1 Oscar Sheynin History of Statistics Berlin, 2012 ISBN 978-3 ...

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1 Oscar Sheynin History of Statistics Berlin, 2012 ISBN 978-3 ...

Chebyshev thought that the limits of integration, α and β, in formula(12.2) describing that theorem, were any. Nekrasov (1911, p. 449) arbitrarilyinterpreted that expression as variable. I discuss Nekrasov in § 13.5; hecould have well indicated that, on the contrary, he had generalized theChebyshev theorem. In his previous polemic paper Liapunov (1901b, p. 61)declared that he had assumed that these limits were given beforehand andthat otherwise the probability, written down in the left side of formula of theCLT, could have no limit at all, – but nevertheless be asymptoticallyexpressed by the normal law of distribution.13.5. NekrasovHis life and work (Sheynin 2003a) are separated into two stages. From1885 and until about 1900 he had time to publish remarkable memoirs notconnected with probability both in Russia and Germany and to becomeProfessor and Rector of Moscow University. In 1898 he sketched the proofof the CLT for sums of lattice random variables. Then, however, hispersonality changed. His writings became unimaginably verbose, sometimesobscure and confusing, and inseparably linked with ethical, political andreligious considerations. Here is a comparatively mild example (1906, p. 9):mathematics accumulatedpsychological discipline as well as political and social arithmetic or themathematical law of the political and social development of forcesdepending on mental and physiological principles.Furthermore, Nekrasov’s work began to abound with elementarymathematical mistakes and senseless statements. For example (1901, p.237): it is possible to assume roughly, that x n , n > 0, is the limit of sin x as |x|→ 0, and the conclusions made by [Chebyshev, Markov and Liapunov]never differ much from such an understanding of limit. And here is hisastounding declaration (Archive, Russian Academy of Sciences, fond 173,inventory 1, 55, No. 5) from his letter of 1913 to Markov:I distinguish the viewpoints of Gauss and Laplace [on the MLSq] by themoment with regard to the experiment. The first one is posterior and thesecond one is prior. It is more opportune to judge à posteriori because moredata are available, but this approach is delaying, it lags behind, drags afterthe event.At least the attendant reasons for such a change were Nekrasov’s religiousupbringing (before entering Moscow University he graduated from aRussian Orthodox seminary), his work from 1898 onward as a high officialat the Ministry of People’s Education, and his reactionary views. In his letterof 1916 to the religious philosopher P. A. Florensky (Sheynin 1993a, p. 196)Nekrasov stated that the German – Jewish culture and literature pushed usto the crossroads. World War I was then going on which only partlyexonerates Nekrasov. I shall now dwell on some concrete issues.1) Teaching the theory of probability. In § 13.2-7 I mentioned Nekrasov’sproposal for teaching probability in school and the rejection of thecurriculum drawn up by him.134

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