In England he did postgraduate research at the University of Cambridge, his doctoral dissertation being on
p-adic analogues of
Baker's method. In 1969, Coates was appointed assistant professor of mathematics at
Harvard University in the United States, before moving again in 1972 to
Stanford University where he became an associate professor. and took up a lectureship. Here he supervised the PhD of
Andrew Wiles, and together they proved a partial case of the
Birch and Swinnerton-Dyer conjecture for
elliptic curves with
complex multiplication. In 1977, Coates moved back to Australia, becoming a professor at the
Australian National University, His research interests included
Iwasawa theory, number theory and arithmetical algebraic geometry. He served on the Mathematical Sciences jury for the
Infosys Prize in 2009. ==Awards and honours==