He then moved to the University of California, Berkeley, completing his Ph.D. in June 1948 with a dissertation titled Geology of the Mount Garibaldi map-area, southwestern British Columbia.

Mathews received the Willet G. Miller Medal for "outstanding research in any branch of the earth sciences" from the Royal Society of Canada in 1989.

After his retirement from teaching duties, he maintained an active research program and began writing a book on the geology of southern British Columbia, working part-time on the project until his death in 2003.

Mathews scientific work embraced a broad spectrum of topics, including volcanoes, glaciers, regional geomorphology, landslides, hydrogeology, stratigraphy, coal geology, and mineral deposits.

A large portion of this body of work is devoted to the numerous fascinating volcanic, glacial, and limnological features of Garibaldi Provincial Park, which he examines, analyzes, and interprets in meticulous detail and with far-reaching insight.