Mathews was born at Pawhuska, Oklahoma as the only surviving son of five children of William Shirley and Eugenia (Girard) Mathews. His banker father was part Osage, the son of John Allan Mathews, a noted trader, and Sarah Williams, the mixed-race daughter of "A-Ci'n-Ga," a full-blood Osage, and "Old Bill" Williams, a noted missionary and later Mountain Man who lived with the Osage. Because the Osage had a patrilineal kinship system, the Mathews descendants were excluded from belonging to one of the tribe's clans, as their Osage ancestry was through the maternal line of "A-Ci'-Ga", rather than through a direct male ancestor.