David James Foulis (July 26, 1930- April 3, 2018) was an American mathematician known for his research on the algebraic foundations of quantum mechanics.He spent much of his career at the University of Massachusetts Amherst, retiring in 1997 but continuing to be very active in mathematics as professor emeritus. He is the namesake of Foulis semigroups, an algebraic structure that he studied extensively under the alternative name of Baer *-semigroups.