CHEBYSHEV, PAFNUTY LVOVICH

born May 4 [May 16, New Style], 1821, Okatovo, Russia died Nov. 26 , 1894, St. Petersburg founder of the St. Petersburg mathematical school (sometimes called the Chebyshev school), who is remembered primarily for his work on the theory of prime numbers. Chebyshev became assistant professor of mathematics at the University of St. Petersburg in 1847. In 1860 he became a correspondent and in 1874 a foreign associate of the Institut de France. He developed a basic inequality of probability theory called Chebyshev's inequality, a generalized form of the Bienaym-Chebyshev inequality, and used the latter inequality to give a very simple and precise demonstration of the generalized law of large numbers. Chebyshev's work on prime numbers included the determination of the number of primes below a given number. He studied theoretical mechanics and devoted much attention to the problem of obtaining rectilinear motion from rotary motion by mechanical linkage. The Chebyshev parallel motion is a three-bar linkage that gives a very close approximation to exact rectilinear motion. His mathematical writings covered a wide range of subjects, including the theory of probabilities, quadratic forms, orthogonal functions, the theory of integrals, gearings, the construction of geographic maps, and formulas for the computation of volumes. His Teoria sravneny (1849; Theory of Congruences) made him widely known in the mathematical world and was used as a textbook in Russian universities for many years.