A. P. Nekrasov and the central limit theorem of probability theory (Q2713165)

Pavel Alekseevich Nekrasov (1853-1924) contributed to algebra, analysis, probability theory and to mechanics. The author studies his work on the central limit theorem and concludes that he, by essentially applying the complex variable theory, had proved it for lattice variables (which he, however, understood in a wrongly excessive sense) in the new case of large deviations. The author remarks that some of Nekrasov's conditions were too strict and his other restrictions could not be checked. The author agrees with earlier commentators in that Nekrasov's pompous style, his lumping together of mathematics, pseudophilosophy and religion as well as his glaring mistakes (e.g., his misunderstanding of the notion of infinitesimal) caused Markov and Lyapunov to dismiss his work.NEWLINENEWLINENEWLINEThe author also participates in describing Nekrasov's role in originating the saddle point method [\textit{S. S. Petrova} and \textit{A. D. Solov'ev}, Istor. Mat. Issled. 35, 148-164 (1994; Zbl 0906.01009)] and now he properly mentions \textit{E. Seneta} [Math. Sci. 9, 37-77 (1984; Zbl 0542.01003)].NEWLINENEWLINENEWLINENekrasov's debates with Markov and Lyapunov (seven papers, 1899-1911, and correspondence) are translated in ``From Davidov to Romanovsky. More Russian papers on probability and statistics. Egelsbach (1998; Zbl 0941.01034) (selected and translated by the reviewer).