Editing Andrey Markov

{{short description|Russian mathematician (1856–1922)}}
{{Other people}}
{{More citations needed|date=May 2023}}
{{Use dmy dates|date=April 2014}}
{{Infobox scientist
| name              = Andrey Markov
| native_name       = Андрей Марков
| native_name_lang  = ru
| image             = Andrei Markov.jpg
| image_size        = 
| caption           = Markov in 1886
| birth_date        = {{birth date|df=yes|1856|6|14}} [[New Style|N.S.]]
| birth_place       = [[Ryazan]], [[Russian Empire]]
| nationality       = [[Russians|Russian]]
| death_date        = {{death date and age|df=yes|1922|7|20|1856|6|14}}
| death_place       = [[Petrograd]], [[Russian SFSR]]
| field             = [[Mathematics]], specifically [[probability theory]] and [[statistics]]
| known_for         = [[Markov chain]]s <br /> [[Markov process]]es <br /> [[Stochastic process]]es
| work_institutions = [[St. Petersburg University]]
| alma_mater        = [[St. Petersburg University]]
| doctoral_advisor  = [[Pafnuty Chebyshev]]
| doctoral_students = {{Plainlist|
* [[Abram Besicovitch]]
* [[Nikolai Günther]]
* [[Veniamin Kagan]]
* [[Vsevolod Ivanovich Romanovsky|V. I. Romanovsky]]
* [[Jacob Tamarkin]]
* [[J. V. Uspensky]]
* [[Georgy Voronoy]]
}}
| children          = [[Andrey Markov Jr.]]
| prizes            = 
| footnotes         = 
}}

'''Andrey Andreyevich Markov'''{{efn|({{langx|ru|link=no|Андре́й Андре́евич Ма́рков}}, first name also spelled "Andrei", in older works also spelled '''Markoff'''<ref>E.g. {{cite journal |author=Shannon, Claude E. |author-link=Claude Shannon |title=A Mathematical Theory of Communication |url=http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf|journal=Bell System Technical Journal |volume=27 |issue=3 |pages=379–423 |date=July–October 1948 |access-date=29 August 2012 |archive-date=10 August 2012 |archive-url=https://web.archive.org/web/20120810102533/http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf |doi=10.1002/j.1538-7305.1948.tb01338.x|hdl=11858/00-001M-0000-002C-4314-2 |hdl-access=free }}</ref>)}} (14 June 1856 – 20 July 1922) was a Russian mathematician best known for his work on [[stochastic process]]es. A primary subject of his research later became known as the [[Markov chain]]. He was also a strong, close to master-level, chess player.

Markov and his younger brother [[Vladimir Markov (mathematician)|Vladimir Andreyevich Markov]] (1871–1897) proved the [[Markov brothers' inequality]].
His son, another [[Andrey Markov (Soviet mathematician)|Andrey Andreyevich Markov]] (1903–1979), was also a notable mathematician, making contributions to [[constructive mathematics]] and [[Recursion#Functional recursion|recursive function]] theory.<ref>{{Cite book|last=Драгалин|title=Математический интуиционизм. Введение в теорию доказательств|publisher=Наука|year=1979|pages=256}}</ref>

== Biography ==
Andrey Markov was born on 14 June 1856 in Russia. He attended the St. Petersburg Grammar School, where some teachers saw him as a rebellious student. In his academics he performed poorly in most subjects other than mathematics.  Later in life he attended Saint Petersburg Imperial University (now [[Saint Petersburg State University]]). Among his teachers were [[Yulian Sokhotski]] (differential calculus, higher algebra), [[Konstantin Posse]] (analytic geometry), Yegor Zolotarev (integral calculus), [[Pafnuty Chebyshev]] (number theory and probability theory), [[Aleksandr Korkin]] (ordinary and partial differential equations), Mikhail Okatov (mechanism theory), [[Osip Somov]] (mechanics), and Nikolai Budajev (descriptive and higher geometry).  He completed his studies at the university and was later asked if he would like to stay and have a career as a mathematician. He later taught at high schools and continued his own mathematical studies. In this time he found a practical use for his mathematical skills. He figured out that he could use chains to model the alliteration of vowels and consonants in Russian literature. He also contributed to many other mathematical aspects in his time. He died at age 66 on 20 July 1922.

== Timeline ==
In 1877, Markov was awarded a gold medal for his outstanding solution of the problem

''About Integration of Differential Equations by [[Continued Fractions]] with an Application to the Equation'' <math> (1+x^2) \frac{dy}{dx} = n (1+y^2)</math>.

During the following year, he passed the candidate's examinations, and he remained at the university to prepare for a lecturer's position.

In April 1880, Markov defended his [[master's degree|master's thesis]] "On the Binary Square Forms with Positive Determinant", which was directed by Aleksandr Korkin and Yegor Zolotarev. Four years later in 1884, he defended his doctoral thesis titled "On Certain Applications of the Algebraic Continuous Fractions".

His [[pedagogy|pedagogical]] work began after the defense of his master's thesis in autumn 1880. As a [[privatdozent]] he lectured on differential and integral calculus. Later he lectured alternately on "introduction to analysis", probability theory (succeeding Chebyshev, who had left the university in 1882) and the calculus of differences. From 1895 through 1905 he also lectured in [[differential calculus]].

[[File:AAMarkov.jpg|right|thumb|alt=Markov|Markov]]
One year after the defense of his doctoral thesis, Markov was appointed extraordinary professor (1886) and in the same year he was elected adjunct to the Academy of Sciences. In 1890, after the death of Viktor Bunyakovsky, Markov became an extraordinary member of the academy. His promotion to an ordinary professor of St. Petersburg University followed in the fall of 1894.

In 1896, Markov was elected an ordinary member of the academy as the successor of [[Chebyshev]]. In 1905, he was appointed merited professor and was granted the right to retire, which he did immediately. Until 1910, however, he continued to lecture in the calculus of differences.

In connection with student riots in 1908, professors and lecturers of St. Petersburg University were ordered to monitor their students. Markov refused to accept this decree, and he wrote an explanation in which he declined to be an "agent of the governance". Markov was removed from further teaching duties at St. Petersburg University, and hence he decided to retire from the university.

Markov was an [[atheist]]. In 1912, he responded to [[Leo Tolstoy]]'s [[excommunication]] from the [[Russian Orthodox Church]] by requesting his own excommunication. The Church complied with his request.<ref>"Of course, Markov, an atheist and eventual excommunicate of the Church quarreled endlessly with his equally outspoken counterpart Nekrasov. The disputes between Markov and Nekrasov were not limited to mathematics and religion, they quarreled over political and philosophical issues as well."  Gely P. Basharin, [[Amy Langville|Amy N. Langville]], Valeriy A. Naumov, [https://wayback.archive-it.org/all/20121218173228/https://netfiles.uiuc.edu/meyn/www/spm_files/Markov-Work-and-life.pdf The Life and Work of A. A. Markov], page 6.</ref><ref>{{cite book|title=Naming Infinity: A True Story of Religious Mysticism and Mathematical Creativity|year=2009|publisher=Harvard University Press|isbn=978-0-674-03293-4|author1=Loren R. Graham|author2=Jean-Michel Kantor|page=69|quote=Markov (1856–1922), on the other hand, was an atheist and a strong critic of the Orthodox Church and the tzarist government (Nekrasov exaggeratedly called him a Marxist).}}</ref>

[[File:Literator Bridges Grave Markov.jpg|right|thumb|alt=Markov's headstone|Markov's [[headstone]]]]
In 1913, the council of St. Petersburg elected nine scientists honorary members of the university. Markov was among them, but his election was not affirmed by the minister of education. The affirmation only occurred four years later, after the [[February Revolution]] in 1917. Markov then resumed his teaching activities and lectured on probability theory and the calculus of differences until his death in 1922.

== See also ==
{{Div col|colwidth=20em}}
* [[List of things named after Andrey Markov]]
* [[Chebyshev–Markov–Stieltjes inequalities]]
* [[Gauss–Markov theorem]]
* [[Gauss–Markov process]]
* [[Hidden Markov model]]
* [[Markov blanket]]
* [[Markov chain]]
* [[Markov decision process]]
* [[Markov's inequality]]
* [[Markov brothers' inequality]]
* [[Markov information source]]
* [[Markov random field|Markov network]]
* [[Markov number]]
* [[Markov property]]
* [[Markov process]]
* [[Stochastic matrix]] (also known as Markov matrix)
* [[Subjunctive possibility]]
{{div col end}}

==Notes==
{{notelist}}

== References==
{{Reflist}}

== Further reading ==
* {{cite book|author=Karl-Georg Steffens|title=The History of Approximation Theory: From Euler to Bernstein|url=https://books.google.com/books?id=IjFJNoq638kC&pg=PA98|date=28 July 2007|publisher=Springer Science & Business Media|isbn=978-0-8176-4475-8|pages=98–105}}
* 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, с. 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.
* {{cite news |last1=Pavlyk |first1=Oleksandr |title=Centennial of Markov Chains |url=http://blog.wolfram.com/2013/02/04/centennial-of-markov-chains/ |work=Wolfram Blog |date=February 4, 2013 |language=en}}

== External links ==
{{Commons category|Andrey Markov}}
* {{MathGenealogy|title=Andrei Andreyevich Markov}}

{{Authority control}}

{{DEFAULTSORT:Markov, Andrey}}
[[Category:1856 births|Markov, Andrei Andreyevich]]
[[Category:1922 deaths|Markov, Andrei Andreyevich]]
[[Category:19th-century mathematicians from the Russian Empire]]
[[Category:20th-century Russian mathematicians]]
[[Category:Russian atheists]]
[[Category:Former Russian Orthodox Christians]]
[[Category:Probability theorists]]
[[Category:Saint Petersburg State University alumni]]
[[Category:Full members of the Saint Petersburg Academy of Sciences]]
[[Category:Full Members of the Russian Academy of Sciences (1917–1925)]]
[[Category:People from Ryazan]]
[[Category:Russian statisticians]]
[[Category:Russian scientists]]