Green was a doctoral student of the Nobel Laureate Max Born at Edinburgh, with whom he was involved in the development of the modern kinetic theory.

He is often credited for the development of parastatistics, one of several alternatives to the better known particle statistics models.

[1][2] Born in Ipswich, England, he graduated with a PhD from the University of Edinburgh in 1947 with a thesis entitled A Unitary Quantum Electrodynamics.

From 1950 to 1951 Green worked as a professor at the Dublin Institute for Advanced Studies in the school of Theoretical Physics.

From 1951 till his death in 1999, Green lectured mathematical physics at the University of Adelaide, Australia.