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I have been reading this blog post which mentions that:

during World War II Kolmogorov applied his mathematical gifts to artillery problems, helping to protect Moscow from German bombardment.

So, what were the mathematical solutions did Kolmogorov use in helping protect Moscow in the World War 2?

  • The quote is wrong on one point; Kolmogorov applied statistical analysis to the targeting by Russian artillery crews. So while this contributed to the defence of Moscow, it was essentially on offensive rather than a defensive technique. – Pieter Geerkens Aug 16 '17 at 6:25
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    One of the distinctions Kolmogorov made clear to artillery crews was to distinguish between whether the goal of a barrage was to maximize the chance of a hit, or to maximize the number of hits. then he showed them how different targeting strategies could be applied to make each goal more obtainable. For instance, one wishes to maximize the chance of a hit on a key opposing unit such as a large tank, while maximizing the number of hits on a widely dispersed target such as an opposing infantry unit. – Pieter Geerkens Aug 16 '17 at 6:27
  • @PieterGeerkens Interesting. Possible to add it as an answer? – Dawny33 Aug 16 '17 at 6:31
  • Kind of like how Archimedes helped protect Syracuse. – Tom Au Aug 16 '17 at 11:27
  • The sentence which you cite us simply untrue. – Alex Aug 16 '17 at 22:52
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The Wikipedia article on Kolmogorov is a good starting point and will give you some search terms that could be fruitful.

For example, Shiryaev A.N. (2003) On the Defense Work of A. N. Kolmogorov during World War II. In: Booß-Bavnbek B., Høyrup J. (eds) Mathematics and War. Birkhäuser, Basel.

This survey references his 1941/42 paper "Estimation of the center and spread of dispersion for a bounded sample"

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    This doesn't really answer the question for anyone not already familiar with said books (because it gives no hint as to how Kolmogorov's maths helped protecting Moscow, just pointers where one could read up about it). – DevSolar Aug 16 '17 at 7:09
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In the end of 1941 and beginning of 1942, the Soviets had multiple problems with artillery.

The first one was shell and batteries availability: there was not enough of them for field artillery. It was not that much a problem since the mud, and later the snow, reduced the capacity of artillery to inflict damages. So the Soviets relied on infiltration tactics with mobile units made for low intensity fights: light armoured cars, cavalry units, skiing units, airborne troops...

The second problem they faced was numerous air attacks made by the Luftwaffe againt the cities. Despite primitive radars and an increasing number of airplanes, front line operations were the priority and Soviets had to rely a lot on anti aircraft artillery to repel German raids. This artillery needed multiple data to be effective: how airplane behave, deflection, ballistic, how to stop a group of planes rather than destroy each airplane one by one (which is impossible in fact).... According to colonel Proektor, out of 4 000 airplanes targeting Moscow during eponym battle, only 120 airplanes actually reached and bombed targets over Moscow.

So I don't have primary sources on Kolmogorov, but it is probable that he helped in anti aircraft artillery based in Moscow rather than field artillery.

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