Mathews moved to Brookings, Dakota Territory (now South Dakota) in 1879. He became prosecuting attorney of the fifth judicial circuit for the Territory of Dakota and a member of the Territorial council (serving as its president). He was elected as a Republican to the House, serving from March 4, 1889 to November 2, 1889, when the Territory was admitted into the Union.
He was mayor of the city of Brookings from 1897 -1903. In 1910 he moved to Los Angeles, California, where he died. He was cremated and his ashes deposited in Greenwood Cemetery, Brookings.