Andrey Markov

This article is about the mathematician. For the hockey player, see Andrei Markov (hockey player).

Andrey Markov
Andrey Andreyevich Markov
Born	June 14, 1856 N.S. Ryazan, Russia
Died	July 20, 1922 Petrograd, Russia
Nationality	Russian
Alma mater	St Petersburg University
Known for	Markov chains
Scientific career
Fields	Mathematician
Institutions	St Petersburg University
Doctoral advisor	Pafnuty Chebyshev
Doctoral students	Abram Besicovitch Georgy Voronoy

Andrey (Andrei) Andreyevich Markov (Russian: Андрей Андреевич Марков) (June 14, 1856 N.S. – July 20, 1922) was a Russian mathematician. He is best known for his work on theory of stochastic processes. His research later became known as Markov chains. In late 19th century, the Moscow school of probability mixed math and religion assuming that the stability of frequencies proves free will, hence existence of God. Markov, an atheist, proved that Central Limit Theorem works also for random variables that are not independent, discrediting the ideas from Moscow school.

His son another Andrey Andreevich Markov (1903-1979) was also a notable mathematician.

Biography

Andrej Andreevich Markov was born in Ryazan as the son of the secretretary of the public forest management of Ryazan, Andrey Grigorevich Markov, and his first wife, Nadezhda Petrovna Markova.

In the beginning of the 1860s Andrey Grigorevich moved to St Petersburg to adopt the job as an asset manager of the princess Ekaterina Aleksandrovna Valvatyeva.

In 1866 Andrey Andreevich’s school life began with his entrance into Saint Petersburg’s fifth grammar school. Already during his school time Andrey was intensily engaging in higher mathematics. As a 17 years old grammar school pupil he informed Bunyakovski, Korkin and Zolotarev about an apparently new method to solve linear ordinary differential equations and was invited to the so-called Korkin Saturdays, where Korkin's students regularly met. At last in 1874 he finished the school and began his studies at the physico-mathematical faculty of St~Petersburg university.

Among his teachers were Sochocki (differential calculus, higher algebra), Posse (analytic geometry), Zolotarev (integral calculus), Chebyshev (number theory, probability theory), Korkin (ordinary and partial differential equations), Okatov (mechanism theory), Somov (mechanics) and Budaev (descriptive and higher geometry).

In 1877 he was awarded the gold medal for his outstanding solution of the problem “About Integration of Differential Equations by Continuous Fractions with an Application to the Equation $(1+x^2) \frac{dy}{dx} = n (1+y^2)$. In the following year he passed the candidate examinations and remained at the university to prepare the lecturer’s job.

In April, 1880 Andrey Markov defended his master thesis “About Binary Quadratic Forms with Positive Determinant“, which was encouraged by Korkin and Zolotarev.

Another five years later, in January 1885, there followed his doctoral thesis “About Some Applications of Algebraic Continuous Fractions.

His pedagogical job began after the defence of his master thesis in autumn 1880. As a privatdozent he lectured differential and integral calculus. Later he lecutured alternately „introduction to analysis“, probability theory (succeeding Chebyshev who had left the university in 1882) and calculus of differences. From 1895/96 until 1905 he additionally lectured again diefferential calculus.

One year after the defence of the doctoral thesis he was appointed extraordinary professor (1886) and in the same year he was elected adjunkt of the academy of sciences. In 1890, After the death of the academician Bunyakovski Markov became extraordinary member of the academy. His promotion to an ordinary professor of St~Petersburg university followed in autumn 1894.

Finally in 1896 he was elected ordinary member of the academy as the successor of Chebyshev. In 1905 he was appointed merited professor and got the right to retire which he immediately used. Till 1910, however, he continued to lecture calculus of differences.

Protesting against a decree of the ministry of education Markov rejected from a further teaching activity at the Saint Petersburg university. In connection with student’s riots in 1908 professor and lecturers of Saint Petersburg university were ordered to observe their students. Firstly Markov rejected from accepting this decree and after that he wrote an explanation where he expressed his decline from being an “agent of the governance”. Finally he did not see any way except from a full retirement from the university.

In 1913 the council of St~Petersburg elected nine scientists honorary members of the university. Markov was among them, but only his election was not affirmed by the minister of education. The affirmation was done only four years later, after the February revolution in 1917.

In the following Markov again resumed his teaching activity. Until his death in 1922 he lectured probability theory and calculus of differences.

See also

• Markov chain
• Markov chain Monte Carlo
• Gauss-Markov theorem
• Gauss–Markov process
• Hidden Markov model
• Markov number
• Markov property
• Markov's inequality
• Markov process
• Markov blanket
• Markov network
• Markov decision process

References

• А. А. Марков. "Распространение закона больших чисел на величины, зависящие друг от друга". "Известия Физико-математического общества при Казанском университете", 2-я серия, том 15, ст. 135-156, 1906.
• A.A. Markov. "Extension of the limit theorems of probability theory to a sum of variables connected in a chain". reprinted in Appendix B of: R. Howard. Dynamic Probabilistic Systems, volume 1: Markov Chains. John Wiley and Sons, 1971.

External links

• Andrey Markov at the Mathematics Genealogy Project
• O'Connor, John J.; Robertson, Edmund F., "Andrey Markov", MacTutor History of Mathematics Archive, University of St Andrews
• Biography of A.A. Markov
• Biography of A.A. Markov by his son, A.A. Markov-jnr Template:Ru icon
• Andrey Andreevich Markov (1903-1979) (biography of Markov's son, located at the Steklov Institute of Mathematics at St.Petersburg)