P. L. Chebyshev life and his works
P. L. Chebyshev life and his works
Assist Prof. Dr. Alaa Adnan auad
alaa.adnan.auad@uoanbar.edu.iq
The aim of this article is to outline the life and work of Chebyshev, creator in St. Petersburg of the largest prerevolutionary school of mathematics in Russia, who permitted him to be equated only with Archimedes. Chebyshev, who wasregularly in Paris, at the latest by 1852, if not already by 1842, a friend of Liouville and Hermite, was the author of ca 80 publications, covering approximation theory, probability theory, number theory, theory of mechanisms, as well as many problems of analysis and practical mathematics. He was also proud to be a constructor of various mechanisms, including an arithmomancy tree. Although the article is intended for an approximation theorist readership, an attempt is made to give proportionate coverage of the broad spectrum of Chebyshev's achievements, emphasis being placed upon their background. The article is based in part upon the authors' studies during 1985-1991. Pafnutii Lvovich Chebyshev was born on May 16, 1821 in Okatovo, Kaluga region of Russia, on the small estate of his parents, Lev Pavlovich Chebyshev and Agrafena Ivanovna Pozniakova Chebysheva. He was one of nine children; his younger brother Vladimir, a general and professor at the St. Petersburg Artillery Academy, also is well known. His father was a retired army officer who had fought in the war against Napoleon.
Chebyshev received his primary education at home; his mother taught him reading and writing. Avdotia Kvintillianova Soukhareva, apparently a cousin, fulfilled the role of governess, teaching him French and arithmetic .The Chebyshev family moved in 1832 to Moscow where Pafnutii completed his secondary education at home. His tutor in mathematics was P. N. Pogorelski, the author of popular mathematical textbooks. He enrolled in the department of physics and mathematics of Moscow University in 1837, studying mathematics, in particular, under N. D. Brashman2 and N. E. Zernov (1804-1862). Chebyshev always expressed deep respect for his teacher Brashman, to whom he attributed the greatest influence on his mathematical development. He was also nominated a junior academician of the St. Petersburg Academy of Sciences with the chair of applied mathematics in 1853, as an extraordinary academician in 1856 and an ordinary academician in 1859. The chairs for pure mathematics at the Academy were then occupied by P. H. Fuss (1798-1855) a great grandson of Euler, M. V. Ostrogradskii (1801-1862), and V. Ya. Bunyakovskii (1804-1889). After 35 years of teaching at St. Petersburg University in 1882 he decided to retire from his professorship but continued his research work at the Academy to the very end. He died at St. Petersburg on December 8, 1894.
Although he never married, Chebyshev had a daughter whom he did not acknowledge officially, but supported financially. Later he would meet her, together with her husband, a colonel Leer, and their own daughter, at the house of his sister Nadiejda in Rudakovo. The ``two young and beautiful daughters'' seen at Chebyshev's funeral according to Grave's autobiographical notes were, presumably, Mrs. Leer and her daughter. Chebyshev's merits were recognized early in his career. He was elected a Corresponding Member of the Society Royale des Sciences of Liege and of the Society Philomathique in 1856, of the Paris Academy of Sciences in 1860, and a Foreign Associate in 1874 (the first Russian since Peter the Great), as well as a corresponding or foreign member of the Berlin Academy of Sciences (1871), the Bologna Academy (1873), the Royal Society of London (1877), the Italian Royal Academy (1880), and the Swedish Academy of Sciences (1893). An extended selection of Chebyshev's research was published in two volumes by A. Markoff and N. Sonin, while his complete works appeared in five volumes much later . Chebyshev is regarded as the creator of the largest prerevolutionary school of mathematics in Russia. Its most prominent members included A. N. Korkin (1837-1908) , Y. V. Sohotski ,J. W. Sochozki 9 (1842-1927), E. I. Zolotarev (1847-1878) , C. A. Posse (1847-1928), A. V. Vassiliev (1853-1929) , A. A. Markov (1856-1922) , V. A. Markov (1871-1897), A. M. Lyapunov (1857-1918) , D. A. Grave (1863-1939) [25, 36], V. A. Steklov (1864-1926) [91], G. F. Voronoi (1868-1908), and A. N. Krylov (1863-1945) [56], I. L. Ptaszycki (1854-1912), and I. I. Ivanov (1862-1939). O. Sheynin mentions further students of Chebyshev, namely the educationalists N. A. Artemiev, Latyshev, and Lermantov.
Chebyshev is the author of 80 or so publications; they span a wide area of mathematics, namely approximation theory, probability theory, number theory, theory of mechanisms, as well as many problems of analysis and practical mathematics. Many of these papers were published in major jour- nals abroad: 17 of them in Liouville's journal, at least 10 in other French journals. Three papers appeared in Crelle's journal (Germany), and five in Acta Mathematica (Sweden, after 1885). Most of the remaining publications are to be found in the two journals of the St. Petersburg Academy, renowned since Euler's days at the Academy. Chebyshev began his work in analysis while working on his master exams; then he turned to probability in his Moscow master thesis, then to integration in finite terms in his venia legendi thesis at St. Petersburg, then to number theory and to approximation theory, etc. We shall treat these fields successively. The courses Chebyshev taught at St. Petersburg, roughly from 1847 to 1850, were concerned with spherical trigonometry, analytical geometry, higher algebra, elliptic functions, and practical mechanics. As an extra- ordinary professor he taught number theory, integral calculus, theory of interpolation and theoretical mechanics. In his capacity as an ordinary pro- fessor he continued teaching the number theory course, began teaching probability theory a subject he taught almost continuously for 22 years as well as the theory of definite integrals and integration of differential equations. The latter course he left to a colleague in 1875. Apart from the theory of interpolation there is no course under the specific name of approximation theory, or better still, constructive function theory, as S. N. Bernstein coined it and the Russians still call it (perhaps such lectures existed nowhere in the world at the time). However, in 1849-1851 and 1852-1856 he lectured on practical mechanics in the (short-lived) department of practical knowledge (thus quasi engineering) of St. Petersburg University and at the Alexander Lyceum in Tsarskoe Selo (now Pushkin), respectively. It is perhaps in these lectures that he developed his original ideas on the construction of mechanisms and introduced his first personal views anticipating the constructive theory of functions. Chebyshev was also very active as an educator. As a member of the Scientific Committee of the Ministry of Education from 1856-1873, Chebyshev was, like Lobachevskii, Ostrogradskii and other Russian scientists, active in working for the improvement of the teaching of mathematics, physics and astronomy in secondary schools, both in regard to curricula and textbooks intended for school use. He also participated in preparing a new university charter.