During the 1980s Coates's work was concerned with elliptic curves, Iwasawa theory and p-adic L-functions, all work closely related to the direction that would eventually yield the proof of Fermat's Last Theorem.
Sa panahon ng 1980 Coates ng trabaho ay nagmamalasakit sa tambilugin kurva, Iwasawa teorya at p-adic L-function, lahat ng trabaho may malapit na kaugnayan sa dakong huli na ani ng patunay ng Fermat's Last teorama.