Leonhard Euler (15.04.1707-18.09.1783) — a mathematician, mechanician and physicist. Born in Basel (Switzerland). Studied (1720—24) at the University of Basel, where his teachers were the well-known mathematicians of the time Jakob and Johann Bernoulli. Possessing outstanding abilities, especially for mathematics, he received the degree of Master of Arts as early as 1722. In 1727, on the recommendation of the brothers Nikolaus and Daniel Bernoulli (sons of J. Bernoulli), with whom he had been on friendly terms in Basel, he began work as an adjunct in mathematics at the St Petersburg Academy of Sciences; all his later activity was connected with it. He lived in St Petersburg in 1727—41 and from 1766 to the end of his life. In 1741 —66 he worked at the Berlin Academy of Sciences, but maintained close ties with the St Petersburg Academy of Sciences. Both St Petersburg periods of Euler's life were extremely fruitful scientifically; about 500 scientific works were prepared by him here. The total number of Euler's works reaches almost 850, among them about 20 fundamental books. His scientific correspondence (about 3 000 letters) is also of considerable interest.
Euler's research related to many branches of mathematics and its applications, where he laid the foundations of a number of scientific fields. In particular, he began the theory of functions of a complex variable, the calculus of variations, the theory of special functions, and others.
Euler's physical research concerned mechanics, optics, acoustics, thermoelectricity and mathematical physics. He tried to construct a unified picture of the world and of physical processes. According to Euler, all optical, electrical, magnetic, thermal and other phenomena are the interaction of “coarse” matter and a more “subtle” substance, less dense but more elastic — the ether. Mechanical displacements of the ether created, in Euler's opinion, the whole variety of the phenomena of nature. In optics he created his own wave theory of light, trying to explain the best-known light phenomena by oscillations of the ether; he derived a formula for the dependence of the refractive index on the parameters of the medium and of the refracted ray, and a formula for the focal length of a biconvex lens; he considered (1752) that the colour of bodies depends on the frequency of the light ray, that the maximum wavelength corresponds to red rays and the minimum to violet ones, and so on. In the opinion of S. I. Vavilov, Euler was the first to write down the equation of a plane harmonic wave.
He established the law of conservation of angular momentum (1746), developed the theory of moments of inertia, and laid the foundations for the transformation of mechanics from geometric to analytic (1736).
He worked on the theory of heat, considering that “heat is a certain motion of the smallest particles of bodies”, investigated the nature of electricity and tried to explain electrical phenomena, and developed a theory of magnetism based on vortices.
Together with D. Bernoulli he is the creator of the mechanics of liquids and gases. In particular, he formulated the basic laws of motion of an ideal fluid (1755). His works also concerned acoustics (the mathematical theory of music, the propagation of sounds in tubes of variable cross-section, the theory of musical instruments), the theory of elasticity, strength of materials, the theory of the stability of ships, ballistics and mathematical physics (problems of the oscillations of strings, plates, membranes and others). In his philosophical views he was a spontaneous materialist.
A member of many academies of sciences, in particular the St Petersburg (1742), Berlin and Paris academies and the Royal Society.