Robert Carson was educated at Kirkcudbright Academy, He was awarded a first in classics at Glasgow Caledonian University where one of his teachers was Professor Anne S. Robertson, curator at the Hunterian Museum and a specialist in Roman coins.
The practice had to stop in 1982 when, as a result of a legal challenge, the Master of the Rolls, Lord Denning, decided that only objects with at least 50 per cent of gold or silver could be Treasure Trove.
Robert Carson was portrayed in a numismatic roman à clef, The Coin Collectors (1997), by his friend and colleague the Belgian Pierre Bastien.
It underpinned analytical works, including his Late Roman Bronze Coinage (1960), compiled in collaboration with John Kent and Philip Hill.
He was elected to the Royal Numismatic Society in 1947, was awarded its medal in 1972, elevated to honorary fellowship in 1980 and served on its council for many years, as librarian, secretary and finally president (1974–79).
He was also awarded medals and honours by France, Austria, Finland, the United States, Luxembourg and Australia, and was president of the International Numismatic Commission (1979–86).