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The most significant mathematician of all time, Leonhard Euler
was born in Basel in 1707
. He contributed to areas of both pure and applied mathematics, including calculus, analysis, number theory, topology, algebra, geometry, trigonometry, analytical mechanics
, hydrodynamics, and the theory of the moon’s motion.
By means of his numerous books and memoirs that he submitted to the academy, Euler carried integral calculus to a higher degree of perfection, developed the theory of trigonometric and logarithmic functions, reduced analytical operations to a greater simplicity, and threw new light on nearly all parts of pure mathematics. Overtaxing himself, Euler in 1735 lost the sight of one eye. Then, invited by Frederick the Great in 1741, he became a member of the Berlin Academy, where for 25 years he produced a steady stream of publications, many of which he contributed to the St. Petersburg Academy, which granted him a pension. In 1748, in his Introductio in analysin infinitorum, he developed the concept of function in mathematical analysis, through which variables are related to each other and in which he advanced the use of infinitesimals and infinite quantities. He did for modern analytic geometry and trigonometry what the Elements of Euclid had done for ancient geometry, and the resulting tendency to render mathematics and physics in arithmetical terms has continued ever since. He is known for familiar results in elementary geometry; for example, the Euler line through the orthocentre (the intersection of the altitudes in a triangle), the circumcentre (the centre of the circumscribed circle of a triangle), and the barycentre (the “centre of gravity,” or centroid) of a triangle. He was responsible for treating trigonometric functions--i.e., the relationship of an angle to two sides of a triangle--as numerical ratios rather than as lengths of geometric lines and for relating them, through the so-called Euler identity (eix = cos x + i sin x) , with complex numbers (e.g., 1 + −1 ). He discovered the imaginary logarithms of negative numbers and showed that each complex number has an infinite number of logarithms.