Joan Sylvia Lyttle Birman (born May 30, 1927 in New York City) is an American mathematician, specializing in low-dimensional topology.
She has made contributions to the study of knots, 3-manifolds, mapping class groups of surfaces, geometric group theory, contact structures and dynamical systems.
Birman is currently Research Professor Emerita at Barnard College, Columbia University, where she has been since 1973.