In 1930, Kupradze was enrolled for the postgraduate study in the USSR Academy of Sciences, which he finished in 1931.
In 1933-35, Kupradze worked at the Institute of Mathematics of the USSR Academy of Sciences as a Scientific Secretary and Senior Scientific Worker. In 1935, Kupradze maintained his thesis and received a Ph. D. degree.
In 1936, Kupradze returned to his homeland. Afterwards, he became Director of the Institute of Mathematics of the USSR Academy of Sciences. At the same time, he was Head of chairs in two organisations (Tbilisi State University and State Polytechnic Institute).
During World War II, Kupradze was in the Soviet army and worked as an editor-in-chief of the frontline newspaper. Afterwards, Kupradze was Deputy Rector of the Tbilisi State University. In 1943, he was awarded the title of the Honoured Scientist. In 1946, he was elected Academician of the Georgian Academy of Sciences.
In 1944-53, Kupradze was Minister of Education of Georgia; in 1954-58, he became Rector of the Tbilisi State University.
In 1963, Kupradze was elected Academician-Secretary of the newly founded department at the Georgian Academy of Sciences. In the same period, he was Head of the Chair of Differential and Integral Calculus at Tbilisi State University.
In 1971, Kupradze was awarded the USSR State Prize in Science and Technology and many other prizes.
V. Kupradze’s works deal with the issues of mathematical physics, theory of differential and integral equations, etc. Many of his works were translated and published in foreign languages.
Viktor Kupradze died on November 24, 1985.