Euler, Leonhard (lāˈônhärt oiˈlər) [key], 1707–83, Swiss mathematician. Born and educated at Basel, where he knew the Bernoullis, he went to St. Petersburg (1727) at the invitation of Catherine I, becoming professor of mathematics there on the departure of Daniel Bernoulli (1733). He was invited to Berlin (1741) by Frederick the Great and remained there until 1766, when he returned to St. Petersburg. Euler was the most prolific mathematician who ever lived; his collected works run to more than seventy volumes. He contributed to numerous areas of both pure and applied mathematics, including the calculus of variations, analysis, number theory, algebra, geometry, trigonometry, analytical mechanics, hydrodynamics, and the lunar theory (calculation of the motion of the moon). Euler was one of the first to develop the methods of the calculus on a wide scale. Though half-blind for much of his life and totally blind for the last seventeen years, he retained to the end a near-legendary skill at calculation. Among his results are the differential equation named for him, the formula relating the number of faces, edges, and vertices of a polyhedron ( *F* + *V* = *E* + 2), and the famous equation *e* ^{ i π} + 1 = 0 connecting five fundamental numbers in mathematics.

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