Andrei Andreevich Markov is a well-known Russian mathematician, academician who made a great contribution to science, studying the theory of probability. Also in his area of interest were number theory and mathematical analysis. It is noteworthy that at the same time Andrei Andreyevich raised his son, who also became a scientist. He is considered the founder of the Soviet school for the study of constructive mathematics.
Biography of a scientist
Andrei Andreyevich Markov was born in 1856. He was born in Ryazan. His father, named Andrei Grigorievich, was an official who served as a college adviser in the Forestry Department. After he retired from this post, he moved to St. Petersburg, where he became an attorney and general manager on the estate of Ekaterina Alexandrovna Valvateva.
The grandfather of the hero of our article, Grigory Markovich, was a rural deacon. The biography of Andrei Andreyevich Markov is now well known to everyone who is interested in mathematics. He was twice married. His first wife was Nadezhda Petrovna Fedorova, the daughter of an official. They gave birth to six children. The boy Paul died in childhood. The remaining children were called Peter, Eugene, Maria, Michael and Andrew.
The second time he married Anna Iosifovna, from whom he had three more children - Lydia, Vladimir and Catherine. Vladimir Andreevich was a talented scientist who showed great promise in mathematics. But he died at the age of 26 from tuberculosis.
The sister of his father, whose name was Evgenia Andreevna, is well known. She entered Russian history as one of the first Russian female doctors.
Andrei Andreyevich Markov himself has suffered from tuberculosis of the knee joint since childhood. Because of this, he had to walk on crutches for up to ten years. Only when the famous surgeon Kade performed the operation, he got the opportunity to move normally.
Education
In 1866, Andrei Andreyevich Markov entered the fifth gymnasium in St. Petersburg. At that time, this educational institution was considered classical, Greek and Latin were taught in it. The humanities did not like the hero of our article, so he did not have time for most subjects, putting almost all his efforts only to study mathematics.
He managed to finish high school in 1874. After that, Andrei Andreevich Markov Sr. became a student at St. Petersburg University. He studied at the university with the famous professors Zolotarev, Korkin, as well as with the legendary Pafnuti Chebyshev (pictured above), who played a significant role in the fate of the hero of our article.
He became a graduate of the university in 1878. At St. Petersburg University he graduated from the Faculty of Physics and Mathematics with a mathematical degree, receiving a Ph.D. He distinguished himself by becoming the owner of a gold medal for an essay on the integration of differential equations using continued fractions. He was invited to stay at the university in order to start preparing for a professorship.
Master's dissertation
In 1880, Andrei Andreevich Markov Sr. defended his famous work on binary quadratic forms of a positive determinant. This dissertation immediately made him one of the most influential scientists in this field.
Soon after, he successfully defended his doctoral dissertation on applications of algebraic continued fractions. Since 1880, he has been teaching at the University of St. Petersburg as a privat-docent. After three years of successful work, she receives a course called Introduction to Analysis, which Posset and Sokhotsky taught before. It so happened that in parallel the famous Chebyshev left the university, so the mathematician Andrei Andreyevich Markov began to teach students the basics of probability theory.
In 1886, the hero of our article was chosen as an adjunct in the physics and mathematics department, since then he began to study exclusively pure mathematics. Since 1896 he became an ordinary academician at the Imperial Academy of Sciences in St. Petersburg.
In increasing order, his career developed at the Physics and Mathematics Faculty. In 1886, he received the post of professor, and in 1898 - a full state councilor.
In 1922, Markov died in Petrograd. He was 66 years old. The scientist was buried at Mitrofanievsky cemetery. In 1954, he was reburied at the Literary bridges at the Volkovsky cemetery.
Scientific work
Speaking about the mathematics of Andrei Andreyevich Markov and his achievements, it should be noted that he made the greatest contribution to the study of probability theory. Markov became the pioneer of a large class of stochastic processes, which were accompanied by a continuous time and discrete component. In the future they were named after him.
Its processes can be described in this way. The state of the process itself depends directly on the current state. The probability theory itself in those years was constructed in such a way that it was considered exclusively abstract, but at present it is being put into practice.
Markov deduced the theory of chains, which immediately became an important area of scientific research. The so-called theory of Markov processes was the basis for a more global theory dedicated to stochastic processes. This is also known as Markov inequality. The mathematician played a large role in promoting the classical studies of his predecessors, which related to large numbers and the central theorem of probability theory, dealt with the problem of their distribution to the so-called Markov chains.
Separately, it is worth noting that Markov's landmark discovery was work related to the theory of random processes, as well as to probability theory in general. Similar successes were achieved in the future by Kolmogorov, who proposed a rigorous and clear theoretical and probabilistic formulation, putting forward it on the basis of measure theory.
Advances in Mathematical Analysis
The scientist, to whom this article is devoted, made a great contribution to mathematical analysis. In the exhaustive list of works on which Markov worked, mathematical analysis occupies about a third. First of all, he diligently studied the theory of continued fractions, the calculation of finite differences, extremal problems to be solved in the so-called function spaces, and also studied the theory of interpolation of functions, the problem of moments, quadrature formulas, the theory of orthogonal polynomials, differential equations, the theory of functions, which is least likely to deviate from zero. In most of these sections, Markov was able to achieve the most important results.
Markov basically adopted the thoughts of his immediate teacher Chebyshev, having begun to deal with the solution of the problems identified in his writings. The key and classical works of Markov and Chebyshev were devoted to the limit values of the integrals, constituted the key foundations of the theory of moments and extremal problems in the field of function spaces.
The scientist also worked on number theory. Moreover, he has only about fifteen specific publications. But each of them is crucial for this theory as a whole. These include, first of all, the master's thesis on binary quadratic forms of the positive determinant, which saw the light of day in 1880.
This theory adjoined the studies of Zolotarev and Korkin, it was highly appreciated by Chebyshev, many strongly advising her to study. This dissertation was devoted to the problems of arithmetic minima, which are used in indefinite binary quadratic forms. In most of his subsequent articles, Markov considered this problem as indefinite ternary and quaternary quadratic forms. The results of the work and ideas of Markov himself had a huge impact on the development of number theory as a whole.
Conflict with the church
At the very beginning of the 20th century, Markov had a conflict with the Russian Orthodox Church. In 1901, a mathematical scientist sharply criticized the decision of the Synod, which excommunicated Leo Tolstoy from the church.
In 1912, Markov sent a letter to the Holy Synod at the Russian Orthodox Church, in which he independently asked him to excommunicate. The academician, in particular, wrote that he does not see any significant difference between relics and icons, as well as idols and gods, on the one hand, and on the other hand, does not sympathize with any world religion, each of which, like Orthodoxy, is supported exclusively by fire and sword.
In February, the synod considered Markov’s appeal, instructing the St. Petersburg metropolitan to persuade the academician. But the hero of our article even refused to meet with the priest. He officially stated that he considered this a waste of his time.
Then Metropolitan Anthony signed a resolution in which he called on everyone to officially consider Markov to have fallen from Orthodoxy and to be immediately removed from the lists of Orthodox people.
In September 1912, the spiritual consistory of St. Petersburg officially approved this decision. Once again, the case was considered by the synod in October. The ministers of the Orthodox Church decided to notify his immediate superiors, officials in the Ministry of Education about this case. After that, they requested detailed information about his parents, the date and place of baptism. In response, Markov refused to provide this information, because of which it was decided to apply for it to the Academy of Sciences. However, they replied that they did not have such information. The same answer came from Petersburg University and the police.
If we list the main works of Markov, then it is necessary to mention such works as the “Calculus of Probabilities”, “Selected Works on the Theory of Continued Fractions and Function Theories that Least Least from Zero”, “Selected Works. Number Theory. Probability Theory”.
Markov was a very versatile and educated person, he had many hobbies, which many of his friends, acquaintances and colleagues knew about. First of all, Andrei Andreyevich was an avid chess player. He participated in a large number of correspondence tournaments. Basically, these were tournaments and individual matches, which were organized under the auspices of all kinds of print media. Markov was engaged in a chess composition, was close friends with Chigorin, they were even sparring partners. Incidentally, to the delight of the future academician, their meeting ended with a score of 1.5: 2.5. Markov managed to win one game, brought the next one in a draw, only after that Chigorin won two victories in a row, playing with white pieces. If we evaluate his success in chess by modern standards, it becomes obvious that Markov played chess at the level of a modern master of sports.
In total, the chess archive of the scientist and mathematician contains about one and a half thousand letters. Of particular value is the archive of his correspondence with his son. Partially, materials from this archive were published with the direct assistance of Romanov and Grodzensky.
Markov Jr
Andrei Andreevich Markov Jr. was born in 1903. He was born in St. Petersburg. Andrei Andreyevich, to whom the first part of this article is devoted, was his father. The son followed in his footsteps, but not in tsarist Russia, but in the Soviet Union, becoming one of the most famous Soviet mathematicians. It is believed that it was he who became the founders of the national school of constructive mathematics. In the biography of Andrei Andreevich Markov, Jr., whose childhood was spent in St. Petersburg, the upbringing that his father gave him and the education that the young man himself chose played a large role. All this had a direct impact on the future of Markov Jr.
Andrei Andreevich Markov, Jr. became a graduate of the Eighth Petrograd Gymnasium in 1919. In 1924 he became a graduate of Leningrad State University, going to graduate school at the Astronomical Institute of Leningrad.
Briefly telling the biography of A. A. Markov Jr., it is necessary to mention that he received the scientific degree of Doctor of Physical and Mathematical Sciences in 1935 without an official defense of the dissertation, his work and achievements were already appreciated at that time. In 1953, an important event took place in the biography of Andrei Andreevich Markov Jr. Briefly, this fact is definitely worth mentioning. He became a member of the Academy of Sciences of the Soviet Union. In the same year, he became a member of the CPSU.
Scientific career
Andrey Andreyevich Markov made a great contribution to computer science. His labor and scientific career developed like that. In 1933, he began working at the University of Leningrad, in 1936 he received the post of professor there. Then, until 1942, and also from 1943 to 1953, he headed the department of geometry. At the same time, he spent a little less than a year in the besieged Leningrad, which was occupied by the Nazis during the Great Patriotic War.
From 1959 to 1979, Markov headed the Department of Mathematical Logic at Moscow State University. In parallel, he began working at the Steklov Institute of Mathematics of the Academy of Sciences of the Soviet Union. In this institution, he served until 1972.
Advances in Computer Science
After the war, a new page opens in the biography of Andrei Andreevich Markov Jr. On the basis of the computer center, which operates at the Academy of Sciences of the Soviet Union, he creates a real laboratory of logic and structure of machines, which he personally manages for more than two decades.
Speaking briefly about the most important thing in the biography of A.A. Markov, Jr., it should be noted that work in this laboratory had an impact on his entire future career.
Markov’s social and political position on the so-called Letter 99 is well known. This is a collective appeal, which was signed in 1968 by a number of famous Soviet mathematicians, seeking to protect their colleague Alexander Yesenin-Volpin. The latter was forcibly sent to a psychiatric hospital due to the fact that he conducted dissident activities. The letter became an important event not only in the life of prominent figures of Soviet mathematics, but also in the domestic history of the human rights movement. Markov signed this letter together with other famous scientists.
It is noteworthy that this letter was an important milestone in the relationship between the government and the Soviet mathematical community. Many of those who decided to sign it were subjected to repression. At a minimum, signatories lost their jobs or enviable privileges. Because of this letter, there was a change in the leaders of Soviet education and mathematical science. And yet, on Markov his signature, put under the letter, did not affect much, unlike many others.
Yesenin-Volpin himself, who, incidentally, was the son of Sergei Yesenin, emigrated to the United States in 1972, which the Soviet authorities insisted on. He died in Boston only in 2016.
