Short answers, pulled from the story.
Pafnuty Chebyshev was a Russian mathematician born in the village of Okatovo in the province of Kaluga and considered the founding father of Russian mathematics. He made foundational contributions to probability, statistics, mechanics, and number theory, and a range of mathematical concepts bear his name, including the Chebyshev inequality, Chebyshev polynomials, Chebyshev linkage, and Chebyshev bias.
The Chebyshev inequality states that if a random variable has standard deviation greater than zero, the probability that an outcome falls a given distance or more from the mean is bounded by a calculable maximum. It can be used to prove the weak law of large numbers.
The Bertrand-Chebyshev theorem, established in two stages in 1845 and 1852, states that for any integer there always exists a prime number between that integer and its double. It was a key result in number theory and produced useful inequalities for estimating the count of primes below a given bound.
Chebyshev began his formal studies in September 1837 at the second philosophical department of Moscow University. He later promoted his thesis at St Petersburg University in 1847 and rose through its faculty to become a merited professor in 1872 after twenty-five years of teaching. Between 1852 and 1858 he also taught practical mechanics at the Alexander Lyceum in Tsarskoe Selo.
Chebyshev's well-known students included the mathematicians Dmitry Grave, Aleksandr Korkin, Aleksandr Lyapunov, and Andrei Markov. As of January 2025, the Mathematics Genealogy Project counts more than seventeen thousand mathematical descendants tracing their lineage to him.
The name has been transliterated in at least ten different ways across European languages. In English, the spelling Chebyshev has gained widespread acceptance and was adopted by the American Mathematical Society in its Mathematical Reviews. The correct transliteration according to ISO 9 is Cebyshev with diacritics.