Pafnuty Chebyshev

Pafnuti Lvovitch Chebyshev ( see below notation ) (* 4.jul / May 16 1821greg in Okatowo in a circle Borovsk (now in the Kaluga oblast ). . † on 26 Novemberjul / December 8 1894greg in Saint Petersburg.. ) Was a Russian mathematician. Chebyshev is considered together with Nikolai Ivanovich Lobachevsky as the most important Russian mathematician of the 19th century.

His name is spelled Russian Пафнутий Львович Чебышёв what is by today's transcription Pafnuti Lvovitch Chebyshev ( emphasis on the last syllable ); Scientific transliteration Pafnutij L' vovič Chebyshev, formerly ( incorrectly, as stressed on the first syllable) transcribed as Chebyshev or Chebyshev or Chebyshev and particularly in English than Chebyshev.

Life

Chebyshev came from the family of the landowner Lev Pavlovich Chebyshev. He was one of nine children, in 1832 he moved with his family to Moscow, where he was taught by one of the best private mathematics teacher PN Pogorelski.

He studied from 1837 at the Moscow State University with Nikolai Dmitrievich Braschman ( in which he heard already on probability theory ) and Nikolai Zernov. In 1846 he defended his master's thesis, 1847, he handed in his dissertation, a Saint Petersburg (per venia legendi ), after which he got a job at the university. He was promoted in Saint Petersburg from Viktor Yakovlevich Bunjakowski, which he published in 1849 the number-theoretic work of Leonhard Euler. Finally, in 1849 he defended his doctoral dissertation famous ( habilitation thesis ) " theory of congruences ", which was published as a book and was translated into several languages. She received an Academy Award.

In 1850 he became an associate professor in St. Petersburg, in 1860 a full professor. In St. Petersburg he lectured on algebra, analysis, number theory, and on probability theory. During his teaching career in St. Petersburg Chebyshev taught 1852-1858 among other things, " Practical Mechanics" at the Alexander Lyceum.

Chebyshev spoke French very well and also wrote his first mathematical work mostly in French. He also had early contact with French and foreign mathematicians and later attended regularly the mathematical centers in Western Europe.

In 1882 he retired, but had continued at the St. Petersburg Academy and maintained a weekly open house for his many former students. In 1894 he died of heart failure.

He was never married. His younger brother Wladimir Lvovitch Chebyshev was a general and a professor at the St. Petersburg Artillery Academy and funded the first edition of the collected works of Chebyshev.

Work

Chebyshev worked in the fields of interpolation, approximation, function theory, probability theory, number theory (especially prime number theory ), mechanics and ballistics (with which he was involved in a committee of the Academy ).

Named after him are the Chebyshev polynomials ( the first in his book of 1854 appear on mechanisms ) those that Chebyshev 's inequality, the Chebyshev distance, the Chebyshev filter, the set of Chebyshev, the set of Bertrand- Chebyshev, and Chebyshev - Summenungleichung, the Chebyshev iteration and Chebyshev function. Further, the supremum is also sometimes called Chebyshev standard.

His Master's dissertation of 1846 treated " An attempt to elemental analysis of the probability theory." The title of his dissertation (1847, per venia legendi ) was "On the Integration Using logarithms ," in which he discussed the elementary methods of integration; his doctoral dissertation ( Habilitation Thesis ) " theory of congruences " treated aspects of number theory.

Chebyshev also dealt intensively with mechanical inventions, in particular joint mechanisms. Some of his models are in the Mathematical Institute of the Russian Academy of Sciences and the Paris Conservatoire des Arts et Métiers. There is also a copy of a built by him in the 1870s adding machine (another copy is in the Historical Museum in Moscow). He described his calculating machine in 1882 in a short article. 1893 several of its mechanisms at the World Fair in Chicago were (World's Columbian Exposition ) issued.

Chebyshev wrote his first mathematical work mostly in French. He already published in 1843 in the journal of Joseph Liouville.

He is the founder of the St. Petersburg Mathematical School. Among his students Andrei Andreyevich Markov, Alexander Mikhailovich Lyapunov, Alexander Nikolayevich Korkin, Yegor Ivanovich Zolotarev, Dmitry Alexandrovich Grawe, Georgi Feodosjewitsch Woronoi, Vladimir Andreevich Steklov.

Honors and Memberships

He was a corresponding member of the Prussian Academy of Sciences ( 1871), Fellow of the Royal Society (1877 ), member of the royal Italian and Swedish Academy of Sciences. He was a full member of the French Academy of Sciences, the first Russian scientists since 1860 and corresponding 1874. In 1856 he became extraordinary and in 1858 a full member of the St. Petersburg Academy of Sciences. In 1893 he was made an honorary member of the recently founded the St. Petersburg Mathematical Society. He was a member of the Legion of Honour.

Writings

  • Oeuvres, 2 volumes, St. Petersburg 1899, 1907, Commission of the Academy of Sciences, Andrei Markov and N. Sonin (Editor ), French, Reprint New York, Chelsea 1962 Online: Volume 1, Volume 2
  • Collected Works, 5 volumes, Russian, Moscow, Leningrad, 1944-1951
  • Theory of congruences, Berlin, Mayer and Müller, 1889, Online
  • Théorie des sous le nom de Mécanismes connus parallelogram, St. Petersburg 1854
  • Definite integrals, the theory of finite differences, theory of probability (lectures 1879-1880, by Lyapunov recorded), Berlin, NG -Verlag, 2004
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