Vainshtein was born on 24 February 1942 in Novokuznetsk, Russia. He got his Ph.D. from Budker Institute of Nuclear Physics in Novosibirsk, Russia and master's degree from Novosibirsk University[2] where he became a Professor. He was the director of William I Fine Theoretical Physics Institute, University of Minnesota where he currently serves as the Gloria Becker Lubkin chair[2] and also holds a position as Professor since 1990.