A report about Leonhard Euler will tell you everything about the life of the great mathematician, physicist, mechanic and astronomer.

The life and work of Leonhard Euler briefly

The future scientist (the years of the life of Leonhard Euler 1707-1783) was born in Basel in Switzerland on April 15, 1707. After graduating from a local school, he attended Bernoulli's lectures at the University of Basel. He received his master's degree in 1723 and 3 years later he received an invitation from the St. Petersburg Academy of Sciences to the post of adjunct in mathematics.

In 1730 he took the chair of physics. In 1733, Euler received the title of academician. Euler spent 15 years in Russia and here he wrote the world's first textbook on theoretical mechanics and a course on mathematical navigation.

In 1741 Euler was invited by the Prussian King Frederick II to move to Berlin. Having accepted this offer, he changes his place of residence and issues 3 volumes of articles on the subject of ballistics. In 1747, a mathematician invented a complex lens.

In 1749, Euler published a two-volume work, in which he was the first to present the problems of navigation in mathematical form. He made many discoveries in the field of mathematical analysis, describing them in a book called "Introduction to the analysis of infinitesimal quantities." The great mathematician Leonhard Euler never ceases to explore differential, variational and integral calculus. He took up the issue of the passage of light through different media and how the effect of chromatism is connected with this.

He returned to Russia in 1766 and published his work "Elements of Algebra". By the way, he did not write it with his own hand, but dictated it, since by 1768 the mathematician was completely blind. But this illness did not prevent him from issuing several more publications and books, memoirs and volumes of integral calculus.

The Paris Academy of Sciences in 1775 accepted Euler as its 9th member of the society, while circumventing the laws of the academy and its statute, according to which only 8 people could be accepted into the society.

In general, mathematician Euler conducted more than 865 studies throughout his life, having a huge impact on the development of mathematics in Russia. He died in Petersburg on September 18, 1783.

Leonhard Euler interesting facts

• In 1733, the scientist marries Katharina, the daughter of the artist Georg Gzel. During the 40 years of marriage, the wife gave Leonard 13 children. But only 5 of them survived - 2 daughters and 3 sons. In 1773, his beloved wife died and after 3 years Euler married a second time. On Katarina Salome, half-sister of the deceased wife.
• In Russia, the scientist was called Leonty.
• Euler was the first to systematically expound calculus. The mathematician is the founder of the scientific mathematical Russian school. He wrote many books on the theory of the motion of the planets and the Moon, on mechanics, geography, the theory of shipbuilding and the theory of music.
• He didn't like theaters, and when his wife still managed to introduce him to the beautiful, Leonard mentally calculated complex mathematical schemes until the end of the performance, so as not to die of boredom.
• He was a very capable person. Total at the age of 13 he became a student, and at 17 received a master's degree and received an invitation to head the Department of Physics at the Russian Academy of Sciences.
• Despite his Swiss birth, Euler spent most of his adult life in St. Petersburg, Russia and in Berlin, Prussia.
• Euler is remembered as the most important mathematician of the 18th century. He is remembered for his contributions to mechanics, fluid dynamics, optics, astronomy and music.
• Leonhard Euler remained a faithful Calvinist all his life.
• He lost sight in his right eye quite early, probably due to overwork.
• He worked for 25 years at the Berlin Academy and then returned to Petersburg at the age of 59, during which time he lost sight in his other eye. Blindness did not stop him. In fact, he blindly completed a comprehensive analysis of the theory of the motion of the moon. All complex analysis was done entirely in his head.
• In 1771 his house burned down. In 1776 his wife died. He died in 1783 at the age of 76.
• It is known that he published more than 500 books and articles throughout his life, and another 400 were published posthumously. It has been estimated that he averaged about 800 pages per year.

Euler Leonard (1707-1783), mathematician, physicist, mechanic, astronomer.

Born April 15, 1707 in Basel (Switzerland). He graduated from the local gymnasium, listened to the lectures of I. Bernoulli at the University of Basel. In 1723 he received a master's degree. In 1726, at the invitation of the St. Petersburg Academy of Sciences, he came to Russia and was appointed adjunct in mathematics.

In 1730 he took the chair of physics, and in 1733 he became an academician. During his 15 years in Russia, Euler managed to write the world's first textbook on theoretical mechanics, as well as a course on mathematical navigation and many other works.

In 1741, he accepted the offer of the Prussian King Frederick II and moved to Berlin. But even at that time, the scientist did not break ties with St. Petersburg. In 1746, three volumes of Euler's articles on ballistics were published.

In 1749, he published a two-volume work, which for the first time presented the problems of navigation in mathematical form. The numerous discoveries made by Euler in the field of mathematical analysis were later compiled in the book An Introduction to the Analysis of Infinitely Small Quantities (1748).

The Introduction was followed by a treatise in four volumes. The 1st volume, devoted to differential calculus, was published in Berlin (1755), and the rest, devoted to integral calculus, in St. Petersburg (1768-1770).

In the last, 4th volume, the calculus of variations created by Euler and J. Lagrange is considered. At the same time, Euler investigated the question of the passage of light through various media and the effect of chromatism associated with this.

In 1747 he proposed a complex lens.

In 1766 Euler returned to Russia. The work "Elements of Algebra", which was published in 1768, the scientist was forced to dictate, since by this time he was blind. At the same time, three volumes of integral calculus, two volumes of elements of algebra, and memoirs were published (“Computation of the Comet 1769”, “Calculation of the Solar Eclipse”, “New Theory of the Moon”, “Navigation”, etc.).

In 1775, the Paris Academy of Sciences, bypassing the statute and with the consent of the French government, appointed Euler as its ninth (there should be only eight) "affiliated member".

Euler is the author of more than 865 investigations on the most varied and most difficult questions. He had a great and fruitful influence on the development of mathematical education in Russia in the 18th century. The Petersburg School of Mathematics, which included academicians S. K. Kotelnikov, S. Ya Rumovsky, N. I. Fuss, M. E. Golovin, and other scientists, under the guidance of Euler, carried out a huge educational work, created an extensive and remarkable for its time educational literature, performed a number of interesting studies.

Leonhard Euler - one of the greatest mathematicians of all time - was distinguished by an irrepressible craving for knowledge and irrepressible energy. Many classical theorems in all areas of mathematics are named after him.

Leonhard Euler was born in Basel, Switzerland on April 15, 1707. Paul Euler - the boy's father - was a pastor and dreamed that his son would follow in his footsteps. From the first years of his life, he teaches Leonard all kinds of sciences, wanting to instill in him a craving for new knowledge. Euler showed a special talent for precise objects, and his father immediately began to develop his abilities. Paul himself devoted almost all his free time to mathematics, and in his youth he even attended the lessons of the famous Jacob Bernoulli.

Home schooling has become a solid foundation for the further education of the boy. When he entered the Basel gymnasium, all subjects were given to him with extraordinary ease. However, the level of teaching in secondary school left much to be desired, and Euler began to look for new opportunities to gain knowledge. At the age of 13, Leonard entered the University of Basel at the Faculty of Liberal Arts. So he gets to lectures on mathematics by the younger brother of Jacob Bernoulli - Johann.

The professor notices a capable student and assigns individual lessons to Euler. Under the strict guidance of Bernoulli, the boy gets acquainted with the most complex works of great mathematicians, learns to understand and analyze them. This approach to learning allowed Leonard to receive his first degree at the age of 16, when he was able to conduct a comparative analysis of the works of Descartes and Newton in Latin. So Euler becomes a master of arts.

After graduating from university, Paul again intervened in his son's education. Being sure that Leonard will become a priest, his father forces him to learn languages: Hebrew and Greek. Euler did not achieve much success, so his father had to come to terms with his passion for mathematics. However, the 17-year-old boy is unable to find a job in his specialty - all the places at the university are occupied. He continues to visit Professor Bernoulli's house and develops a close friendship with his sons: Daniel and Nikolai.

In 1727, following the Bernoulli brothers, the scientist left for St. Petersburg. Here Euler becomes an adjunct of higher mathematics. In 1730, Leonhard Euler was offered the chair of physics, and in January 1731 he became a professor. Since 1733, under his leadership, there was already a department of higher mathematics. For 14 years spent in St. Petersburg, he publishes works on hydraulics, navigation, mechanics, cartography and, of course, mathematics. In total, he has more than 70 scientific papers to his credit. In the West, Euler is recognized precisely as a Russian scientist. The Swiss roots of Leonard remind of themselves only in his personal life - he marries a Swiss woman, Katerina Gzel.

Petersburg Academy of Sciences at that time could boast of a unique teaching staff. Such well-known scientists as J. German, D. Bernoulli, H. Goldbach and many others teach and conduct scientific activities here. Such a company allows Euler to delve into his research as much as possible, and the scientist publishes more and more new works in the publications of the Academy. The most significant of them is the two-volume Mechanics.

Frederick II, being King of Prussia, decides to open the Berlin Academy on the basis of the Society of Sciences. He invites Euler to work in Berlin on very favorable terms. In 1841, the scientist decided to move, nevertheless, he actively corresponded with Russian scientists, in particular, with Lomonosov. In Berlin, Leonard Euler met the president of the Academy of Sciences Moreau de Maupertuis and actually became his deputy - Moreau often gets sick, and Euler fulfills his duties.

In Germany, the scientist continues to work in the field of number theory, mathematical analysis and calculus of variations, applies a new approach to the study of geometry. The result of Euler's research is a new science - topology. At the same time, shipbuilding and celestial mechanics fell into the field of Leonard's interests. In the latter, he achieves unprecedented success - he creates a theory of the motion of the Moon, taking into account the attraction of the Sun.

Euler did not receive the long-awaited post of president of the Academy, which became one of the main reasons for his return to St. Petersburg. Here he is warmly received by the patroness of sciences - Catherine II. The scientist enthusiastically begins to work for the good of Russia.

Age makes itself felt, and at the age of 60 Euler almost completely loses his sight, however, he does not stop his scientific activity. After returning, he manages to print 200 essays in various fields of science.

Leonard's first wife dies shortly after the move and, a couple of years later, the scientist marries her own sister, Salome-Abigail Gzel. His children take Russian citizenship.

The government highly appreciates the achievements of the scientist and his contribution to the development of science. Even having stopped their scientific activity, Euler and his family were fully provided with everything necessary at the expense of the state. Leonhard Euler dies in 1783 in St. Petersburg at the age of 75. By this time he had 5 children and 26 grandchildren. After himself, he left 800 scientific articles and 72 volumes devoted to various fields of science.

During his scientific career, Leonhard Euler founded the theory of functions with complex variables, ordinary differential equations, and partial differential equations. He became a pioneer in the calculus of variations and topology, applied new methods of integration. Many theorems of algebra and number theory are named after him, which later became classical.

Using the results of Stirling and Newton, Euler in 1732 (at the same time as MacLaren) discovered the general summation law. In other words, he expressed the partial sum, integral and derivative of the infinite series sn= ∑ u (k) through a series with a common term u (n). Examining the obtained data, as well as the ratio of Bernoulli numbers B2n+2:B2n, Euler determined that this series is divergent, however, he was able to calculate its approximate value. For this, the scientist used the sum of all members of the series, which are decreasing. This discovery led to the concept of an asymptotic series, to which many famous mathematicians later devoted their works. Among them are Laplace, Legendre, Lagrange, Poisson and Cauchy. The Euler-McLaren formula became the basis of the theory of finite differences.

Fascinated by the work of d'Alembert, Euler began to study string theory. In his article "On Vibration of a String", the scientist finds a general solution to the equation of oscillation, taking the initial velocity as zero. It had the form y \u003d φ (x + at) + ψ (x - at), where a is a constant, and differed little from d'Alembert's solution. However, in 1766, Euler also found his own method, which would later be included in his "Integral Calculus" (1770). To do this, he introduced new coordinates, which brought the equation to a simpler form for integration: u \u003d x + at, v \u003d x - at. In modern textbooks on differential equations, such coordinates are called characteristic and are widely used for various kinds of calculations.

One of Euler's main discoveries was the formula named after him. It states that for any real x, the equality eix= cosx + isinx (i is the imaginary unit, e is the base of the natural logarithm) is true. Thus, the scientist connected the trigonometric function and the complex exponent. The formula was published in the book "Introduction to the analysis of infinitesimals" (1748). Continuing research in this area, Euler obtained the exponential form of a complex number of the form z = reiφ.

In addition, he greatly simplified and shortened mathematical notation - he introduced the notation for trigonometric functions: tg x, ctg x, sec x, cosec x and was the first to consider them as functions of a numerical argument, which became the basis of modern trigonometry.

As Laplace later argued, all the mathematicians of the 18th century studied with Euler. However, even after several centuries, his mathematical methods are used in maritime affairs, ballistics, optics, music theory and insurance.

Leonhard Euler is an outstanding mathematician and physicist. The most accurate definition that can be used to characterize the works created by Euler is the brilliant materials that have become the property of all mankind.
It is by his methods that students of many generations are taught in schools and higher educational institutions. Leonard made a colossal contribution to the development of mathematical and physical sciences, became the founder of the main series of scientific discoveries. Thanks to his achievements, Euler was an honorary academician in many countries of the world.
Euler's main focus was mathematics, but he worked in many areas of science, which allowed him to leave a huge number of important works in astronomy, physics, mechanics and several types of applied sciences. Euler became not only the most important representative of history in the creation of educational literature for students of schools and universities, but was also a teacher for many outstanding mathematicians of several generations who became followers of Euler's teachings. Many famous mathematicians, both past and present, have based their studies of the mathematical sciences to a large extent on the work of Leonard. Among them are such "kings" of mathematics as Laplace and Carl Friedrich Gauss. Until now, after many years since Euler's death, he is an inspiration for many scientists from all over the world in reaching new heights in the field of mathematics and its branches.
Even in the modern world, in the age of high technology, Leonhard Euler's teaching materials remain in high demand. In the branches of mathematics, Euler's concepts are widely known, such as:
- straight line;
- a straight line in a circle;
- dot;
- theorem for polyhedra;
- method of broken lines (method of solving differential equations);
- integral of beta function and gamma function;
- angle (in mechanics - to determine the movement of bodies);
- number (for work in hydrodynamics).
It is probably impossible to find at least one area in mathematical science that is not based on the teachings of such a brilliant scientist as Euler. He left a truly significant mark in science.
But it is not only the contribution of Leonhard Euler in various scientific fields that is interesting and significant. No less interesting was his life. Leonard was born on April 15, 1707 in Basel. He was raised by his father, a theologian by education and a clergyman by occupation. The boy received his initial education at home. His father, Paul, once studied mathematics with Jacob Bernoulli. And now he shared his knowledge with his son. Developing logical thinking in his child, Paul still hoped that Leonard would continue his spiritual career in the future. But the little genius was so fascinated by exact science that he did not spend a single day without learning more and more from his father about this entertaining science.
However, when the time came to start serious studies and get a specialty, his father sent Leonard to the University of Basel, where the young man became an art student. There they were to make a spiritual person out of him and send him along the path of his father, the pastor. But childhood love for mathematics changed all Paul's plans, and directed the guy along a different path - the path of exact calculations, formulas and numbers. Leonard became the best student in his class, thanks to his impeccable memory and high abilities. And Bernoulli himself noticed the mathematical successes of the young genius. He invited Euler to study at his home, and these studies became weekly.
At the age of 17, Leonard was awarded a master's degree for an excellent lecture in Latin on the philosophy of the views of Newton and Deckard. Euler was noted for several other outstanding works, one of which (in physics) won the competition at the University of Basel for the position of professor. His work caused a storm of admiration and a flurry of positive reviews. But despite the high recognition of the talent of the young talent, he was considered too young to take the responsible position of a university professor.
Soon, thanks to the recommendations of Bernoulli's sons, with whom Leonhard had warm friendly relations, Euler got his chance to improve his skills. He was invited to St. Petersburg to head the Department of Physiology. Realizing that he will not reach significant heights in his native city, Leonard accepts the invitation, leaves Switzerland and goes to St. Petersburg.
Meanwhile, there was an active development of science in Europe. The ingenious Leibniz presented to the world a project designed to create scientific academies. Having learned about the development of this project, Peter I approved the plan for the creation of the St. Petersburg Academy. Outstanding professors were invited to it. To promote the teaching of sciences and the development of Russian scientists, a university and a gymnasium were built at the academy. The members of the academy were faced with the task of compiling methodological manuals for the initial study of mathematics, mechanics, physics and other specialties. Euler wrote a manual on the study of arithmetic, which was soon translated into Russian. This recommendation was the first in Russian education, according to which they began to teach schoolchildren,
and she forever marked Euler in history as a man, an external colossal contribution to the development of society.
Soon the power changed, instead of Peter I, Anna Ioannovna took the throne. Politics has changed, views on the state have changed, including in terms of education. The training academy began to be seen as an institution that brought great losses and did not bring much benefit to the government. Rumors began to circulate about its closure.
But despite all the difficulties, the academy survived and continued its activities. Some professors left, fearing the new government. Thanks to this, Leonard took the vacant position of professor of physics, which also allowed him to receive a fairly large salary. A couple of years later, Leonhard Euler became an academician of the Department of Mathematics.
In addition to a brilliant career, Leonard also had a happy life. At the age of 26, he married the beautiful and sophisticated Ekaterina Gzel, the daughter of a famous painter. The wedding day was appointed for the New Year, and all the employees of the academy became invited guests. Two families of the great Euler gathered to celebrate two holidays. A family of relatives and a family from the Academy of Sciences. After all, for him, work has become a second home, and colleagues have become close people.
Euler's performance was amazing. He could not live without his scientific career. Once he took on the development task received by the academy. The peculiarity was that the task was incredibly large. Three months were allocated for its implementation. However, Euler wanted to stand out, show his outstanding abilities, and completed this task in three days. This caused a storm of positive discussions and admiration for the talent of the professor. But a strong overvoltage had a negative impact on the scientist's body - unable to withstand the powerful load, Leonard went blind in one eye. But Euler showed steadfastness and philosophical wisdom, declaring that now he will be able to devote more time to his family and personal life, since from now on he will be less distracted by mathematics.
After that, Euler became even more famous among the luminaries of science, and his grandiose work, which deprived him of half of his sight, brought him truly world fame. His brilliant analytical exposition of mechanics as a method of motion was the discovery of a new milestone in the world of science.
As the world improved, so did science. Euler began studying the description of physical phenomena with the help of integrals. The difficulty was that Leonard lived in St. Petersburg, where the scientific academy was not considered outstanding and did not have due respect. The development of science worsened by the fact that a new ruler was announced in Russia - the young John. According to Euler, the state of development of scientific research became unstable and did not have a developed bright future. Therefore, Euler gladly accepted the invitation to work for the Berlin Academy. But at the same time, the mathematician gave his word not to forget the St. Petersburg Academy, to which he gave many years of his life, and to help as much as possible. After 25 years, he will return to Russian soil. But for now, he is moving to Berlin with his family, wife and children. However, all the time that Euler stays in Berlin, he continues to write works for the Russian Academy, edit new methods of Russian scientists, acquire Russian scientific books, and also host students from Russia who were sent on an internship to the great scientist. And most importantly, he remains an honorary member of the St. Petersburg Academy.
Soon the collected works of Bernoulli are published, which the old professor sends to his student in Berlin with a request to continue his work. And Euler did not disappoint his teacher. Despite health problems, he began to actively produce works, which later gained tremendous success and recognition. These works were:
- "Introduction to the analysis of infinite";
- "Instructions on differential calculus";
- "Theory of the motion of the moon";
- "Marine Science";
- "Letters on various physical and philosophical matters."
The last of these works was Euler's next great breakthrough, which was translated into dozens of languages ​​and published in many publications around the world. In addition, Euler wrote many scientific articles that were very successful.
Despite his scientific education, the professor did not seek to write abstruse articles. He always wrote in a language understandable to people of any level of knowledge. He described his works as if he were studying the topic at the same time as the reader, starting from the opening of the topic, understanding the purpose of the work, from reasoning leading to a logical conclusion. Having independently gone through the path of learning, having gone through all its difficult stages, Euler knew what people feel when they begin to delve into the complex structure of science. Therefore, he tried to make his work interesting and understandable.
A great achievement was the discovery of formulas that determine the critical load during compression of the rod. In those years, this work did not cause a need for its use, but after almost a century, it became necessary in the construction of railway bridges in England.
Leonard performed a huge amount of work based on his discoveries and calculations. About 1000 pages of his works were published per year. This is a serious scale even for literary works. But the fact that on these pages there were numbers and formulas in such a volume ... The genius of the professor is admirable!
The new Empress Catherine II allocated impressive sums for the development of science, and drawing attention to a talented professor, she invited him to return to St. Petersburg and head the management of the mathematical department at the academy. In her proposal, she indicated a fairly solid salary, while noting that if this amount was not enough for the professor, she was ready to accept his conditions, if only he agreed to come to St. Petersburg. Euler agrees to this advantageous offer, but they do not want to let him go from service in Berlin. After the refusal of several of his petitions, Euler goes to the trick and simply stops publishing scientific papers. This paid off and he was finally allowed to leave for Russia. Upon arrival in St. Petersburg, the Empress gave the professor all sorts of benefits, including allocating funds for the purchase of a personal home and for its comfortable environment. The first request of Catherine the Great was a project of ideas that would modernize the academy.
Active work and intense stress finally deprived Leonhard Euler of his precious vision. But even this did not stop the scientific genius from improving the scientific world. He dictates all his thoughts, discoveries, scientific works to a young boy, who diligently writes everything down in German.
Soon a terrible unforeseen situation happened - a grandiose fire broke out in St. Petersburg, the victims of which were many buildings. Including the professor's house. It was difficult to save him. Fortunately, his scientific work was practically not affected. Only one work burned down - "A new theory of the motion of the moon." But thanks to the impeccable, phenomenal memory that Leonard had even in his old age, the destroyed work was restored.
Euler was forced to move with his family to a new home. This caused the professor, who had lost his sight, a lot of inconvenience, since everything in this house was unfamiliar to him, and it was difficult for him to navigate by touch. Soon an outstanding German oculist, Wenzel, arrived in St. Petersburg. He intended to restore the great professor's sight. The operation, which lasted only a few minutes, restored Euler's sight in his left eye. The doctor urged Leonard to protect his eyes, avoid prolonged exertion, and not write or read. But the professor's obsessive love for science did not allow him to adhere to the recommendations of the ophthalmologist. He again began to work actively, which led to terrible consequences - he finally lost his sight. To the surprise of others, the genius with incredible calmness refers to everything that happened. His scientific activity even increased - a clear stream of thoughts allowed him to comprehend a number of scientific achievements that appeared on paper thanks to his students who wrote from dictation.
Soon Leonard's wife died, and this was a serious shock for him, a man insanely attached to his family. Having lived with his beloved wife for 40 years, Euler could no longer imagine life without her. Science helped him take his mind off grief. Until the last days of his life, Euler continued to work actively and productively. His main assistant in writing was the eldest son, as well as several faithful students. All of them were the professor's eyes, allowing the scientific world to present the last thoughts of a genius.
In 1793, Leonard felt a sharp deterioration in his health, strong and regular headaches caused him serious anxiety and no longer allowed him to work productively. At one of the important meetings with Leksel, discussing the discovery of the new planet Uranus, Euler felt very dizzy. Having managed to utter the words “I am dying”, the brilliant professor lost consciousness. Later, a medical examination found out that he had died of a cerebral hemorrhage.
The great mathematician Leonhard Euler was buried in the St. Petersburg Smolensk cemetery. The world has lost a talented, excellent scientist, professor and incredible person. But after himself, he left a grandiose volume necessary for mankind open.

Switzerland (1707-1727)

Basel University in the 17th-18th centuries

In the next two years, the young Euler wrote several scientific papers. One of them, "Thesis on 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 feedback, the 19-year-old Euler was considered too young to be included in the number of candidates for a professorship. It should be noted that the number of scientific vacancies in Switzerland was quite small. Therefore, the brothers Daniel and Nikolai Bernoulli left for Russia, where the organization of the Academy of Sciences was in progress; they promised to work there for a position for Euler as well.

Euler was a phenomenal worker. According to contemporaries, for him to live meant doing mathematics. And the young professor had a lot of work: cartography, all kinds of expertise, consultations for shipbuilders and gunners, drafting training manuals, designing fire pumps, etc. They even require him to draw up horoscopes, which order Euler with all possible tact forwarded 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 papers. A significant part of the academic "Notes" is filled with the works of Euler. He made presentations at scientific seminars, gave public lectures, participated in the implementation of various technical orders from government departments.

All these dissertations are not only good, but also very excellent, for he [Lomonosov] writes about very necessary physical and chemical matters, which even the most witty people did not know and could not interpret today, what he did with such success that I am quite sure the validity of his explanations. In this case, Mr. Lomonosov must do justice, that he has an excellent talent for explaining physical and chemical phenomena. One should wish that other Academies would be able to produce such revelations, as Mr. Lomonosov showed. Euler, in reply to His Excellency Mr. President, 1747

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

Portrait from 1756 by Emanuel Handmann (Kunstmuseum, Basel)

According to contemporaries, Euler remained a modest, cheerful, extremely sympathetic person all his life, always ready to help another. However, relations with the king do not add up: Friedrich finds the new mathematician unbearably boring, completely unsecular, and treats him dismissively. Maupertuis, president of the Berlin Academy of Sciences, died in 1759. 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.

Again Russia (1766-1783)

Euler worked actively until his last days. In September 1783, the 76-year-old scientist began to feel headaches and weakness. On September 7 () after a dinner spent with his family, talking with Academician 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 brain hemorrhage.

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

Euler was a caring family man, willingly helping his colleagues and young people, generously sharing 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 math, read Euler."

Contribution to science

Euler left important works on the most diverse branches of mathematics, mechanics, physics, astronomy, and a number of applied sciences. Mathematically, the 18th century is the age of Euler. If before him achievements in the field of mathematics were scattered and not always consistent, then 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 been taught since then "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 modulus, the complete theory of continued fractions, the analytical foundation of mechanics, numerous methods of integrating and solving differential equations, the number e, notation i for the imaginary unit , the gamma function with its environment, and much more.

In essence, it was he who created several new mathematical disciplines - number theory, calculus of variations, the 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, a variety of European and ancient languages.

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

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

number theory

He refuted Fermat's conjecture that all numbers of the form are prime; turned out to be divisible by 641.

where is real. Euler deduced 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 that were overlooked 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 the same straight line - " Euler's 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 to the orthocenter all lie on the same circle (the Euler circle).
• The number of vertices (B), faces (D) and edges (P) of any convex polyhedron are related by a simple formula: B + G = P + 2.

The second volume of "Introduction to Infinitely Small Analysis" () is the world's first textbook on analytic geometry and foundations of differential geometry. The term affine transformations is 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, introduced the Euler numbers into consideration.

Other areas of mathematics

• Graph theory began with Euler's solution of the seven-bridge problem 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. The 29-year-old Euler abandoned the traditional geometric approach to mechanics and laid a rigorous analytical foundation under it. Essentially, from that moment on, mechanics becomes an applied mathematical discipline.

Engineering

• 29 volumes in 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

• A new theory of the motion of the moon. - L .: Ed. Academy of Sciences of the USSR, 1934.
• A method for finding curved lines that have the properties of either a maximum or a minimum. - M.-L.: GTTI, 1934.
• Fundamentals 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 infinite. 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 / transl. 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. Sc., 1739.)

see also

• Astronomical Observatory of the St. Petersburg Academy of Sciences

Notes

References

1. Mathematics of the 18th century. Decree. op. - S. 32.
2. Glazer G.I. History of mathematics in the school. - M .: Education, 1964. - S. 232.
3. , with. 220.
4. Yakovlev A. Ya. Leonard Euler. - M .: Enlightenment, 1983.
5. , with. 218.
6. , with. 225.
7. , with. 264.
8. , with. 230.
9. , with. 231.
10. On the 150th anniversary of Euler's death: a collection. - Publishing House of the Academy of Sciences of the USSR, 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, repondit-il, parce que je viens d'un pays où, quand on parle, on est pendu
13. Bell E.T. Decree. op. - S. 123.