1911 Encyclopædia Britannica/Chebichev, Pafnutiy Lvovich

CHEBICHEV, PAFNUTIY LVOVICH (1821–1894), Russian mathematician, was born at Borovsk on the 26th of May 1821. He was educated at the university of Moscow, and in 1859 became professor of mathematics in the university of St Petersburg, a position from which he retired in 1880. He was chosen a correspondent of the Institute of France in 1860, and succeeded to the high honour of associé étranger in 1874. He was also a foreign member of the Royal Society of London. After N. I. Lobachevskiy he probably ranks as the most distinguished mathematician Russia has produced. In 1841 he published a valuable paper, “Sur la convergence de la serié de Taylor,” in Crelle’s Journal. His best-known papers, however, deal with prime numbers; in one of these (“Sur les nombres premiers,” 1850) he established the existence of limits within which must be comprised the sum of the logarithms of the primes inferior to a given number. Another question to which he devoted much attention was that of obtaining rectilinear motion by linkage. The parallel motion known by his name is a three-bar linkage, which gives a very close approximation to exact rectilinear motion, but in spite of all his efforts he failed to devise one that produced absolutely true rectilinear motion. At last, indeed, he came to the conclusion that to do so was impossible, and in that conviction set to work to find a rigorous proof of the impossibility. While he was engaged on this task the desired linkage, which moved the highest admiration of J. J. Sylvester, was discovered and exhibited to him by one of his pupils, named Lipkin, who, however, it was afterwards found, had been anticipated by A. Peaucellier. Chebichev further constructed an instrument for drawing large circles, and an arithmetical machine with continuous motion. His mathematical writings, which account for some forty entries in the Royal Society’s catalogue of scientific papers, cover a wide range of subjects, such as the theory of probabilities, quadratic forms, theory of integrals, gearings, the construction of geographical maps, &c. He also published a Traité de la théorie des nombres. He died at St Petersburg on the 8th of December 1894.