As a student at Prince Alfred College Raymond Wilton was profoundly influenced by his mathematics teacher Mr Sidney Vanes, who recognised his wide ranging abilities. He vied with future headmaster and contemporary J.F. Ward for PAC honours and received seven credits for his eight subjects.
Wilton was awarded the Angas Engineering Scholarship to Adelaide University but chose to study mathematics under Professor William Bragg, who rated Wilton as his most outstanding student and arranged for him to study mathematics at Cambridge University. Here he met with great success and came fifth in the tripos examinations in 1907, the news of which prompted Headmaster Chapple to give the boys a half holiday!
Wilton became a lecturer in mathematics at the University of Sheffield until the interruption of the First World War. Because he was a conscientious objector, Wilton was working as a hospital orderly when he was invited to become the inaugural Elder Professor of Mathematics at the University of Adelaide, a position he held from 1920 to 1944. During his tenure he revised school and university mathematical courses and continued his research.
In 1914 the University of Adelaide conferred on Wilton a DSc by for his work in applied mathematics. His study of Analytical Number Theory was recognised with a DSc from Cambridge University in 1930. In 1935 he was awarded the Lyle Medal for the most outstanding work in Australian mathematics or physics.
In 1941 Wilton suffered a stroke, which so affected his memory that he had to reteach himself, with great forebearance, most of the mathematics he had previously known so well.