Joseph Leonard Walsh (September 21, 1895 – December 6, 1973) was an American mathematician who worked mainly in the field of analysis.

The Grace–Walsh–Szegő coincidence theorem is important in the study of the location of the zeros of multivariate polynomials.

[1][2] He became a member of the National Academy of Sciences in 1936 and served 1949–51 as president of the American Mathematical Society.

Altogether he published 279 articles (research and others) and seven books, and advised 31 PhD students.

After his retirement from Harvard in 1966 he accepted a position at the University of Maryland where he continued to work up to a few months before his death.