Mathews was a native of Walker County, Alabama. He graduated from Jacksonville State College (now Jacksonville State University) in 1949 and received a graduate degree from Vanderbilt University in 1950.

He became part of the Tennessee gubernatorial staff after his time at Vanderbilt, successively serving governors Gordon Browning, Frank G. Clement, and Buford Ellington. In 1961 he was named to the Cabinet as Commissioner of Finance and Administration, a position he held until 1971. In 1962, he graduated from the YMCA Night Law School, now Nashville School of Law.

With the accession to office of Republican Winfield Dunn in January, 1971, Mathews left the Cabinet and entered the private sector for two years. In 1973 he became the legislative assistant to the longtime Tennessee Comptroller of the Treasury. In 1974 he was elected State Treasurer by the Tennessee General Assembly when his predecessor, Tom Wiseman, resigned to run for governor. He served in this office until January, 1987, when he became deputy to the newly-elected governor, Ned R. McWherter.

Mathews served as deputy governor until January, 1993. Albert Gore, Jr., who had been Tennessee's junior Senator since 1985, was elected Vice President of the United States as Bill Clinton's running mate in November, 1992, and resigned his position as Senator in preparation for his inauguration as Vice President on January 2, 1993. McWherter then appointed his deputy as Gore's successor in the Senate.

From the beginning, it was understood that Mathews role in the Senate would be one of caretaker; he had no ambition of running for the office for election in his own right. The appointment served two purposes; firstly, to reward a longtime government insider who had served his state and his party faithfully for many years, largely out of view of the general public, and secondly, to allow McWherter to remain above the fray in the scramble to succeed Gore in the Senate and not identify himself with any particular party faction.

Mathews' service in the Senate was of a decidedly low-key nature; he largely supported the Democratic agenda of President Clinton and the then-majority in the Senate. The passion for the contest for the Democratic senatorial nomination to succeed him was quelled somewhat when it became apparent that the Republican nominee would be attorney and prominent actor Fred Thompson. The highest-profile Democrat to enter the primary was Representative Jim Cooper, who was the eventual nominee and lost to Thompson in a landslide.

Thompson was sworn in to office in December of 1994 in order to give him a slight advantage in seniority over other Senators elected in that year, as is traditionally done when someone is elected to the balance of an unexpired term. Mathews left office as quietly as he had served in it and currently practices law in Nashville, Tennessee.