Brief biography of Leonard Euler. The great mathematician Euler Leonard: achievements in mathematics, interesting facts, short biography Interesting facts from the life of Euler

Switzerland (1707-1727)

University of Basel in the 17th-18th centuries

Over the next two years, young Euler wrote several scientific papers. One of them, “Thesis in Physics on Sound,” which received a favorable review, was submitted to the competition to fill the unexpectedly vacant position of professor of physics at the University of Basel (). But, despite the positive review, 19-year-old Euler was considered too young to be included in the list of candidates for the professorship. It should be noted that the number of scientific vacancies in Switzerland was very small. Therefore, the brothers Daniel and Nikolai Bernoulli left for Russia, where the organization of the Academy of Sciences was just underway; they promised to work there for a position for Euler.

Euler was distinguished by his phenomenal efficiency. According to contemporaries, for him living meant doing mathematics. And the young professor had a lot of work: cartography, all kinds of examinations, consultations for shipbuilders and artillerymen, drawing up training manuals, designing fire pumps, etc. He was even required to compile horoscopes, which Euler forwarded with all possible tact to the staff astronomer. But all this does not prevent him from actively conducting his own research.

During the first period of his stay in Russia, he wrote more than 90 major scientific works. A significant part of the academic “Notes” is filled with the works of Euler. He made reports at scientific seminars, gave public lectures, and participated in the implementation of various technical orders from government departments.

This high assessment was not hindered even by the fact that Lomonosov did not write mathematical works and did not master higher mathematics.

Portrait of 1756 by Emanuel Handmann (Kunstmuseum, Basel)

According to contemporaries, Euler remained a modest, cheerful, extremely sympathetic person all his life, always ready to help others. However, relations with the king do not work out: Frederick finds the new mathematician unbearably boring, not at all secular, and treats him dismissively. In 1759, Maupertuis, president of the Berlin Academy of Sciences, died. King Frederick II offered the post of president of the Academy to D'Alembert, but he refused. Friedrich, who did not like Euler, nevertheless entrusted him with the leadership of the Academy, but without the title of president.

Euler returns to Russia, now forever.

Russia again (1766-1783)

Euler worked actively until his last days. In September 1783, the 76-year-old scientist began to experience headaches and weakness. On September 7 () after lunch spent with his family, talking with Academician A. I. Leksel about the recently discovered planet Uranus and its orbit, he suddenly felt unwell. Euler managed to say: “I’m dying,” and lost consciousness. A few hours later, without regaining consciousness, he died of a cerebral hemorrhage.

“He stopped calculating and living,” Condorcet said at the funeral meeting of the Paris Academy of Sciences (fr. Il cessa de calculer et de vivre ).

Euler was a caring family man, willingly helped colleagues and young people, and generously shared his ideas with them. There is a known case when Euler delayed his publications on the calculus of variations so that the young and then unknown Lagrange, who independently came to the same discoveries, could publish them first. Lagrange always admired Euler both as a mathematician and as a person; he said: “If you really love mathematics, read Euler.”

Contribution to science

Euler left important works in various branches of mathematics, mechanics, physics, astronomy and a number of applied sciences. From the point of view of mathematics, the 18th century is the century of Euler. If before him achievements in the field of mathematics were scattered and not always coordinated, Euler was the first to link analysis, algebra, trigonometry, number theory and other disciplines into a single system, and added many of his own discoveries. A significant part of mathematics has since been taught “according to Euler.”

Thanks to Euler, mathematics included the general theory of series, the amazingly beautiful “Euler formula”, the operation of comparison over an integer modulo, the complete theory of continued fractions, the analytical foundation of mechanics, numerous methods of integration and solving differential equations, number e, designation i for the imaginary unit, the gamma function with its environment and much more.

Essentially, it was he who created several new mathematical disciplines - number theory, calculus of variations, theory of complex functions, differential geometry of surfaces, special functions. Other areas of his work: Diophantine analysis, astronomy, optics, acoustics, statistics, etc. Euler's knowledge was encyclopedic; in addition to mathematics, he deeply studied botany, medicine, chemistry, music theory, and many European and ancient languages.

• Dispute with D'Alembert about the properties of the complex logarithm.
• Dispute with English optician John Dollond about whether it was possible to create an achromatic lens.

In all the cases mentioned, Euler defended the correct position.

Number theory

He refuted Fermat's hypothesis that all numbers of the form are prime; It turned out that it is divisible by 641.

where is real. Euler derived an expansion for it:

where the product is taken over all prime numbers. Thanks to this, he proved that the sum of a series of inverse primes diverges.

The first book on the calculus of variations

Geometry

In elementary geometry, Euler discovered several facts not noticed by Euclid:

• The three altitudes of a triangle intersect at one point (orthocenter).
• In a triangle, the orthocenter, the center of the circumscribed circle and the center of gravity lie on one straight line - the “Euler straight line”.
• The bases of the three altitudes of an arbitrary triangle, the midpoints of its three sides and the midpoints of the three segments connecting its vertices with the orthocenter all lie on the same circle (Eulerian circle).
• The number of vertices (B), faces (G) and edges (P) of any convex polyhedron are related by the simple formula: B + G = P + 2.

The second volume of Introduction to Infinitesimal Analysis () is the world's first textbook on analytical geometry and the foundations of differential geometry. The term affine transformations was first introduced in this book along with the theory of such transformations.

When solving combinatorial problems, he deeply studied the properties of combinations and permutations and introduced Euler numbers into consideration.

Other areas of mathematics

• Graph theory began with Euler's solution to the problem of the seven bridges of Königsberg.
• Polyline method Euler.

Mechanics and mathematical physics

Many of Euler’s works are devoted to mathematical physics: mechanics, hydrodynamics, acoustics, etc. In 1736, the treatise “Mechanics, or the science of motion, in an analytical presentation” was published, marking a new stage in the development of this ancient science. 29-year-old Euler abandoned the traditional geometric approach to mechanics and laid a strict analytical foundation for it. Essentially, from this moment mechanics becomes an applied mathematical discipline.

Engineering

• 29 volumes on mathematics;
• 31 volumes on mechanics and astronomy;
• 13 - in physics.

Eight additional volumes will be devoted to Euler's scientific correspondence (over 3,000 letters).

Stamps, coins, banknotes

Bibliography

• New theory of the moon's motion. - L.: Publishing house. USSR Academy of Sciences, 1934.
• A method for finding curved lines that have the properties of either a maximum or a minimum. - M.-L.: GTTI, 1934.
• Basics of point dynamics. - M.-L.: ONTI, 1938.
• Differential calculus. - M.-L., 1949.
• Integral calculus. In 3 volumes. - M.: Gostekhizdat, 1956-58.
• Selected cartographic articles. - M.-L.: Geodesizdat, 1959.
• Introduction to the analysis of infinites. In 2 volumes. - M.: Fizmatgiz, 1961.
• Ballistics research. - M.: Fizmatgiz, 1961.
• Letters to a German princess about various physical and philosophical matters. - St. Petersburg. : Nauka, 2002. - 720 p. - ISBN 5-02-027900-5, 5-02-028521-8
• Experience of a new theory of music, clearly stated in accordance with the immutable principles of harmony / trans. from lat. N. A. Almazova. - St. Petersburg: Ros. acad. Sciences, St. Petersburg scientific center, publishing house Nestor-History, 2007. - ISBN 978-598187-202-0(Translation Tentamen novae theoriae musicae ex certissismis harmoniae principiis dilucide expositae (Tractatus de musica). - Petropol.: Typ. Acad. Sci., 1739.)

see also

• Astronomical Observatory of the St. Petersburg Academy of Sciences

Notes

References

1. Mathematics of the 18th century. Decree. Op. - P. 32.
2. Glazer G.I. History of mathematics in school. - M.: Education, 1964. - P. 232.
3. , With. 220.
4. Yakovlev A. Ya. Leonard Euler. - M.: Education, 1983.
5. , With. 218.
6. , With. 225.
7. , With. 264.
8. , With. 230.
9. , With. 231.
10. To the 150th anniversary of Euler's death: collection. - Publishing House of the USSR Academy of Sciences, 1933.
11. A. S. Pushkin. Anecdotes, XI // Collected Works. - T. 6.
12. Marquis de Condorcet. Eulogy of Euler. History of the Royal Academy of Sciences (1783). - Paris, 1786. - P. 37-68.; see original text: fr. Madame, répondit-il, parce que je viens d’un pays où, quand on parle, on est pendu
13. Bell E.T. Decree. Op. - P. 123.
14. Stroik D. Ya. Chapter VII // Brief outline of the history of mathematics / Translation by I. B. Pogrebyssky. - 3rd ed. - M., 1984.
15. Litvinova E. F. Euler // Copernicus, Galileo, Kepler, Laplace and Euler, Quetelet. Biographical narratives. - Chelyabinsk, Ural, 1997. - T. 21. - P. 315. - (F. Pavlenkov Library). - ISBN 5-88294-071-0

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 on Various Subjects of Natural Philosophy, Addressed to the 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 Euler’s amazing ability 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, the Russian Academy of Sciences placed a bust at 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 as we know them today, introducing the letter “e” for the base of the natural logarithm (known as “Euler’s number”), the Greek letter “Σ” for the total, and the letter “i” to determine the imaginary unit.

Analysis

Euler approved the use of exponential functions and logarithms in analytical proofs. He discovered a way to expand various logarithmic functions into 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 solving 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 applied 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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Euler is the author of more than 800 works on mathematical analysis, differential geometry, number theory, approximate calculations, celestial mechanics, mathematical physics, optics, ballistics, shipbuilding, music theory, etc. Many of his works had a significant influence on the development of science.

He spent almost half his life in Russia, where he made a significant contribution to the development of national science. In 1726 he was invited to work in St. Petersburg. In 1731-1741 and, starting from 1766, he was an academician of the St. Petersburg Academy of Sciences (in 1741-1766 he worked in Berlin, remaining an honorary member of the St. Petersburg Academy). He knew the Russian language well, and published some of his works (especially textbooks) in Russian. The first Russian academic mathematicians (S.K. Kotelnikov) and astronomers (S.Ya. Rumovsky) were students of Euler. Some of his descendants still live in Russia.

Biography

Switzerland (1707-1727)

Leonhard Euler was born in 1707 into the family of a Basel pastor, a friend of the Bernoulli family. He discovered mathematical abilities early. He received his primary education at home under the guidance of his father, who had once studied mathematics with Jacob Bernoulli. The pastor was preparing his eldest son for a spiritual career, but he also studied mathematics with him, both as entertainment and to develop logical thinking. While studying at the gymnasium, the boy enthusiastically studied mathematics under the guidance of Jacob Bernoulli, and in his last years at the gymnasium he attended university lectures by Jacob’s younger brother, Johann Bernoulli.

On October 20, 1720, 13-year-old Leonhard Euler became a student at the Faculty of Arts at the University of Basel. But Leonard's love for mathematics led him down a different path. Soon the capable boy attracted the attention of Professor Johann Bernoulli. He gave the gifted student mathematical articles to study, and on Saturdays he invited him to come to his home to jointly analyze the incomprehensible. In his teacher's house, Euler met and became friends with Bernoulli's sons, Daniel and Nikolai, who were also enthusiastic about mathematics.

On June 8, 1724, 17-year-old Leonhard Euler gave a speech in Latin about comparing the philosophical views of Descartes and Newton and was awarded a master's degree.

Over the next two years, young Euler wrote several scientific papers. One of them, “A Dissertation in Physics on Sound,” which received a favorable review, was submitted to the competition to fill the unexpectedly vacant position of professor of physics at the University of Basel (1725). But, despite the positive review, 19-year-old Euler was considered too young to be included in the list of candidates for the professorship.

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It should be noted that the number of scientific vacancies in Switzerland was very small. Therefore, the brothers Daniel and Nikolai Bernoulli left for distant Russia, where the organization of the Academy of Sciences was just underway; they promised to work hard for a place for Euler there.

At the beginning of the winter of 1726, Euler was informed from St. Petersburg: on the recommendation of the Bernoulli brothers, he was invited to the post of adjunct in physiology with a salary of 200 rubles. Receiving an advance to compensate for travel expenses lasted almost a year, and only on April 5, 1727, Euler left his native Switzerland forever.

First visit to Russia (1727-1741)

On January 22, 1724, Peter I approved the project for the organization of the St. Petersburg Academy. On January 28, the Senate issued a decree on the creation of the Academy. Of the 22 professors and adjuncts invited in the first years, there were 8 mathematicians who also worked in mechanics, physics, astronomy, cartography, the theory of shipbuilding, and the service of weights and measures.

One of the most important tasks of the Academy was the training of domestic personnel. Later, a university and a gymnasium were created at the Academy. Due to the acute shortage of textbooks in Russian, the Academy turned to its members with a request to compile such manuals. Euler, although he was listed as a physiologist, compiled a very good “Manual to Arithmetic” in German, which was immediately translated into Russian and served for many years as an initial textbook. The translation of the first part was carried out in 1740 by the first Russian adjunct of the Academy, Euler's student Vasily Adodurov. This was the first systematic presentation of arithmetic in Russian. To everyone’s surprise, Euler began to speak Russian fluently the very next year after his arrival.

In 1730, when Anna Ioannovna ascended the Russian throne, interest in the Academy fell. During the years of her reign, the Empress visited the Academy only once. Some of the invited professors began to return to their homeland. The vacant position of professor of physics was offered to Euler (1731), at the same time he received an increase in salary to 400 rubles. Two years later, Daniil Bernoulli returned to Switzerland, and Euler took over his department, becoming an academician and professor of pure mathematics with a salary of 600 rubles (however, Daniil Bernoulli received twice as much). Nicholas Bernoulli, a talented mathematician, died suddenly of illness shortly after arriving in Russia, in 1726.

On one of the last days of 1733, 26-year-old Leonard Euler married his peer, the daughter of a painter (a St. Petersburg Swiss) Katharina Gsell (German: Katharina Gsell). The newlyweds purchased a house on the Neva embankment, where they settled. 13 children were born into the Euler family, but 3 sons and 2 daughters survived.

Euler was distinguished by his phenomenal efficiency. According to contemporaries, for him living meant doing mathematics. And the young professor had a lot of work: cartography, all kinds of examinations, consultations for shipbuilders and artillerymen, drawing up training manuals, designing fire pumps, etc. He was even required to compile horoscopes, which Euler forwarded with all possible tact to the staff astronomer. But all this does not prevent him from actively conducting his own research.

During the first period of his stay in Russia, he wrote more than 90 major scientific works. A significant part of the academic “Notes” is filled with the works of Euler. He made reports at scientific seminars, gave public lectures, and participated in the implementation of various technical orders from government departments.

In 1735, the Academy received the task of performing an urgent and very cumbersome astronomical (according to other sources, cartographic) calculation. A group of academicians asked for three months to complete this work, but Euler undertook to complete the work in 3 days - and did it on his own. However, the overexertion did not pass without a trace: he fell ill and lost sight in his right eye. However, the scientist reacted to the misfortune with the greatest calm: “Now I will be less distracted from doing mathematics,” he noted philosophically.

In the 1730s, Euler became famous in Europe. The two-volume work “Mechanics, or the science of motion, in an analytical presentation,” published in 1736, brought him worldwide fame. In this monograph, Euler brilliantly applied the methods of mathematical analysis to the solution of problems of motion in vacuum and in a resistive medium. “Whoever has sufficient skill in analysis will be able to see everything with extraordinary ease and will read the entire work without any help,” Euler ends his preface to the book. From this moment on, theoretical mechanics becomes the applied part of mathematics.

Circumstances worsened when Empress Anna Ioannovna died in 1740, and the young John VI was declared king. “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.” In fact, during the regency of Anna Leopoldovna, the St. Petersburg Academy finally fell into disrepair. Euler is considering returning home. In the end, he accepts the offer of the Prussian King Frederick, who invited him to the Berlin Academy on very favorable terms, to the post of director of its Mathematics Department. The Academy was created on the basis of the Prussian Royal Society, founded by Leibniz, but in those years was in a deplorable state.

Prussia (1741-1766)

Euler submitted his resignation to the leadership of the St. Petersburg Academy:

For this reason, I am forced, both for the sake of poor health and other circumstances, to seek the most pleasant climate and accept the summons 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.

The Academy did not object. Euler was “released from the Academy” in 1741 and confirmed as an honorary academician with a salary of 200 rubles. In return, he promised to help the St. Petersburg Academy to the best of his ability - and indeed, during all the years spent in Prussia, he conscientiously participated in the publications of the Academy, edited the mathematical departments of Russian journals, and purchased books and instruments for St. Petersburg. Young Russian scientists sent on an internship lived in Euler’s apartment on full board (the payment for which, by the way, was sent very late by the Academy’s office) for years. It is known that Euler had a lively correspondence with Lomonosov, in whose work he highly valued the “happy combination of theory and experiment.” In 1747 he gave a favorable review of Lomonosov's papers on physics and chemistry, stating:

All these works are not only good, but excellent, for he [Lomonosov] explains the most necessary and difficult physical and chemical matters, which were completely unknown and impossible for the most witty scientists to interpret, with such thoroughness that I am completely confident in the validity of his explanations . At the same time, I must give justice to Mr. Lomonosov that he is gifted with the happiest wit for explaining physical and chemical phenomena.

This high assessment was not hindered even by the fact that Lomonosov did not write mathematical works and did not master higher mathematics.

In June 1741, Leonhard Euler arrived in Berlin with his wife, two sons and four nephews. He spent 25 years here and published about 260 works.

At first, Euler was greeted kindly in Berlin. He is even invited to court balls, although it is unlikely that this event particularly attracted him.

The king is constantly away due to continuous wars, but Euler has a lot of work. In addition to mathematics, he is involved in many practical matters, including even lotteries, minting coins, laying new water pipes and organizing pensions.

In 1742, a four-volume collected works of Johann Bernoulli was published. 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 after another, his works of great importance for science came out: “Introduction to the Analysis of Infinitesimals” (1748), “Marine Science” (1749), “The Theory of the Motion of the Moon” (1753), “Manual on Differential Calculus” (lat. Institutiones calculi differentialis, 1755). Numerous articles on specific issues are published in publications of the Berlin and St. Petersburg Academies. In 1744, Euler discovered the calculus of variations. His work uses well-thought-out terminology and mathematical symbolism, largely preserved to this day, and takes the presentation to the level of practical algorithms. Euler was soon elected a member of the four leading Academies of Sciences.

In 1753, Euler bought an estate in Charlottenburg (a suburb of Berlin) with a garden and grounds. Euler's mother notified him of his father's death in Switzerland; she soon moved in with Euler.

Euler’s “Letters on various physical and philosophical matters, written to a certain German princess...”, which went through over 40 editions in 10 languages ​​(including 4 editions in Russian), gained enormous popularity in the 18th century, and partly in the 19th century as well. . This is a wide-ranging popular science encyclopedia, written vividly and accessible to everyone.

Euler's performance remained exceptional until the end of his life. It produced an average of 800 in-quarto pages (a page ¼ the size of a paper sheet) per year. This is a lot even for a novelist; For a mathematician, such a volume of scientific work can be considered a record.

World fame did not go to Euler's head. According to contemporaries, all his life he remained a modest, cheerful, extremely sympathetic person, always ready to help others. However, relations with the king do not work out: Frederick finds the new mathematician unbearably boring, not at all secular, and treats him dismissively.

In 1759: Maupertuis, president of the Berlin Academy of Sciences, died. King Frederick II offered the post of president of the Academy to D'Alembert, but he refused. Friedrich, who did not like Euler, nevertheless entrusted him with the leadership of the Academy, but without the title of president.

During the Seven Years' War, Russian artillery destroyed Euler's house; Upon learning of this, Field Marshal Saltykov immediately compensated for the losses, and later Empress Elizabeth sent another 4,000 rubles from herself.

1765: Euler's new masterpiece, The Theory of the Motion of Rigid Bodies. In 1766, “Elements of the Calculus of Variations” was published. It was here that the name of the new branch of mathematics created by Euler and Lagrange first appeared.

From the early 1760s, Euler, increasingly bullied by the king, weighed the prospect of moving to London. However, his plans soon changed. In 1762, Catherine II ascended the Russian throne and pursued a policy of enlightened absolutism. Well understanding the importance of science both for the progress of the state and for her own prestige, she carried out a number of important, favorable for science, transformations in the system of public education and culture. The Empress offered Euler 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,” said the letter to her representative, “he would be pleased to communicate his conditions, so long as he doesn’t hesitate to come to St. Petersburg.”

Euler submitted a petition to the king for dismissal from service, but received no response. He applied again - but Friedrich did not even want to discuss the issue of his departure. In response to this, Euler stopped working for the Berlin Academy.

Euler received decisive support from persistent petitions from the Russian mission on behalf of the Empress. On April 30, 1766, Frederick finally allowed the great scientist to leave Prussia, releasing several malicious witticisms (in letters of that period). True, Christoph, Euler’s youngest son, who served as an artillery lieutenant colonel (German: Oberstleutnant), the king flatly refused to release from the army. Later, thanks to the intercession of Catherine II, he was still able to join his father; in the Russian army he rose to the rank of lieutenant general.

Euler returns to Russia, now forever.

Russia again (1766-1783)

In July 1766, 60-year-old Euler, his family and household (18 people in total) arrived in the Russian capital. Immediately upon arrival he was received by the empress. Catherine, now the Second, greeted him as an august person and showered him with favors: she granted 8,000 rubles 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.

Unfortunately, after returning to St. Petersburg, Euler developed a cataract in his second, left eye - he stopped seeing. Probably for this reason, he never received the promised post of vice-president of the Academy. However, blindness did not affect his performance. Euler dictated his works to a tailor boy, who wrote everything down in German. The number of works he published even increased; during the decade and a half of his second stay in Russia, he dictated more than 400 articles and 10 books.

1767-1770: work on the two-volume classic monograph “Universal Arithmetic” (also published under the titles “Principles of Algebra” and “Complete Course of Algebra”). This wonderful work was published in Russian immediately (first volume: 1768), in German - two years later. The book was translated into many languages ​​and reprinted about 30 times (three times in Russian). All subsequent algebra textbooks were created under the strong influence of Euler's book.

In the same years, the three-volume book “Optics” (Latin: Dioptrica, 1769-1771) and the fundamental “Integral Calculus” (Latin: Institutiones calculi integralis), also in 3 volumes, were published.

In 1771, 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 saved with difficulty. 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. Euler had to temporarily move to another house.

In September of the same year, at the special invitation of the Empress, the famous German ophthalmologist Baron Wentzel arrived in St. Petersburg to treat Euler. After an examination, he agreed to perform surgery on Euler and removed a cataract from his left eye. Euler began to see again. The doctor ordered to protect the eye from bright light, not to write, not to read - just gradually get used to the new condition. However, just a few days after the operation, Euler removed the bandage, and soon lost his sight again. This time it's final.

1772: "A New Theory of the Motion of the Moon." Euler finally completed his many years of work, having approximately solved the three-body problem.

In 1773, on the recommendation of Daniel Bernoulli, Bernoulli's 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 mainly dictated his works to him, although sometimes he used the “eyes of his eldest son” and his other students.

In 1773, Euler's wife, with whom he lived for almost 40 years, died; they had three sons (the youngest son, Christopher, was later a lieutenant general in the Russian army and commander of the Sestroretsk arms factory). This was a great loss for the scientist, who was sincerely attached to his family. Soon Euler married her half-sister Salome.

1779: General Spherical Trigonometry, the first complete exposition of the entire system of spherical trigonometry, is published.

Euler worked actively until his last days. In September 1783, the 76-year-old scientist began to experience headaches and weakness. On September 7 (18), after lunch spent with his family, talking with astronomer A. I. Leksel about the recently discovered 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,” Condorcet said at the funeral meeting of the Paris Academy of Sciences (French: Il cessa de calculer et de vivre).

He was buried at the Smolensk Lutheran cemetery in St. Petersburg. The inscription on the monument read: “Here lie the mortal remains of the wise, just, famous Leonhard Euler.”

In 1955, the ashes of the great mathematician were transferred to the “Necropolis of the 18th century” at the Lazarevskoye cemetery of the Alexander Nevsky Lavra. The poorly preserved tombstone was replaced.

A. S. Pushkin gives a romantic story: supposedly Euler compiled a horoscope for the newborn Ivan Antonovich (1740), but the result frightened him so much that he did not show it to anyone, and only after the death of the unfortunate prince told Count K. G. Razumovsky about it . The reliability of this historical anecdote is extremely doubtful.

The Marquis of Condorcet reports that shortly after moving to Berlin, Euler was invited to a court ball. When asked by the Queen Mother why he was so taciturn, Euler replied: “I beg your pardon, but I have just come from a country where they can be hanged for saying too much.”

Another Condorcet story: One day two students, independently performing complex astronomical calculations, obtained slightly different results in the 50th digit, and turned to Euler for help. Euler did the same calculations in his head and indicated the correct result.

They say that Euler did not like the theater, and if he got there, succumbing to the persuasion of his wife, then in order not to get bored, he performed complex calculations in his head, selecting their volume so that it was enough just until the end of the performance.

In 1739, Euler's work Tentamen novae theoriae musicae on the mathematical theory of music was published. There was a running joke about this work that there was too much music for mathematicians and too much mathematics for musicians.

Ratings

According to contemporaries, Euler’s character was good-natured, gentle, and practically did not quarrel with anyone. Even Johann Bernoulli, whose difficult character was experienced by his brother Jacob and son Daniel, invariably treated him warmly. He needed only one thing to complete his life - the opportunity for regular mathematical creativity. At the same time, he was cheerful, sociable, loved music and philosophical conversations.

Euler was a caring family man, willingly helped colleagues and young people, and generously shared his ideas with them. There is a known case when Euler delayed his publications on the calculus of variations so that the young and then unknown Lagrange, who independently came to the same discoveries, could publish them first. Lagrange always admired Euler both as a mathematician and as a person; he said: “If you really love mathematics, read Euler.”

Academician S.I. Vavilov wrote: “Together with Peter I and Lomonosov, Euler became the good genius of our Academy, who determined its glory, its strength, its productivity.”

“Read, read Euler, he is our common teacher,” Laplace also liked to repeat (French Lisez Euler, lisez Euler, c "est notre maître à tous.). Euler’s works were also studied with great benefit by the “king of mathematicians” Carl Friedrich Gauss, and almost all famous scientists of the 18th-19th centuries.

He is among the top five greatest mathematicians of all time. He was born into a pastor's family and 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. The following 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 in mechanics, soon brought him worldwide fame, and later contributed to the fame 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 to 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 the academic gymnasium, worked at the astronomical observatory, collaborated in the publication of the St. Petersburg Gazette, 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 great 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 work. 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 the last years of 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 authored the famous six-volume course on 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 Having the Properties of Maximum or Minimum (1744). Euler's significant contributions were to the development of function theory, differential geometry, computational mathematics, and number theory. Euler's two-volume course Complete Guide to 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 the mechanics of a material point, having examined in his two-volume Mechanics (1736) the motion of a free and non-free point in emptiness and in a resisting medium. Later, Euler laid the foundations of kinematics and rigid body dynamics, receiving the corresponding

current general equations. The results of these studies by Euler are collected in his Theory of the Motion of Rigid Bodies (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.”

In 1752, Euler’s article “Discovery of a new principle of mechanics” was published, in which he formulated in general form Newton’s equations of motion in a fixed coordinate system, opening the way for the study of continuum mechanics. 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 are remarkable, among which the most famous is his New Theory of the Motion of the Moon (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 issues of the structural mechanics of a ship were developed in subsequent works. He gave a more accessible presentation of the theory of the ship in the Complete Theory of the Structure and Driving of Ships (1773), which was used as a practical guide not only in Russia.

Euler's comments to B. Robins's New Principles of Artillery (1745) were a significant success, containing, along with his other works, important elements of external ballistics, as well as an explanation of the hydrodynamic “D'Alembert's 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. Of particular note are the three volumes of Letters to a German Princess on various subjects of physics and philosophy published by Euler (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.

The modern five-volume Mathematical Encyclopedia lists 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, a large number of his technical examinations, 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 of the St. Petersburg Academy of Sciences, 130 articles published in Berlin, 30 articles in various European journals, 15 memoirs awarded prizes and encouragements from the Paris Academy sciences, and 40 books of individual works. All this will amount to 72 volumes of the near-complete Complete Works (Opera omnia) of Euler, published in Switzerland since 1911. All works are printed here in the language in which they were originally published (i.e. in Latin and French, which were in the middle of the 18th century the main working languages ​​of, respectively, the St. Petersburg and Berlin academies). To this will be added another 10 volumes of his Scientific Correspondence, the publication of which began 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 of the Russian army and navy, as well as statesmen and scientists. Only in the troubled times of the 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.”)

Publications: 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

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 of the Russian Empire, a 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 that theoretical mechanics became the 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. A 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 the 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 his conditions were accepted at the highest 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 “Complete Course of 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. What he could not save, he restored in a short time, 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 latest 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 of the Patriotic War of 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.