[1] Mathews was educated at King Charles I School, Kidderminster, served his articles in Birmingham and London from 1851, and was admitted solicitor in 1856.
One of the founders and subsequently chairman of the parliamentary committee of the National Education League, he founded in 1864 the Birmingham Children's Hospital, in conjunction with Thomas Pretious Heslop, and took part for many years in its management; he set on foot the agitation which led to the reorganisation of King Edward's School, and served as a governor of the school from its reconstitution in 1878 till his death; a lifelong friend of Joseph Chamberlain, he was from 1886 one of the local leaders of the Liberal Unionist Party.
[1] He was introduced to the Alps in 1856 by his brother William, with whom the idea of forming the Alpine Club originated; and the foundation of the club was definitely decided upon in November 1857 by the two brothers, a cousin, Benjamin Attwood Mathews, and Edward Shirley Kennedy; the last, aided by Thomas Woodbine Hinchliff, taking the leading share in its actual formation (December 1857 to January 1858).
[1] Mathews played his part in the exploration of the High Alps that followed during the succeeding decade, and he continued to climb vigorously for more than forty years, long after all the other original members of the Alpine Club had retired from serious mountaineering.
[1] Besides numerous papers in the Alpine Journal (volumes i–xxii) Mathews contributed articles about the guides Melchior Anderegg and Jakob Anderegg to Pioneers of the Alps (1887), and a retrospective chapter to C. T. Dent's Mountaineering in the Badminton Library (1892); but his most important work in Alpine literature is The Annals of Mont Blanc (1898), an exhaustive monograph, containing a critical analysis of tho original narratives of the early ascents of tho mountain, and a history and description of all the later routes by which its summit has been reached.