Mathews scientific work embraced a broad spectrum of topics, including volcanoes, glaciers, regional geomorphology, landslides, hydrogeology, stratigraphy, coal geology, and mineral deposits. But his most influential work was in the fields of subglacial eruptions and volcano-ice interactions. He discovered several ideal field laboratories for this research in his home province of British Columbia, including the numerous volcanoes in Garibaldi Provincial Park just north of Vancouver and the remote Tuya Volcanic Field in far northern British Columbia. While still in graduate school at Berkeley in 1947, he published a paper, Tuyas, Flat-Topped Volcanoes in Northern British Columbia, in which he coined the term tuya to refer to the distinctive, flat-topped, steep-sided volcanoes formed when lava erupts through a thick glacier or ice sheet. He took the name from Tuya Butte, a near-ideal specimen of the type, and this name has since become standard worldwide among volcanologists in referring to and writing about these volcanic formations. Late in his career, other scientists named a previously unnamed tuya in the Tuya Volcanic Field in honor of him as Mathews Tuya.