Pafnuty Chebyshev
From Wikipedia, the free encyclopedia
 Pafnuty Lvovich Chebyshev |
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| Born | May 26 [O.S. May 14] 1821 Borovsk, Kaluga, Russia |
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| Died | December 8 [O.S. Nov. 26] 1894 St Petersburg, Russia |
| Residence |  Russia |
| Nationality | Russian |
| Field | Mathematician |
| Institution | St Petersburg University |
| Alma mater | Moscow University |
| Academic advisor | Nikolai Brashman |
| Notable students | Dmitry Grave Aleksandr Korkin Aleksandr Lyapunov Andrei Markov |
| Known for | Mechanics and analytical geometry |
| Notable prizes | Demidov Prize (1836) |
Pafnuty Lvovich Chebyshev (Russian: Пафну́тий Льво́вич Чебышёв) ( May 26 [O.S. May 14] 1821 – December 8 [O.S. November 26] 1894) was a Russian mathematician. His name is also transliterated in various ways, e. g. as Chebychev, Chebyshov, Tchebycheff or Tschebyscheff (French and German transcriptions).
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[edit] Biography
[edit] Early years
One of nine children, he was born in the village of Okatovo, the district of Borovsk, province of Kaluga. His father was the wealthy landowner Lev Pavlovich Chebyshev. Pafnuty Lvovich got his first education at home from his mother Agrafena Ivanovna Chebysheva (reading and writing) and his cousin Avdotya Kvintillianovna Sukhareva (French and arithmetic). His music-teacher also played an important role in Chebyshev's education, for she "brought up his mind to exactness and analysis", as Chebyshev himself mentioned.
Possibly a physical handicap, whose reasons are yet unknown, was important for Chebyshev's adolescence and development: He limped since his childhood and walked with a stick. Therefore his parents had to give up the idea to make an officer's career possible for him, although he would have followed the family's tradition. His complaint prevented him from most of the usual children's games, so very soon he devoted himself to a passion, which would determine his whole life: the construction of mechanisms.
In 1832, the family moved to Moscow mainly to attend to the education of their eldest sons (Pafnuty and Pavel, who would become a lawyer). The education continued at home, P.N. Pogorelski was engaged as a teacher for mathematics and physics, who was held as one of the best teachers in Moscow and, e. g. had educated the writer Ivan Sergeevich Turgenev. For the other subjects teachers with excellent reputation were invited, too.
[edit] University studies
In summer 1837, Chebyshev passed the registration examinations and in September he started the studies of mathematics at the second philosophical department of Moscow university. Among his teachers were counted N.D. Brashman, N.E. Zernov and D.M. Perevoshchikov. No doubt that among them Brashman had the greatest influence on Chebyshev. He instructed him in practical mechanics and probably showed him the work of the French engineer J.V. Poncelet. In 1841 Chebyshev was awarded the silver medal for his work "calculation of the roots of equations" which had already been finished in 1838. In this contribution Chebyshev derived an approximating algorithm for the solution of algebraic equations of nth degree based on Newton's algorithm. In the same year he finished his studies as "most outstanding candidate".
In 1841, Chebyshev's financial situation drastically changed. In Russia a famine broke out, Chebyshev's parents were forced to leave the city and were not able to support their son anymore. Nevertheless, he decided to continue his mathematical studies and prepared the master examinations which spread over half a year. He passed the final examination in October 1843. In 1846 he defended his master thesis "An Attempt to an Elementary Analysis of Probabilistic Theory". The biographer Prudnikov assumes that Chebyshev was directed to this mathematical branch after getting knowledge about recently edited books on probabilistic theory or the revenue of the insurance industry in Russia.
[edit] Adult years
In 1847, Chebyshev defended his dissertation pro venia legendi "About integration with the help of logarithms" at St Petersburg University and thus obtained the right to teach there as a lecturer. At that time some of Leonhard Euler's works were rediscovered by P. N. Fuss and were being edited by V. Ya. Bunyakovsky, who encouraged Chebyshev to engage in the study of them, something that would come to direct his life's work. Already in 1848, he had submitted his work theory of congruences for his doctorate, which he defended in May, 1849. After one year he was elected for an extraordinary professor at St Petersburg University, 1860 he became ordinary professor. In 1872, after 25 years of lectureship, he became merited professor. In 1882 he left the university and completely devoted his life to research.
Besides his lectureship at the university from 1852 to 1858, Chebyshev taught practical mechanics at the Alexander Lyceum in Tsarskoe Selo (now Pushkin), a southern suburb of St Petersburg.
His scientific achievements give the reasons for his election for a junior academician (adjunkt) in 1856. Later on, he became an extraordinary (1856) and in 1858 an ordinary member of the Imperial Academy of Sciences. In the same year he became honorable member of Moscow University. Moreover, he assumed other honourable appointments and was decorated several times: in 1856, Chebyshev became member of the scientific committee of the ministry of national education. In 1859, he became an ordinary member of the ordnance department of the academy with the adoption of the headship of the commission for mathematical questions according to ordnance and experiments related to the theory of shooting. The Paris academy elected him corresponding member in 1860 and full foreign member in 1874. In 1893, he was elected honorable member of the St. Petersburg Mathematical Society, recently founded in 1890.
Pafnuty Lvovich Chebyshev died November 26, 1894, in St Petersburg.
[edit] Mathematical contributions
Chebyshev is known for his work in the field of probability, statistics and number theory. Chebyshev's inequality says that if X is a random variable with standard deviation σ, the probability that the outcome of X is no less than aσ away from its mean is no more than 1/a2:
Chebyshev's inequality is used to prove the weak law of large numbers.
The Bertrand-Chebyshev theorem (1845|1850) states that for any n > 1, there exists a prime number p such that n < p < 2n. It is a consequence of Chebyshev inequalities for the number π(x) of prime numbers less than x, which state that π(x) is of the order of n / log(n). A more precise form is given by the celebrated prime number theorem: the quotient of the two expressions approaches 1 as n tends to infinity.
[edit] Legacy
Chebyshev is considered one of the founding fathers of Russian mathematics. Among his students were Dmitry Grave, Aleksandr Korkin, Aleksandr Lyapunov and Andrei Markov, themselves well known and prolific mathematicians. According to the Mathematics Genealogy Project, Chebyshev has about 4,000 mathematical descendants.
[edit] See also
- Chebyshev's inequality
- Chebyshev distance
- Chebyshev filter, in electronics and signal processing, a family of electronic filters
- Chebyshev function, in number theory
- Chebyshev polynomials
- Chebyshev's sum inequality
- Chebyshev's equation
- Chebyshev linkage, a straight line generating linkage.
- Chebyshev-Markov-Stieltjes inequalities
[edit] External links
- Pafnuty Chebyshev at the Mathematics Genealogy Project
- O'Connor, John J., and Edmund F. Robertson. "Pafnuty Chebyshev". MacTutor History of Mathematics archive.
- Biography, another one, and yet another (all in Russian).
- Œuvres de P.L. Tchebychef (in French)
| Persondata | |
|---|---|
| NAME | Chebyshev, Pafnuty |
| ALTERNATIVE NAMES | |
| SHORT DESCRIPTION | Mathematician |
| DATE OF BIRTH | May 26 [O.S. May 14] 1821 |
| PLACE OF BIRTH | Borovsk, Kaluga, Russia |
| DATE OF DEATH | December 8 [O.S. November 26] 1894 |
| PLACE OF DEATH | St Petersburg, Russia |
