Mathematical works of Vladimir A. Uspensky: a commentary (Enlgish and Russian texts)

Vladimir Andreevich Uspensky [1930-2018] was one of the Soviet pioneers of the theory of computation and mathematical logic in general. This paper is the survey of his mathematical works and their influence. (His achievements in linguistics and his organizational role are outside the scope of this survey.) Harmonic functions The first paper of Uspensky [3] appeared when he was an undergraduate student. It suggests an elementary approach to harmonic functions that is based on the definition of a harmonic function on R 2 as a function that has the mean value property. The main tool in the following observation: for fixed two poinst A, B the oriented angle ACB is a harmonic function of C, 1 and this function is a locally constant function on any circle that goes through A and B. * Vladimir Andreevich Uspensky was my teacher (and undegraduate and Ph.D advisor). Here I concentrate on his mathematical works; I hope to express my deep gratitude to him elsewere.