# Pafnuty Chebyshev

**Pafnuty Chebyshev** (1821-1894) was one of the greatest Russian mathematicians, who made significant contributions to number theory. He also advanced knowledge concerning the convergence of Taylor series, probability, and Poisson's weak law of large numbers.

He was homeschooled by his mother and a cousin until age eleven, and then homeschooled by a tutor until entering Moscow University in 1837.

He co-authored a complete edition of Euler's 99 number theory papers, in a two-volume set published in 1849. In 1850, Chebyshev proved Bertrand's conjecture that there is always at least one prime between n and 2n, for n > 3. Chebyshev also made progress on proving the Prime Number Theorem.

Subsequently, Chebyshev made his greatest contribution by advancing the understanding of orthogonal polynomials, and "Chebyshev polynomials" are named after him. This generalized the work of Legendre and Laplace.

In probability, Chebyshev was the first to clarify the concepts of "random quantity" and its "expectation (mean) value."

Students praised his lecturing style as follows:^{[1]}

- Chebyshev was a wonderful lecturer. His courses were very short. As soon as the bell sounded, he immediately dropped the chalk, and, limping, left the auditorium. On the other hand he was always punctual and not late for classes. Particularly interesting were his digressions when he told us about what he had spoken outside the country or about the response of Hermite or others. Then the whole auditorium strained not to miss a word.