Born at Penally, Pembrokeshire son of Charles Mathias (1817-88) MRCS 1839, Surgeon IMS, he was educated at Clifton College and King's College, Cambridge where he gained an entrance scholarship and was awarded a first class in both parts of the Natural Sciences Tripos, despite a long period of illness during his second year. Having obtained a Price scholarship, he went to the London Hospital for his clinical studies, and qualifying in 1913 he held a house surgeon's appointment at the London Hospital and an appointment as senior house surgeon at Poplar Hospital. In 1914 he joined the RAMC and served throughout the war, principally on the Italian Front. He was admitted a Fellow in 1920, and then joined his brother in the family practice in Tenby as surgical partner. With the introduction of the National Health Service he was graded as a Senior Hospital Medical Officer, which enabled him to continue in the dual role of a general practitioner and of a surgeon, but as time passed he devoted himself more and more to surgery. The last year of his life was spent in hospital, but he endured his failing health with patience and cheerfulness. He married Elsie Ann Salmon in 1922, and their only son David is a doctor in Norfolk. Mathias died on 23 February 1963 aged 75.