The Adams prize of the University of Cambridge was awarded to Proudman in 1923 for an essay on tides, which proved to be a remarkable seed-bed of ideas from which there developed a series of papers, many of them jointly with Doodson, of theoretical and practical importance. Proudman used to say that his partnership with Doodson was so successful because he liked to do the algebra while Doodson preferred the arithmetic, an understatement of their work which nevertheless indicated their complementary interests. In addition to his work in developing the departments of applied mathematics and oceanography, Proudman took a full part in University administration and acted as Pro-Vice-Chancellor during the war years 1940-46. Quoting the maxim that "the quickest way to get a lot of things done is to do one thing at a time" he was able to go straight to the heart of a problem, whether scientific or administrative, with an intuition which matched his intellectual ability. After his retirement the University of Liverpool conferred on him the honorary LLD degree. He was a fellow of the Royal Society (elected 1925) which awarded him the Hughes Medal in 1957 and he served on many scientific and government committees.