Is there a theorem of prominent Russian mathematicians that played an important role in the development of machine learning?
A search on Google Scholar yielded
NeuralComputation 1991 article
That is

Kolmogorov's Theorem Is Relevant
Abstract We show that Kolmogorov's theorem on representations of
continuous functions of n-variables by sums and superpositions of
continuous functions of one variable is relevant in the context of
neural networks. We give a version of this theorem with all of the
one-variable functions approximated arbitrarily well by linear
combinations of compositions of affine functions with some given
sigmoidal function. We derive an upper estimate of the number of
hidden units.&quot;

This theorem of Kolmogorov is surely the one referred to in the seminar I attended. But I somewhat erred I first thought in using the plural of mathematician.
But then I see the terminology
&quot;Kolmogorov–Arnold representation theorem (or superposition theorem)&quot; is also employed.
Wikipedia gives the following references:

Andrey Kolmogorov, &quot;On the representation of continuous functions of
several variables by superpositions of continuous functions of a
smaller number of variables&quot;, Proceedings of the USSR Academy of
Sciences, 108 (1956), pp. 179–182; English translation: Amer. Math.
Soc. Transl., 17 (1961), pp. 369–373.
Vladimir Arnold, &quot;On functions
of three variables&quot;, Proceedings of the USSR Academy of Sciences, 114
(1957), pp. 679–681; English translation: Amer. Math. Soc. Transl., 28
(1963), pp. 51–54.