I think, the reference is to Kolmogorov's work on anti-aircraft artillery in 1942 (the theory of artificial scattering of shells).
The following is taken from the article
V.I. Arnolʹd, A. N. Kolmogorov and the natural sciences. Uspekhi Mat. Nauk 59 (2004), no. 1(355), 25–44; translation in
Russian Math. Surveys 59 (2004), no. 1, 27–46.
Pages 35-36 (of the English trianslation):
During a state examination on military training, a general of artillery, who came to Moscow State University to evaluate the graduates, asked me: “Who is the best
mathematician in Russia at present?” I mentioned Kolmogorov, and the general
was pleased: “He did a lot of useful things for us as well, we remember it and also appreciate him.”
Kolmogorov told me with pleasure that in 1942 the Artillery Command requested that he come from Kazan (to which the Academy of Sciences had been evacuated) to Moscow for consultations; according to him, Kolmogorov got a sofa as a lodging (as
he told me) in Neskuchnyi garden (in the building of the Presidium of the Academy of Sciences) and worked out a statistical basis for his suggestions about how to
organize antiaircraft fire against the massive bombing raids of the enemy. These suggestions, called a theory of artificial scattering of shells, show that under certain conditions it is preferable to shoot at random rather than aim, creating a curtain of shell bursts in the path of the enemy aircraft. The point is that, when trying to hit an individual aircraft, several antiaircraft guns or even a whole battery of guns can choose the same target, and then the nearby enemy aircraft would remain undamaged (if one tries to hit only chosen targets).
A caveat: Many things claimed by Arnold should be taken with a grain of salt. But this story, I think, is solid.