Pafnuty Chebyshev | |
|---|---|
Пафнутий Чебышёв | |
 Pafnuty Lvovich Chebyshev | |
| Born | (1821-05-16)16 May 1821[1] |
| Died | 8 December 1894(1894-12-08) (aged 73)[1] |
| Other names | Chebysheff, Chebyshov, Tschebyscheff, Tschebycheff, Tchebycheff |
| Alma mater | Moscow University |
| Known for | Work onprobability,statistics,mechanics,analytical geometry andnumber theory |
| Awards | Demidov Prize (1849) |
| Scientific career | |
| Fields | Mathematician |
| Institutions | St. Petersburg University |
| Academic advisors | Nikolai Brashman |
| Notable students | Dmitry Grave Aleksandr Korkin Aleksandr Lyapunov Andrey Markov Vladimir Andreevich Markov Konstantin Posse Yegor Ivanovich Zolotarev |
| Signature | |
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Pafnuty Lvovich Chebyshev (Russian:Пафну́тий Льво́вич Чебышёв,IPA:[pɐfˈnutʲɪjˈlʲvovʲɪtɕtɕɪbɨˈʂof]) (16 May [O.S. 4 May] 1821 – 8 December [O.S. 26 November] 1894)[3] was aRussian mathematician and considered to be the founding father of Russian mathematics[further explanation needed].
Chebyshev is known for his fundamental contributions to the fields ofprobability,statistics,mechanics, andnumber theory. A number of important mathematical concepts are named after him, including theChebyshev inequality (which can be used to prove theweak law of large numbers), theBertrand–Chebyshev theorem,Chebyshev polynomials,Chebyshev linkage, andChebyshev bias.
The surname Chebyshev has beentransliterated in several different ways, giving rise to one of the most well known data-retrieval nightmares in mathematical literature. Examples include Tchebichef, Tchebychev, Tchebycheff, Tschebyschev, Tschebyschef, Tschebyscheff, Čebyčev, Čebyšev, Chebysheff, Chebychov and Chebyshov (which provides the closest pronunciation in English to the correct pronunciation in old Russian).Chebychev is an erroneous mixture between English and French transliterations. In English, the transliterationChebyshev has gained widespread acceptance. The correcttransliteration according toISO 9 isČebyšëv. TheAmerican Mathematical Society adopted the transcriptionChebyshev in itsMathematical Reviews.[4]
His first name comes from theGreekPaphnutius (Παφνούτιος), which in turn takes its origin in theCopticPaphnuty (Ⲡⲁⲫⲛⲟⲩϯ), meaning "that who belongs to God" or simply "the man of God".
One of nine children,[5] Chebyshev was born in the village of Okatovo in the district ofBorovsk,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 (inFrench andarithmetic). 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]
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]
In 1832, the family moved toMoscow, 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 seniorMoscow University teacherPlaton Pogorelsky [ru], who had taught, among others, the future writerIvan Turgenev.[citation needed]
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] His teachers includedN.D. Brashman,N.E. Zernov andD.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 engineerJ.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 ofnth degree based onNewton's method. In the same year, he finished his studies as "most outstanding candidate".[citation needed]
In 1841, Chebyshev's financial situation changed drastically. There was famine in Russia, and his parents were forced to leave Moscow.[citation needed] 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]
In 1847, Chebyshev promoted his thesispro venia legendi "On integration with the help of logarithms" atSt Petersburg University and thus obtained the right to teach there as a lecturer. At that time some ofLeonhard Euler's works were rediscovered by P. N. Fuss and were being edited byViktor Bunyakovsky, who encouraged Chebyshev to study them. This would come to influence Chebyshev's work. In 1848, he submitted his workThe Theory of Congruences for a doctorate, which he defended in May 1849.[1] He was elected anextraordinary 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]
During his lectureship at the university (1852–1858), Chebyshev also taught practical mechanics at theAlexander Lyceum inTsarskoe Selo (now Pushkin), a southern suburb ofSt Petersburg.[citation needed]
His scientific achievements were the reason for his election as junioracademician (adjunkt) in 1856. Later, he became an extraordinary (1856) and in 1858 an ordinary member of theImperial Academy of Sciences. In the same year he became an honorary member ofMoscow 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. TheParis 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 byÉdouard Lucas, to the French Association for the Advancement of the Sciences.[6]
In 1893, he was elected honorable member of theSt. Petersburg Mathematical Society, which had been founded three years earlier.[citation needed]
Chebyshev died inSt Petersburg on 8 December 1894.[1][2]
Chebyshev is known for his work in the fields ofprobability,statistics,mechanics, andnumber theory. TheChebyshev inequality states that if is arandom variable withstandard deviationσ > 0, then the probability that the outcome of is or more away from its mean is at most:
The Chebyshev inequality can be used toprove the weak law of large numbers.
TheBertrand–Chebyshev theorem (1845, 1852) states that for any, there exists aprime number such that. This is a consequence of the Chebyshev inequalities for the number ofprime numbers less than:
Fifty years later, in 1896, the celebratedprime number theorem was proved, independently, byJacques Hadamard[8] andCharles Jean de la Vallée Poussin:[9]
using ideas introduced byBernhard Riemann.
Chebyshev is also known for theChebyshev polynomials and theChebyshev bias – the difference between the number of primes that are congruent to 3 (modulo 4) and 1 (modulo 4).[10]
Chebyshev was the first person to think systematically in terms ofrandom variables and theirmoments andexpectations.[11]
Chebyshev is considered to be a founding father ofRussian mathematics.[1] Among his well-known students were the mathematiciansDmitry Grave,Aleksandr Korkin,Aleksandr Lyapunov, andAndrei Markov. According to theMathematics Genealogy Project, Chebyshev has 17,533 mathematical "descendants" as of January 2025.[12]
The lunar craterChebyshev and the asteroid2010 Chebyshev were named to honor his major achievements in the mathematical realm.[13]
Media related toPafnuty Chebyshev at Wikimedia Commons
