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The life and work of A. A. Markov. (English) Zbl 1049.01014

This is a careless essay on Markov’s life and on his work in probability theory. Repeating mistakes made by previous contributors, the authors believe that Tolstoy (who died in 1910) was excommunicated from the Russian Orthodox Church in 1912 (actually, in 1901) and they attribute to Markov rather than to Pushkin the verse (not limerick) “Count (not Duke!) Dundook”. They also state that Markov “implicitly accused” Chebyshev of plagiarism; actually, of failing to cite his predecessors. Some inaccuracies are also present and the references are given without page numbers which makes it difficult to check the provided formulations of Markov’s findings. Missing references include important papers by Markov jun. and Linnik et al. Describing Markov’s correspondence with Chuprov, the authors are unaware that in 1996, the reviewer published a book on Chuprov containing newly found letters betweed these scholars.

MSC:

01A60 History of mathematics in the 20th century
01A70 Biographies, obituaries, personalia, bibliographies
60-03 History of probability theory

Biographic References:

Markov, Andrei A.
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References:

[3] Bernstein, S. N., Sur l’extension du théoremé limite du calcul des probabilies etc., Math. Annalen, Bd., 97, 1-59 (1926) · JFM 52.0517.03
[7] Chebyshev, P. L., An experience in the elementary analysis of the probability theory, Crelle’s J. Angew. Math. (1846)
[8] Chebyshev, P. L., Des valuers moyennes, J. Math. Pures Appl., 12, 177-184 (1867)
[9] Chebyshev, P. L., Sur deux theoremes relatifs aux probabilities, Acta Math., 14 (1891)
[10] Fletcher, A., (An Index of Mathematical Tables, vol. 1 (1962), Oxford)
[11] Frobenius, G. F., Uber Matrizen aus nicht negativen Elementeen, Sitzungsber. Preuss. Akad. Wiss., Berl., 456-477 (1912) · JFM 43.0204.09
[12] Hostinsky, B., Sur les probabilités des phénomenes liés en chaine de Markoff, C.R. Acad. Sci., Paris, 189, 78-80 (1929) · JFM 55.0916.03
[14] Markonv, A. A., Ob odnom voproce D.I. Mendeleeva, Zapiski Imperatorskoi Akad. Nauk SP6, 62, 1-24 (1890)
[15] Markov, A. A., Application des fonctions continues au calcul des probabilités, Kasan Bull., 9, 2, 29-34 (1899)
[20] Markov, A. A., Issledovanie obschego sluchaya ispytanij, svyazannyh v cep’, Zapiski Akad. Nauk po Fiziko-matematicheskomu otdeleniyu, VIII seriya, 25, 93 (1910)
[21] Markov, A. A., Ob odnom sluchae ispytanij, svyazannyh v slozhnuyu cep’, Izv. Akad. Nauk, SPb, VI seriya, 5, 93, 171-186 (1911)
[22] Markov, A. A., Ob ispytaniyah, svyazannyh v cep’ ne nablyudaemymi sobytiyami, Izv. Akad. Nauk, SPb, VI seriya, 6, 98, 551-572 (1912)
[23] Markov, A. A., Primer statisticheskogo issledovaniya nad tekstom “Evgeniya Onegina”, illyustriruyuschij svyaz’ ispytanij v cep’, Izv. Akad. Nauk, SPb, VI seriya, 7, 93, 153-162 (1913)
[24] Nekrasov, P. A., General properties of numerous independent events in connection with approximate calculation of functions of very large numbers, Mat. Sbornik, 20, 431-442 (1898), (in Russian)
[27] (Ondar, Kh. O., The Correspondence between A.A. Markov and A.A. Chuprov on the Theory of Probability and Mathematical Statistics (1981), Springer-Verlag: Springer-Verlag New York) · Zbl 0476.62002
[29] Schneider, H., The concepts of irreducibility and full indecomposability of a matrix in the works of Frobenius, Konig and Markov, Linear Algebra Appl., 18, 139-162 (1977) · Zbl 0365.15009
[30] Seneta, E., Markov and the birth of chain dependence theory, Int. Statist. Rev., 64, 3, 255-263 (1996) · Zbl 0918.60008
[31] Seneta, E., Review of the correspondence between A.A. Markov and A.A. Chuprov on the theory of probability and mathematical statistics, Ann. Sci., 39, 614-617 (1982)
[32] Sheynin, O. B., A.A. Markov’s work on probability, Arch. His. Exact Sci., 39, 337-377 (1988) · Zbl 0764.01007
[33] Sheynin, O. B., Laplace’s work on probability, Arch. Hist. Exact Sci., 16, 137-187 (1976) · Zbl 0363.60005
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