Mathews was born in Charleston, South Carolina, in 1744. At the age of 16, he joined the South Carolina Provincial Regiment, rising to the rank of lieutenant. He later attended school in London and became a lawyer. Returning to South Carolina, he became active in politics, serving on the First and Second Provincial Congresses in 1775 and 1776.
Following his retirement, Mathews died in Charleston on November 17, 1802.
- In 1782, he was elected Governor of South Carolina, and served in that office until 1783.