On the Defense Work of A. N. Kolmogorov during World War II

Similarly to his great predecessors P. L. Tschebyshev and A. M. Lyapunov, the academician A. N. Kolmogorov (25.04.1903– 20.10.1987) was not only a universal mathematician, proposing and developing fruitful ideas, he also readily answered challenges presented to him in his capacity as an applied mathematician. He had an amazing ability to get to the root of a problem, to determine fundamental issues, and to clarify debatable situations. A typical example of such work by Kolmogorov are his investigations on firing dispersion theory that he performed during World War II. His paper Estimation of the center and spread of dispersion for a bounded sample, [Kolmogorov 1942], was dated September 15th, 1941, i.e., three months after the war began on the Soviet territory. It was published in response to a request from the appropriate military agencies to “give his conclusion on the subject of discrepancies among the existing methods to estimate precision from experimental data.” Kolmogorov remarked that this paper presents primarily methodological interest due to critical comparison of distinct approaches. Nevertheless, Kolmogorov and his colleagues from the Mathematical Institute of the Academy of Sciences, Department of Mechanics and Mathematics at Moscow State University, as well as the immediate practitioners from the Institute of Marine Artillery Research, developed large scale theoretical and computational efforts toward measuring the efficiency of firing strategies. Simultaneously, he taught a course at the university on firing dispersion theory. He made it compulsory for students majoring in probability. This work concluded in the publication of a separate volume of “Proceedings of the Steklov Mathematical Institute” (1945), nicknamed by Kolmogorov himself Collection of Articles on the Theory of Firing, [Kolmogorov 1945]. It included two of his articles, On the number of hits among several shots and general principles of characterizing efficiency of firing strategies and Artificial dispersion in case of single shot kill and one dimensional dispersion, as well as two articles by his