Pafnuty Chebyshev

The surname Chebyshev has been transliterated in several different ways, like Tchebichef, Tchebychev, Tchebycheff, Tschebyschev, Tschebyschef, Tschebyscheff, Čebyčev, Čebyšev, Chebysheff, Chebychov, Chebyshov (according to native Russian speakers, this one provides the closest pronunciation in English to the correct pronunciation in old Russian), and Chebychev, a mixture between English and French transliterations considered erroneous. It is one of the most well known data-retrieval nightmares in mathematical literature. Currently, the English transliteration Chebyshev has gained widespread acceptance, except by the French, who prefer Tchebychev. The correct transliteration according to ISO 9 is Čebyšëv. The American Mathematical Society adopted the transcription Chebyshev in its Mathematical Reviews.[3]

His first name comes from the Greek Paphnutius (Παφνούτιος), which in turn takes its origin in the Coptic Paphnuty (Ⲡⲁⲫⲛⲟⲩϯ), meaning "that who belongs to God" or simply "the man of God".

Pafnuty Chebyshev

Chebyshev is known for his work in the fields of probability, statistics, mechanics, and number theory. The Chebyshev inequality states that if ${\displaystyle X}$ is a random variable with standard deviation σ > 0, then the probability that the outcome of ${\displaystyle X}$ is no less than ${\displaystyle a\sigma }$ away from its mean is no more than ${\displaystyle 1/a^{2}}$:

${\displaystyle \Pr(|X-{\mathbf {E} }(X)|\geq a\ )\leq {\frac {\sigma ^{2}}{a^{2}}}.}$

The Chebyshev inequality is used to prove the weak law of large numbers.

The Bertrand–Chebyshev theorem (1845, 1852) states that for any ${\displaystyle n>3}$, there exists a prime number ${\displaystyle p}$ such that ${\displaystyle n<p<2n}$. This is a consequence of the Chebyshev inequalities for the number ${\displaystyle \pi (n)}$ of prime numbers less than ${\displaystyle n}$, which state that ${\displaystyle \pi (n)}$ is of the order of ${\displaystyle n/\log(n)}$. A more precise form is given by the celebrated prime number theorem: the quotient of the two expressions approaches 1.0 as ${\displaystyle n}$ tends to infinity.

Chebyshev is also known for the Chebyshev polynomials and the Chebyshev bias – the difference between the number of primes that are congruent to 3 (modulo 4) and 1 (modulo 4).

Chebyshev was the first person to think systematically in terms of random variables and their moments and expectations.[5]

Chebyshev on a 2021 stamp of Russia

Chebyshev is considered to be a founding father of Russian mathematics.[1] Among his well-known students were the mathematicians Dmitry Grave, Aleksandr Korkin, Aleksandr Lyapunov, and Andrei Markov. According to the Mathematics Genealogy Project, Chebyshev has 13,709 mathematical "descendants" as of January 2020.[6]

The lunar crater Chebyshev and the asteroid 2010 Chebyshev were named to honor his major achievements in the mathematical realm.[7]

• Tchebychef, P. L. (1899), Markov, Andrey Andreevich; Sonin, N. (eds.), Oeuvres, vol. I, New York: Commissionaires de l'Académie impériale des sciences, MR 0147353, Reprinted by Chelsea 1962
• Tchebychef, P. L. (1907), Markov, Andrey Andreevich; Sonin, N. (eds.), Oeuvres, vol. II, New York: Commissionaires de l'Académie impériale des sciences, MR 0147353, Reprinted by Chelsea 1962
• Butzer (1999), "P. L. Chebyshev (1821–1894): A Guide to his Life and Work", Journal of Approximation Theory, 96: 111–138, doi:10.1006/jath.1998.3289

• List of things named after Pafnuty Chebyshev

• Media related to Pafnuty Chebyshev at Wikimedia Commons

Wikisource has the text of the 1911 Encyclopædia Britannica article "Chebichev, Pafnutiy Lvovich".

• Mechanisms by Chebyshev – short 3d films – embodiment of Tchebishev's inventions
• Pafnuty Chebyshev at the Mathematics Genealogy Project
• O'Connor, John J.; Robertson, Edmund F., "Pafnuty Chebyshev", MacTutor History of Mathematics Archive, University of St Andrews
• Biography, another one, and yet another (all in Russian).
• Biography in French.
• Œuvres de P.L. Tchebychef Vol. I, Vol. II (in French)