View source for Pafnuty Chebyshev

{{Short description|Russian mathematician (1821–1894)}}
{{redirect|Chebyshev|other uses|Chebyshev (disambiguation)}}
{{Use dmy dates|date=May 2018}}
{{Infobox scientist
|name = Pafnuty Chebyshev
|image = Pafnuty Lvovich Chebyshev.jpg
|image_size = 240px
|caption = Pafnuty Lvovich Chebyshev
|birth_date = {{Birth date|df=yes|1821|05|16}}<ref name=brit>[https://www.britannica.com/biography/Pafnuty-Lvovich-Chebyshev Pafnuty Chebyshev]. Encyclopaedia Britannica</ref>
|birth_place = [[Zhukovsky District, Kaluga Oblast|Akatovo]], [[Kaluga Governorate]], [[Russian Empire]]<ref name=brit/>
|death_date = {{death date and age|df=yes|1894|12|08|1821|05|16}}<ref name=brit/>
|death_place = [[St. Petersburg]], [[Russian Empire]]<ref name=brit/><ref name=McT>{{cite web|title=Pafnuty Lvovich Chebyshev|website=MacTutor|url=https://mathshistory.st-andrews.ac.uk/Biographies/Chebyshev/|access-date=22 November 2024}}</ref>
| other_names = Chebysheff, Chebyshov, Tschebyscheff, Tschebycheff, Tchebycheff
|nationality = [[Russia]]n
|alma_mater = [[Moscow University]]
|academic_advisors = [[Nikolai Brashman]]
|notable_students = [[Dmitry Grave]]<br />[[Aleksandr Korkin]]<br />[[Aleksandr Lyapunov]]<br />[[Andrey Markov]]<br />[[Vladimir Andreevich Markov]]<br />[[Konstantin Posse]]<br>[[Yegor Ivanovich Zolotarev]]
|known_for  = Work on [[probability]], [[statistics]], [[mechanics]], [[analytical geometry]] and [[number theory]]
|footnotes = 
|field = [[Mathematician]]
|work_institution = [[St. Petersburg University]]
|prizes = [[Demidov Prize]] (1849)
| signature=Pafnuty Chebyshev signature.png
}}

'''Pafnuty Lvovich Chebyshev''' ({{lang-rus|Пафну́тий Льво́вич Чебышёв|p=pɐfˈnutʲɪj ˈlʲvovʲɪtɕ tɕɪbɨˈʂof}}) ({{OldStyleDate|16 May|1821|4 May}} – {{OldStyleDate|8 December|1894|26 November}})<ref>[http://www.britannica.com/eb/article-9022729/Pafnuty-Lvovich-Chebyshev Pafnuty Lvovich Chebyshev – Britannica Online Encyclopedia]</ref> was a [[list of Russian mathematicians|Russian 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]] (which can be used to prove the [[weak law of large numbers]]), the [[Bertrand's postulate|Bertrand–Chebyshev theorem]], [[Chebyshev polynomial]]s, [[Chebyshev linkage]], and [[Chebyshev bias]].

==Transcription==

<!-- this was part of the lead, and made it look like the lead said something about the man's career, but it was only this crud after all --> 
<!-- His name can be alternatively [[Romanization of Russian|transcribed]] as ''Chebysheff'', ''Chebychov'', ''Chebyshov''; or ''Tchebychev'', ''Tchebycheff'' (French transcriptions); or ''Tschebyschev'', ''Tschebyschef'',  ''Tschebyscheff'' (German transcriptions); or, rarely, ''Čebyčev''.-->

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]].<ref>[https://mathscinet.ams.org/mathscinet/search/author.html?mrauthid=191693 Chebyshev, Pafnutiĭ L'vovich], on [[MathSciNet]].</ref>

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

== Biography ==
=== Early years ===
One of nine children,<ref Name=MacTutor>[http://www-history.mcs.st-andrews.ac.uk/Biographies/Chebyshev.html Biography in MacTutor Archive]</ref> Chebyshev was born in the village of Okatovo in the district of [[Borovsk]], [[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 language|French]] and [[arithmetic]]). Chebyshev mentioned that his music teacher also played an important role in his education, for she "raised his mind to exactness and analysis".{{citation needed|date= October 2022}}

[[Trendelenburg gait|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.{{citation needed|date= October 2022}}

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) the senior [[Moscow University]] teacher {{ill|Platon Pogorelsky|ru|Погорельский, Платон Николаевич}}, who had taught, among others, the future writer [[Ivan Turgenev]].{{citation needed |date= October 2022}}

=== 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.{{citation needed|date= October 2022}} His teachers included [[Nikolai Brashman|N.D. Brashman]], [[N.E. Zernov]] and [[Dmitri Perevoshchikov|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 [[Jean-Victor Poncelet|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 ''n<sup>th</sup>'' degree based on [[Newton's method]]. In the same year, he finished his studies as "most outstanding candidate".{{citation needed|date= October 2022}}

In 1841, Chebyshev's financial situation changed drastically. There was famine in Russia, and his parents were forced to leave Moscow.{{citation needed|date= October 2022}} 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.{{citation needed|date= October 2022}}

=== Adult years ===
In 1847, Chebyshev promoted his thesis ''[[pro venia legendi]]'' "On 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 [[Viktor 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.<ref name=brit/> He was elected an [[Professor|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.{{citation needed |date= October 2022}}

During his lectureship at the university (1852–1858), Chebyshev also taught practical mechanics at the [[Tsarskoye Selo Lyceum|Alexander Lyceum]] in [[Tsarskoe Selo]] (now Pushkin), a southern suburb of [[St Petersburg]].{{citation needed|date= October 2022}}

His scientific achievements were the reason for his election as junior [[academician]] (adjunkt) in 1856. Later, he became an extraordinary (1856) and in 1858 an ordinary member of the [[Russian Academy of Sciences|Imperial Academy of Sciences]]. 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 [[French Academy of Sciences|Paris academy]] elected him corresponding member in 1860 and full foreign member in 1874. In 1878, Chebyshev presented a paper on garment cutting, inspired by a lecture by [[Édouard Lucas]], to the French Association for the Advancement of the Sciences.<ref>{{cite journal |last1=Tapia |first1=Victor |year=2025 |title=Chebyshev and Garment Cutting: Debunking Some Myths |url=https://link.springer.com/article/10.1007/s00283-025-10409-x |journal=The Mathematical Intelligencer |volume= |issue= |pages=1–5 |doi=10.1007/s00283-025-10409-x|url-access=subscription }}</ref>

In 1893, he was elected honorable member of the [[St. Petersburg Mathematical Society]], which had been founded three years earlier.{{citation needed|date= October 2022}}

Chebyshev died in [[St Petersburg]] on 8 December 1894.<ref name=brit/><ref name=McT/>

== Mathematical contributions ==
[[File:Чебышёв, Пафнутий Львович.jpg|thumb|right|Pafnuty Chebyshev]]
Chebyshev is known for his work in the fields of [[probability]], [[statistics]], [[mechanics]], and [[number theory]]. The [[Chebyshev inequality]] states that if <math>X</math> is a [[random variable]] with [[standard deviation]] ''σ'' > 0, then the probability that the outcome of <math>X</math> is <math>d = k\sigma</math> or more away from its mean is at most <math>1/k^2 = \sigma^2/d^2</math>:

: <math>\Pr(|X - {\mathbf E}(X)| \ge d\ )\le \frac {\sigma^2}{d^2}.</math>

The Chebyshev inequality is used to prove the [[weak law of large numbers]].{{citation needed|date= October 2022}}

The [[Bertrand's postulate|Bertrand–Chebyshev theorem]] (1845, 1852) states that for any <math>n > 3</math>, there exists a [[prime numbers|prime number]] <math>p</math> such that <math>n < p < 2n</math>. This is a consequence of the Chebyshev inequalities for the number <math>\pi(n)</math> of [[prime numbers]] less than <math>n</math>:

: for <math> x </math> sufficiently large, <math> A\frac{x}{\log(x)}  < \pi(x) < \frac{6A}{5}\frac{x}{\log(x)}  \; \text{, with } \; A \approx 0.92129.</math><ref>{{cite journal | author=Tchebichef | title=Mémoire sur les nombres premiers | journal=Journal de Mathématiques Pures et Appliquées | date=1852 | issn=1776-3371 | pages=366–390 | url=https://eudml.org/doc/234762 | access-date=26 November 2024 | lang=fr}}  [https://nonagon.org/ExLibris/chebyshevs-memoire-nombres-premiers-section-1 English translation] by Mike Bertrand (November 5, 2020).</ref>

Fifty years later, in 1896, the celebrated [[prime number theorem]] was proved, independently, by [[Jacques Hadamard]]<ref name="Hadamard1896">{{Citation|last=Hadamard|first=Jacques|author-link=Jacques Hadamard|year=1896|title=Sur la distribution des zéros de la fonction ζ(s) et ses conséquences arithmétiques.|journal=Bulletin de la Société Mathématique de France|publisher=Société Mathématique de France|volume=24|pages=199–220|url=http://www.numdam.org/item/?id=BSMF_1896__24__199_1 |archive-url=https://web.archive.org/web/20240910153636/http://www.numdam.org/item/?id=BSMF_1896__24__199_1 |archive-date=2024-09-10 }}</ref> and [[Charles Jean de la Vallée Poussin]]:<ref name="de la Vallée Poussin1896">{{Citation|last=de la Vallée Poussin|first=Charles-Jean|author-link=Charles Jean de la Vallée Poussin|year=1896|title=Recherches analytiques sur la théorie des nombres premiers.|journal=Annales de la Société scientifique de Bruxelles|publisher=Imprimeur de l'Académie Royale de Belgique|volume=20 B; 21 B|pages=183-256, 281-352, 363-397; 351-368|url=http://sciences.amisbnf.org/fr/livre/recherches-analytiques-de-la-theorie-des-nombres-premiers}}</ref>

: <math>\lim_{x\to\infty}\frac{\;\pi(x)\log(x)\;}{x\;} = 1</math>

using ideas introduced by [[Bernhard Riemann]].

Chebyshev is also known for the [[Chebyshev polynomial]]s and the [[Chebyshev bias]] – the difference between the number of primes that are congruent to 3 (modulo 4) and 1 (modulo 4).<ref>{{cite journal | last1=Rubinstein | first1=Michael | last2=Sarnak | first2=Peter | title=Chebyshev's Bias | journal=Experimental Mathematics | volume=3 | issue=3 | date=1994 | issn=1058-6458 | doi=10.1080/10586458.1994.10504289 | pages=173–197}}</ref>

Chebyshev was the first person to think systematically in terms of [[random variables]] and their [[moment (mathematics)|moments]] and [[expected value|expectations]].<ref>{{cite journal|journal=Bulletin of the American Mathematical Society |series=New Series|volume=3|number=1|date=July 1980|last=Mackey|first=George|title=Harmonic analysis as the exploitation of symmetry-a historical survey|page=549|doi=10.1090/S0273-0979-1980-14783-7|doi-access=free|hdl=1911/63317|hdl-access=free}}</ref>

== Legacy ==
[[File:Pafnuty Chebyshev 2021 stamp of Russia.jpg|thumb|Chebyshev on a 2021 stamp of Russia]]

Chebyshev is considered to be a founding father of [[Russia]]n mathematics.<ref name=brit/> Among his well-known students were the mathematicians [[Dmitry Grave]], [[Aleksandr Korkin]], [[Aleksandr Lyapunov]], and [[Andrey Markov|Andrei Markov]]. According to the [[Mathematics Genealogy Project]], Chebyshev has 17,533 mathematical "descendants" as of January 2025.<ref>{{MathGenealogy|12542}}</ref>

The lunar crater ''[[Chebyshev (crater)|Chebyshev]]'' and the asteroid [[2010&nbsp;Chebyshev]] were named to honor his major achievements in the mathematical realm.<ref name="springer" />

== Publications ==
* {{Citation | last1=Tchebychef | first1=P. L. | editor1-last=Markov | editor1-first=Andrey Andreevich | editor2-last=Sonin | editor2-first=N. | title=Oeuvres | url=https://archive.org/stream/oeuvresdepltche01chebrich | publisher=Commissionaires de l'Académie impériale des sciences | location=New York | mr=0147353 |id=Reprinted by Chelsea 1962 | year=1899 | volume=I}}
* {{Citation | last1=Tchebychef | first1=P. L. | editor1-last=Markov | editor1-first=Andrey Andreevich | editor2-last=Sonin | editor2-first=N. | title=Oeuvres | url=https://books.google.com/books?id=1mBtAAAAMAAJ | publisher=Commissionaires de l'Académie impériale des sciences | location=New York | mr=0147353 |id=Reprinted by Chelsea 1962 | year=1907 | volume=II}}
* {{Citation | last1=Butzer | first1  = Paul | last2=Jongmans | first2= Francois | title=P. L. Chebyshev (1821–1894): A Guide to his Life and Work | journal = Journal of Approximation Theory| volume = 96| pages = 111–138| doi=10.1006/jath.1998.3289| year = 1999| doi-access = free}}

== See also ==
* [[List of things named after Pafnuty Chebyshev]]

== References ==
{{reflist|refs=

<ref name="springer">{{cite book
  |last       = Schmadel | first = Lutz D.
  |title = Dictionary of Minor Planet Names |publisher  = Springer Berlin Heidelberg
  |page       = 163
  |date       = 2007
  |isbn       = 978-3-540-00238-3
  |doi       = 10.1007/978-3-540-29925-7_2011 |chapter       = (2010) Chebyshev }}</ref>

}} <!-- end of reflist -->


== Further reading ==

* {{cite web | last=Papadopoulos | first=Athanase | title=Pafnuty Chebyshev (1821-1894) | website=Bhāvanā – The mathematics magazine| publisher=The Bhavana Trust | date=14 May 2019 | url=https://bhavana.org.in/pafnuty-chebyshev-1821-1894/ | access-date=25 November 2024}}

== External links ==
*{{Commons category-inline}}
{{EB1911 poster|Chebichev, Pafnutiy Lvovich}}
* [http://tcheb.ru Mechanisms by Chebyshev] – short 3d films – embodiment of Tchebishev's inventions
* {{MathGenealogy |id=12542}}
* {{MacTutor Biography|id=Chebyshev}}
* [https://web.archive.org/web/20060829211200/http://www.bashedu.ru/konkurs/tarhov/russian/chebish.htm Biography], [http://www.mathsoc.spb.ru/pantheon/chebyshe/b-e.html another one], and [https://web.archive.org/web/20060713072728/http://www.univer.omsk.su/omsk/Edu/Math/chchebishev.htm yet another] (all in [[Russian language|Russian]]).
* [https://archive.org/details/pltchbychefets00vasiuoft Biography] in French.
* ''Œuvres de P.L. Tchebychef'' [https://archive.org/details/oeuvresdepltche01chebrich/ Vol. I], [https://archive.org/details/oeuvresdepltche02chebrich Vol. II] (in [[French language|French]])
* [https://www.youtube.com/watch?v=1EoUBwwl8-k When Mathematicians use Geometry to Cut Cloth] –  A presentation by [[Étienne Ghys]] on the work of Chebyshev, with a special focus on his research on [[Chebyshev nets]] in [[differential geometry]].

{{Authority control}}

{{DEFAULTSORT:Chebyshev, Pafnuty Lvovich}}
[[Category:1821 births]]
[[Category:1894 deaths]]
[[Category:People from Kaluga Oblast]]
[[Category:People from Borovsky Uyezd]]
[[Category:19th-century mathematicians from the Russian Empire]]
[[Category:Probability theorists]]
[[Category:Inventors from the Russian Empire]]
[[Category:Number theorists]]
[[Category:Numerical analysts]]
[[Category:Ballistics experts]]
[[Category:Statisticians from the Russian Empire]]
[[Category:Moscow State University alumni]]
[[Category:Full members of the Saint Petersburg Academy of Sciences]]
[[Category:Members of the French Academy of Sciences]]
[[Category:Demidov Prize laureates]]
[[Category:Foreign members of the Royal Society]]