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Pafnuty Lvovich Chebyshev ( rus, Пафну́тий Льво́вич Чебышёв, p=pɐfˈnutʲɪj ˈlʲvovʲɪtɕ tɕɪbɨˈʂof) ( – ) was a
Russian Russian(s) refers to anything related to Russia, including: *Russians (, ''russkiye''), an ethnic group of the East Slavic peoples, primarily living in Russia and neighboring countries * Rossiyane (), Russian language term for all citizens and p ...
mathematician and considered to be the founding father of Russian mathematics. Chebyshev is known for his fundamental contributions to the fields of probability, statistics, mechanics, and number theory. A number of important mathematical concepts are named after him, including the
Chebyshev inequality In probability theory, Chebyshev's inequality (also called the Bienaymé–Chebyshev inequality) guarantees that, for a wide class of probability distributions, no more than a certain fraction of values can be more than a certain distance from th ...
(which can be used to prove the weak law of large numbers), the Bertrand–Chebyshev theorem, Chebyshev polynomials, Chebyshev linkage, and Chebyshev bias.


Transcription

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 of the entire 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 The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
adopted the transcription ''Chebyshev'' in its Mathematical Reviews. His first name comes from the Greek Paphnutius (Παφνούτιος), which in turn takes its origin in the
Coptic Coptic may refer to: Afro-Asia * Copts, an ethnoreligious group mainly in the area of modern Egypt but also in Sudan and Libya * Coptic language, a Northern Afro-Asiatic language spoken in Egypt until at least the 17th century * Coptic alphabet, t ...
Paphnuty (Ⲡⲁⲫⲛⲟⲩϯ), meaning "that who belongs to God" or simply "the man of God".


Biography


Early years

One of nine children,Biography in MacTutor Archive
/ref> Chebyshev was born in the village of Okatovo in the district of
Borovsk Borovsk (russian: Бо́ровск) is a town and the administrative center of Borovsky District of Kaluga Oblast, Russia, located on the Protva River just south from the oblast's border with Moscow Oblast. Population: 12,000 (1969). History It ...
, province of Kaluga. His father, Lev Pavlovich, was a Russian nobleman and wealthy landowner. Pafnuty Lvovich was first educated at home by his mother Agrafena Ivanovna Pozniakova (in reading and writing) and by his cousin Avdotya Kvintillianovna Sukhareva (in French and
arithmetic Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th c ...
). Chebyshev mentioned that his music teacher also played an important role in his education, for she "raised his mind to exactness and analysis." Trendelenburg's gait affected Chebyshev's adolescence and development. From childhood, he limped and walked with a stick and so his parents abandoned the idea of his becoming an officer in the family tradition. His disability prevented his playing many children's games and he devoted himself instead to mathematics. In 1832, the family moved to Moscow, mainly to attend to the education of their eldest sons (Pafnuty and Pavel, who would become lawyers). Education continued at home and his parents engaged teachers of excellent reputation, including (for mathematics and physics)
P.N. Pogorelski PN may refer to: Arts and entertainment * '' Purple Noon'', a 1960 film * Patriotic Nigras, a griefing group in the game ''Second Life'' Business and economics * Pacific National, a rail freight company in Australia * Participatory notes, i ...
, held to be one of the best teachers in Moscow and who had taught (for example) the writer Ivan Sergeevich Turgenev.


University studies

In summer 1837, Chebyshev passed the registration examinations and, in September of that year, began his mathematical studies at the second philosophical department of Moscow University. His teachers included N.D. Brashman,
N.E. Zernov NE, Ne or ne may refer to: Arts and entertainment * Neutral Evil, an alignment in the American role-playing game ''Dungeons & Dragons'' * New Edition, an American vocal group * Nicomachean Ethics, a collection of ten books by Greek philosopher Ar ...
and D.M. Perevoshchikov of whom it seems clear that Brashman had the greatest influence on Chebyshev. Brashman instructed him in practical mechanics and probably showed him the work of French engineer J.V. Poncelet. In 1841 Chebyshev was awarded the silver medal for his work "calculation of the roots of equations" which he had finished in 1838. In this, Chebyshev derived an approximating algorithm for the solution of algebraic equations of ''nth'' degree based on Newton's method. In the same year, he finished his studies as "most outstanding candidate". In 1841, Chebyshev's financial situation changed drastically. There was famine in Russia, and his parents were forced to leave Moscow. Although they could no longer support their son, he decided to continue his mathematical studies and prepared for the master examinations, which lasted six months. Chebyshev passed the final examination in October 1843 and, in 1846, defended his master thesis "An Essay on the Elementary Analysis of the Theory of Probability." His biographer Prudnikov suggests that Chebyshev was directed to this subject after learning of recently published books on probability theory or on the revenue of the Russian insurance industry.


Adult years

In 1847, Chebyshev promoted his thesis pro venia legendi "On integration with the help of logarithms" at
St Petersburg University Saint Petersburg State University (SPBU; russian: Санкт-Петербургский государственный университет) is a public research university in Saint Petersburg, Russia. Founded in 1724 by a decree of Peter the G ...
and thus obtained the right to teach there as a lecturer. At that time some of
Leonhard Euler Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in ...
's works were rediscovered by P. N. Fuss and were being edited by V. Ya. Bunyakovsky, who encouraged Chebyshev to study them. This would come to influence Chebyshev's work. In 1848, he submitted his work ''The Theory of Congruences'' for a doctorate, which he defended in May 1849. He was elected an extraordinary professor at St Petersburg University in 1850, ordinary professor in 1860 and, after 25 years of lectureship, he became merited professor in 1872. In 1882 he left the university and devoted his life to research. During his lectureship at the university (1852–1858), Chebyshev also taught practical mechanics at the Alexander Lyceum in Tsarskoe Selo (now Pushkin), a southern suburb of St Petersburg. His scientific achievements were the reason for his election as junior
academician An academician is a full member of an artistic, literary, engineering, or scientific academy. In many countries, it is an honorific title used to denote a full member of an academy that has a strong influence on national scientific life. In syst ...
(adjunkt) in 1856. Later, he became an extraordinary (1856) and in 1858 an ordinary member of the
Imperial Academy of Sciences The Russian Academy of Sciences (RAS; russian: Росси́йская акаде́мия нау́к (РАН) ''Rossíyskaya akadémiya naúk'') consists of the national academy of Russia; a network of scientific research institutes from across ...
. In the same year he became an honorary member of Moscow University. He accepted other honorary appointments and was decorated several times. In 1856, Chebyshev became a 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 ballistics. The
Paris academy The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. It was at the ...
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, which had been founded three years earlier. Chebyshev died in St Petersburg on 26 November 1894.


Mathematical contributions

Chebyshev is known for his work in the fields of probability, statistics, mechanics, and number theory. The
Chebyshev inequality In probability theory, Chebyshev's inequality (also called the Bienaymé–Chebyshev inequality) guarantees that, for a wide class of probability distributions, no more than a certain fraction of values can be more than a certain distance from th ...
states that if X is a random variable with
standard deviation In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, whil ...
''σ'' > 0, then the probability that the outcome of X is no less than a\sigma away from its mean is no more than 1/a^2: : \Pr(, X - (X), \ge a\,\sigma )\le \frac . The Chebyshev inequality is used to prove the weak law of large numbers. The Bertrand–Chebyshev theorem (1845, 1852) states that for any n > 3, there exists a prime number p such that n < p < 2n. This is a consequence of the Chebyshev inequalities for the number \pi(n) of prime numbers less than n, which state that \pi(n) 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 1.0 as 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.


Legacy

Chebyshev is considered to be a founding father of
Russia Russia (, , ), or the Russian Federation, is a transcontinental country spanning Eastern Europe and Northern Asia. It is the largest country in the world, with its internationally recognised territory covering , and encompassing one-eight ...
n mathematics. Among his well-known students were the mathematicians
Dmitry Grave Dmitry Aleksandrovich Grave (russian: Дми́трий Алекса́ндрович Гра́ве; September 6, 1863 – December 19, 1939) was an Imperial Russian and Soviet mathematician. Naum Akhiezer, Nikolai Chebotaryov, Mikhail Kravchuk, a ...
,
Aleksandr Korkin Aleksandr Nikolayevich Korkin (russian: Александр Николаевич Коркин; – ) was a Russian mathematician. He made contribution to the development of partial differential equations, and was second only to Chebyshev among th ...
,
Aleksandr Lyapunov Aleksandr Mikhailovich Lyapunov (russian: Алекса́ндр Миха́йлович Ляпуно́в, ; – 3 November 1918) was a Russian mathematician, mechanician and physicist. His surname is variously romanized as Ljapunov, Liapunov, Liapo ...
, and Andrei Markov. According to the Mathematics Genealogy Project, Chebyshev has 13,709 mathematical "descendants" as of January 2020. The lunar crater ''
Chebyshev Pafnuty Lvovich Chebyshev ( rus, Пафну́тий Льво́вич Чебышёв, p=pɐfˈnutʲɪj ˈlʲvovʲɪtɕ tɕɪbɨˈʂof) ( – ) was a Russian mathematician and considered to be the founding father of Russian mathematics. Chebyshe ...
'' and the asteroid 2010 Chebyshev were named to honor his major achievements in the mathematical realm.


Publications

* * *


See also

*
List of things named after Pafnuty Chebyshev {{Short description, none Mathematics * Chebyshev center * Chebyshev constants * Chebyshev cube root * Chebyshev distance * Chebyshev equation * Chebyshev's equioscillation theorem * Chebyshev filter, a family of analog filters in electronics and ...


References


External links

*
Mechanisms by Chebyshev
– short 3d films – embodiment of Tchebishev's inventions * * *

an

(all in
Russian Russian(s) refers to anything related to Russia, including: *Russians (, ''russkiye''), an ethnic group of the East Slavic peoples, primarily living in Russia and neighboring countries * Rossiyane (), Russian language term for all citizens and p ...
).
Biography
in French. * ''Œuvres de P.L. Tchebychef'
Vol. IVol. II
(in French) {{DEFAULTSORT:Chebyshev, Pafnuty Lvovich 1821 births 1894 deaths People from Kaluga Oblast People from Borovsky Uyezd Russian people of Tatar descent 19th-century mathematicians from the Russian Empire Probability theorists Inventors from the Russian Empire Number theorists Numerical analysts Ballistics experts Statisticians from the Russian Empire Moscow State University alumni Full members of the Saint Petersburg Academy of Sciences Members of the French Academy of Sciences Demidov Prize laureates Foreign Members of the Royal Society