Joseph Leonard "Joe" Walsh (September 21, 1895 – December 6, 1973) was an American mathematician who worked mainly in the field of analysis. The Walsh function and the Walsh–Hadamard code are named after him. The Grace–Walsh–Szegő coincidence theorem is important in the study of the location of the zeros of multivariate polynomials.He became a member of the National Academy of Sciences in 1936 and served 1949–51 as president of the American Mathematical Society.