Born into an upper class family in Ryazan, Russia, Markov suffered from poor health throughout his childhood, but he exhibited keen intelligence and had a talent for mathematics that attracted the attention of his high school teachers. He studied mathematics under Pafnuty Chebychev (1821-1894) at the University of St. Petersburg, where he received his B.A. in 1878, and after spending some years studying and tutoring, Markov finally received his doctorate in 1884 for his dissertation on continued fractions. The use of continued fractions was Markov's mathematical tool of choice for much of his life's work. Markov combined mathematical research and a heavy teaching load for 25 years at St. Petersburg University, where he reached the position of full professor in 1893. During these years, Markov explored problems in many areas of mathematics, including number theory, approximate quadrature formulas, differential equations, and probability theory.

The prototypal absent-minded professor, Markov paid little attention...