Kolmogorov, stochastics in Bulgaria, and probabilistic problems with unexpected solutions

Abstract

In this talk, I am going to share with the readers my memories of personal meetings with Andrey Nikolaevich Kolmogorov (1903–1987), the content of our conversations, and the fruitful consequences. The reader is familiar with, or could read, the timely prepared recent comprehensive paper [34], presented by N.M. Yanev at the 52nd Spring Conference of the UBM. Included here are several new details about Andrey Nikolaevich and the great influence of the Moscow Probability School on the development of Stochastics in Bulgaria. I have used MathSciNet and introduced the ‘Kolmogorov number’, a ‘collaboration distance’ between a mathematician and Kolmogorov, with a focus on Bulgarian stochasticians. I am writing about Kolmogorov’s approach to doing mathematics in general and the role of counterexamples. Discussed are two specific probabilistic problems which, according to him, are with most unusual solutions, ‘Skitovich-Darmois theorem’ and ‘Plackett problem’. Several related short stories and not well-known facts are presented.