Mathews was a male Human Starfleet crewman who lived during the mid-23rd century. He served in the operations division aboard the USS Enterprise under Captain James T. Kirk, during a historic five-year mission that starship undertook. In 2266, he served as one of the ship's security guards.
That same year, Mathews was a late assignment to the landing party that arrived on the surface of Exo III. When Kirk and Chapel were beamed to the caverns of Exo III, their expectation was that Dr. Roger Korby would be waiting for them. After beaming down and not finding him waiting for them, Kirk requested a security team; the team consisted of Mathews and Rayburn. Mathews accompanied Kirk and Chapel as they probed deeper into the caverns. As he was following behind them, Mathews was murdered when he was pushed off a precipice in the outer junction by Ruk. (TOS: "What Are Little Girls Made Of?")