Pavel Alexeyevich Nekrasov

Pawel Alexejewitsch Nekrasov , Russian Павел Алексеевич Некрасов , English transcription Pavel Alekseevich Nekrasov, (born February 1, 1853 in Ryazan Governorate ; † December 20, 1924 in Moscow ) was a Russian mathematician who dealt with probability.

Pavel Alexeyevich Nekrasov

Life

Nekrasov studied at the Orthodox theological seminary and from 1874 at Moscow University. There he was a student of the mathematician Nikolai Vasilyevich Bugayev . Several years after his graduation, he became a private lecturer there in 1885 (after he had received his Russian doctorate in the same year, corresponding to a habilitation in the West) and in 1885 or 1886 extraordinary professor at Moscow University (where he had been since 1883). In 1890 he was given a full professorship. In 1893 he became rector. After his tenure as rector, he actually wanted to retire, but was not allowed to do so. He also taught probability theory and higher mathematics at the Moscow Land Surveying Institute from 1885 to 1891. From 1898 he was almost exclusively occupied with administrative tasks for the Ministry of Education (he was curator of the university and responsible for the schools in Moscow and the surrounding area) and in 1905 he moved to St. Petersburg as a member of the Council of the Ministry of Education. After the Russian Revolution he tried to adapt to the new rulers, dealt with mathematical economics (which he lectured on in 1918/19) and studied Marxism. He died of pneumonia in 1924. His approach to Marxism, however, brought him no recognition; on the contrary, with some of his writings after his death he was a main target of attacks against religiously influenced mathematicians, which later culminated in the arrest of Yegorov and the Lusin affair .

In 1891 he became vice president of the Moscow Mathematical Society and was its president from 1903 to 1905. From 1891 to 1894 he was vice-president of the Society of Friends of Natural Sciences in Moscow.

He dealt with algebra, analysis, mechanics and probability theory. In the latter area he made significant contributions, which were criticized at his time by Andrei Markow and Alexander Mikhailovich Lyapunov , because he could not present them in a satisfactory form, and later he was forgotten. Markov and Lyapunov are mostly mentioned today as representatives of the St. Petersburg School (founded by Tschebyschow) when it comes to the question of the first mathematically strict treatment of the Central Limit Theorem, whereby the discussion and argument with Nekrasov played an important role (especially a Essay from 1898). In his work, however, he anticipated results that only reappeared in mathematical literature fifty years later. The works from 1900 to 1902 (in Matematichesky Sbornik), in which he elaborates on the statements of his essay from 1898 and which comprise over 1000 pages, are so unclear and unsystematic, according to E. Seneta (1984), that they make reading very difficult complicate.

Loren Graham and Jean-Michel Kantor see the confrontation between Nekrasov and Markov as an expression of the confrontation between the liberal-secular, government-critical thinking of the St. Petersburg School (Markov, who was an atheist) with the conservative thinking of Nekrasov in Moscow, which was arrested by the Orthodox Church . After Graham and Kantor, he also mixed philosophical and religious considerations with his mathematical work, and his concept of statistical independence from random variables was directly linked to his philosophical concern about the existence of free will. Markov was repulsed by this and even changed the direction of his research to refute Nekrasov (according to Markov, statistical independence is not a prerequisite for the validity of the law of large numbers, it also applies to dependent variables, which led him to consider Markov chains).

He was a pioneer in the evaluation of integrals of exponential functions in complex with the saddle point method and in 1885 he wrote a paper on the convergence of the Gauß-Seidel method .

One of his students was the statistician Alexander Ivanovich Tschuprov , who did his doctorate with him.

Fonts

• Determination of unknowns using the least squares method (Russian), Matematichesky Sbornik, Volume 12, 1885, pp. 189–204
• The Lagrange series and approximations for functions for very large numbers (Russian), Matematichesky Sbornik, Volume 12, 1885, pp. 12: 49–188, 315–376, 483–578, 643–724
• The general properties of mass-independent phenomena in connection with the approximate calculation of functions for very large numbers (Russian), Matematichesky Sbornik, Volume 20, 1898, pp. 431-442
• Probability Theory (Russian), Moscow University 1896, 2nd edition St. Petersburg 1912
• The theory of probability: central limit theorem, method of least squares, reactionary views, teaching of probability theory, further developments (OB Sheynin Hrsg.), Berlin, NG-Verlag 2004

literature

• E. Seneta: The central limit theorem and linear least squares in pre-revolutionary Russia: the background, Mathematical Scientist, Volume 9, 1984, pp. 37-77
• Oscar B. Sheynin: Nekrasov's work on probability: the background, Archive for History of Exact Sciences, Volume 57, 2003, pp. 337-353
• AD Soloviev: PA Nekrasov and the central limit theorem of the theory of probability, IMI ser. 2, 1997, 2 (37),: 9-22,

Web links

Commons : Pavel Nekrasov  - collection of pictures, videos and audio files

• Mathnet.ru

Individual evidence

1. ↑ Eugene Seneta: Mathematics, religion, and Marxism in the Soviet Union in the 1930s, Historia Mathematica, Volume 31, 2004, 337-367
2. ^ Hans Fischer, History of the Central Limit Theorem, Springer p. 196, referring to E. Seneta and AD Soloviev
3. ^ Graham, Kantor, Naming Infinity, Harvard UP 2009, p. 69
4. ^ Hans Fischer, History of the Central Limit Theorem, Springer, p. 196
5. ↑ There the patronymic is given with Alexandrovich, in Sheynin with Alexejewitsch