The great mathematician Euler Leonard: achievements in mathematics, interesting facts, brief biography

Leonard Euler is a Swiss mathematician and physicist, one of the founders of pure mathematics. He not only made a fundamental and shaping contribution to geometry, calculus, mechanics and number theory, but he also developed methods for solving problems in observational astronomy and applied mathematics in engineering and public affairs.

Euler (mathematician): brief biography

Leonard Euler was born on April 15, 1707. He was the firstborn of Paulus Euler and Margaret Brucker. Father was a descendant of a modest kind of artisans, and the ancestors of Margaret Brucker was a number of famous scientists. Paulus Euler at that time served as vicar in the church of St. Jacob. As a theologian, Leonard's father was interested in mathematics, and during the first two years of studying at the university he attended the courses of the famous Jacob Bernoulli. About a year and a half after the birth of his son, the family moved to Rien, a suburb of Basel, where Paulus Euler became pastor in the local parish. There he conscientiously and faithfully served until the end of his days.

The family lived in cramped conditions, especially after the birth of the second child, Anna Maria, in 1708. The couple will have two more children - Mary Magdalena and Johann Heinrich.

The first lessons of mathematics Leonard received at home from his father. At about the age of eight he was sent to a Latin school in Basel, where he lived in his maternal grandmother's house. To compensate for the poor quality of school education at that time, the father hired a private tutor, a young theologian named Johannes Burkhardt, a passionate mathematics lover.

In October 1720, at the age of 13, Leonard entered the University of Basel at the Faculty of Philosophy (usually at that time), where he attended the introductory classes in elementary mathematics of Johann Bernoulli, the younger brother of Jacob, who was dead by then.

Young Euler began to study with such zeal that soon attracted the attention of the teacher, who encouraged him to study more complex books of his own work and even offered to help in studies on Saturdays. In 1723, Leonard completed his education with a master's degree and read a public lecture in Latin, in which he compared Descartes' system with Newton's natural philosophy.

Following the wishes of his parents, he entered the theological faculty, devoting, however, most of the time to mathematics. Eventually, probably, at the insistence of Johann Bernoulli, the father took for granted the son's destiny to make a scientific, not a theological career.

At the age of 19, mathematician Euler dared to compete with the largest scientists of that time, taking part in the competition for the solution of the problem of the Paris Academy of Sciences on the optimal placement of ship masts. At that moment he, never seen ships in his life, won the first prize, but took the prestigious second place. A year later, when there was a vacancy at the Department of Physics at the University of Basel, Leonard, with the support of his mentor Johann Bernoulli, decided to compete for the place, but lost because of his age and lack of an impressive list of publications. In a sense, he was lucky, as he was able to accept the invitation of the St. Petersburg Academy of Sciences, founded several years earlier by Tsar Peter I, where Euler found a more promising field that allowed him to develop to the fullest. The main role in this played Bernoulli and his two sons, Nicklaus II and Daniel I, who were active there.

St. Petersburg (1727-1741): rapid take-off

Euler spent the winter of 1726 in Basel, studying anatomy and physiology in preparation for the execution of his expected duties in the academy. When he arrived in St. Petersburg and began to work as an adjunct, it became obvious that he must fully devote himself to the mathematical sciences. In addition, Euler was required to participate in the examinations in the Cadet Corps and advise the government on various scientific and technical issues.

Leonard easily adapted to the new harsh living conditions in northern Europe. Unlike most other foreign members of the academy, he immediately began to learn Russian and quickly mastered it, both in written and oral forms. For some time he lived with Daniel Bernoulli and was friends with Christian Goldbach, the permanent secretary of the academy, known today for his still unsolved problem, according to which any even number, starting at 4, can be represented by the sum of two primes. Extensive correspondence between them is an important source on the history of science in the eighteenth century.

Leonard Euler, whose achievements in mathematics instantly brought him world fame and increased his status, held the Academy's most fruitful years.

In January 1734 he married Katarina Gzel, the daughter of a Swiss artist who taught with Euler, and they moved to their own house. In the marriage 13 children were born, of whom, however, only five have reached adulthood. The firstborn, Johann Albrecht, also became a mathematician, and later helped his father in his work.

Euler did not avoid adversity. In 1735 he became seriously ill and almost died. To the great relief of all, he recovered, but three years later he fell ill again. This time the disease cost him his right eye, which is clearly visible in all the portraits of the scientist since that time.

Political instability in Russia, which came after the death of Queen Anne Ivanovna, forced Euler to leave St. Petersburg. Moreover, he had an invitation from the Prussian King Frederick II to come to Berlin and help establish the Academy of Sciences there.

In June 1741, Leonard, along with his wife Katarina, 6-year-old Johann Albrecht and one-year-old Karl, left St. Petersburg for Berlin.

Work in Berlin (1741-1766)

The military campaign in Silesia postponed Friedrich II's plans to establish an academy. And only in 1746 it was finally formed. The president was Pierre-Louis Moro de Maupertuis, and Euler took the post of director of the mathematical department. But before that he did not stay idle. Leonard wrote about 20 scientific articles, 5 basic treatises and made more than 200 letters.

Despite the fact that Euler performed many duties - he was responsible for the observatory and botanical gardens, he solved personnel and financial issues, he was engaged in selling the almanacs, which formed the main source of the Academy's income, not to mention various technological and engineering projects, its mathematical performance was not affected.

He was also not too distracted by the scandal about the primacy of the discovery of the principle of least action, which broke out in the early 1750s, which Maupertuis claimed, which was disputed by the Swiss scientist and newly elected academician Johann Samuel Koenig, who spoke of his mentioning Leibniz in a letter to the mathematician Jacob Herman. Koenig was close to Maupertuis's accusation of plagiarism. When he was asked to present a letter, he could not do it, and Euler was instructed to investigate the case. Not having sympathy for the philosophy of Leibniz, he took the side of the president and accused Koenig of fraud. The boiling point was reached when Voltaire, who took the side of Koenig, wrote a derogatory satire, ridiculed Maupertuis and did not spare Euler. The President was so upset that he soon left Berlin, and Euler had to conduct business, de facto heading the academy.

The family of a scientist

Leonard became so wealthy that he bought an estate in Charlottenburg, a western suburb of Berlin, large enough to provide a comfortable stay for his widowed mother, who brought to Berlin in 1750, his half-sister and all his children.

In 1754, his first-born Johann Albrecht, on the recommendation of Maupertuis at the age of 20, was also elected a member of the Berlin Academy. In 1762, his work on perturbations of the comet orbits attracted the planets to the prize of the Petersburg Academy, which he shared with Alexis Claude Claire. The second son of Euler, Karl, studied medicine in Halle, and the third, Christophe, became an officer. His daughter Charlotte married a Dutch aristocrat, and her elder sister Helena in 1777 - for a Russian officer.

The King's Treason

The relationship of the scientist with Frederick II was not easy. Partly this was due to a noticeable difference in personal and philosophical inclinations: Frederic - a proud, confident, elegant and witty companion, sympathetic to French enlightenment; Mathematician Euler is a modest, inconspicuous, down-to-earth and devout Protestant. Another, perhaps more important, reason was Leonard's insult to the fact that he was never offered the post of president of the Berlin Academy. This resentment only increased after Maupertuis's departure and Euler's efforts to keep the institution afloat when Friedrich was trying to interest the presidential chair of Jean Léron D'Alembert. The latter actually came to Berlin, but only to inform the king of his disinterest and recommend Leonard. Friedrich not only ignored the advice of D'Alembert, but demonstratively declared himself the head of the academy. This, along with many other failures of the king, eventually led to the fact that the biography of the mathematician Euler again made a sharp turn.

In 1766, despite the obstacles on the part of the monarch, he left Berlin. Leonard accepted the invitation of Empress Catherine II to return to St. Petersburg, where he was solemnly met again.

Again St. Petersburg (1766-1783)

Honored in the academy and adored at the court of Catherine, the great mathematician Euler held an extremely prestigious position and enjoyed the influence, in which he was so long denied in Berlin. In fact, he played the role of spiritual leader, if not the head of the academy. Unfortunately, however, with his health, not everything developed so well. The cataract of the left eye, which began to bother him in Berlin, became more serious, and in 1771 Euler decided on an operation. Its consequence was the formation of an abscess, which almost completely destroyed sight.

Later that year, during a big fire in St. Petersburg, his wooden house broke out, and almost blind Euler managed not to burn out alive only thanks to the heroic rescue of Peter Grimm, a master from Basel. To ease the misfortune, the Empress allocated funds for the construction of a new house.

Another severe blow was struck by Euler in 1773, when his wife died. Three years later, in order not to depend on his children, he married for the second time at her half-sister Salome-Avigeye Gzel (1723-1794).

Despite all these fatal events, the mathematician L. Euler remained devoted to science. Indeed, about half of his work was published or was born in St. Petersburg. Among them, two of his "best-selling books" are "Letters to the German Princess" and "Algebra." Naturally, he would not be able to do this without a good secretary and the technical assistance that he was provided, among others, by Nicklaus Fuss, a compatriot from Basel and the future husband of Euler's granddaughter. His son Johann Albrecht also participated in the process. The latter also acted as a stenographer of the academy sessions, at which the scientist, as the oldest active member, was to preside.

Death

The great mathematician Leonard Euler died of a stroke on September 18, 1783, while playing with his grandson. On the day of his death on two of his large slate boards , formulas were found describing the flight in a balloon, committed June 5, 1783 in Paris, the brothers Montgolfier. The idea was developed and prepared for publication by the son Johann. This was the last article of the scientist, published in the 1784th volume of Memoires. Leonard Euler and his contribution to mathematics were so great that the flow of articles awaiting their turn in academic publications was still printed for 50 years after the death of the scientist.

Scientific activity in Basel

During the short Basel period, Euler's contributions to mathematics were compiled on isochronous and reciprocal curves, as well as work for the Prize of the Paris Academy. But the main work at this stage was Dissertatio Physica de sono, submitted in support of his nomination to the Department of Physics at the University of Basel, about the nature and distribution of sound, in particular, about the speed of sound and its generation by musical instruments.

The first St. Petersburg period

Despite the health problems experienced by Euler, the achievements in the mathematics of the scientist can not but surprise. During this time, in addition to major works in mechanics, music theory, and naval architecture, he wrote 70 articles on a wide range of subjects, from mathematical analysis and number theory to specific problems in physics, mechanics and astronomy.

The two-volume "Mechanics" was the beginning of a far-reaching idea of a comprehensive review of all aspects of mechanics, including the mechanics of rigid, flexible and elastic bodies, as well as liquids and celestial mechanics.

As can be seen from the notebooks of Euler, even in Basel, he thought a lot about music and musical composition and planned to write a book. These plans matured in St. Petersburg and gave rise to the work of Tentamen, published in 1739. The work begins with a discussion of the nature of sound as a vibration of air particles, including its propagation, the physiology of auditory perception and the generation of sound by string and wind instruments.

The core of the work was the theory of pleasure, caused by music, which Euler created by assigning a range of tone, chord or their sequences to numerical values, the degrees that make up the "pleasantness" of a given musical construction: the lower the degree, the higher the pleasure. The work is done in the context of the diatonic chromatic temperament loved by the author, but also a complete mathematical theory of temperaments (both ancient and modern) is given. Euler was not the only one who tried to turn music into an exact science: Descartes and Mersenne did the same before him, like D'Alembert and many others after him.

The two-volume Scientia Navalis is the second stage of its development of rational mechanics. The book outlines the principles of hydrostatics and develops the theory of equilibrium and vibrations of three-dimensional bodies immersed in water. The work contains the rudiments of the mechanics of solids, which later crystallizes in the book Theoria Motus corporum solidorum seu rigidorum, the third major treatise on mechanics. In the second volume, the theory is applied to ships, shipbuilding and navigation.

Incredibly, Leonard Euler, whose achievements in mathematics were impressive during this period, had the time and endurance to write a 300-page work on elementary arithmetic for use in the gymnasiums of St. Petersburg. How fortunate were the children taught by the great scientist!

Berlin works

In addition to 280 articles, many of which were very important, during this period the mathematician Leonard Euler created a number of epoch-making scientific treatises.

The problem of brachistochrone - the search for the way in which the point mass moves under the action of gravity from one point in the vertical plane to the other in the shortest time - is an early example of the problem created by Johann Bernoulli in finding a function (or curve) that optimizes the analytic expression, Which depends on this function. In 1744, and then in 1766 Euler significantly generalizes this problem, creating an entirely new section of mathematics - "calculus of variations".

Two smaller treatises, about trajectories of planets and comets and on optics, appeared approximately in 1744 and 1746. The latter is of historical interest, since it began a discussion about Newtonian particles and the wave theory of Euler light.

As a sign of respect for his employer, King Frederick II, Leonard translated important work on the ballistics of the Englishman Benjamin Robins, although he unfairly criticized his "Mechanics" in 1736. He added, however, so many comments, explanatory notes and corrections that as a result The book "Artillery" (1745) by volume was 5 times higher than the original.

In the two-volume "Introduction to the analysis of infinitesimal" (1748), the mathematician Euler positions the analysis as an independent discipline, generalizes his numerous discoveries in the field of infinite series, infinite products and continued fractions. He develops a clear concept of the function of real and complex values and emphasizes a fundamental role in the analysis of the number e, exponential and logarithmic functions. The second volume is devoted to analytic geometry: the theory of algebraic curves and surfaces.

"Differential calculus" also consists of two parts, the first of which is devoted to the calculation of differences and differentials, and the second - the theory of power series and summing formulas with a large number of examples. Here, by the way, the first printed Fourier series is contained .

In the three-volume "Integral calculus" the mathematician Euler considers the quadratures (i.e., infinite iterations) of elementary functions and the techniques of reducing linear differential equations to them, and he describes in detail the theory of second-order linear differential equations.

Throughout the years in Berlin and later Leonard was engaged in geometric optics. His articles and books on this subject, including the monumental three-volume Dioptric, amounted to seven volumes of Opera Omnia. The central theme of this work was the improvement of optical instruments, such as telescopes and microscopes, methods for eliminating chromatic and spherical aberrations through a complex system of lenses and filling fluids.

Euler (mathematician): interesting facts of the second St. Petersburg period

This was the most productive time during which the scientist published more than 400 papers on the topics already mentioned, as well as on geometry, probability theory and statistics, cartography, and even on pension funds for widows and agriculture. Of these, three treatises on algebra, the theory of the moon and naval science, as well as on number theory, natural philosophy and dioptric, can be distinguished.

Here was his next "bestseller" - "Algebra". The name of the mathematician Euler adorned this 500-page work, which was written with the goal of teaching this discipline to the absolute beginner. He dictated the book to a young apprentice, whom he had brought with him from Berlin, and when the work was completed, he understood everything and was able to solve algebraic tasks given him with great ease.

"The second theory of the courts" was also intended for people who do not have knowledge in mathematics, namely, sailors. Not surprisingly, thanks to the author's unusual didactic skill, the work was very successful. The Minister of Navy and Finance of France Anne-Robert Turgot invited King Louis XVI to oblige all students of naval and artillery schools to study Euler's treatise. It is very likely that Napoleon Bonaparte was one of those students. The king even paid mathematics 1000 rubles for the privilege of reprinting the work, and Empress Catherine II, unwilling to yield to the king, doubled the amount, and the great mathematician Leonard Euler additionally received 2000 rubles!