This volume contains nine papers presented as 45-minute or one-hour addresses at the International Congress of Mathematicians in Berkeley in 1986. In the original proceedings volume of ICM-86, published by the AMS in 1988, these papers appeared in the Russian. They have since been translated and collected in the present volume, to insure their broad dissemination. Among the topics represented here are stochastic processes, logic, number theory, functions of a complex variable, functional analysis, Fourier analysis, numerical analysis, and theoretical computer science.

Table of Contents

• A. V. Skorokhod -- Random processes in infinite-dimensional spaces
• M. G. Peretyat'kin -- Finitely axiomatizable theories
• G. V. Belyĭ -- On the commutator subgroup of the absolute Galois group
• A. A. Gonchar -- Rational approximations of analytic functions
• E. D. Gluskin -- Probability in the geometry of Banach spaces
• A. M. Olevskiĭ -- Homeomorphisms of the circle, modifications of functions, and Fourier series
• S. K. Godunov -- The problem of guaranteed precision in numerical methods of linear algebra
• A. A. Razborov -- Lower bounds for monotone complexity of Boolean functions
• I. G. Bashmakova -- Diophantine equations and the evolution of algebra