Born at Ryazan in Russia, Markov studied at the University of St. Petersburg and later held a variety of teaching posts at the same university, eventually becoming a professor in 1893. He was an extremely enthusiastic and effective teacher. His mathematical interests were very wide, ranging over number theory, the theory of continued fractions, and differential equations. It was, however, his work in probability theory that constituted his most profound and enduring contribution to mathematics.

Among Markov's teachers was the eminent Russian mathematician Pafnuti Chebyshev, whose central interest was in probability. One of Markov's first pieces of important research centered on a key theorem of Chebyshev's – ‘the central limit theorem’. He was able to show that Chebyshev's supposed proof of this result was erroneous, and to provide his own, correct, proof of a version of the theorem of much greater generality than that attempted by Chebyshev. In 1900 Markov published his important and influential textbook Probability Calculus, and by 1906 he had arrived at the fundamentally new concept of a Markov chain. A sequence of random variables is a Markov chain if the two probabilities conditioned on different amounts of information about the early part of the sequence are the same. This aspect of Markov's work gave a major impetus to the subject of stochastic processes.

The great importance of Markov's work was that it enabled probability theory to be applied to a very much wider range of physical phenomena than had previously been possible. As a result of his work a whole range of subjects, among them genetics and such statistical phenomena as the behavior of molecules, became amenable to mathematical probabilistic treatment.