Leonard Euler is a Swiss mathematician and physicist, one of the founders of pure mathematics. He not only made a fundamental and formative contribution to geometry, calculus, mechanics and number theory, but also developed methods for solving problems of observational astronomy and applied mathematics to technology and social affairs.
Euler (mathematician): short biography
Leonard Euler was born on April 15, 1707. He was the first-born of Paulus Euler and Margaret Brucker. His father came from a modest kind of artisans, and the ancestors of Margareta Brucker were 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 study at the university he attended the courses of the famous Jacob Bernoulli. About a year and a half after the birth of a son, the family moved to Rien, a suburb of Basel, where Paulus Euler became a pastor in a 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 their second child, Anna Maria, in 1708. The couple will have two more children - Maria Magdalena and Johann Heinrich.
Leonard received his first math lessons 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 of that time, his father hired a private tutor, a young theologian named Johannes Burkhardt, a passionate lover of mathematics.
In October 1720, at the age of 13, Leonard entered the University of Basel at the Faculty of Philosophy (a common thing at that time), where he attended introductory classes in elementary mathematics by Johann Bernoulli, the younger brother of Jacob, who had died by then.
The young Euler began his studies with such zeal that he soon attracted the attention of a teacher who encouraged him to study more complex books of his own composition and even offered to help with studies on Saturdays. In 1723, Leonard completed his master's degree and gave a public lecture in Latin, in which he compared the Descartes system with Newton's natural philosophy.
Following the wishes of his parents, he entered the theological faculty, however, devoting most of his time to mathematics. In the end, probably, at the insistence of Johann Bernoulli, the father took for granted his son's destiny to pursue a scientific rather than a theological career.
At the age of 19, the mathematician Euler dared to compete with the largest scientists of that time by taking part in a competition to solve the problem of the Paris Academy of Sciences on the optimal placement of ship masts. At that moment, he had never seen ships in his life, he did not win the first prize, but took the prestigious second place. A year later, when a vacancy appeared 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 the 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 fully develop. Bernoulli and his two sons, Nicklaus II and Daniel I, who actively worked there, played the main role in this.
St. Petersburg (1727-1741): rapid take-off
Euler spent the winter of 1726 in Basel, studying anatomy and physiology in preparation for fulfilling his expected duties at the academy. When he arrived in St. Petersburg and began working as an adjunct, it became obvious that he should devote himself fully to the mathematical sciences. In addition, Euler was required to participate in 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 study 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 from 4, can be represented as the sum of two prime numbers. Extensive correspondence between them is an important source on the history of science in the 18th century.
Leonard Euler, whose achievements in mathematics instantly brought him worldwide fame and raised his status, spent his most fruitful years at the academy.
In January 1734, he married Katarina Gzel, the daughter of a Swiss artist who taught with Euler, and they moved to their own home. 13 children were born in the marriage, of which, however, only five reached the age of majority. The first-born, Johann Albrecht, also became a mathematician, and later helped his father in his work.
Euler did not escape adversity. In 1735, he became seriously ill and nearly died. To the great relief of all, he recovered, but after three years 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.
The political instability in Russia that occurred after the death of Tsarina Anna Ivanovna forced Euler to leave St. Petersburg. Moreover, he had an invitation from the Prussian king Frederick II to come to Berlin and help create an academy of sciences there.
In June 1741, Leonard, together 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 the plans of Frederick II to establish an academy. And only in 1746 she was finally educated. Pierre-Louis Moreau de Maupertuis became president, and Euler took up the post of director of the mathematics department. But before that, he did not remain idle. Leonard wrote about 20 scientific articles, 5 basic treatises and composed more than 200 letters.
Despite the fact that Euler performed many duties - he was responsible for the observatory and botanical gardens, solved personnel and financial issues, was engaged in the sale of almanacs, which constituted the main source of income for the academy, 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 erupted in the early 1750s, which claimed Maupertuis, which was disputed by the Swiss scientist and newly elected academician Johann Samuel Koenig, who spoke of his mention in mathematician Jacob Leibniz. Koenig was close to accusing Maupertuis of plagiarism. When asked to present a letter, he could not do this, and Euler was assigned to investigate the case. Not sympathetic to Leibniz's philosophy, he sided with the president and accused Koenig of fraud. The boiling point was reached when Voltaire, who took the side of Koenig, wrote a derogatory satire that 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 leading the academy.
Scientist's family
Leonard became so wealthy that he acquired a manor in Charlottenburg, a western suburb of Berlin, large enough to provide a comfortable living for his widowed mother, whom he 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 orbits of comets by the attraction of planets received the prize of the St. Petersburg Academy, which he shared with Alexis-Claude Claireau. Euler's second son, Carl, studied medicine in Halle, and the third, Christoph, became an officer. His daughter Charlotte married a Dutch aristocrat, and her older sister Helena in 1777, a Russian officer.
King's wiles
The scientist’s relationship with Frederick II was not easy. This was partly due to a noticeable difference in personal and philosophical inclinations: Frederick is a proud, confident, elegant and witty conversationalist who sympathizes with French enlightenment; the mathematician Euler is a modest, inconspicuous, mundane and devout Protestant. Another, perhaps more important reason was Leonard’s resentment at the fact that he was not offered the post of president of the Berlin Academy. This resentment only increased after the departure of Maupertuis and Euler's efforts to keep the institution afloat when Frederick tried to interest Jean Leron D'Alembert in the presidency. 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 defiantly declared himself the head of the academy. This, along with many other failures of the king, in the end, led to the fact that the biography of the mathematician Euler again made a sharp turn.
In 1766, despite the obstacles from 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)
Highly respected at 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 had been denied in Berlin for so long. In fact, he played the role of a spiritual leader, if not the head of the academy. Unfortunately, however, with his health, not everything went so well. The cataract of the left eye, which began to bother him in Berlin, was becoming more serious, and in 1771 Euler decided on an operation. Its consequence was the formation of an abscess, which almost completely destroyed vision.
Later that year, during a great fire in St. Petersburg, his wooden house broke out, and the almost blind Euler managed not to be burned alive only thanks to the heroic rescue by Peter Grimm, a craftsman from Basel. To alleviate the misfortune, the empress allocated funds for the construction of a new house.
Euler suffered another heavy blow in 1773 when his wife died. After 3 years, so as not to depend on his children, he married for the second time to her half-sister Salome-Avigey Gzel (1723-1794).
Despite all these fatal events, the mathematician L. Euler remained devoted to science. Indeed, about half of his works were published or originated in St. Petersburg. Among them are two of his "best sellers" - "Letters to the German Princess" and "Algebra." Naturally, he would not have been able to do this without the good secretary and technical assistance that he received, among others, from Niklaus Fuss, a compatriot from Basel and the future husband of Euler’s granddaughter. A feasible part in the process was taken by his son Johann Albrecht. The latter also acted as a stenographer of the Academy sessions, at which the scientist, as the oldest full 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, formulas describing a balloon flight performed on June 5, 1783 in Paris by the Montgolfier brothers were found on his two large slate boards . The idea was developed and prepared for publication by son Johann. This was the last article by a scientist published in the 1784th volume of Memoires. Leonhard Euler and his contribution to mathematics were so great that the stream of articles awaiting their turn in academic journals was still published for 50 years after the death of the scientist.
Scientific activities in Basel
For a short Basel period, Euler's contribution to mathematics consisted of works 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, filed in support of his promotion to the Department of Physics at the University of Basel, about the nature and distribution of sound, in particular, 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 cannot but be surprising. During this time, in addition to the main works in mechanics, music theory, as well as naval architecture, he wrote 70 articles on a wide variety of topics, 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 plan of a comprehensive review of all aspects of mechanics, including the mechanics of solid, flexible and elastic bodies, as well as liquids and celestial mechanics.
As you can see from Euler’s notebooks, back 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 vibration of air particles, including its distribution, 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 numerical values to the tone interval, chord or their sequence, degrees that make up the “pleasantness” of this musical construction: the lower the degree, the higher the pleasure. The work was done in the context of the author's favorite diatonic chromatic temperament, 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 exact science: Descartes and Mersenne did the same before him, as did D'Alembert and many others after him.
The two-volume Scientia Navalis is the second phase of his development of rational mechanics. The book sets out the principles of hydrostatics and develops a theory of equilibrium and vibrations of three-dimensional bodies immersed in water. The work contains the rudiments of solid mechanics, which later crystallizes in Theoria Motus corporum solidorum seu rigidorum, the third major treatise on mechanics. In the second volume, the theory applies 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 St. Petersburg gymnasiums. How lucky those 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 brachistochrone problem - finding the path in which a point mass moves under the influence of gravity from one point in a vertical plane to another in the shortest time - is an early example of a task created by Johann Bernoulli to find a function (or curve) that optimizes an analytical expression, dependent on this function. In 1744, and then in 1766, Euler significantly generalizes this problem, creating a completely new branch of mathematics - “calculus of variations”.
Two smaller treatises on the trajectories of planets and comets and on optics appeared around 1744 and 1746. The latter is of historical interest, since he began a discussion about Newtonian particles and the Euler wave theory of light.
As a sign of respect to his employer, King Frederick II, Leonard translated an important work on the ballistics of the Englishman Benjamin Robins, although he unfairly criticized his Mechanics of 1736. He added, however, so many comments, explanatory notes and corrections that as a result the book "Artillery" (1745) in volume 5 times exceeded the original.
In the two-volume “Introduction to the Analysis of the Infinitesimals” (1748), the mathematician Euler positions analysis as an independent discipline, summarizes his many 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 the fundamental role in the analysis of the number e, the 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 calculus of differences and differentials, and the second to the theory of power series and summing formulas with a large number of examples. Here, by the way, contains the first printed Fourier series.
In the three-volume Integral Calculus, the mathematician Euler considers quadratures (that is, infinite iterations) of elementary functions and techniques for reducing linear differential equations to them, and 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 “Diopter”, composed 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 liquids.
Euler (mathematician): interesting facts of the second St. Petersburg period
This was the most productive time, during which the scientist published more than 400 works on the topics already mentioned, as well as on geometry, probability theory and statistics, cartography, and even about pension funds for widows and agriculture. Of these, three treatises can be distinguished on algebra, the theory of the moon and naval science, as well as on number theory, natural philosophy and diopter.
Here appeared his next "best seller" - "Algebra". The name of the mathematician Euler graced this 500-page work, which was written with the aim of teaching this discipline an absolute beginner. He dictated the book to a young apprentice, whom he brought with him from Berlin, and when the work was finished, he figured out everything and was able to solve the algebraic problems assigned to him with great ease.
The "Second Ship Theory" was also intended for people without knowledge of mathematics, namely, sailors. Not surprisingly, thanks to the extraordinary didactic mastery of the author, the work was very successful. The Minister of the Navy and Finance of France, Ann-Robert Turgot, invited King Louis XVI to oblige all students of naval and artillery schools to study the Euler 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, not wanting to yield to the king, doubled the amount, and the great mathematician Leonard Euler received an additional 2000 rubles!