In 1923 he was elected to the Chair of Mathematics in the University College of the South West at Exeter, and here he remained until his retirement in 1958. The Mathematics department is his monument. During the first twenty-five years or so of his professorship, he prepared a steady stream of students for external degrees in Mathematics of London University, with a staff which for the greater part of that period varied between three and five, including himself As a result, Professor Brown had to undertake a considerable amount of teaching in both Pure and Applied Mathematics, apart from the inevitable administrative duties. As a result, he found it impossible to devote much time to research, in which he had made so promising a beginning. Nevertheless, he maintained his interest in Mathematics and when, in the period after the war, the opportunity came to expand the department, he seized it with both hands and the department grew considerably in stature, two of his appointments during this period being of men who obtained chairs elsewhere within ten years of their original appointment at Exeter.
When he retired in 1958, the department, in what had now become the University of Exeter, could look forward to the future with confidence in the foundations he had laid. During his retirement he remained in Exeter, and was a constant visitor in the department. He died on May 13, 1965, leaving a widow and two sons.
He had been a Fellow of the Society since 1924.