Born in Los Alamos, New Mexico, Foreman earned his Ph.D. from the University of California, Berkeley in 1980 under Robert M. Solovay.

From 2000–2008 they sailed Veritas to the Arctic, the Shetland Islands, Scotland, Ireland, England, France, Spain, North Africa and Italy.

Further south they sailed through the Chenal du Four and Raz de Sein, across the Bay of Biscay and around Cape Finisterre.

[5][6] Foreman's later work in set theory was primarily concerned with developing the consequences of generic large cardinal axioms.

With Randall Dougherty he settled the Marczewski problem (1930) by showing that there is a Banach–Tarski decomposition of the unit ball in which all pieces have the property of Baire (see Banach–Tarski paradox).

With Friedrich Wehrung, Foreman showed that the Hahn–Banach theorem implied the existence of a non-Lebesgue measurable set, even in the absence of any other form of the axiom of choice.