Jon Peter May (born September 16, 1939, New York) is an American mathematician, working in the fields of algebraic topology, category theory, homotopy theory, and the foundational aspects of spectra. He is known, in particular, for inventing the term operads and for the May spectral sequence.
He received a B.A. from Swarthmore College in 1960, and a Ph.D. from Princeton University in 1964. His thesis, written under the direction of John Moore, was titled The cohomology of restricted Lie algebras and of Hopf algebras: Application to the Steenrod algebra. From 1964 to 1967 he taught at Yale University. He has been a faculty member at the University of Chicago since 1967, and a Professor since 1970. He has advised at least 50 doctoral students, among them Ib Madsen.
In 2012 he became a fellow of the American Mathematical Society.