[1][2] Room was born in London and educated at St John's College, Cambridge he moved to Sydney, Australia, in 1935.
In January 1940, with the encouragement of the Australian Army, he, together with some colleagues at the University of Sydney, began to study Japanese codes.
As a result it was agreed that Room's group, with the agreement of the University of Sydney, would move in August 1941 to work under Nave at the Special Intelligence Bureau in Melbourne.
[9][10][11] He retired from Sydney in 1968 but took short-term positions afterwards at Westfield College in London and the Open University before returning to Australia in 1974.
[9][12] Room's PhD work concerned generalizations of the Schläfli double six, a configuration formed by the 27 lines on a cubic algebraic surface.
[1][13] In the postwar period, Room shifted the focus of his work to Clifford algebra and spinor groups.
[1] Despite retiring in 1968, Room remained active mathematically for several more years, and published the book Miniquaternion geometry: An introduction to the study of projective planes in 1971 with his student Philip B.
[1] In 1941, Room won the Thomas Ranken Lyle Medal of the Australian National Research Council and was elected as a Fellow of the Royal Society.