His teaching career began at Leeds and Liverpool Universities, and in 1926 he was appointed to the Chair of Pure Mathematics at the newly founded Egyptian University at Cairo. A successful tenure of this post had to be terminated for family reasons, and after returning to this country in 1931 he held lectureships in the mathematical departments of the Imperial College of Science and of the University of Edinburgh.
Ince's research work was for the most part devoted to differential equations, and in particular Mathieu's Equation and Lamé's Equation. It was to Mathieu's Equation that Professor Whittaker directed his attention in his post-graduate period, and his work on the Mathieu functions culminated in a series of papers, published in our Proceedings, in which he proved the impossibility of Mathieu's Equation having more than one periodic solution, and also prepared the way for and actually carried out the numerical tabulation of the functions. Professor Whittaker has referred to this as "a splendid achievement, performed single-handed save for some help by an Egyptian assistant, which will be more and more appreciated as the progress of physics and astronomy reveals fresh problems for which these tables provide the solution." Lamé's Equation attracted Ince in his later years, and his work on the Lamé functions is marked by the introduction of a new notation, exhibiting the essential relations between the different classes, and also of a novel method of expansion - based on a suggestion by Hermite - which has the advantage of orthogonality. His papers on Lamé's Equation were also published in our Proceedings, and shortly before he was, taken away, at the early age of forty-nine, he was cheered with the announcement that our Council had decided to award him the Makdougall-Brisbane Prize for the period 1938 to 1940.
In addition to his many published papers on these and other mathematical subjects Ince was the author of an extensive treatise on Ordinary Differential Equations (1927), an introductory text-book on the same subject, published in 1939, and also two books on Descriptive Geometry (1915 and 1933).
He was elected a Fellow in 1923, and died on March 16, 1941.