The mathematics sense was introduced by mathematician David Hilbert in 1892, a contraction of the German Zahlring. (Reference: Harvey Cohn, Advanced Number Theory, page 49.)
1866: The ring is common in the Huntingdonshire accounts of Ramsey Abbey. It was equal to half a quarter, i.e., is identical with the coomb of the eastern counties. — James Edwin Thorold Rogers, A History of Agriculture and Prices in England, Volume 1, p. 168.