lyceum were pleased with the diligent and inquisitive student. The essay in French, which he wrote at the end of the ninth grade, was called by the lyceum professor "a small masterpiece" for its style and inspirational and emotional presentation. Mathematics, or rather arithmetic, did not touch his soul, although he coped with the material presented without much difficulty. But one day, when Henri was in the fourth grade, one of the Lyceum teachers came to Poincaré's house. Very excited, he told the hostess who met him: "Madame, your son will be a mathematician!" And since the face of Madame Puncaré did not reflect either delight or surprise, the new-born prophet hastened to add: "I mean, he will be a great mathematician!"

Despite encouraging and unequivocal successes in mathematics, he moves to the department of literature. Apparently, this was the desire of his parents, who believed that their son must certainly receive a full liberal arts education. Henri intensively studies Latin, studies ancient and new classics.

On July 19, 1870, the French government declares war on Prussia. Upliftment and general enthusiasm reign in the capital and in the departments. No one doubts the easy and speedy victory of enlightened France over barbarian Prussia. As an unexpected and terrible revelation, the French come to the realization that the country is completely unprepared for war. The Parisian newspapers are still enthusiastically shouting about the victories of French weapons, and the remnants of the defeated, exhausted unequal battles French parts.

In these harsh days Leon Poincaré, as a member of the city municipality, headed the entire medical unit that served the wounded. Sixteen-year-old Henri, who cannot yet be called to military service, is inseparably with his father as a voluntary secretary and outpatient assistant. On August 14, German units entered the city, and on March 18 an uprising took place in Paris and the power of the Commune was proclaimed. The government led by Thiers fled to Versailles. Now the siege of Paris is no longer carried out by the Prussians, but by government troops, who complete it at the end of May with the "bloody week". All these events are carried by some kind of whirlwind before Henri's shocked mind.

In the troubling spring of 1871, Henri contemplates a dissertation written work to be submitted at the end of the first class. The theme he has chosen speaks for itself: "How can a nation rise?" On the pages student notebook his pure and noble thoughts are reflected, his pain and anxiety for the defeated Fatherland are hidden.

On August 5, 1871, the lyceum student Poincare successfully passed the exams for a bachelor of literature with a mark of "good". His Latin composition surpassed even that in French and deserved the highest mark. The ranks of French philologists could have been replenished with a very talented, outstanding thinker if Henri had chosen the philological faculty of the university. But these hopes of some teachers of the lyceum were not destined to come true. A few days later, Henri expressed his desire to participate in the examinations for the degree of Bachelor of Science.

The exam took place on November 7, 1871. Poincaré passed it, but only with a "satisfactory" rating. His written work in mathematics failed, which Henri simply failed. The story of this incident is as follows: being late for the exam, very excited and unsettled, Henri did not understand the task well. It was required to derive a formula for the sum of a geometric progression. But Poincaré digressed from the topic and began to present a completely different question. As a result, the work he wrote deserved only an unsatisfactory rating. According to the formal rules, Henri had to drop out of the examination in this case. But the fame of his unusual mathematical abilities even reached the walls of the university, where the bachelor's examinations took place. University professors regarded his failure as an unfortunate misunderstanding and turned a blind eye to some violation of formal canons for the sake of justice. They did not have to regret it when they attended the oral exam. Henri answered confidently and brilliantly, demonstrating fluency in the material. He was awarded a Bachelor of Science degree.

After receiving a Bachelor of Science degree, Henri enters the elementary mathematics class. Only now does he truly fully and selflessly surrender to his future calling. Not content with the recommended textbooks, he studies more serious mathematical literature: Rouchet's "Geometry", Joseph Bertrand's "Algebra", Duhamel's "Analysis", Chall's "Higher Geometry".

Two next summer The years 1872 and 1873 were marked by the fact that Henri Poincaré took first place in the General Competition in Elementary Mathematics and in the General Competition in Special Mathematics.

Education at the Polytechnic School and at the School of Mines. Working as a mining engineer

In October 1873, Henri became a student at the Polytechnic School, which recruited and prepared applicants for the highest technical positions in the state apparatus and in the army. After the entrance exams, Poincaré comes out on top of the list best students school, but then gradually loses it. This was due to such subjects as military affairs, drafting and drawing. As in the Lyceum, Henri shows no signs of artistic talent. Even in mathematics classes, if he draws straight lines on the board that converge at one point, then they turn out to be neither straight nor converging.

In the first place comes a friend of Poincaré - Bonfoy, who got complete collection works of Laplace, traditionally awarded to the best student of the Polytechnic School from the Academy of Sciences. Poincaré is in second place, but Henri is ahead of everyone in basic physical and mathematical disciplines and in chemistry. All the first three students of the Polytechnic School enter the Mining School, the most authoritative specialized higher educational institution at that time.

In the second year of study at the School of Mines, Henri already seriously took up Scientific research. Ideas are swarming in his head, which two years later will form the basis of his doctoral dissertation. Therefore, the special courses he takes do not affect his imagination, if they are not related to mathematics. The only subject that really interested Henri was mineralogy. Not even mineralogy itself, but crystallography, which, along with the kinematics of solids, represented one of the few points of application of group theory, one of the most abstract sections of mathematics at that time. Checking the status of the dissertation was entrusted to Darboux, Laguerre and Bonnet, who are in no hurry to answer. Poincare even describes his troubles related to obtaining recommendations from the members of this commission in a playful poem he composed.

Philosophical views

The scientific work of Poincaré in the last ten years of his life proceeded in the atmosphere of the beginning revolution in natural science, which undoubtedly determined his interest in these years in the philosophical problems of science. Brief summary of his own philosophical views boils down to the following: the main provisions (principles, laws) of any scientific theories are neither synthetic a priori truths nor models objective reality. They are an agreement whose only absolute condition is consistency. The choice of certain provisions from the set of possible ones is arbitrary, if we ignore the practice of their application. But since we are guided by the latter, the productivity of choosing the basis of the principle (laws) is limited, on the one hand, by the need in our thought for the maximum simplicity of theories, and on the other, by the need for their successful use. Within the boundaries of these requirements lies a certain freedom of choice, due to the relative nature of these requirements themselves. This philosophical doctrine of Poincaré was subsequently called conventionalism.

Awards and titles

During his life, Poincaré managed to receive many scientific titles and awards, including:

Poiselet Prize of the Paris Academy of Sciences (1885),
- Member of the French Academy of Sciences (1887),
- Prize of the King of Sweden Oscar II (1889),
- Member of the Royal Society of London (1894),
- foreign corresponding member of the St. Petersburg Academy of Sciences (1895),
- President of the French Astronomical Society,
- member of the Bureau of Longitudes in Paris (1893),
- Jean Reino Prize of the Paris Academy of Sciences (1896),
- gold medal of the Royal Astronomical Society of London (1900),
- J. Sylvester Medal of the Royal Society of London (1901),
- gold medal of the Fund. N.I. Lobachevsky Physical and Mathematical Society of Kazan,
- Prize to them. J. Bolyai of the Hungarian Academy of Sciences (1905),
- President of the French Academy of Sciences (1906),
- Gold medal of the French Association for the Promotion of Science (1909).

The Mathematical Institute in Paris is named after Poincare, as well as a crater on the far side of the moon.

Links to literature and web pages

1. The principle of relativity. Collection of works of the classics of relativism(G.A. Lorentz, A. Poincaré, A. Einstein, G. Minkowski). Ed. and notes by V.K. Frederiks and D.D. Ivanenko. M.-L.: ONTI, 1935.
2. Pauly W. Theory of relativity. M.-L.: Gostekhizdat, 1947.
3. Questions of the history of natural science and technology, 1956, no. 2, p. 114-123.
4. Subbotin M.F. Works of Henri Poincaré in the field of celestial mechanics. Questions of the history of natural science and technology, 1956, no. 2, p. 114-123.
5. Poincare A. Selected writings, tt. 1-3. M .: Nauka, 1971-1974 (files of these books can be found).
6. The principle of relativity. Sat. works on the special theory of relativity. M .: Atomizdat, 1973 (the file of this book can be found).
7. Julia G. Henri Poincare, his life and work. In: Henri Poincaré. Fav. works. M.: Nauka, 1974, v. 3, p. 664-673.
8. Tyapkin A.A., Shibanov A.S. . Moscow: Young guard, 1979.
9. Bogolyubov A.N. Mathematicians, Mechanics: Biographer. right. Kyiv: Naukova Dumka, 1983.
10. Logunov A.A. To the works of Henri Poincaré "On the dynamics of the electron"(2nd edition). M.: MSU, 1988.
11. Mathematical encyclopedic Dictionary . M.: Soviet Encyclopedia, 1988, p. 739-740.
12. Logunov A.A. Henri Poincaré and the Theory of Relativity. M.: Nauka, 2004.
13. Apple P. Henri Poincare. Paris: Plon, 1925.
14. Whittaker E. A History of the Theories of Aether and Electricity. The Modern Theories 1900-1926, London: Thomos Nelson, 1953.
15. Par Renard de la Taille. Relativite Poincare a precedent Einstein, Science et Vie, no. 931, Avril 1995, p. 114-119 (original article in djvu format, translation of the article in html format).
16. Tyapkin A.A. On the history of the "theory of relativity". Dubna: JINR, 2004.
17. . Virtual school for young mathematicians.

Jules Henri Poincaré (French Jules Henri Poincaré; April 29, 1854, Nancy, France - July 17, 1912, Paris, France) was a 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).

He studied at the Lycée Nancy. Higher education received at the Polytechnic School in Paris, then at the School of Mines, which he graduated in 1879. In the same year he defended his doctoral dissertation. Since 1881 - professor of mechanics at the University of Paris, head of the department of physics, astronomy and celestial mechanics.

A significant number of works by Poincaré in mathematics are connected with the solution of problems in celestial mechanics, in particular, the problems of three bodies. Dealing with its solution, the scientist studied divergent series and built the theory of asymptotic expansions, developed the theory of integral invariants, studied the stability of orbits and the shape of celestial bodies. The fundamental discoveries of Poincaré concerning the behavior of integral curves of differential equations are also connected with the solution of problems of celestial mechanics. Poincaré published big number works on the theory of so-called automorphic functions, as well as on differential equations, topology, and probability theory.

Among his works are the 10-volume Course of Mathematical Physics (Cours de physique mathématique, 1889 et seq.), the monograph Maxwell's Theory and Hertzian Oscillations (Théorie de Maxwell et les oscillations hertziennes, 1907). Poincare is the author of a number of popular science works - The Value of Science (Valeur de la science, 1905) and Science and Method (Science et méthode, 1908).

Poincaré used the methods of mathematical physics to solve problems of heat conduction, electromagnetism, hydrodynamics, and the theory of elasticity. In 1904-1905 he formulated the principle of relativity, showed that it is impossible to detect absolute motion based on the concepts of the ether and the Maxwell-Lorentz equations. He proposed the first version of the relativistic theory of gravity. Poincare was a member of many academies of sciences, was awarded the medals of J. Sylvester, N.I. Lobachevsky and others.

Books (9)

Selected works. In three volumes. Volume I. New methods of celestial mechanics

This book includes the first two volumes of New Methods of Celestial Mechanics. The third volume will be included in the second book of this edition. This fundamental work of the remarkable French mathematician and physicist is published in Russian for the first time.

In the "New Methods of Celestial Mechanics" A. Poincare developed the theory of integral invariants, built the theory of asymptotic expansions, investigated periodic orbits, made a significant contribution to the solution of a number of other problems applied mathematics, mechanics, astronomy. This work, which became a classic, had a great influence on the development of the exact sciences and has not lost its significance even today.

Selected works. In three volumes. Volume II. New methods of celestial mechanics. Topology. number theory

This book includes the third volume of "New Methods of Celestial Mechanics", as well as the second part of the memoir "On the problem of three bodies and on the equations of dynamics", which served as the basis for the creation of "New methods of celestial mechanics".

In addition, the book includes the classic works of A. Poincaré on topology and memoirs "On geodesic lines on convex surfaces" and "On one geometric theorem”, which adjoin both the“ New methods of celestial mechanics ”and the topological works of A. Poincaré.

AT real volume also included arithmetic work A. Poincare "On ternary and quaternary cubic forms" and "On the arithmetic properties of algebraic curves".

Selected works. In three volumes. Volume III. Mathematics. Theoretical physics. Analysis of the mathematical and natural science works of Henri Poincaré

This book includes four large articles by A. Poincaré on linear differential equations and automorphic functions, as well as two articles on algebraic geometry, a number of Poincaré's papers on electrodynamics, relativity theory, quantum theory, and kinetic theory gases.

The volume ends with reviews of Poincare's mathematical and natural science works written by himself and other mathematicians and physicists: L. de Broglie, J. Hadamard, G. Julia, A. Weyl, G. Freudenthal and L. Schwartz.

Mathematics and Logic

The book contains articles by prominent French mathematicians A. Poincaré and L. Couture, arguing on the relationship between mathematics and logic.

Critical analysis of the ideas of "logicism" - a direction that aims to justify mathematics by reducing it initial concepts to the concepts of logic, - the outstanding mathematician and philosopher A. Poincare devoted the work "Mathematics and Logic", published in the XIII and XIV volumes of the journal "Revue de Methaphysique et de Morale" (Russian translation appeared in 1915).

Unlike the "logicists", Poincaré does not disassociate himself from philosophy and does not hide the connection of his ideas with the ideas of philosophers, in particular with Kant's doctrine of a priori synthetic judgments of mathematics. But, like the “logicists,” Poincaré, in his discussion of the question of intuition in mathematics, does not clearly separate what in his argument is caused by his philosophical prejudices from what in it is determined specifically by mathematical justifications and what has meaning and value regardless of his philosophical positions. Poincaré leaves the task of this distinction to his readers and critics. Speaking against "logicism", Poincaré had in mind not only the heuristic understanding of intuition, but also the logical-epistemological subject of the dispute. In his polemic with L. Couture, he means by “intuition” no longer “inspiration”, not “guess”, but direct, not based on logic, intellectual insights.

Science and hypothesis

Readers are offered one of the first translations into Russian of the book by the outstanding French mathematician, physicist and philosopher Henri Poincaré, dedicated to the philosophical and methodological problems of science.

The author explores the question of the significance of a hypothesis in science, clarifies the nature mathematical thinking, analyzes the concept of a mathematical quantity, principles, postulates and hypotheses in geometry, mechanics, physics, illustrating his positions with examples from the history of optics and electrodynamics. this work was the first of the famous works of A. Poincare related to the philosophy of science.