Pafnuty Chebyshev

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Pafnuty Lvovich Chebyshev (16 May 1821 – 8 December 1894) was a Russian mathematician and is widely considered the founder of Russian mathematics. He made important advances in probability, statistics, mechanics and number theory, and several key ideas in math are named after him, including the Chebyshev inequality, the Bertrand–Chebyshev theorem, Chebyshev polynomials, and Chebyshev bias.

- Early life: Chebyshev was born in Okatovo, in the Kaluga region, into a noble family. He walked with a limp from childhood and spent much of his early education at home. The family later moved to Moscow for better schooling.

- Education and early career: He studied at Moscow University under the influential teacher N. D. Brashman. In 1841 he won a silver medal for his work on solving equations and graduated as an outstanding candidate. He wrote a master’s thesis on probability in 1846 and earned a doctorate in 1849 for The Theory of Congruences. He began teaching at St. Petersburg University in 1847 and progressed to full professor by 1860, continuing to contribute to research for many years.

- Major contributions: Chebyshev helped lay the foundations of probability and statistics, and made lasting contributions to mechanics and number theory. He is best known for:
- Chebyshev inequality, which helps bound the probability of deviations from the mean.
- Bertrand–Chebyshev theorem, about primes between n and 2n.
- Chebyshev polynomials, a powerful tool in approximation theory.
- Chebyshev bias, the observed imbalance in prime residues.
He is also regarded as a pioneer in thinking about random variables and their moments.

- Notable students: Dmitry Grave, Aleksandr Korkin, Aleksandr Lyapunov, Andrey Markov, Vladimir Markov, Konstantin Posse, and Yegor Zolotarev.

- Death and legacy: Chebyshev died in St. Petersburg in 1894. He left a lasting impact on mathematics, and his name remains attached to many fundamental concepts. The spelling of his surname appears in many forms across languages, with Chebyshev being the common English form.