[1] Mathews began a 41-year career with Frost Bros. as a fashion buyer, ascending to president of its specialty clothing store at North Star Mall in 1963.
In 1971, the Federal Reserve System Board of Governors appointed Mathews director of the San Antonio branch.
A native of Toledo, Ohio, he attended the University of Michigan, where he received a bachelor's degree in economics in 1938.
Irving's father, Samuel Henry Mathews (1893–1951), had owned an apparel retail store in Toledo, Ohio.
On September 1, 1945 — while a Lieutenant in the U.S. Army stationed at Fort Sam Houston — Irving married Jeanne Lang, daughter of Sylvan Lang, co-owner of Frost Bros. Mathews was a past director of the San Antonio Symphony, United Fund, the Jewish Social Service Federation of San Antonio and the National Board of the American Jewish Committee.