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BIOGRAPHIES OF GREAT SCIENTISTS
Euler Leonard. Biography of a scientist
Directory / Biographies of great scientists
During the existence of the Academy of Sciences in Russia, apparently, one of its most famous members was the mathematician Leonhard Euler. He was the first who in his work began to erect a consistent edifice of infinitesimal analysis. Only after his research, outlined in the grandiose volumes of his trilogy "Introduction to Analysis", "Differential Calculus" and "Integral Calculus", analysis became a fully formed science - one of the most profound scientific achievements of mankind. Leonhard Euler was born in Basel, Switzerland on April 15, 1707. His father, Pavel Euler, was a pastor in Richen (near Basel) and had some knowledge of mathematics. The father intended his son for a spiritual career, but he himself, being interested in mathematics, taught it to his son, hoping that it would later be useful to him as an interesting and useful lesson. At the end of his home schooling, thirteen-year-old Leonard was sent by his father to Basel to study philosophy. Among other subjects, elementary mathematics and astronomy were studied at this faculty, taught by Johann Bernoulli. Bernoulli soon noticed the talent of the young listener and began to study with him separately. After receiving a master's degree in 1723, after delivering a speech in Latin on the philosophy of Descartes and Newton, Leonard, at the request of his father, began to study oriental languages \uXNUMXb\uXNUMXband theology. But he was increasingly attracted to mathematics. Euler began to visit his teacher's house, and between him and the sons of Johann Bernoulli - Nikolai and Daniel - a friendship arose that played a very important role in Euler's life. In 1725, the Bernoulli brothers were invited to become members of the St. Petersburg Academy of Sciences, recently founded by Empress Catherine I. When leaving, Bernoulli promised Leonard to notify him if there was a suitable occupation for him in Russia. The next year they reported that there was a place for Euler, but, however, as a physiologist in the medical department of the academy. Upon learning of this, Leonard immediately enrolled as a medical student at the University of Basel. Diligently and successfully studying the sciences of the medical faculty, Euler also finds time for mathematical studies. During this time, he wrote a dissertation published later, in 1727, in Basel, on the propagation of sound and a study on the placement of masts on a ship. In St. Petersburg, there were the most favorable conditions for the flowering of Euler's genius: material security, the opportunity to do what he loved, the presence of an annual journal for publishing his works. The largest group of experts in the field of mathematical sciences in the world then worked here, which included Daniil Bernoulli (his brother Nikolai died in 1726), the versatile H. Goldbach, with whom Euler was connected by common interests in number theory and other issues, the author of the works in trigonometry F. H. Mayer, astronomer and geographer J. N. Delisle, mathematician and physicist G. V. Kraft and others. Since that time, the St. Petersburg Academy has become one of the main centers of mathematics in the world. Euler's discoveries, which, thanks to his lively correspondence, often became known long before publication, make his name more and more widely known. His position at the Academy of Sciences is improving: in 1727 he began work with the rank of adjunct, that is, the junior academician, and in 1731 he became a professor of physics, that is, a full member of the academy. In 1733 he received the chair of higher mathematics, which was previously held by D. Bernoulli, who returned in the same year to Basel. The growth of Euler's authority found a peculiar reflection in the letters to him of his teacher Johann Bernoulli. In 1728, Bernoulli refers to "the most learned and gifted young man Leonhard Euler", in 1737 - to "the most famous and witty mathematician", and in 1745 - to "the incomparable Leonhard Euler - the head of mathematicians." In 1735, the academy had to do a very difficult job of calculating the trajectory of a comet. According to academicians, it took several months of labor to do this. Euler undertook to do this in three days and completed the work, but as a result he fell ill with a nervous fever with inflammation of his right eye, which he lost. Shortly thereafter, in 1736, two volumes of his analytical mechanics appeared. The need for this book was great; many articles were written on various questions of mechanics, but there was no good treatise on mechanics. In 1738, two parts of an introduction to arithmetic appeared in German, in 1739, a new theory of music. Then, in 1840, Euler wrote an essay on the ebb and flow of the seas, crowned with one-third of the prize of the French Academy; the other two thirds were awarded to Daniil Bernoulli and Maclaurin for essays on the same subject. At the end of 1740, power in Russia fell into the hands of the regent Anna Leopoldovna and her entourage. An alarming situation has developed in the capital. At this time, the Prussian King Frederick II decided to revive the Society of Sciences in Berlin, founded by Leibniz, which had been almost inactive for many years. Through his ambassador in Petersburg, the king invited Euler to Berlin. Euler, believing that "the situation began to appear rather uncertain," accepted the invitation. In Berlin, Euler at first gathered around him a small scientific society, and then was invited to the newly restored Royal Academy of Sciences and appointed dean of the mathematical department. In 1743 he published five of his memoirs, four of them on mathematics. One of these works is remarkable in two respects. It indicates a way of integrating rational fractions by decomposing them into partial fractions, and, in addition, the now usual way of integrating higher-order linear ordinary equations with constant coefficients is outlined. In general, most of Euler's work is devoted to analysis. Euler so simplified and supplemented entire large sections of the analysis of infinitesimals, integration of functions, the theory of series, differential equations, which had already begun before him, that they acquired approximately the form that they have largely retained to this day. Euler also started a whole new chapter of analysis, the calculus of variations. This initiative of his was soon picked up by Lagrange and thus a new science was formed. In 1744, Euler published three works on the motion of the stars in Berlin: the first is the theory of the motion of planets and comets, which contains a presentation of the method for determining orbits from several observations; the second and third are about the movement of comets. Euler devoted seventy-five papers to geometry. Some of them, although interesting, are not very important. Some just made up an era. First, Euler must be considered one of the pioneers of research on geometry in space in general. He was the first to give a coherent exposition of analytic geometry in space (in "Introduction to Analysis") and, in particular, introduced the so-called Euler angles, which make it possible to study rotations of a body around a point. In the 1752 work "Proof of some remarkable properties to which bodies limited by flat faces are subject", Euler found a relation between the number of vertices, edges and faces of a polyhedron: the sum of the number of vertices and faces is equal to the number of edges plus two. This ratio was assumed by Descartes, but Euler proved it in his memoirs. This is, in a sense, the first major theorem in the history of mathematics in topology - the deepest part of geometry. Dealing with questions about the refraction of light rays and writing many memoirs on this subject, Euler published an essay in 1762, which proposes the construction of complex lenses in order to reduce chromatic aberration. The English artist Doldond, who discovered two types of glass of different refraction, followed Euler's instructions and built the first achromatic lenses. In 1765, Euler wrote an essay where he solves the differential equations of rotation of a rigid body, which are called the Euler equations of rotation of a rigid body. The scientist wrote many works on the bending and vibration of elastic rods. These questions are interesting not only in mathematical but also in practical terms. Frederick the Great gave the scientist instructions of a purely engineering nature. So, in 1749, he instructed him to inspect the Funo Canal between Havel and Oder and make recommendations for correcting the shortcomings of this waterway. Next, he was instructed to fix the water supply in Sanssouci. This resulted in more than twenty memoirs on hydraulics, written by Euler at various times. Equations of hydrodynamics of the first order with partial derivatives of the projections of velocity, density to pressure are called Euler's hydrodynamic equations. After leaving St. Petersburg, Euler retained the closest connection with the Russian Academy of Sciences, including the official one: he was appointed an honorary member, and a large annual pension was determined for him, and he, for his part, undertook obligations regarding further cooperation. He bought books, physical and astronomical instruments for our academy, selected employees in other countries, giving detailed characteristics of possible candidates, edited the mathematical department of academic notes, acted as an arbitrator in scientific disputes between St. Petersburg scientists, sent topics for scientific competitions, as well as information about new scientific discoveries, etc. Students from Russia lived in Euler's house in Berlin: M. Sofronov, S. Kotelnikov, S. Rumovsky, the latter later became academicians. From Berlin, Euler, in particular, corresponded with Lomonosov, in whose work he highly valued the happy combination of theory and experiment. In 1747, he gave a brilliant review of Lomonosov's articles on physics and chemistry sent to him for conclusion, which greatly disappointed the influential academic official Schumacher, who was extremely hostile to Lomonosov. In Euler's correspondence with his friend Goldbach, an academician of the St. Petersburg Academy of Sciences, we find two famous "Goldbach problems": to prove that every odd natural number is the sum of three prime numbers, and every even number is the sum of two. The first of these assertions was already proved in our time (1937) by Academician I. M. Vinogradov with the help of a very remarkable method, while the second has not been proved so far. Euler was drawn back to Russia. In 1766, through the ambassador in Berlin, Prince Dolgorukov, he received an invitation from Empress Catherine II to return to the Academy of Sciences on any terms. Despite persuasion to stay, he accepted the invitation and arrived in St. Petersburg in June. The Empress provided Euler with funds to buy a house. The eldest of his sons, Johann Albrecht, became an academician in the field of physics, Karl took a high position in the medical department, Christopher, who was born in Berlin, Frederick II did not let go of military service for a long time, and it took the intervention of Catherine II so that he could come to his father. Christopher was appointed director of the Sestroretsk arms factory. Back in 1738, Euler became blind in one eye, and in 1771, after an operation, he almost completely lost his sight and could only write with chalk on a black board, but thanks to his students and assistants. I. A. Euler, A. I. Loksel, V. L. Kraft, S. K. Kotelnikov, M. E. Golovin, and most importantly N. I. Fuss, who arrived from Basel, continued to work no less intensively than before . Euler, with his brilliant abilities and remarkable memory, continued to work, dictating his new memoirs. Only from 1769 to 1783, Euler dictated about 380 articles and essays, and during his life he wrote about 900 scientific papers. Euler's 1769 paper "On Orthogonal Trajectories" contains brilliant ideas about obtaining, using a function of a complex variable, from the equations of two mutually orthogonal families of curves on a surface (i.e., such lines as meridians and parallels on a sphere), an infinite number of other mutually orthogonal families. This work turned out to be very important in the history of mathematics. In the next work of 1771 "On bodies whose surface can be turned into a plane", Euler proves the famous theorem that any surface that can be obtained only by bending the plane, but not stretching it and not compressing it, if it is not conical and not cylindrical , is a set of tangents to some spatial curve. Equally remarkable is Euler's work on map projections. One can imagine what a revelation for the mathematicians of that era were at least Euler's work on the curvature of surfaces and on developable surfaces. The papers in which Euler studies surface mappings that preserve similarity in the small (conformal mappings), based on the theory of functions of a complex variable, must have seemed downright transcendent. And the work on polyhedra began a completely new part of geometry and, in its principledness and depth, stood in line with the discoveries of Euclid. Euler's indefatigability and perseverance in scientific research were such that in 1773, when his house burned down and almost all the property of his family perished, he continued to dictate his research even after this misfortune. Shortly after the fire, a skilled oculist, Baron Wentzel, performed a cataract operation, but Euler could not stand the proper time without reading and became completely blind. In the same year, 1773, Euler's wife died, with whom he had lived for forty years. Three years later he married her sister, Salome Gsell. Enviable health and a happy character helped Euler "resist the blows of fate that befell him ... Always an even mood, soft and natural cheerfulness, some kind of good-natured mockery, the ability to talk naively and amusingly made a conversation with him as pleasant as it was desirable ... "He could sometimes flare up, but" he was not able to harbor anger against anyone for a long time ... "- recalled N. I. Fuss. Euler was constantly surrounded by numerous grandchildren, often a child was sitting in his arms, and a cat lay on his neck. He himself worked with children in mathematics. And all this did not prevent him from working! On September 18, 1783, Euler died of apoplexy in the presence of his assistants, professors Kraft and Leksel. He was buried at the Smolensk Lutheran cemetery. The Academy commissioned a marble bust of the deceased from the well-known sculptor Zh. D. Rachette, who knew Euler well, and Princess Dashkova presented a marble pedestal. Until the end of the 1826th century, I. A. Euler remained the conference secretary of the academy, who was replaced by N. I. Fuss, who married the daughter of the latter, and in XNUMX - the son of Fuss Pavel Nikolaevich, so the descendants of Leonard were in charge of the organizational side of the life of the academy for about a hundred years Euler. The Euler traditions also had a strong influence on Chebyshev's students: A. M. Lyapunov, A. N. Korkin, E. I. Zolotarev, A. A. Markov and others, defining the main features of the St. Petersburg mathematical school. There is no scientist whose name is mentioned in educational mathematical literature as often as the name of Euler. Even in high school, logarithms and trigonometry are still studied to a large extent "according to Euler." Euler found proofs of all Fermat's theorems, showed the falseness of one of them, and proved Fermat's famous Last Theorem for "three" and "four". He also proved that every prime number of the form Euler began to consistently build elementary number theory. Starting with the theory of power residues, he then moved on to quadratic residues. This is the so-called quadratic law of reciprocity. Euler also spent many years solving indefinite equations of the second degree in two unknowns. In all these three fundamental questions, which for more than two centuries after Euler constituted the bulk of elementary number theory, the scientist went very far, but in all three he failed. Gauss and Lagrange received a complete proof. Euler also initiated the creation of the second part of the theory of numbers - the analytic theory of numbers, in which the deepest secrets of integers, for example, the distribution of prime numbers in a series of all natural numbers, are obtained from consideration of the properties of certain analytic functions. The analytic number theory created by Euler continues to develop today. Author: Samin D.K.
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