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# Andrey Markov

Andrey (Andrei) Andreyevich Markov (Андрей Андреевич Марков) (June 14, 1856 N.S. – July 20, 1922) was a Russian mathematician. He is best known for his work on theory of stochastic processes. His research later became known as Markov chains.

He and his younger brother Vladimir Andreevich Markov (1871-1897) proved Markov brothers' inequality. His son, another Andrey Andreevich Markov (1903-1979), was also a notable mathematician, making contributions on constructive mathematics and recursive function theory.

## Biography

Andrey Andreevich Markov was born in Ryazan as the son of the secretary of the public forest management of Ryazan, Andrey Grigorevich Markov, and his first wife, Nadezhda Petrovna Markova.

In the beginning of the 1860s Andrey Grigorevich moved to St Petersburg to become an asset manager of the princess Ekaterina Aleksandrovna Valvatyeva. In 1866 Andrey Andreevich’s school life began with his entrance into Saint Petersburg’s fifth grammar school. Already during his school time Andrey was intensely engaged in higher mathematics. As a 17-year-old grammar school student he informed Bunyakovsky, Korkin and Yegor Zolotarev about an apparently new method to solve linear ordinary differential equations and was invited to the so-called Korkin Saturdays, where Korkin's students regularly met. In 1874 he finished the school and began his studies at the physico-mathematical faculty of St Petersburg University.

Among his teachers were Yulian Sokhotski (differential calculus, higher algebra), Konstantin Posse (analytic geometry), Yegor Zolotarev (integral calculus), Pafnuty Chebyshev (number theory, probability theory), Aleksandr Korkin (ordinary and partial differential equations), Okatov (mechanism theory), Somov (mechanics) and Budaev (descriptive and higher geometry).

In 1877 he was awarded the gold medal for his outstanding solution of the problem “About Integration of Differential Equations by Continuous Fractions with an Application to the Equation $\left(1+x^2\right) frac\left\{dy\right\}\left\{dx\right\} = n \left(1+y^2\right).$“ In the following year he passed the candidate examinations and remained at the university to prepare for the lecturer’s position.

In April 1880 Markov defended his master thesis “About Binary Quadratic Forms with Positive Determinant“, which was encouraged by Aleksandr Korkin and Yegor Zolotarev. Five years later, in January 1885, there followed his doctoral thesis “About Some Applications of Algebraic Continuous Fractions“.

His pedagogical work began after the defense of his master thesis in autumn 1880. As a privatdozent he lectured on differential and integral calculus. Later he lectured alternately on “introduction to analysis“, probability theory (succeeding Chebyshev who had left the university in 1882) and calculus of differences. From 1895/96 until 1905 he additionally lectured on differential calculus.

One year after the defense of the doctoral thesis, he was appointed extraordinary professor (1886) and in the same year he was elected adjunct to the Academy of Sciences. In 1890, after the death of Viktor Bunyakovsky, Markov became extraordinary member of the academy. His promotion to an ordinary professor of St Petersburg University followed in autumn 1894.

In 1896, he was elected ordinary member of the academy as the successor of Chebyshev. In 1905 he was appointed merited professor and got the right to retire which he immediately used. Till 1910, however, he continued to lecture calculus of differences.

In connection with student riots in 1908, professors and lecturers of Saint Petersburg University were ordered to observe their students. Markov initially refused to accept this decree and wrote an explanation in which he declined to be an “agent of the governance”. Markov was rejected from a further teaching activity at the Saint Petersburg University, and he eventually decided to retire from the university.

In 1913 the council of Saint Petersburg elected nine scientists honorary members of the university. Markov was among them, but his election was not affirmed by the minister of education. The affirmation was done only four years later, after the February revolution in 1917. Markov then resumed his teaching activities and lectured probability theory and calculus of differences until his death in 1922.