In 1961 Platonov graduated with highest distinction from Belarus State University. Two years later (in 1963) he received his Doctor of Philosophy from Academy of Sciences of Belarus. Platonov received his Doctor of Science degree from the Academy of Sciences of Union of the Soviet Socialist Republics in 1967.
In 1992–2004 he worked at various research centers of the United States, Canada and Germany. At the age of 28 Platonov received a title of full professor of the Belarus State University. This made him the youngest full professor in the history of Belarus.
Since 1972 he has been an Academician of the National Academy of Sciences of Belarus and its President (1987–1993).
Academician of the Russian /Union of the Soviet Socialist Republics Academy of Sciences since 1987. He was the Director of the Institute of Mathematics of the Academy of Sciences of Belarus from 1977 to 1992.
His interests are algebra, algebraic geometry, and number theory. He solved the Strong approximation problem, developed the reduced K-theory and solved the Tannaka–Artin problem.
He solved also the Kneser–Tits and Grothendieck problems.Together with F.Grunewald he solved the arithmeticity problem for finite extensions of arithmetic groups and the rigidity problem for arithmetic subgroups of algebraic groups with radical.
Platonov solved also the rationality problem for spinor varieties and the Dieudonne problem on spinor norms. Platonov was an invited speaker of the International Congresses of Mathematicians in Vancouver (1974), Helsinki (1978) and the European Congress of Mathematicians in Budapest (1996). He is the author, with Andrei Rapinchuk, of Algebraic Groups and Number Theory
He currently works as a Chief Science Officer of Scientific Research Institute of System Development (NIISI RAN).
The court gave him a conditional sentence of two years.
Later, in September 2001, Platonov took early retirement as a professor of the University of Waterloo.
1968: Lenin Communist Youth League Prize, for a series of works in topological group theory 1978: Lenin Prize in Science and Technology, for a fundamental series of works "Arithhmetics of Algebraic Groups and Reduced K-Theory" ("Арифметика алгебраических групп и приведенная К-теория") 1993: Humboldt Prize.
Russian Academy of Sciences. Academy of Sciences of the Union of the Soviet Socialist Republics. Central Committee of the Communist Party of the Soviet Union]
He is a member of the Canadian Mathematical Society and was from 1993 to 2001 a Professor of the Faculty of Mathematics of the University of Waterloo in Waterloo, Ontario, Canada.
