Beginning as an undergraduate in mathematics at Trinity College, Cambridge in 1946–1949, he went on to read Part II biochemistry in 1949–1951.
In 1967 he was appointed to a chair in the Department of Mathematics of Bedford College, London, where his inaugural lecture was entitled "The Neural Basis of Conscious Decision".
His early work was in the inorganic chemistry of transition metal ions and ligand field theory.
[3] During the 1960s, Griffith and radiation biologist Tikvah Alper developed the hypothesis that some transmissible spongiform encephalopathies (TSEs) are caused by an infectious agent consisting solely of proteins.
In 1951, when he was just 23, at Francis Crick's suggestion, Griffith performed quantum mechanical calculations on what later became known as complementary base pairing.