Career
Prior to politics, Mathews had a career in primary education and was a tailor and small business owner in South Melbourne, Victoria. In 1914, 1919 and 1928, Mathews was elected to Melbourne Ports unopposed. When he was challenged in 1917 by Nationalist candidate William Fozard, however, his margin was decreased to 16.3%.
In 1922, Mathews was challenged by Nationalist candidate Selwyn Neale and was elected with a 23.1% margin, whereas in 1925, Nationalist candidate Francis Wilder challenged Mathews and decreased his margin by 5.4%.
Jack Holloway replaced Mathews as the next member for Melbourne Ports in 1931.