Pafnuty Lvovich Chebyshev
May 16, 1821|
Akatovo, Kaluga Governorate, Russian Empire
|Died||December 8, 1894
St. Petersburg, Russian Empire
|Institutions||St. Petersburg University|
|Alma mater||Moscow University|
|Doctoral advisor||Nikolai Brashman|
|Doctoral students||Dmitry Grave
Vladimir Andreevich Markov
|Known for||probability, statistics, mechanics, and analytical geometry|
|Notable awards||Demidov Prize (1849)|
Pafnuty Lvovich Chebyshev (Russian: Пафну́тий Льво́вич Чебышёв; IPA: [pɐfˈnutʲɪj ˈlʲvovʲɪtɕ tɕɪbɨˈʂof]) (May 16 [O.S. May 4] 1821 – December 8 [O.S. November 26] 1894) was a Russian mathematician. His name can be alternatively transliterated as Chebychev, Chebysheff, Chebyshov; or Tchebychev, Tchebycheff (French transcriptions); or Tschebyschev, Tschebyschef, Tschebyscheff (German transcriptions).
One of nine children, Chebyshev was born in the central Russian village of Akatovo near Borovsk, to Agrafena Ivanova Pozniakova and Lev Pavlovich Chebyshev. His father had fought as an officer against Napoleon Bonaparte's invading army.
Chebyshev was originally home schooled by his mother and his cousin, Avdotia Kvintillianova Soukhareva. He learned French early in life, which later helped him communicate with other mathematicians. A stunted leg prevented him from playing with other children, leading him to concentrate on his studies instead.
Later he moved to St. Petersburg, where he founded one of the most important schools of mathematics in Russia, and there is today a research institute in mathematics called the Chebyshev Laboratory in that city.
Chebyshev is known for his work in the fields of probability, statistics, mechanics, and number theory. The Chebyshev inequality states that if is a random variable with standard deviation σ > 0, then the probability that the outcome of is no less than away from its mean is no more than :
The Chebyshev inequality is used to prove the Weak Law of Large Numbers.
The Bertrand–Chebyshev theorem (1845,1852) states that for any , there exists a prime number such that . This is a consequence of the Chebyshev inequalities for the number of prime numbers less than , which state that is of the order of . A more precise form is given by the celebrated prime number theorem: the quotient of the two expressions approaches 1.0 as tends to infinity.
Chebyshev is considered to be a founding father of Russian mathematics. 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 7,483 mathematical "descendants" as of 2010.
- Tchebychef, P. L. (1899), Markov, Andreĭ Andreevich; Sonin, N., eds., Oeuvres I, New York: Commissionaires de l'Académie impériale des sciences, MR 0147353, Reprinted by Chelsea 1962
- Tchebychef, P. L. (1907), Markov, Andreĭ Andreevich; Sonin, N., eds., Oeuvres II, New York: Commissionaires de l'Académie impériale des sciences, MR 0147353, Reprinted by Chelsea 1962
- Butzer, P. L. Chebyshev (1821–1894): A Guide to his Life and Work, doi:10.1006/jath.1998.3289
- Chebyshev cube root
- Chebyshev distance
- Chebyshev filter, a family of analog filters in electronics and signal processing
- Chebyshev function in number theory
- Chebyshev polynomials and the "Chebyshev form"
- Chebyshev's inequality in probability and statistics
- Chebyshev's sum inequality
- Chebyshev equation
- Chebyshev iteration
- Chebyshev linkage, a straight line generating linkage
- Roberts–Chebyshev theorem on the generation of cognate coupler-curves.
- Chebyshev–Markov–Stieltjes inequalities
- Chebychev–Grübler–Kutzbach criterion for the mobility analysis of linkages
- Chebyshev nodes
- Chebyshev rational functions
- Chebyshev's bias
- Discrete Chebyshev polynomials
- Chebyshev integral
- 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.
- Works by or about Pafnuty Chebyshev in libraries (WorldCat catalog)
- Biography, another one, and yet another (all in Russian).
- Œuvres de P.L. Tchebychef (in French)