At the University of California, Berkeley, Montague earned an B.A. in Philosophy in 1950, an M.A. in Mathematics in 1953, and a Ph.D. in Philosophy 1957, the latter under the direction of the mathematician and logician Alfred Tarski. Montague, one of Tarski's most accomplished American students, spent his entire career teaching in the UCLA Department of Philosophy, where he supervised the dissertations of Nino Cocchiarella and Hans Kamp.
Montague wrote on the foundations of logic and set theory, as would befit a student of Tarski. His Ph.D. dissertation, titled Contributions to the Axiomatic Foundations of Set Theory, contained the first proof that all possible axiomatizations of the standard axiomatic set theory ZFC must contain infinitely many axioms. In other words, ZFC cannot be finitely axiomatized.
He pioneered a logical approach to natural language semantics which became known as Montague grammar. This approach to language has been especially influential among certain computational linguists—perhaps more so than among more traditional philosophers of language.
Montague was an accomplished organist and a successful real estate investor. He died violently in his own home; the crime is unsolved to this day. Feferman and Feferman argue that he usually went to bars "cruising" and bringing people home with him. On the day that he was murdered, he brought home several people "for some kind of soirée", but they instead robbed his house and strangled him.
His life and work provide the inspiration for the novel The Semantics of Murder (Aifric Campbell 2008: 250 ISBN 978-1852429966).