Pafnuty Lvovich Chebyshev – the founder of the St. Petersburg School of mathematics

We continue our topic about great Petersburgers that we started last year by the posts about Olga Ladyzhenskaya and Leonhard Euler. The new article is about Pafnuty Chebyshev.

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One of nine children, Pafnuty was born in Okatovo, a small town in western Russia, south-west of Moscow, in the small family estate of an upper-class family with an impressive history. His family traced its roots back to a 17th-century Tatar military leader named Khan Chabysh. Unfortunately, because of Trendelenburg’s gait Chebyshev limped and so he could not continue the family tradition and become an officer. His disability prevented him from taking part in many children’s games and he devoted himself instead to mathematics. Chebyshev would greatly benefit from his fluency in French later in his life because it would make France a natural place to visit and provide a link with the leading European mathematicians, he would use French to communicate mathematics on an international stage. In 1832, when Chebyshev was eleven years old, the family moved to Moscow, mainly to attend to the education of their eldest sons. Being well prepared for his study of the mathematical sciences Chebyshev began his mathematical studies in the second philosophical department of Moscow University. During this period the person who influenced Chebyshev most was Nikolai Dmetrievich Brashman, the professor of applied mathematics at the university since 1834. Being particularly interested in mechanics Brashman however, had wide interests. In addition to courses in mechanical engineering and hydraulics, he taught his students the theory of integration of algebraic functions and the calculus of probability. Chebyshev always acknowledged the great influence Brashman had on him during his university studies.

Chebyshev’s very first paper was written in French and was devoted to multiple integrals. His second paper, written again in French, was published in 1844 by Crelle in his journal. This paper was devoted to the convergence of Taylor series. In the summer of 1846 Chebyshev was examined on his Master’s thesis devoted to the theory of probability. In it, the main results of the theory were developed in a rigorous but elementary way. In the same year a paper based on that thesis was published, again in Crelle’s journal. In this paper, he published from his thesis he examined, in particular, Poisson’s weak law of large numbers.

Between July and November 1852, he made a scientific trip to France, UK, Belgium and Germany. During this trip he had the opportunity to get acquainted with the practice of foreign mechanical engineering and discussions with French mathematicians including Liouville, Bienaymé, Hermite, Serret, Poncelet, and English mathematicians including Cayley and Sylvester. After this trip Chebyshev wrote several papers, including “Theory of the mechanisms known as parallelograms” published in 1854. It was in this work that his famous Chebyshev polynomials appeared for the first time. Later he went on to develop a general theory of orthogonal polynomials.

Besides mathematical contributions, Chebyshev invented more than 40 different mechanisms and about 80 of their modifications. Among them are mechanisms, many of which are used in modern auto, motorcycle and instrument making. One of them is Chebyshev linkage which is a mechanical linkage that converts rotational motion to approximate straight-line motion. Based on it, Chebyshev built the world’s first walking mechanism, which had success at the World Exhibition in Paris in 1878.

Chebyshev had received many honors during his career. He was elected an ordinary professor in 1860 and, after 25 years of lectureship, he became merited professor in 1872. In 1882 retired from his professorship at St Petersburg University and devoted his life to research. For Chebyshev, the task of developing the Russian mathematical school has always been of no less importance than scientific results. Numerous students of Chebyshev made a significant contribution to science. Among them are such well-known mathematicians and mechanics as Zolotarev, Lyapunov, Sokhotsky, Vasiliev, Voronoi, Grave, Korkin, Markov, Posse, Ptashitsky.

Chebyshev died on November 26 (December 8), 1894 at a desk.  Chebyshev created the first Russian mathematical, scientific school, the hallmark of which is a clear statement of the problem,  algorithmic, almost engineering solution with the result that is convenient for use and productive in relation to further research. Chebyshev and his students formed the core of the scientific team of mathematicians, which over time became the name of the St. Petersburg School of Mathematics.