— Graduated from Belarusian State University (1961).
— In 1963-1971 - Senior Lecturer, Associate Professor, Professor, Head of the Department of Belarusian State University.
— Since 1971 - Head of the laboratory of the Institute of Mathematics of the Academy of Sciences of the BSSR, in 1977-1992 - Director of this Institute.
— In 1987-1992 - President of the Academy of Sciences of Belarus, in 1992-1996 - Chief Researcher of the Institute of Mathematics of the National Academy of Sciences of Belarus.
— At present - Chief Researcher at the Research Institute of System Studies of the Russian Academy of Sciences and Mathematical Institute named after V.A. Steklov of the RAS.
— Chairman of the Committee on State Prizes of the BSSR (1988-1991), Editor-in-Chief of the journal "Doklady of the National Academy of Sciences of the BSSR" (1987–1992).
— Member of the Presidium of the Academy of Sciences of the USSR (1989–1991).
— In 1989-1991 - Deputy of the Supreme Soviet of the USSR.
— In 1985-1990 - Deputy of the Supreme Council.

Research on algebra, algebraic geometry, algebraic number theory, Lie groups, linear groups and topological algebra, applied algebra and cryptography. Solved the problem of strong approximation in algebraic groups and the Kneser-Tits problem. Developed the above K-theory and decided on this basis the Tannaka-Artin problem. Solved the problem of rationality of spinor varieties. Investigated the local-global principle, according to which the structure of groups defined over arithmetic fields is determined by the structure of their localizations over the corresponding additions. He proved the main approximation theorem for linear groups with a finite number of generators. He discovered a new local-global principle for functional hyperelliptic fields defined over the field of algebraic numbers. Together with the students, he solved the problem of rationality for group algebraic varieties over local and global fields; built the theory of finite dimensional bodies; solved the Grothendieck problem of profinite completions of groups and the problem of rigidity for arithmetic subgroups of algebraic groups with a radical; developed the multiplicative theory of finite-dimensional bodies; solved the problem of arithmeticity for polycyclic groups; developed a new approach to the congruence problem, based on the analysis of combinatorial properties of arithmetic groups.

Author of more than 160 scientific papers.

The Leninist Komsomol Prize in 1968 for a series of works on topological groups. Lenin Prize in 1978 for research on algebraic groups and reduced K-theory. Humboldt Prize (Germany, 1993).

Awarded with the Order of the Red Banner of Labor (1979).