He was educated at Christ's Hospital and St John's College, Cambridge. He started research under the supervision of G.H. Hardy but his work was interrupted by service in World War II after which he turned to algebra under the influence of Emil Artin, whom he had met while visiting Princeton University.
He became a Research Fellow of St John's College in 1948, then moved to the Town Trust Chair of Pure Mathematics at Sheffield University in 1952. He was awarded the London Mathematical Society Junior Berwick Prize in 1953 and served as LMS Vice-President during 1968-69. He was elected Fellow of the Royal Society in 1961.
- Northcott, D. G. Multilinear algebra. Cambridge University Press, Cambridge, 1984. ISBN 0-521-26269-0
- Northcott, D. G. A first course of homological algebra. Reprint of 1973 edition. Cambridge University Press, Cambridge-New York, 1980. ISBN 0-521-29976-4
- Northcott, D. G. Affine sets and affine groups. London Mathematical Society Lecture Note Series, 39. Cambridge University Press, Cambridge-New York, 1980. ISBN 0-521-22909-X
- Northcott, D. G. Finite free resolutions. Cambridge Tracts in Mathematics, No. 71. Cambridge University Press, Cambridge-New York-Melbourne, 1976.
- Northcott, D. G. Lessons on rings, modules and multiplicities. Cambridge University Press, London 1968
- Northcott, D. G. An introduction to homological algebra. Cambridge University Press, New York 1960
- Northcott, D. G. Ideal theory. Cambridge Tracts in Mathematics and Mathematical Physics, No. 42. Cambridge, at the University Press, 1953.
- Rees, D.; Sharp, R. Y. (2007). "Douglas Geoffrey Northcott. 31 December 1916 -- 8 April 2005: Elected FRS 1961". Biographical Memoirs of Fellows of the Royal Society. 53: 247. doi:10.1098/rsbm.2007.0010.
- "Douglas Northcott at the London Mathematical Society (LMS)". Retrieved 2011-07-20.
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