Pafnuty Chebyshev

"Chebyshev" redirects here. For other uses, seeChebyshev (disambiguation).

Pafnuty Chebyshev
Pafnuty Lvovich Chebyshev
Born	(1821-05-16)16 May 1821 Akatovo,Kaluga Governorate,Russian Empire
Died	8 December 1894(1894-12-08)(aged 73) St. Petersburg,Russian Empire
Nationality	Russian
Other names	Chebysheff, Chebyshov, Tschebyscheff, Tschebycheff, Tchebycheff
Alma mater	Moscow University
Known for	Work onprobability,statistics,mechanics,analytical geometryandnumber 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

Pafnuty Lvovich Chebyshev(Russian:Пафну́тий Льво́вич Чебышёв,IPA:[pɐfˈnutʲɪjˈlʲvovʲɪtɕtɕɪbɨˈʂof]) (16 May [O.S.4 May] 1821 – 8 December [O.S.26 November] 1894)was aRussian mathematicianand considered to be the founding father of Russian mathematics.

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.

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 in mathematical literature. Currently, the English transliterationChebyshevhas gained widespread acceptance, except by the French, who preferTchebychev.The correcttransliterationaccording toISO 9isČebyšëv.TheAmerican Mathematical Societyadopted the transcriptionChebyshevin itsMathematical Reviews.

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".

Biography

Early years

One of nine children,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 (inFrenchandarithmetic). 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 gaitaffected 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 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 UniversityteacherPlaton Pogorelsky,who had taught, among others, the future writerIvan 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 includedN.D. Brashman,N.E. ZernovandD.M. Perevoshchikovof 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 ofn^thdegree based onNewton'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 thesispro venia legendi"On integration with the help of logarithms" atSt Petersburg Universityand 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 Congruencesfor a doctorate, which he defended in May 1849.He was elected anextraordinary professorat 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 theAlexander LyceuminTsarskoe Selo(now Pushkin), a southern suburb ofSt Petersburg.

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 academyelected him corresponding member in 1860 and full foreign member in 1874. In 1893, he was elected honorable member of theSt. Petersburg Mathematical Society,which had been founded three years earlier.

Chebyshev died inSt Petersburgon 26 November 1894.

Mathematical contributions

Pafnuty Chebyshev

Chebyshev is known for his work in the fields ofprobability,statistics,mechanics,andnumber theory.TheChebyshev inequalitystates that if$X$is arandom variablewithstandard deviationσ> 0, then the probability that the outcome of$X$is no less than$a\sigma$away from its mean is no more than$1/a^{2}$:

$\Pr(|X-{\mathbf {E} }(X)|\geq a\ )\leq {\frac {\sigma ^{2}}{a^{2}}}.$

The Chebyshev inequality is used to prove theweak law of large numbers.

TheBertrand–Chebyshev theorem(1845, 1852) states that for any$n>3$,there exists aprime number$p$such that$n<p<2n$.This is a consequence of the Chebyshev inequalities for the number$\pi (n)$ofprime numbersless than$n$,which state that$\pi (n)$is of the order of$n/\log(n)$.A more precise form is given by the celebratedprime number theorem:thequotientof the two expressions approaches 1.0 as$n$tends to infinity.

Chebyshev is also known for theChebyshev polynomialsand theChebyshev 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 ofrandom variablesand theirmomentsandexpectations.

Legacy

Chebyshev on a 2021 stamp of Russia

Chebyshev is considered to be a founding father ofRussianmathematics.Among his well-known students were the mathematiciansDmitry Grave,Aleksandr Korkin,Aleksandr Lyapunov,andAndrei Markov.According to theMathematics Genealogy Project,Chebyshev has 16,874 mathematical "descendants" as of February 2024.

The lunar craterChebyshevand the asteroid2010 Chebyshevwere named to honor his major achievements in the mathematical realm.

Publications

• Tchebychef, P. L. (1899), Markov, Andrey Andreevich; Sonin, N. (eds.),Oeuvres,vol. I, New York: Commissionaires de l'Académie impériale des sciences,MR0147353,Reprinted by Chelsea 1962
• Tchebychef, P. L. (1907), Markov, Andrey Andreevich; Sonin, N. (eds.),Oeuvres,vol. II, New York: Commissionaires de l'Académie impériale des sciences,MR0147353,Reprinted by Chelsea 1962
• Butzer (1999), "P. L. Chebyshev (1821–1894): A Guide to his Life and Work",Journal of Approximation Theory,96:111–138,doi:10.1006/jath.1998.3289

See also

• List of things named after Pafnuty Chebyshev

External links

• Media related toPafnuty Chebyshevat Wikimedia Commons

• Mechanisms by Chebyshev– short 3d films – embodiment of Tchebishev's inventions
• Pafnuty Chebyshevat theMathematics Genealogy Project
• O'Connor, John J.;Robertson, Edmund F.,"Pafnuty Chebyshev",MacTutor History of Mathematics Archive,University of St Andrews
• Biography,another one,andyet another(all inRussian).
• Biographyin French.
• Œuvres de P.L. TchebychefVol. I,Vol. II(inFrench)