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Russian Papers on the History of Probability and Statistics Translated by the Author Berlin 2004 (C) Oscar Sheynin

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Russian Papers on the History of Probability and Statistics Translated by the Author Berlin 2004 (C) Oscar Sheynin Russian Papers on the History of Probability and Statistics Translated by the Author Berlin 2004 (C) Oscar Sheynin www.sheynin.de Contents Introduction 1. Review of Kendall, M.G., Doig, A.G. Bibliography of Statistical Literature Pre-1940 with Supplements to the Volumes for 1940 – 1949 and 1950 – 1958. Edinburgh, 1968. Novye Knigi za Rubezhom , ser. A, No. 10, 1969, 2. On the work of Adrain in the theory of errors. Istoriko-Matematicheskie Issledovania (IMI), vol. 16, 1965, pp. 325 – 336 3. On the history of the iterative methods of solving systems of linear algebraic equations. Trudy IX Nauchn Konf. Aspirantov i Mladsh. Nauchn. Sotrundn. Inst. Istorii Estestvoznania iTekhniki , Sektsia istorii fiz. i mat. nauk. Moscow, 1966, pp. 8 – 12 4. On selection and adjustment of direct observations. Izvestia Vuzov. Geodezia i Aerofotos’emka No. 2, 1966, pp. 107 – 112 5. On the history of the adjustment of indirect observations. Ibidem, No. 3, 1967, pp. 25 – 32 6. Some Issues in the History of the Theory of Errors. Abstract of dissertation. Moscow, 1967. Published as a manuscript. Inst. Istorii Estestvoznania i Tekhniki 7. On the work of Bayes in the theory of probability. Trudy XII Nauchn. Konf. Aspirantov i Mladsh. Nauchn. Sotrudn. Inst. Istorii Estestvoznania I Tekhniki , Sektsia istorii mat. i mekh. nauk. Moscow, 1969, pp. 40 – 57 8. On the history of the De Moivre – Laplace limit theorem. Istoria i Metodologia Estestven. Nauk , vol. 9, 1970, pp. 199 – 211 9. On the appearance of the Dirac delta-function in a memoir of Laplace. IMI, vol. 20, 1975, pp. 303 – 308 10. History of the theory of probability. Based on Theory of probability before Chebyshev. IMI, vol. 25, 1978, pp. 284 – 306, and History of the Theory of Probability to the Beginning of the 20 th Century . Berlin, 2004 11. Liapunov’s letters to Andreev. IMI, vol. 31, 1989, pp. 306 – 313 . 12. On the history of the statistical method in natural sciences. IMI, vol. 32/33, 1990, pp. 384 – 408 13. Markov’s report on a paper by Galitzin. Ibidem, pp. 451 – 467 14. Markov’s papers in the newspaper Den , 1914 – 1915. IMI, vol. 34, 1993, pp. 194 – 206 15. Correspondence of Nekrasov and Andreev. IMI, vol. 35, 1994, pp. 124 – 147. Coauthor: M.V. Chirikov 16. The notion of randomness from Aristotle to Poincaré. IMI, vol. 1 (36), No. 1, 1995, pp. 85 – 105 17. Correspondence between P.A. Nekrasov and A.I. Chuprov. Ibidem, pp. 159 – 167 18. Markov and life insurance. IMI, vol. 2 (37), 1997, pp. 22 – 33 19. Slutsky: commemorating the 50 th anniversary of his death. IMI, vol. 3 (38), 1999, pp. 128 – 137 20. History of the theory of errors. IMI, vol. 5 (40), 2000, pp. 310 – 332 Introduction I am presenting translations of my papers originally published in Russian, mainly in Istoriko- Matematicheskie Issledovania (IMI) . Only a fraction of historians of mathematics read Russian and some are unwilling to study the contributions published beyond the usual set of periodicals so that my present work seems justified. In actual fact, I am putting out most of the items from a microfiche collection of the same title published by Hänsel-Hohenhausen in 1999 as Deutsche Hochschulschriften 2621 but hardly examined by more than a dozen readers; the copyright to ordinary publication was, and is mine. Some items below are translations of publications of materials kept at several Russian archives or newspaper articles and among the former is Markov’s critical review of a paper devoted to the treatment of observations. In translating my papers, I corrected a few mistakes and misprints (largely due, in the new series of the IMI, to the impossibility of reading the proofs), left out dated material, and referred not to Russian transla- tions of classical works but to their original editions. Abbreviations used throughout: AHES = Arch. Hist. Ex. Sci. ; DHS = Deutsche Hochschulschriften; IMI = Istoriko-Matematicheskie Isssledovania ; L. = Leningrad; M. = Moscow; MSb = Matematich. Sbornik ; 1 Psb = Petersburg; ( R ) = in Russian; ZhMNP = Zhurnal Ministerstva Narodn. Prosveshchenia. 1. Review of Kendall, M.G., Doig, A.G . (1968), Bibliography of Statistical Literature pre-1940 with Supplements to the Volumes for 1940 – 1949 and 1950 – 1958. Edinburgh. This is vol. 3 of the entire Bibliography covering the period until 1958; the first two volumes appeared in 1962 and 1965. No further volumes are planned since in 1959 the International Statistical Institute began publishing an abstracting journal now called Statistical Theory and Methods Abstracts. According to the authors’ aims and methodology as described in vol. 1, the Bibliography includes almost all the articles from 12 main periodicals and a number of papers from 42 other journals. In addition, the authors made use of the bibliographies appended to many papers and of the abstracting journals (although not of the Soviet Mate- matika ). They believe to have covered 95% of the existing articles on statistics and its applications. Each volume of the Bibliography is actually an author index (no subject indices are provided). The litera- ture published in Russian and in several other languages is described in English, French or German. In all, this vol. 3 lists about 10 thousand monographs and articles separated into two time intervals, – before 1900 and from 1900 to 1939 (2,360 and 7,630 items respectively) as well as 148 sources for 1940 – 1949 and about 1,170 for 1950 – 1958. All the books entered here had appeared before 1900. Neither the second part, nor the first two volumes include any books which is in line with the practice of the abovementioned quar- terly. This is an essential setback but the Bibliography is nevertheless very valuable. Vol. 3 is also useful for historians of mathematics since it lists classical works (of Laplace, Gauss et al) including writings of such authors for whom probability was a minor subject (Euler), forgotten writings of eminent mathematicians, commentaries and essays, translations of various works into any of the three main languages. There are some shortcomings. The selected literature, even of the 20 th century, was not checked in visu ; likely because of the general direction of the Bibliography there are hardly any references to collected works; of the 14 writings of Euler included in t. 7 of his Opera omnia , ser. 1 (1923) and pertaining to probability and statistics, the authors included only seven, and one of these called Wahrscheinlichkeitsrechnung either does not exist or wrongly named; the descriptions contain mistakes and inaccuracies (Süssmilch’s Göttliche Ord- nung first appeared in 1741, then in 1761 – 1762 but not in 1788; the second part of Daniel Bernoulli’s “Mensura sortis” (1771) is omitted); and cross-references are lacking. Finally, the spelling Ladislaus von Bortkiewicz as given in the second part does not coincide with that in the first part, Vladislav Bortkevich. Having emigrated from Russia to Germany in 1901 and being a nobleman, he changed his name accordingly but that fact is not explained. In 1962, the authors estimated that about a thousand articles on their subject were being published yearly. This means that already now it would be expedient to issue a bibliography of this literature for 1959 – 1970. Neither abstracting journals, nor their cumulative author indices are a substitute for bibliographies (to be compiled in the first place by scanning such sources). I also believe that a single bibliography for 1900 – 1970 with books being certainly included is also needed. 2 On the Work of Adrain in the Theory of Errors Istoriko-Matematicheskie Issledovania (IMI), vol. 16, 1965, pp. 325 – 336 In translating my paper I took into account its somewhat revised version appended to my unpublished the- sis of 1967 (Some Issues …, partly translated in this collection). Adrain’s articles are now reprinted (see Bibliography) and I have therefore omitted his original and hardly understandable derivations of the normal law (leaving however their modernized reconstruction [ 8 ] ). Their latest discussion is due to Hald [10, pp. 368 – 373] and Dutka [8a]. Also note that Adrain’s paper [2] apparently appeared in 1809 rather than in 1808 [13, p. 170]. * * * Robert Adrain is meritorious for his remarkable findings in the theory of errors. He published two deriva- tions of the normal law of error a year before [or at the same time as] Gauss did and applied it to establishing the principles of least squares and arithmetic mean as well as to determining the flattening of the earth’s ellipsoid of revolution. Adrain was born in Ireland and died in New Brunswick. He learned mathematics mainly by himself and began teaching it at an early age. Then, after participating in the Irish national movement and being wounded in the revolt of 1798, he fled to the United States. Adrain resumed there his teaching activities becoming, in 1809, Professor of mathematics at Queen’s College (now, Rutgers College) in New Brunswick. From 1813 to 1826 he was Professor at Columbia University, and, from 1827 to 1836, at Pennsylvania (vice-rector from 1828 to 1836). Adrain delivered lectures in various disciplines. Thus, in 1829 he taught elementary mathematics, geodesy, cartography, mathematical analysis, mechanics and astronomy. He and Nathaniel Bowditch (1773 – 1838) 1 were among the first American mathematicians. In 1812 Adrain was elected to the American Philosophical Society, and, in 1813, to the Academy of Sciences and Arts. He actively contributed to the first American mathematical periodicals. Coolidge [8] provided a general description of Adrain’s work, but his account of the latter’s findings in the theory of errors was not comprehensive. In the 19 th century several geodesists and astronomers discussed these in more detail (e.g., [1; 9; 26] from among those which I do not mention below) but still not sufficiently.
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