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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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[2] J. Bernoulli, Ars Conjectandi, Opus Posthumum, Accedit Tractatus de Seriebus infinitis, et Epistola Gallice scripta de ludo Pilae recticularis, Basileae, 1713 (Chapters 1-4 translated into English by B. Sung, Ars Conjectandi, Technical Report No. 2, Department of Statistics, Harvard University, 1966); J. Bernoulli, Ars Conjectandi, Opus Posthumum, Accedit Tractatus de Seriebus infinitis, et Epistola Gallice scripta de ludo Pilae recticularis, Basileae, 1713 (Chapters 1-4 translated into English by B. Sung, Ars Conjectandi, Technical Report No. 2, Department of Statistics, Harvard University, 1966)
[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
[4] A.S. Besikovitch, A Biographic Essay on A.A. Markov, vol. 9, 1924, pp. iii-xiv (in Russian); A.S. Besikovitch, A Biographic Essay on A.A. Markov, vol. 9, 1924, pp. iii-xiv (in Russian)
[5] S.G. Brush, A history of random processes, 1. Brownian movement, 1968. in: M.G. Kendall, R.L. Plackett (Eds.), Stud. Hist. Stat. and Prob., London, vol. 2, 1977, pp. 347-382; S.G. Brush, A history of random processes, 1. Brownian movement, 1968. in: M.G. Kendall, R.L. Plackett (Eds.), Stud. Hist. Stat. and Prob., London, vol. 2, 1977, pp. 347-382
[6] V.Ya. Bunyakovsky, Elements of the Mathematical Theory of Probability, Petersburg, 1846 (in Russian); V.Ya. Bunyakovsky, Elements of the Mathematical Theory of Probability, Petersburg, 1846 (in Russian)
[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
[13] A.M. Lyapunov, Zhizn’ i trudy P.L. Chebysheva, in: P.L. Chebyshev (Ed.), Izbrannye Matematicheskie Trudy, Gostehizdat, M.-L., 1946; A.M. Lyapunov, Zhizn’ i trudy P.L. Chebysheva, in: P.L. Chebyshev (Ed.), Izbrannye Matematicheskie Trudy, Gostehizdat, M.-L., 1946
[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)
[16] A.A. Markov, Ischislenie veroyatnostej, SPb, 1900; 2-e izd., SPb, 1908, Translated into German, Wahrscheinlichkeits-Rechnung, Teubner, Leipzig-Berlin, 1912; 3-e izd., SPb, 1913; 4-e izd., Moskva, 1924; A.A. Markov, Ischislenie veroyatnostej, SPb, 1900; 2-e izd., SPb, 1908, Translated into German, Wahrscheinlichkeits-Rechnung, Teubner, Leipzig-Berlin, 1912; 3-e izd., SPb, 1913; 4-e izd., Moskva, 1924
[17] A.A. Markov, Rasprostranenie zakona bol’shih chisel na velichiny, zavisyaschie drug ot druga, Izvestiya Fiziko-matematicheskogo obschestva pri Kazanskom universitete, 2-ya seriya 15 (94) (1906) 135-156; A.A. Markov, Rasprostranenie zakona bol’shih chisel na velichiny, zavisyaschie drug ot druga, Izvestiya Fiziko-matematicheskogo obschestva pri Kazanskom universitete, 2-ya seriya 15 (94) (1906) 135-156
[18] A.A. Markov, Issledovanie zamechatel’nogo sluchaya zavisimyh ispytanij, Izvestiya Akademii Nauk, SPb, VI seriya 1 (93) (1907) 61-80 (Translated into French, Recherches sur un cas remarquable d’epreuves dependantes, Acta Math., Stockholm 33 (1910) 87-104); A.A. Markov, Issledovanie zamechatel’nogo sluchaya zavisimyh ispytanij, Izvestiya Akademii Nauk, SPb, VI seriya 1 (93) (1907) 61-80 (Translated into French, Recherches sur un cas remarquable d’epreuves dependantes, Acta Math., Stockholm 33 (1910) 87-104)
[19] A.A. Markov, Rasprostranenie predel’nyh teorem ischisleniya veroyatnostej na summu velichin svyazannyh v cep’, Zapiski Akademii Nauk po Fiziko-matematicheskomu otdeleniyu, VIII seriya 25 (3) (1908). Translated into German, Ausdehnung der Satze uber die Grenzwerte in der Wahrscheinlichkeitsrechnung auf eine Summe verketteter Grossen, in: A.A. Markoff (Ed.), Wahrscheinlichkeitsrechnung (translated by H. Liebmann), B.G. Teuber, Leipzig, 1912, pp. 272-298. Translated into English, Extension of the limit theorems of probability theory to a sum of variables connected in a chain (translated by S. Petelin) in: R.A. Howard (Ed.), Dynamic Probabilities Systems, vol. 1, Wiley, New York, 1971, pp. 552-576; A.A. Markov, Rasprostranenie predel’nyh teorem ischisleniya veroyatnostej na summu velichin svyazannyh v cep’, Zapiski Akademii Nauk po Fiziko-matematicheskomu otdeleniyu, VIII seriya 25 (3) (1908). Translated into German, Ausdehnung der Satze uber die Grenzwerte in der Wahrscheinlichkeitsrechnung auf eine Summe verketteter Grossen, in: A.A. Markoff (Ed.), Wahrscheinlichkeitsrechnung (translated by H. Liebmann), B.G. Teuber, Leipzig, 1912, pp. 272-298. Translated into English, Extension of the limit theorems of probability theory to a sum of variables connected in a chain (translated by S. Petelin) in: R.A. Howard (Ed.), Dynamic Probabilities Systems, vol. 1, Wiley, New York, 1971, pp. 552-576
[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)
[25] P.A. Nekrasov. The Philosophy and Logic of Science of Mass Phenomena in Human Activity, Moscow, 1902 (in Russian); P.A. Nekrasov. The Philosophy and Logic of Science of Mass Phenomena in Human Activity, Moscow, 1902 (in Russian)
[26] J.J. O’Connor, E.F. Robertson, Pafnuty Lvovich Chebyshev. Available from <>, 2002; J.J. O’Connor, E.F. Robertson, Pafnuty Lvovich Chebyshev. Available from <>, 2002
[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
[28] S.-D. Poisson, Recherches sur la Probabilité des Jugements en Matiere Criminelle et en Metière Civile, Précédées des Regles Générales du Calcul des Probabilitiés, Paris, Bachelier, Imprimeur-Libraire pour les Mathematiques, 1837; S.-D. Poisson, Recherches sur la Probabilité des Jugements en Matiere Criminelle et en Metière Civile, Précédées des Regles Générales du Calcul des Probabilitiés, Paris, Bachelier, Imprimeur-Libraire pour les Mathematiques, 1837
[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
[34] Photos of Markov and family from web, , August 2003; Photos of Markov and family from web, , August 2003
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