Euler's biography is brief. Leonhard Euler - a Swiss with a Russian soul

On April 15, 1707, a son was born into the family of the Basel pastor Paul Euler, named Leonard. From early childhood, his father prepared him for a spiritual career. According to Paul, a good priest had to have clearly developed logic, so he attached great importance to mathematics. Not only did the pastor himself love this exact science, but he was also friends with the famous mathematician Jacob Bernoulli. When Leonard was barely 13 years old, Jacob's younger brother, university professor Johann Bernoulli, noticed extraordinary mathematical abilities in the boy and invited him to come to his house on Saturdays, where they, together with Johann's sons, Daniel and Nikolai, solved complex mathematical problems in an easy and relaxed atmosphere.

At the age of 17, Leonard received his master's degree. Soon his first serious scientific work, “Dissertation in Physics on Sound,” was published, which received very flattering reviews from serious scientists. In 1725, the young master tried to get a vacant position as a professor of physics at the University of Basel, but even despite Bernoulli’s patronage, the applicant was told that he was too young for such an honorable position. In general, scientific vacancies were so tight in Switzerland at that time that even the children of professors could not find a worthy occupation. But scientific personnel were needed in neighboring Russia, where in 1724 Peter I established the country's first Academy. Daniil and Nikolai were the first to move to St. Petersburg, and already at the beginning of 1726, Leonard received a dispatch saying that, on the recommendation of the Bernoulli Herrs, he was invited to the position of adjunct in physiology with a salary of 200 rubles per year. Although this amount was not particularly large, it was significantly more than what the young mathematician could count on in his homeland. Therefore, already in April 1726, immediately upon receiving the advance, Euler left his native Switzerland. Then he still thought that it would be for a while.

In the capital Russian Empire The young specialist, who had learned to speak Russian quite fluently in less than a year, was immediately loaded with work, not always related to mathematics. The shortage of specialists led to the fact that the scientist was either charged with tasks on cartography, or required written consultations for shipbuilders and artillerymen, or was entrusted with the design of fire pumps, or was even charged with drawing up court horoscopes. Euler carefully carried out all these tasks, and only requests regarding astrology were categorically forwarded to the court astronomers. Predictions in Russia have always been a matter of increased danger and require special caution.

In 1731, Leonard became an academician and received a position as a professor of physics with a salary double the previous one. And two years later he took the position of professor of pure mathematics. Now he was owed 600 rubles a year. With such an income, one could already think about a family. At the end of 1733, the 26-year-old scientist married his peer and compatriot Katharina, daughter of the artist Georg Gsell, and found a small house on the Neva embankment. During their marriage, the wife gave birth to 13 children to Leonard, but only five of them survived, two daughters and three sons.

In 1735, Euler independently, without any outside help, completed an urgent government cartographic (according to other sources, astronomical) task in three days, which other academicians had been asking for for several months. However, such intensity of work could not but affect the scientist’s health: due to extreme overexertion, Leonhard Euler became blind in his right eye.

By that time, his name was already widely known in Russia. And the treatise “Mechanics, or the science of motion, in an analytical presentation” written in 1736 brought the scientist truly worldwide fame. It was from him theoretical mechanics has become an applied part of mathematics.

Over the decade and a half he spent in Russia, Euler wrote and published more than 90 major scientific works. He was also the main author of the academic “Notes” - the central Russian scientific bulletin of that time. The mathematician spoke at scientific seminars, gave public lectures, and performed a wide variety of tasks. Former teacher, Johann Bernoulli, wrote to him: “I devoted myself to the childhood of higher mathematics. You, my friend, will continue her development into maturity.” The fame of Euler as an excellent mathematician grew to such an extent that when in 1740 the position of director of its mathematical department was vacant at the Berlin Academy, the Prussian King Frederick himself invited the scientist to take this position.

By that time, a time of stagnation had begun in the St. Petersburg Academy of Sciences. After the death of Empress Anna Ioannovna, the young John IV became king. The regent Joanna Anna Leopoldovna, who ruled the empire at that time, did not pay any attention to the sciences, and the Academy gradually fell into disrepair. “Something dangerous was foreseen,” Euler later wrote in his autobiography. - After the death of the illustrious Empress Anna during the regency that followed...

the situation began to seem uncertain.” Therefore, the scientist took Frederick’s invitation as a gift of fate and immediately submitted a petition in which he wrote: “For this reason, I am forced, both for the sake of poor health and other circumstances, to seek a pleasant climate and accept the call made to me from His Royal Majesty of Prussia. For this reason, I ask the Imperial Academy of Sciences to most mercifully dismiss me and provide the necessary passport for travel for me and my family.” But, despite the general cool attitude towards science, the state administration was not at all eager to let go of an already recognized world luminary so easily. On the other hand, it was impossible not to let go. Therefore, as a result of short negotiations, we managed to obtain a promise from the mathematician, even while living in Berlin, to help Russia in every possible way. In return, he was awarded the title of honorary member of the Academy with a salary of 200 rubles. Finally, on May 29, 1741, all the documents were corrected, and already in June Euler, along with his entire family, his wife, children and four nephews, arrived in Berlin.

Here, as once in Russia, they also began to actively involve him in a variety of non-core work and projects. He was involved in organizing state lotteries, supervised the work of the mint, supervised the laying of a new water supply system and the organization of pensions. But Leonard’s relationship with King Frederick himself did not work out. The monarch did not like the mathematician, who was kind and smart, but not at all sociable. Indeed, Euler hated social receptions, balls and other entertainment events that interfered with scientific reasoning. When his wife managed to drag him into the theater, the mathematician would invent some complex example for himself, which he solved in his mind throughout the performance.

The scientist kept his word strictly, given before leaving Russia. He continued to publish his articles in Russian magazines, edited the works of Russian scientists, and purchased instruments and books for the St. Petersburg Academy. Young Russian scientists sent for internships lived in his house on full board. It was here that he met and became friends with a promising student of the Moscow “Spassky Schools” Mikhaila Lomonosov, in whom he most noted the “happy combination of theory and experiment.” When in 1747 the President of the Academy of Sciences, Count Razumovsky, asked him to give feedback on the articles of the young scientist, Euler rated them very highly. “All these dissertations,” he wrote in his report, “are not only good, but also very excellent, for he (Lomonosov) writes about very necessary physical and chemical matters, which to this day the wittiest people did not know and could not interpret, that he He did it with such success that I am completely confident in the validity of his explanations. In this case, Mr. Lomonosov must be given justice that he has an excellent talent for explaining physical and chemical phenomena. We should wish that other Academies would be able to produce such revelations as Mr. Lomonosov showed.” It must be said that Mikhail Vasilyevich, very arrogant, proud and difficult to communicate with, also loved his Berlin teacher until the end of his days, wrote him friendly letters and considered him one of the greatest scientists in the world.

Most of the terms, concepts and techniques introduced by Euler almost three centuries ago are still used by mathematicians today. But all this did not in any way affect the cold attitude of the ruling royalty of Prussia towards him. When the president of the Berlin Academy of Sciences, Maupertuis, died in 1759, Frederick II could not find a replacement for him for a long time. The French encyclopedist and simply very clever Jean D'Alembert, to whom the king turned first, refused the tempting offer, believing that there was a more worthy candidate for this post in Berlin. Finally, Friedrich reconciled himself and gave Euler the leadership of the Academy. But he categorically refused to give him the title of president.

Meanwhile, in Russia, Euler's authority, on the contrary, is becoming increasingly stronger. During seven years war Russian artillery accidentally destroyed the scientist's house in Charlottenburg (a suburb of Berlin). Field Marshal Saltykov, who learned about this, immediately compensated the scientist for all the losses caused. And when the news of the unsuccessful shelling reached Empress Elizabeth, she personally ordered another 4,000 rubles to be sent to her Berlin friend, which was a huge amount.

In 1762, Catherine II ascended the Russian throne, dreaming of establishing an “enlightened monarchy” in the country. She saw the return of a prominent mathematician to the country as one of her most important tasks. Therefore, Euler soon received a very interesting offer from her: to head the mathematics class, receiving the title of conference secretary of the Academy and a salary of 1800 rubles per year. “And if you don’t like it,” her instructions to the diplomatic representatives said, “she would be pleased to inform you of her conditions, so long as you don’t delay your arrival in St. Petersburg.”

Euler, indeed, was pleased to put forward counter conditions:

The post of vice-president of the Academy with a salary of 3,000 rubles;

- an annual pension of 1000 rubles to the wife in the event of his death;

- paid positions for his three sons, including the post of secretary of the Academy for the eldest.

Such insolence on the part of some mathematician outraged the representative of the imperial administration, the prominent Russian diplomat Count Vorontsov. However, the empress herself thought differently. “Mr. Euler’s letter to you,” she wrote to the count, “gave me great pleasure, because I learn from it about his desire to re-enter my service. Of course, I find him completely worthy of the desired title of Vice-President of the Academy of Sciences, but for this, some measures must be taken before I establish this title - I say I will, since until now it has not existed. In the current state of affairs, there is no money for a salary of 3,000 rubles, but for a person with such merits as Mr. Euler, I will add to the academic salary from state revenues, which together will amount to the required 3,000 rubles... I am sure that my Academy will be reborn from the ashes from such an important acquisition, and I congratulate myself in advance on having returned a great man to Russia.”

Having received assurances that all its terms and conditions have been accepted in full high level, Euler immediately wrote to Friedrich asking for his resignation. Perhaps because of the reluctance to let go of the prominent scientist, perhaps because of a negative attitude towards him, and most likely because of all this together, the king not only refused, but simply ignored Euler’s appeal without giving any answer to it. Euler wrote another petition. With the same result. Then the mathematician simply demonstratively stopped working at the Academy. Finally, Catherine herself turned to the King of Prussia with a request to release the scientist. Only after such high intervention did Frederick allow the mathematician to leave Prussia.

In July 1766, the scientist, along with 17 members of his household, arrived in St. Petersburg. Here he was immediately received by the Empress herself. And she not only accepted, but granted 8,000 rubles for the purchase of a house and furnishings, and even placed one of her best cooks at his complete disposal.

Already in Russia, Euler began work on one of his main works - “Universal Arithmetic”, also published under the titles “Principles of Algebra” and “ Full course algebra". Moreover, this book was initially published in Russian, and only two years later - in official scientific German. We can fully claim that all subsequent world algebra textbooks were based on this work. Immediately after him, Euler published two more large-scale monographs - “Optics” and “Integral Calculus”. When he was working hard on his new great work, “The New Theory of the Motion of the Moon,” tragedy happened. A large fire swept through St. Petersburg, destroying more than a hundred houses. Euler's house on Vasilyevsky Island also fell into this list. Fortunately, the scientist managed to save most of his manuscripts. The same thing that could not be saved, he is in short term restored by dictating the texts from memory.

Precisely by dictating. For the vision of the scientist, who spent the day and night doing calculations and calculations, was in the most critical condition. Ophthalmologists long ago diagnosed Euler with rapidly progressing cataracts in his only working left eye. Therefore, he had long been “writing” most of his works with the hands of a nimble boy tailor. Empress Catherine, who knew about this, specifically ordered the scientist from Berlin in 1771 to correct the vision of the scientist, the best specialist in this field - the personal ophthalmologist of the Austrian Emperor and the English King, Baron Wenzel. The operation was successful: Wenzel removed the cataract and warned the scientist that for the first few months he should stay away from bright light and stop reading so that the eye would get used to the new condition. But such torture was absolutely unbearable for the scientist. Within a few days, he, secretly from his family, took off the bandage and greedily attacked the fresh scientific journals. The result was immediate: the scientist soon lost his sight again, this time completely. At the same time, his labor productivity not only did not decrease, but even increased. An incorrigible optimist, he sometimes said with a bit of humor that the loss of vision benefited him: he stopped being distracted by external beauties not related to mathematics.

Soon fate dealt him another serious blow. In 1773, his beloved wife Katharina, with whom he lived in a happy marriage for 40 years, died. But this loss did not knock him out of the saddle. Three years later he married a second time. On Katharina's half-sister Salome. She reminded Leonard of his late wife in everything and until the end of the scientist’s life she was his faithful assistant.

In the early 1780s, Euler increasingly began to complain of headaches and general weakness. On September 7, 1883, he had an afternoon conversation with academician Andrei Leksel. Both mathematicians and astronomers, they discussed the recently discovered planet Uranus and its orbit. Suddenly Euler felt ill. He only managed to say: “I’m dying,” after which he immediately lost consciousness. A few hours later he was gone. Doctors determined that death occurred from a cerebral hemorrhage.

The scientist was buried in St. Petersburg, at the Lutheran Smolensk cemetery. The words were carved on the tombstone: “Here lie the mortal remains of the wise, just, famous Leonhard Euler.”

The mathematician's children remained in Russia. The eldest son, also a talented mathematician and mechanic Johann Euler (1734-1800), as Empress Catherine promised, was secretary of the Imperial Academy of Sciences. The younger, Christopher (1743-1808), rose to the rank of lieutenant general and commanded the Sestroretsk arms factory. Grandson, Alexander Khristoforovich (1773-1849) became an artillery general, a hero Patriotic War 1812. Another descendant, who returned to the homeland of his ancestors, Sweden, Hans Karl August Simon von Euler-Helpin (1873-1964) became a famous biochemist, a foreign member of the USSR Academy of Sciences, and a Nobel Prize laureate in chemistry for 1929. Another Nobel Prize, only in 1970, was received by his son, Swedish biologist Ulf von Euler (1905-1983).

There are many monuments erected to Leonhard Euler. Institutes, streets, and scientific awards bear his name. Stamps and coins have been printed in his honor, and an asteroid and a crater on the Moon have been named. But perhaps the most original monument to the scientist can be found in children's notebooks. After all, schoolchildren often try to solve well-known problems: how to move a chess knight through all the cells of a drawn square without passing through the same cell twice, or how to similarly cross several rivers over several bridges. At the same time, they often don’t even realize that it was the great Russian mathematician Leonhard Euler who came up with these problems, and not only thought of them, but also found an exhaustive algorithm for solving them almost three centuries ago. Whose name in Russia was Leonty.

Leonhard Euler, the son of a pastor, was born and took his first steps in the Swiss city of Basel in 1707 on April 15th.

The boy received his primary education at home. His father, Pastor Pavel, prepared his son for the spiritual field from an early age.

The father invested all kinds of knowledge into the boy, hoping for a comprehensive upbringing of his son. The child showed an aptitude for exact sciences from the first steps of studying them. Pavel, who was interested in mathematics, tried to pass on his knowledge to his young son.

The beginning of the career of a genius

The foundation of knowledge Leonard received from his father turned out to be very voluminous and strong. Further studies at the gymnasium of the city of Basel and admission to the University of Liberal Arts, at the age of 13, the result of home preparation.

All subjects were easy for Euler. At the lectures of Johann Bernoulli, Euler immediately attracted the attention of the teacher with his abilities. For a talented student, the world-famous Swiss mathematician, the most famous representative of the Bernoulli family, sets an individual course of study.

Bernoulli introduces Euler to the works of mathematical geniuses, teaches him to understand and analyze mathematical calculations. Thanks to the teaching methods of Johann Bernoulli, Leonhard Euler was awarded his first Master of Arts degree at the age of sixteen. He presented the work of an analytical comparison of the works of Descartes and Newton in Latin.

Euler's further scientific research is associated with the Bernoulli brothers. Their departure to the St. Petersburg Academy of Sciences helped Euler take new steps. Bernoulli informed Leonard about the possibility of obtaining a position as a physiologist at the academy at the medical department. Euler enters the University of Basel at the Faculty of Medicine, but he does not leave mathematics.

Scientific activities in St. Petersburg and Berlin

The extraordinary breadth of interests and creative productivity served as the basis for the rise of the genius of Leonhard Euler in St. Petersburg. Living conditions allowed Euler to devote all his time to his favorite works in the field of mathematics and physics. During this period, the St. Petersburg Academy of Sciences received the status of the main center of mathematics of world significance.

Leonhard Euler's position in the Academy of Sciences improved: from 1727 to 1740, Euler, who took the post of head of the department of mathematics, published his works on geometry, analytical mechanics, and arithmetic. For publishing a work on sea tides, the scientist receives a prize from the French Academy of Sciences.

The beginning of the revival of the Berlin Society of Sciences, whose ancestor was Leibniz, a German philosopher, mathematician, lawyer, diplomat, Prussian King Frederick II began with the invitation of talented scientists. Euler was one of the first scientists to receive an invitation to the post of dean of the mathematics department.

Leonhard Euler publishes several works on mathematics. The scientist devoted almost all of his mathematical works to mathematical analysis. These treatises were formulated so simply and clearly that they are used by mathematicians of the present day.

Return to St. Petersburg

While working in Berlin, Euler did not lose touch with Russia. He corresponds with Lomonosov, his friend, academician of the St. Petersburg Academy of Sciences Goldbach. The scientist could not stop thinking about Russia. In 1766, he accepted the invitation of the Empress and returned to St. Petersburg to the Academy of Sciences.

Euler's sons

senior Johann Albrecht as academician in the field of physics,
Karl accepted a leading position in one of the medical authorities,
the youngest son Christopher came to his father from Berlin after the intervention of the Empress. The Sestroretsk arms factory received a new director in the person of the youngest son of the great scientist.

Last days of a genius

Continuous work, teaching students, writing papers took its toll on the previously injured eye. The scientist began to lose his sight. However, the abilities of a genius, his unique memory helped him in his work. He dictated his articles and thoughts on geometry and mathematics. Their number reached 380 from 1769 to 1793.

From the moment the scientist became a scientist until his last days, he published over 900 scientific works. Each of them consists of brilliant thoughts and conclusions that are applied by modern users in their original writing. Works of recent years:

"On Orthogonal Trajectories", the most important in the mathematical field (1769);

work “On bodies whose surface can be turned into a plane” (1771);

unique works on map projections, in which Euler was the first to scientifically substantiate the choice of section parallels in conic projections.

Euler's works concerned various fields of science. Only this genius, without much difficulty, managed to create a unified system of such mathematical disciplines as algebra, trigonometry, geometry, and number theory. Many scientific discoveries were added by Euler to this system. He created new mathematical disciplines, which are taught to students unchanged to this day.

His scientific research was extensive not only in mathematics. Astronomy, cartography, and engineering also received many discoveries and developments thanks to Euler's research. Leonhard Euler continued his scientific research until his last days, being completely blind. Death occurred on September 18 (29), 1783, as a result of a stroke, surrounded by his assistants, professors Leksel and Kraft.

EULER, LEONARD(Euler, Leonhard) (1707–1783) is one of the top five greatest mathematicians of all time. Born in Basel (Switzerland) on April 15, 1707 in the family of a pastor, he spent his childhood in a nearby village where his father received a parish. Here, in the lap of rural nature, in the pious atmosphere of a modest parsonage, Leonard received his initial education, which left a deep imprint on his entire subsequent life and worldview. Education at the gymnasium in those days was short. In the fall of 1720, thirteen-year-old Euler entered the University of Basel, three years later he graduated from the lower faculty of philosophy and, at the request of his father, enrolled in the theological faculty. In the summer of 1724, at a one-year university act, he read a speech in Latin on a comparison of Cartesian and Newtonian philosophy. Showing an interest in mathematics, he attracted the attention of Johann Bernoulli. The professor began to personally supervise the young man’s independent studies and soon publicly admitted that he expected the greatest success from the insight and sharpness of mind of young Euler.

Back in 1725, Leonhard Euler expressed a desire to accompany the sons of his teacher to Russia, where they were invited to the St. Petersburg Academy of Sciences, which was then opening at the behest of Peter the Great. On next year I received an invitation myself. He left Basel in the spring of 1727 and after a seven-week journey arrived in St. Petersburg. Here he was first enrolled as an adjunct in the department of higher mathematics, in 1731 he became an academician (professor), receiving the department of theoretical and experimental physics, and then (1733) the department of higher mathematics.

Immediately upon his arrival in St. Petersburg, he completely immersed himself in scientific work and then amazed everyone with the fruitfulness of his work. His numerous articles in academic yearbooks, initially devoted primarily to problems of mechanics, soon brought him worldwide fame, and later contributed to the glory of St. Petersburg academic publications in Western Europe. A continuous stream of Euler's writings was published from then on in the proceedings of the Academy for a whole century.

Along with theoretical research, Euler devoted a lot of time and practical activities, fulfilling numerous orders from the Academy of Sciences. Thus, he examined various instruments and mechanisms, participated in a discussion of methods for raising the large bell in the Moscow Kremlin, etc. At the same time, he lectured at an academic gymnasium, worked at an astronomical observatory, and collaborated in the publication of St. Petersburg Vedomosti, carried out extensive editorial work in academic publications, etc. In 1735, Euler took part in the work of the Geographical Department of the Academy, making a major contribution to the development of cartography in Russia. Euler's tireless work was not interrupted even by the complete loss of his right eye, which befell him as a result of illness in 1738.

In the fall of 1740, the internal situation in Russia became more complicated. This prompted Euler to accept the invitation of the Prussian king, and in the summer of 1741 he moved to Berlin, where he soon headed a mathematical class at the reorganized Berlin Academy of Sciences and Letters. The years Euler spent in Berlin were the most fruitful in his scientific activity. This period also marks his participation in a number of heated philosophical and scientific discussions, including the principle of least action. The move to Berlin did not, however, interrupt Euler’s close ties with the St. Petersburg Academy of Sciences. He continued to regularly send his works to Russia, participated in all kinds of examinations, taught students sent to him from Russia, selected scientists to fill vacant positions at the Academy, and carried out many other assignments.

Euler's religiosity and character did not correspond to the environment of the “freethinking” Frederick the Great. This led to a gradual deterioration in the relationship between Euler and the king, who was well aware that Euler was the pride of the Royal Academy. IN last years During his Berlin life, Euler actually acted as president of the Academy, but never received this position. As a result, in the summer of 1766, despite the king’s resistance, Euler accepted the invitation of Catherine the Great and returned to St. Petersburg, where he then remained until the end of his life.

In the same 1766, Euler almost completely lost sight in his left eye. However, this did not prevent the continuation of his activities. With the help of several students who wrote under his dictation and compiled his works, the half-blind Euler prepared several hundred more scientific works in the last years of his life.

At the beginning of September 1783, Euler felt slightly unwell. On September 18, he was still engaged in mathematical research, but suddenly lost consciousness and, in the apt expression of the panegyrist, “stopped calculating and living.”

He was buried at the Smolensk Lutheran Cemetery in St. Petersburg, from where his ashes were transferred in the fall of 1956 to the necropolis of the Alexander Nevsky Lavra.

The scientific legacy of Leonhard Euler is colossal. He is responsible for classic results in mathematical analysis. He advanced its rationale, significantly developed integral calculus, methods for integrating ordinary differential equations and partial differential equations. Euler owns the famous six-volume course of mathematical analysis, including Introduction to Infinitesimal Analysis, Differential calculus And Integral calculus(1748–1770). Many generations of mathematicians around the world studied from this “analytic trilogy.”

Euler obtained the basic equations of the calculus of variations and determined the ways of its further development, summing up the main results of his research in this area in the monograph Method for finding curved lines that have maximum or minimum properties(1744). Euler's significant contributions were to the development of function theory, differential geometry, computational mathematics, number theory. Euler's two-volume course Complete Guide in algebra(1770) went through about 30 editions in six European languages.

Fundamental results belong to Leonhard Euler in rational mechanics. He was the first to give a consistent analytical presentation of mechanics material point, having reviewed in his two-volume Mechanics(1736) the movement of a free and unfree point in emptiness and in a resisting medium. Later, Euler laid the foundations of kinematics and rigid body dynamics, obtaining the corresponding general equations. The results of these studies by Euler are collected in his Theories of movement solids (1765). The set of dynamic equations representing the laws of momentum and angular momentum was proposed by the greatest historian of mechanics, Clifford Truesdell, to be called “Eulerian laws of mechanics.”

Euler's article was published in 1752 Discovery of a new principle of mechanics, in which he formulated in general view Newton's equations of motion in a fixed coordinate system, opening the way for the study of mechanics continuum. On this basis, he derived the classical equations of hydrodynamics for an ideal fluid, finding a number of their first integrals. His work on acoustics is also significant. At the same time, he was responsible for the introduction of both “Eulerian” (associated with the observer’s reference system) and “Lagrangian” (in the reference system accompanying the moving object) coordinates.

Euler's numerous works on celestial mechanics, among which the most famous is his New theory of the moon's movement(1772), which significantly advanced the most important branch of celestial mechanics for navigation of that time.

Along with general theoretical research, Euler contributed to a number of important works in applied sciences. Among them, the first place is occupied by the theory of the ship. Issues of buoyancy, stability of a ship and its other seaworthiness were developed by Euler in his two-volume Ship science(1749), and some questions of the structural mechanics of a ship - in subsequent works. He gave a more accessible presentation of the theory of the ship in Complete theory of the structure and navigation of ships(1773), which was used as a practical guide not only in Russia.

Euler's comments to New beginnings for artillery B. Robins (1745), which, along with his other works, contained important elements of external ballistics, as well as an explanation of the hydrodynamic “D'Alembert paradox”. Euler laid down the theory of hydraulic turbines, the impetus for the development of which was the invention of the reactive “Segner wheel”. He also created the theory of stability of rods under longitudinal loading, which acquired particular importance a century later.

Euler's many works were devoted to various issues of physics, mainly geometric optics. The three volumes published by Euler deserve special mention. Letters to a German princess about various subjects of physics and philosophy(1768–1772), which subsequently went through about 40 editions in nine European languages. These “Letters” were a kind of educational manual on the basics of science of that time, although their philosophical side did not correspond to the spirit of the Enlightenment.

Modern five-volume Mathematical Encyclopedia indicates twenty mathematical objects (equations, formulas, methods) that now bear Euler's name. A number of fundamental equations of hydrodynamics and solid mechanics also bear his name.

Along with numerous scientific results proper, Euler has the historical merit of creating a modern scientific language. He is the only author of the mid-18th century whose works can be read even today without any difficulty.

The St. Petersburg archive of the Russian Academy of Sciences also stores thousands of pages of Euler’s unpublished research, mainly in the field of mechanics, big number his technical expertise, mathematical " notebooks"and colossal scientific correspondence.

His scientific authority during his lifetime was limitless. He was an honorary member of all the largest academies and scientific societies in the world. The influence of his works was very significant in the 19th century. In 1849, Carl Gauss wrote that “the study of all of Euler’s works will forever remain the best, irreplaceable, school in various fields of mathematics.”

The total volume of Euler's works is enormous. More than 800 of his published scientific works amount to about 30,000 printed pages and consist mainly of the following: 600 articles in publications St. Petersburg Academy sciences, 130 articles published in Berlin, 30 articles in various European journals, 15 memoirs that received prizes and encouragements from the Paris Academy of Sciences, and 40 books of individual works. All this will amount to 72 volumes close to completion Complete Works (Opera omnia) by Euler, published in Switzerland since 1911. All works are printed here in the language in which they were originally published (i.e. Latin and French, which were in the middle of the 18th century. the main working languages of the St. Petersburg and Berlin Academies, respectively). To this will be added another 10 volumes of it Scientific correspondence, which began publication in 1975.

It should be noted that Euler was of particular importance to the St. Petersburg Academy of Sciences, with which he was closely associated for over half a century. “Together with Peter I and Lomonosov,” wrote academician S.I. Vavilov, “Euler became the good genius of our Academy, who determined its glory, its strength, its productivity.” It can also be added that the affairs of the St. Petersburg Academy were conducted for almost a whole century under the leadership of Euler’s descendants and students: the indispensable secretaries of the Academy from 1769 to 1855 were successively his son, son-in-law and great-grandson.

He raised three sons. The eldest of them was a St. Petersburg academician in the department of physics, the second was a court doctor, and the youngest, an artilleryman, rose to the rank of lieutenant general. Almost all of Euler's descendants adopted in the 19th century. Russian citizenship. Among them were senior officers Russian army and navy, as well as statesmen and scientists. Only in Time of Troubles beginning of the 20th century many of them were forced to emigrate. Today, Euler's direct descendants bearing his surname still live in Russia and Switzerland.

(It should be noted that Euler’s last name in its true pronunciation sounds like “Oyler.”)

Editions: Collection of articles and materials. M. – L.: Publishing House of the USSR Academy of Sciences, 1935; Digest of articles. M.: Publishing House of the USSR Academy of Sciences, 1958.

Gleb Mikhailov

Euler was born on April 15, 1707 in Basel, Switzerland. His father, Paul Euler, was a pastor of the Reformed Church. His mother's father, Margaret Brooker, was also a pastor. Leonard had two younger sisters - Anna Maria and Maria Magdalena. Soon after the birth of their son, the family moved to the town of Rien. The boy's father was a friend of Johann Bernoulli, a famous European mathematician who had a great influence on Leonard. At the age of thirteen, Euler Jr. entered the University of Basel, and in 1723 received a master's degree in philosophy. In his dissertation, Euler compares the philosophies of Newton and Descartes. Johann Bernoulli, who gave the boy private lessons on Saturdays, quickly recognizes the boy's outstanding abilities in mathematics and convinces him to leave his early theology and concentrate on mathematics.

In 1727, Euler took part in a competition organized by the Paris Academy of Sciences for the best technique for installing ship masts. Leonard takes second place, while first place goes to Pierre Bouguer, who would later become known as the “father of shipbuilding.” Euler takes part in this competition every year, receiving twelve of these prestigious awards in his life.

Saint Petersburg

On May 17, 1727, Euler entered the medical department of the Imperial Russian Academy of Sciences in St. Petersburg, but almost immediately transferred to the Faculty of Mathematics. However, due to unrest in Russia, on June 19, 1741, Euler was transferred to the Berlin Academy. The scientist will serve there for about 25 years, writing more than 380 scientific articles during this time. In 1755 he was elected a foreign member of the Royal Swedish Academy of Sciences.

In the early 1760s Euler receives an offer to teach science to the Princess of Anhalt-Dessau, to whom the scientist will write more than 200 letters, included in the extremely popular collection “Euler’s Letters to various items natural philosophy addressed to a German princess." The book not only clearly demonstrates the scientist's ability to reason on all sorts of topics in the field of mathematics and physics, but is also an expression of his personal and religious views. The interesting thing is that this book is better known than all of his mathematical works. It was published both in Europe and in the United States of America. The reason for such popularity of these letters was amazing ability Euler to convey scientific information to the common man in an accessible form.

The uniqueness of this work also lay in the fact that in 1735 the scientist became almost completely blind in his right eye, and in 1766 his left eye was affected by cataracts. But, even despite this, he continued his work and in 1755 wrote on average one mathematical article per week.

In 1766, Euler accepted the offer to return to the St. Petersburg Academy, and would spend the rest of his life in Russia. However, his second visit to this country turns out to be not so successful for him: in 1771, a fire destroys his house, and, after this, in 1773 he loses his wife Katharina.

Personal life

January 7, 1734 Euler marries Katharina Gsell. In 1773, after 40 years of family life, Katharina dies. Three years later, Euler marries her half-sister, Salome Abigail Gsell, with whom he will spend the rest of his life.

Death and legacy

On September 18, 1783, after a family dinner, Euler suffered a cerebral hemorrhage, after which, a few hours later, he died. The scientist was buried at the Smolensk Lutheran cemetery on Vasilyevsky Island, next to his first wife Katarina. In 1837 Russian Academy Sciences placed a bust on the grave of Leonhard Euler on a pedestal in the shape of a rector’s chair, next to the gravestone. In 1956, on the 250th anniversary of the scientist’s birth, the monument and remains were moved to the 18th-century cemetery at the Alexander Nevsky Monastery.

In memory of his enormous contribution to science, Euler's portrait appeared on the Swiss 10-franc banknotes of the sixth series, as well as on a number of Russian, Swiss and German marks. The asteroid 2002 Euler is named in his honor. On May 24, the Lutheran Church honors his memory according to the calendar of saints, since Euler was a staunch adherent of Christianity and fervently believed in the biblical commandments.

Mathematical notation system

Among all of Euler's various works, the most notable is his presentation of function theory. He was the first to introduce the notation f(x) – the function “f” given the argument “x”. Euler also defined the mathematical notation for trigonometric functions in the form in which we know them now, introduced the letter “e” for the base natural logarithm(known as "Euler's number"), the Greek letter "Σ" for the total, and the letter "i" for the imaginary unit.

Analysis

Euler approved the application exponential function and logarithms in analytical proofs. He discovered a method for decomposing various logarithmic functions V power series, and also successfully proved the application of logarithms to negative and complex numbers. Thus, Euler significantly expanded the mathematical application of logarithms.

This great mathematician also explained in detail the theory of higher transcendental functions and presented an innovative approach to solve quadratic equations. He discovered the technique of calculating integrals using complex limits. He also developed a formula for the calculus of variations, called the Euler-Lagrange equation.

Number theory

Euler proved Fermat's little theorem, Newton's identities, Fermat's theorem on the sum of two squares, and also significantly advanced the proof of Lagrange's theorem on the sum of four squares. He made valuable additions to the theory of perfect numbers, on which more than one mathematician worked with enthusiasm.

Physics and astronomy

Euler made a significant contribution to the solution of the Euler-Bernoulli beam equation, which became one of the main equations used in engineering. The scientist used his analytical methods not only in classical mechanics, but also in solving celestial problems. For his achievements in the field of astronomy, Euler received numerous awards from the Paris Academy. Based on knowledge of the true nature of comets and calculating the parallax of the Sun, the scientist clearly calculated the orbits of comets and other celestial bodies. Using these calculations, accurate tables of celestial coordinates were compiled.

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, differential geometry, number theory, approximate calculations, celestial mechanics, mathematical physics, optics, ballistics, shipbuilding, music theory, etc., which had a significant impact on the development of science. In 1726 was invited to work in St. Petersburg, and then moved to live in Russia. In - and starting from the years. was an academician of the St. Petersburg Academy of Sciences (in - years he worked in Berlin, remaining an honorary member of the St. Petersburg Academy).

Contribution to science

Euler is one of the geniuses whose work has become the property of all mankind. Until now, schoolchildren in all countries study trigonometry and logarithms in the form that Euler gave them. Students study higher mathematics using manuals, the first examples of which were Euler's classical monographs. He was primarily a mathematician, but he knew that the soil on which mathematics flourishes is practical activity.

He left important works in various branches of mathematics, mechanics, physics, astronomy and a number of applied sciences. It is difficult to even list all the industries in which the great scientist worked.

“Read, read Euler, he is our common teacher,” Laplace liked to repeat. And Euler’s works were read with great benefit - or rather, studied - by the “king of mathematicians” Carl Friedrich Gauss, and almost all the famous scientists of the last two centuries.

Euclidean geometry

Euler points;

Graph theory

Solution of the problem of the seven bridges of Königsberg.

Topology

Euler's formula for polyhedra.

Computational Mathematics

Euler's method of broken lines, one of the simplest methods for approximate solution of differential equations, widely used until very recent years.

Combinatorics

Elementary theory of partitions;
Method of generating functions.

Mathematical analysis

Euler integrals: beta function and Euler gamma function.

Mechanics

Euler's equations describing the motion of an inviscid medium;
Euler angles when describing the motion of bodies;
Euler's kinematic formula for the distribution of velocities in a solid;
Euler - Poisson equations of rigid body dynamics;
The case of Euler integrability in rigid body dynamics.

Engineering

Involute profile in gears.

Biography

Throughout his stay in Berlin, Euler continued to remain an honorary member of the St. Petersburg Academy. As he promised upon leaving St. Petersburg, he continued to publish many of his works in publications of the St. Petersburg Academy; edited the mathematical sections of Russian journals; purchased books and instruments from St. Petersburg; In his apartment, on full board, of course, for the appropriate payment (which, by the way, the Academy office sent with a great delay), young Russian scientists sent for an internship lived for years.

A four-volume collected works of I. Bernoulli was published in the city. Sending him from Basel to Euler in Berlin, the old scientist wrote to his student: “I devoted myself to the childhood of higher mathematics. You, my friend, will continue her development into maturity.”

Euler lived up to his teacher's hopes. One by one they come out scientific works of colossal importance: “Introduction to the Analysis of Infinites” (g.), “Marine Science” (g.), “The Theory of the Motion of the Moon” (g.), “Manual on Differential Calculus” (1755) - not to mention dozens articles on certain private issues published in publications of the Berlin and St. Petersburg Academies.

They gained enormous popularity in the 18th and partly in the 19th centuries. Euler's “Letters on various physical and philosophical matters, written to a certain German princess...”, which went through over 40 editions in 10 languages.

Euler did not seek to surprise the reader; he, together with the reader, seems to go through the entire path leading to the discovery, showing the entire chain of reasoning and conclusions leading to the result. He knows how to put himself in the position of a student; he knows where the student may encounter difficulty - and strives to prevent this difficulty.

In the city, Euler, for the first time in history, found formulas for determining the critical load during compression of an elastic rod. However, in those years these formulas could not find practical application. Almost a hundred years later, when in many countries - and especially in England - they began to build railways, it was necessary to calculate the strength of railway bridges. Euler's model brought practical benefits in conducting experiments.

Euler produced an average of 800 quarto pages per year. This would be a lot even for a novelist; For a mathematician, such a volume of scientific works, very clearly presented, including mechanics and number theory, analysis and music, astronomy and physics, probability theory and optics... - simply does not fit in the mind! However, in the city, Catherine II, who received the nickname “The Great,” ascended the Russian throne and pursued a policy of enlightened absolutism. She well understood the importance of science both for the prosperity of the state and for her own prestige; carried out a number of important at that time transformations in the system of public education and culture.

Frederick II “allocated” only 13 thousand thalers a year to the Berlin Academy, and Catherine II allocated over 60 thousand rubles - a more significant amount. The Empress ordered that Euler be offered management of a mathematical class (department), the title of conference secretary of the Academy and a salary of 1800 rubles per year. “And if you don’t like it,” the letter said, “he would be pleased to inform you of his conditions, so long as he doesn’t hesitate to come to St. Petersburg.”

Euler submits a request for dismissal from service to Friedrich. He doesn't answer. Euler writes a second time - but Friedrich does not even want to discuss the issue of Euler's departure. In response to this, he stops working for the Berlin Academy. On April 30, Mr. Friedrich finally allows the great scientist to leave for Russia. Immediately upon his arrival, Euler was received by the Empress. Catherine showered the scientist with favors: she granted money for the purchase of a house on Vasilievsky Island and for the purchase of furnishings, provided one of her cooks for the first time, and instructed him to prepare ideas for the reorganization of the Academy.

After returning to St. Petersburg, Euler developed a cataract in his second, left eye - he stopped seeing. However, this did not affect its performance. He dictates his work to a tailor boy, who wrote everything down in German.

Two serious events occurred in Euler's life. In May, a large fire broke out in St. Petersburg, destroying hundreds of buildings, including Euler’s house and almost all of his property. The scientist himself was barely saved by the Swiss artisan Peter Grimm, who had arrived earlier from Basel. All manuscripts were saved from fire; Only part of the “New Theory of the Motion of the Moon” burned down, but it was quickly restored with the help of Euler himself, who retained a phenomenal memory into old age. The blind old man had to move to another house, the arrangement of rooms and objects in which was unfamiliar to him. However, this trouble turned out to be, fortunately, only temporary.

In September of the same year, the famous German ophthalmologist Baron Wenzel arrived in St. Petersburg, who agreed to perform an operation on Euler - and removed a cataract from his left eye. Nine local medical luminaries prepared to observe the work of the visiting celebrity. But the whole operation took 3 minutes - and Euler began to see again! A skilled ophthalmologist prescribed to protect the eye from bright light, not to write, not to read - just gradually get used to the new state. But how could Euler “not calculate”? A few days after the operation, he removed the bandage. And soon he lost his sight again. This time it's final. However, oddly enough, he reacted to the event with the greatest calm. His scientific productivity even increased: without assistants, he could only think, and when assistants came, he dictated to them or wrote with chalk on the table, by the way, quite legibly, because he could somehow distinguish white from black.

In the city, on the recommendation of D. Bernoulli, his student Niklaus Fuss came to St. Petersburg from Basel. This was a great success for Euler. Fuss had a rare combination of mathematical talent and the ability to conduct practical affairs, which gave him the opportunity to immediately take charge of Euler's mathematical works after his arrival. Soon Fuss married Euler's granddaughter. In the next ten years - until his death - Euler dictated his works to him.

Euler's wife, with whom he lived for almost 40 years, died in the city. This was a great loss for the scientist, who was sincerely attached to his family. In the last years of his life, the scientist continued to work hard, using the “eyes of his eldest son” and a number of his students to read.

In September, the scientist began to feel headaches and weakness. September 7 () after lunch spent with family, talking with A. I. Leksel about recently open planet Uranus and its orbit, he suddenly felt ill. Euler managed to say “I’m dying” - and lost consciousness. A few hours later, without regaining consciousness, he died of a cerebral hemorrhage. “Euler stopped living and calculating.” He was buried at the Smolensk cemetery in St. Petersburg. The inscription on the monument read: “To Leonard Euler - St. Petersburg Academy.”

In 1955 the ashes of the great mathematician and the tombstone were transferred to the “Necropolis of the 18th century.” at the Lazarevskoye Cemetery, Kvant, No. 11, 1983

B. Delaunay, "Leonard Euler" Kvant, No. 5, 1974

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