**A A Markov** was a Russian mathematician who is is best known for his work in probability and for stochastic processes especially Markov chains.

- Andrei Grigorievich Markov studied at a church seminary, then got a job as a clerk.
- Andrei Andreyevich was the oldest of the two boys while the younger was Vladimir.
- In his early years Markov was in poor health and up to the age of ten he could only walk with the assistance of crutches.
- It was clear that mathematics was the right subject for Markov to study at university and, in 1874, he entered the Physics and Mathematics Faculty of St Petersburg University.
- These were particularly stimulating to Markov, since Chebyshev often encouraged an atmosphere of research by posing new questions and problems for his students to investigate.
- Markov graduated in 1878 having won the gold medal for submitting the best essay for the prize topic set by the faculty in that year - On the integration of differential equations by means of continued fractions.
- It is enough to recall the sorts of questions in the field of rational approximation which at that time preoccupied the most prominent number theorists of France and Germany, to appreciate how much deeper into the field Markov had penetrated.
- it is therefore perhaps not surprising that, although the dissertation was published immediately (in French in Mathematische Annalen), it did not become generally absorbed by west European mathematicians, until from 1910 to the 1920s the Berlin mathematicians Frobenius and Remak attempted to master the set of ideas contained in Markov's work.
- After submitting his master's thesis, Markov began to teach at St Petersburg University as a privatdozent while working for his doctorate (equivalent to the habilitation).
- Markov had tutored Maria Ivanova in mathematics and later he proposed marriage to her.
- Markov became an extraordinary professor at St Petersburg University in 1886 and an ordinary professor in 1893.
- Chebyshev proposed Markov as an adjunct of the Russian Academy of Sciences in 1886.
- Markov's early work was mainly in number theory and analysis, algebraic continued fractions, limits of integrals, approximation theory and the convergence of series.
- 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.
- 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.
- His profound analysis in the spirit of Chebyshev of the dependencies among observed random phenomena allowed Markov to extend probability theory in an essential way through the introduction and investigation of dependent random quantities.
- Markov was also interested in poetry and he made studies of poetic style - perhaps surprisingly Kolmogorov had similar interests.
- It is worth pointing out, however, that although Markov developed his theory of Markov chains as a purely mathematical work without considering physical applications, he did apply the ideas to chains of two states, namely vowels and consonants, in literary texts.
- Markov protested strongly and refused to accept honours awarded him on the following year.
- Markov repudiated his membership and might have expected to suffer severe consequences but the authorities chose not to make an example of an elderly and distinguished academician.
- Markov showed his disapproval of the celebration but holding celebrations of his own - he celebrated 200 years of the Law of Large Numbers! The Russian Revolution began early in 1917 as food supplies ran low.
- In September of that year Markov requested the Academy to send him to a disadvantaged town in the Russian interior.

Born 14 June 1856, Ryazan, Russia. Died 20 July 1922.

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Algebra, Group Theory, Origin Russia

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive