Gerstenhaber was an assistant professor in the Department of Mathematics at the University of Pennsylvania from 1953 to 1958, rising to associate professor (1958–61), and full professor (1961–2024) and chairman. His research interests include: Algebraic Deformation Theory, Universal Algebra, Quantum Groups, and Statistics for Law. He is best known for his contributions to theoretical physics with his discovery of Gerstenhaber algebra.