His ten books included six that he authored, two scholarly translations (one with S. Marc Cohen), and two edited collections (one with Susan Turner).
He also lectured widely (making scholarly and educational presentations on hundreds of occasions) and participated in many conferences and workshops.
He was well-known as a scholar of ancient philosophy and medieval philosophy, with about a dozen publications each on Plato and Aristotle, and over twenty, including two books, on Augustine, along with several on other medieval thinkers, including Anselm (some co-authored with Lynne Rudder Baker), Ockham, and Aquinas.
He directed reading groups for graduate students on Wittgenstein's Philosophical Investigations and Heidegger's Being and Time.
He was a member of the Institute for Advanced Study in Princeton in 1986 and directed four summer seminars sponsored by the National Endowment for the Humanities.
Matthews lectured regularly in the US and abroad and conducted philosophy discussions with elementary-school children in Austria, Australia, China, Israel, Germany, Japan, Norway, and Scotland, as well as in various schools in the U.S.