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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 becomePr**of**essor and Rector **of** Moscow University. In 1898 he sketched the pro**of****of** 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 **of**ficialat the Ministry **of** People’s Education, and his reactionary views. In his letter**of** 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