He collaborated with R. J. C. Atkinson, who supervised him when he directed archaeological excavations at Cricklade and Dorchester in Oxfordshire.
In 1949, Maddison was a member of the British School at Rome expedition to Leptis Magna, Tripolitana (now Libya, northern Africa).
Maddison's expertise in Arabic, initially learnt under the tutelage of his father, was reinforced through the museum's extensive collection of Arabic-Islamic astrolabes.
He also has research interests in the history of horology, time measurement, and early sea navigation.
On his retirement in 1994 he was presented with a festschrift containing essays by 20 eminent academics from the disciplines of linguistics and the history of science.