Andrei Andreyevich Markov

Andrei A Markov was a graduate of Saint Petersburg University (1878), where he began a professor in 1886. Markov's early work was mainly in number theory and analysis, continued fractions, limits of integrals, approximation theory and the convergence of series.

After 1900 Markov applied the method of continued fractions, pioneered by his teacher Pafnuty Chebyshev. He also studied sequences of mutually dependent variables, hoping to establish the limiting laws of probability in their most general form. He proved the central limit theorem under fairly general assumptions.

Markov is particularly remembered for his study of Markov chains, sequences of random variables in which the future variable is determined by the present variable but is independent of the way in which the present state arose from its predecessors. This work launched the theory of stochastic processes.

In 1923 Norbert Wiener became the first to treat rigorously a continuous Markov process. The foundation of a general theory was provided during the 1930s by Andrei Kolmogorov.

Markov was also interested in poetry and he made studies of poetic style, interestingly Kolmogorov had similar interests.

Markov had a son (of the same name) who was born on September 9, 1903 and followed his father in also becoming a renowned mathematician.

1. Biography in Dictionary of Scientific Biography (New York 1970-1990).
2. Biography in Encyclopaedia Britannica.

Books:


3. S Ya Grodzenskii, Andreii Andreevich Markov. 1856-1922 (Russian), Nauchno-Biograficheskaya Literatura (Moscow, 1987).

Articles:


4. Andrei Andreevich Markov (1856-1922) (Russian), Mat. v Shkole (1) (1982), i.
5. O B Sheynin, A A Markov's Work on Probability, Archive for History of Exact Science 39 (1988), 337-377.
6. O B Sheynin, Errata for the contribution: "A A Markov's work on probability", Archive for History of Exact Science 40 (4) (1989), 387.
7. V A Steklov, Andrei Andreyevich Markov, Izvestiya Rossiiskoi akademii nauk 16 (1922), 169-184.