Mathew was born in Aberdeen, Scotland, the fourth child (and eldest son) of Alexander Mathew, a factory overseer, and his wife Jean, née Mortimer. Mathew was initially educated at Kidd"s school, Aberdeen, at nine years of age his father died and went to live with his maternal grandmother at Insch then at the Insch Free Church School where he was a pupil-teacher from 1862 to 1864.
Mathew worked there for six years as a Stockrider, bookkeeper, and storeman becoming familiar with the culture and language of the Kabi and Wakawaka (see List of Indigenous Australian group names#West people. Then he moved to Victoria, Australia and graduated from the University of Melbourne (Bachelor, 1884. Master of Arts, 1886) with first-class honours despite working at times as a tutor and station-manager.
This was the basis for his best-known publication, Eaglehawk and Crow (1899).
This publication was criticized (as Mathew had expected) by the ethnographers Walter Baldwin Spencer, Alfred William Howitt and Lorimer Fison. There was however, more support from Daisy Bates and Robert Hamilton Mathews.
Mathew returned to Queensland in 1906, visiting the Kabi and Wakawaka people at the Barambah Government Aboriginal Station. He published Two Representative Tribes of Queensland (1910) and although his linguistic studies and ethnographic reporting are still well regarded, his controversial theory of a tri-hybrid origin of Australian Aborigines is not supported by current data.
