Andrey Andreyevich Markov, first name also spelled "Andrei", in older works also spelled Markoff) (14 June 1856 – 20 July 1922) was a Russian mathematician best known for his work on
stochastic processes. A primary subject of his research later became known as the
Markov chain.
Markov and his younger brother
Vladimir Andreevich Markov (1871–1897) proved the
Markov brothers' inequality.
His son, another
Andrey Andreyevich Markov (1903–1979), was also a notable mathematician, making contributions to
constructive mathematics
In the philosophy of mathematics, constructivism asserts that it is necessary to find (or "construct") a specific example of a mathematical object in order to prove that an example exists. Contrastingly, in classical mathematics, one can prove th ...
and
recursive function theory.
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 Julian Karol Sochocki (russian: Юлиан Васильевич Сохоцкий; pl, Julian Karol Sochocki; February 2, 1842 in Warsaw, Congress Poland, Russian Empire – December 14, 1927 in Leningrad, Soviet Union) was a Russian- Polish mathem ...
(differential calculus, higher algebra),
Konstantin Posse
__notoc__
Konstantin Alexandrovich Posse (russian: Константин Александрович Поссе; September 29, 1847 - August 24, 1928) was a Russian mathematician known for contributions to analysis and in particular approximation t ...
(analytic geometry), Yegor Zolotarev (integral calculus),
Pafnuty Chebyshev
Pafnuty Lvovich Chebyshev ( rus, Пафну́тий Льво́вич Чебышёв, p=pɐfˈnutʲɪj ˈlʲvovʲɪtɕ tɕɪbɨˈʂof) ( – ) was a Russian mathematician and considered to be the founding father of Russian mathematics.
Chebyshe ...
(number theory and probability theory),
Aleksandr Korkin
Aleksandr Nikolayevich Korkin (russian: Александр Николаевич Коркин; – ) was a Russian mathematician. He made contribution to the development of partial differential equations, and was second only to Chebyshev among the ...
(ordinary and partial differential equations), Mikhail Okatov (mechanism theory),
Osip Somov
Osip Ivanovich Somov (russian: Ио́сиф (О́сип) Ива́нович Со́мов; 13 June 1815, Moscow Governorate – 8 May 1876, Saint Petersburg) was a Russian mathematician
A mathematician is someone who uses an extensive knowle ...
(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''
.
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 thesis
A thesis ( : theses), or dissertation (abbreviated diss.), is a document submitted in support of candidature for an academic degree or professional qualification presenting the author's research and findings.International Standard ISO 7144: ...
"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
pedagogical
Pedagogy (), most commonly understood as the approach to teaching, is the theory and practice of learning, and how this process influences, and is influenced by, the social, political and psychological development of learners. Pedagogy, taken as ...
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.
![Andrei Markov](https://upload.wikimedia.org/wikipedia/commons/a/a8/Andrei_Markov.jpg)
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
Pafnuty Lvovich Chebyshev ( rus, Пафну́тий Льво́вич Чебышёв, p=pɐfˈnutʲɪj ˈlʲvovʲɪtɕ tɕɪbɨˈʂof) ( – ) was a Russian mathematician and considered to be the founding father of Russian mathematics.
Chebyshe ...
. 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
Count Lev Nikolayevich TolstoyTolstoy pronounced his first name as , which corresponds to the romanization ''Lyov''. () (; russian: link=no, Лев Николаевич Толстой,In Tolstoy's day, his name was written as in pre-refor ...
's excommunication from the
Russian Orthodox Church
, native_name_lang = ru
, image = Moscow July 2011-7a.jpg
, imagewidth =
, alt =
, caption = Cathedral of Christ the Saviour in Moscow, Russia
, abbreviation = ROC
, type ...
by requesting his own excommunication. The Church complied with his request.
![Literator Bridges Grave Markov](https://upload.wikimedia.org/wikipedia/commons/5/57/Literator_Bridges_Grave_Markov.jpg)
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
*
List of things named after Andrey Markov {{Short description, none
This article is a list of things named after Andrey Markov, an influential Russian mathematician.
* Chebyshev–Markov–Stieltjes inequalities
* Dynamics of Markovian particles
* Dynamic Markov compression
* Gauss–Ma ...
*
Chebyshev–Markov–Stieltjes inequalities
*
Gauss–Markov theorem
In statistics, the Gauss–Markov theorem (or simply Gauss theorem for some authors) states that the ordinary least squares (OLS) estimator has the lowest sampling variance within the class of linear unbiased estimators, if the errors in the ...
*
Gauss–Markov process
Gauss–Markov stochastic processes (named after Carl Friedrich Gauss and Andrey Markov) are stochastic processes that satisfy the requirements for both Gaussian processes and Markov processes. A stationary Gauss–Markov process is unique up to r ...
*
Hidden Markov model
A hidden Markov model (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process — call it X — with unobservable ("''hidden''") states. As part of the definition, HMM requires that there be an o ...
*
Markov blanket
In statistics and machine learning, when one wants to infer a random variable with a set of variables, usually a subset is enough, and other variables are useless. Such a subset that contains all the useful information is called a Markov blanket. ...
*
Markov chain
*
Markov decision process
*
Markov's inequality
In probability theory, Markov's inequality gives an upper bound for the probability that a non-negative function of a random variable is greater than or equal to some positive constant. It is named after the Russian mathematician Andrey Markov, ...
*
Markov brothers' inequality
*
Markov information source
*
Markov network
In the domain of physics and probability, a Markov random field (MRF), Markov network or undirected graphical model is a set of random variables having a Markov property described by an undirected graph. In other words, a random field is said to ...
*
Markov number
A Markov number or Markoff number is a positive integer ''x'', ''y'' or ''z'' that is part of a solution to the Markov Diophantine equation
:x^2 + y^2 + z^2 = 3xyz,\,
studied by .
The first few Markov numbers are
: 1, 2, 5, 13, 29, 34, 89 ...
*
Markov property
In probability theory and statistics, the term Markov property refers to the memoryless property of a stochastic process. It is named after the Russian mathematician Andrey Markov. The term strong Markov property is similar to the Markov propert ...
*
Markov process
A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happe ...
*
Stochastic matrix
In mathematics, a stochastic matrix is a square matrix used to describe the transitions of a Markov chain. Each of its entries is a nonnegative real number representing a probability. It is also called a probability matrix, transition matrix, ...
(also known as Markov matrix)
*
Subjunctive possibility
Notes
References
Further reading
*
* 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.
*
External links
*
*
{{DEFAULTSORT:Markov, Andrey
Markov, Andrei Andreyevich
Markov, Andrei Andreyevich
19th-century mathematicians from the Russian Empire
20th-century Russian mathematicians
Russian atheists
Former Russian Orthodox Christians
Probability theorists
Saint Petersburg State University alumni
Full members of the Saint Petersburg Academy of Sciences
Full Members of the Russian Academy of Sciences (1917–1925)
People from Ryazan
Russian statisticians