In the period of 1926–1934 Wilton published 26 research papers on analysis and number theory.
For which he gained the Doctorate in science from the University of Cambridge in 1930 and in 1935 he was the first person to receive the Thomas Ranken Lyle Medal from the Australian National Research Council.
[3] At the University of Adelaide, Wilton graduated with first-class honours in mathematics and in physics (B.Sc).
Professor Sir William Bragg praised Wilton for his natural genius in mathematics among any of his students.
[4] On 12 April 1944, he died of a cerebral hemorrhage and was buried in West Terrace Cemetery, Adelaide.