Mathu was born in Waithaka to a Kikuyu family. He was educated at the Alliance High School and qualified as a teacher. In 1929 he became the first African master at Alliance. Between 1932-34 he studied at Fort Hare College in South Africa and passed the South Africa matriculation. He returned to teach at Alliance and pursued a Bachelor of Arts degree through a correspondence course. In 1938 he moved to the United Kingdom to complete a one year teaching diploma from Exeter University, and study history at Balliol College, Oxford. Mathu returned to Kenya in 1940, teaching at Alliance until he left in 1942 to open his own school in Waithaka.
In October 1944, Mathu was nominated to the Legislative Council of Kenya to represent the African community. He became the first African member of the Council. He co-founded the Kenya African Study Union to help co-ordinate and represent African interests in the Council. During the Mau Mau Uprising rival politicians from tribes deemed loyal to the government accused him of organising the Mau Mau. Despite remaining loyal himself, as a Kikuyu, he became disqualified from serving in the Council. At the 1957 election Mathu was replaced by Bernard Mate, a member of the Meru tribe who had the support of the government.
- History, Parliament of the Republic of Kenya
- Andrew Burton, Andrew Ross Burton, Helene Charton-Bigot, Generations Past: Youth in East African History, Ohio University Press, 19 Oct 2010
- Marshall Clough (April–June 1978). "Review: Understanding Kenya in the '50s: New Resources, but More Needed: Reviewed Works: Mathu of Kenya: A Political Study by Jack R. Roelker; Counter-Insurgency in Kenya 1952-60: A Study of Military Operations against Mau Mau by Anthony Clayton". Africa Today. 25 (2): 79–81. JSTOR 4185774.
- Munene, Macharia, Historical Reflections on Kenya: Intellectual Adventurism, Politics and International Relations, University of Nairobi Press, 16 Mar 2015
- Kenya Gazette, 7 Oct 1994, Vol. 96, No. 48