Andrei Markov

Born on June 14, 1856, in Ryazan, Andrei Andreyevich Markov was a Russian mathematician, best known for his work on probability and stochastic processes, especially Markov chains.

The mother ofAndreiwas Nadezhda Petrovna, daughter of a state worker, and her father was Andrei Grigorievich Markov, son of a rural deacon. Andrei was the elder of two brothers, while the youngest was Vladimir. His brother Vladimir died of tuberculosis at the age of 25, but he had already earned an international reputation as a mathematician.

In its early years,MarkovHe was in poor health and until he was ten years old, he could only walk with the help of crutches. His secondary education was at the Gymnasium No. 5 in St. Petersburg, where he showed outstanding talent for mathematics, but performed quite poorly in other subjects. He wrote his first math article while at the Gymnasium, but his results on integrating linear differential equations that were presented in the article were not new. However, the writing of the article allowed him to meet Korkin and Zolotarev, two of the main professors of the university.

It was clear that mathematics was the right subject forMarkovstudied at the university and, in 1874, he entered the Faculty of Physics and Mathematics of the University of Saint Petersburg. There he enrolled in the seminar led by Korkin and Zolotarev, but also attended lectures by Chebyshev, the head of the mathematics department. These were particularly stimulating toMarkovas Chebyshev often fostered an investigative atmosphere by posing new questions and problems for his students to investigate.

MarkovHe had known Maria Ivanova Valvatyeva since they were children because she was the daughter of the owner of the farm that her father managed. He had tutored her in math and then proposed to her. However, Maria Ivanova’s mother would not allow her daughter to marry the son of the estate administrator until Markov had gained sufficient social status. In 1883 Maria Ivanova’s mother accepted the marriage that took place that year.

The first works ofMarkovthey were mainly in number theory and analysis, algebraic continued fractions, limits of integrals, approximation theory and the convergence of series. After 1900, he applied the method of continuous fractions, pioneered by his teacher Pafnuty Chebyshev, to the theory of probability.

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. He is particularly remembered for his study of theMarkov chains, sequences of random variables in which the future variable is determined by the present variable but is independent of the way the current state arose from its predecessors. This work founded an entirely new branch of probability theory and launched the theory of stochastic processes. In 1923 Norbert Wiener became the first to deal rigorously with a continuous process ofMarkov. Andrei Kolmogorov provided the basis for a general theory during the 1930s.

MarkovHe lived through a period of great political activity in Russia and, having strong opinions, became strongly involved. Maksim Gorky, the Russian leftist short story writer, novelist and activist, was elected to the Russian Academy of Sciences in 1902, but his election was soon withdrawn for political reasons by order of the Tsar.Markovhe protested vigorously and refused to accept the honors awarded to him the following year. In June 1907, Tsar Nicholas II dissolved the Second Duma, which had been elected by a left majority.Markovhe repudiated his membership and could have expected to suffer dire consequences, but the authorities chose not to make an example of an elderly and distinguished scholar. In 1913, the Romanov dynasty, which had been in power in Russia since 1613, celebrated its 300 years of power. This was not likely to improve his already weak position. The Russian Revolution began in early 1917 when the food supply ran out. In September of that year,Markovhe asked the Academy to send him to a disadvantaged city in the interior of Russia. He was sent to Zaraisk, a small rural town, where he taught high school mathematics without receiving any remuneration. He returned to St. Petersburg, but his health was deteriorating and he underwent surgery on one eye. Although in 1921 he was so ill that he could barely stand up, he continued to lecture on probability at the university. His death in July 1922 came after months of severe suffering.

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