Mathews made his fortune in mining shares, and moved to England in 1902. In 1910 he was elected a Fellow of the Royal Society of Edinburgh. His proposers were William Eagle Clarke, Ramsay Heatley Traquair, John Alexander Harvie-Brown and William Evans.
Mathews was a controversial figure in Australian ornithology. He was responsible for bringing trinomial nomenclature into local taxonomy, however he was regarded as an extreme splitter. He recognised large numbers of subspecies on scant evidence and few notes. In particular, this drew a hostile response from Archibald James Campbell, a leading Australian figure in birds at the time. He later began splitting genera. Dominic Serventy foretold that although a great many of these subspecies ceased to be recognised, future research would have to resort to the use of some of them if and when evidence supported their distinct status.
In 1939 he was elected a Fellow of the Royal Australasian Ornithologists Union, and served as its president 1946–1947. He donated his ornithological library to the National Library of Australia in 1939.
He married Mrs Marian Wynne, a widow.
Mathews contributed numerous papers to the ornithological literature, especially on avian taxonomy and nomenclature, as well as founding, funding, editing and being the principal contributor to the journal The Austral Avian Record. Monographic or book-length works authored or coauthored by him include:
- 1908 – The Handlist of the Birds of Australia. (Based on A Handlist of Birds by Bowdler Sharpe).
- 1910–1927 – The Birds of Australia Witherby: London. (12 volumes, assisted by Tom Iredale).
- 1912 – The Reference List of the Birds of Australia. (Novitates Zoologicae, 18 January 1912).
- 1913 – A List of the Birds of Australia. Witherby: London.
- 1920 – The Name List of the Birds of Australia.
- 1921 – A Manual of the Birds of Australia. Volume I: Orders Casuarii to Columbae. Witherby: London. (With Tom Iredale. Only one volume published of a projected four).
- 1924 – The Check-List of the Birds of Australia. Witherby: London. (Comprising Supplements 1-3 of The Birds of Australia).
- 1925 – The Bibliography of the Birds of Australia. Witherby: London. (Comprising Supplements 4 and 5 of The Birds of Australia).
- 1927 – Systema Avium Australasianarum. a Systematic List of the Birds of the Australasian Region. BOU: London. (2 volumes).
- 1928 – The Birds of Norfolk and Lord Howe Islands and the Australian South Polar Quadrant. Witherby: London.
- 1931 – A List of the Birds of Australasia, Including New Zealand, Lord Howe and Norfolk Islands, and the Australasian Antarctic Quadrant.
- 1936 – A Supplement to the Birds of Norfolk and Lord Howe Islands to which is Added those Birds of New Zealand not figured by Buller. Witherby: London.
- 1942 – Birds and Books: the Story of the Mathews Ornithological Library. Verity Hewitt Bookshop: Canberra.
- 1943 – Notes on the Order Procellariiformes. (With Edward Hallstrom).
- 1946 – A Working List of Australian Birds, including the Australian Quadrant and New Zealand. Shepherd Press: Sydney.
- Biographical Index of Former Fellows of the Royal Society of Edinburgh 1783–2002 (PDF). The Royal Society of Edinburgh. July 2006. ISBN 0 902 198 84 X.
- Serventy, Dominic (1950). "Taxonomic Trends in Australian Ornithology—with Special Reference to the Work of Gregory Mathews President's Address to the Annual Congress, Hobart, 1949". Emu. 49 (4): 257–67. doi:10.1071/MU949257.
- Bull. B.O.C. Vol. 58
- Bull. B.O.C. Vol. 59
- Mathews, G.M. (1922). The Birds of Australia. London: Witherby Vol. 10 .
- Robin, Libby. (2001). The Flight of the Emu: a hundred years of Australian ornithology 1901-2001. Carlton, Vic. Melbourne University Press. ISBN 0-522-84987-3
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