 Brown began his teaching career during his doctorate work, serving as an assistant lecturer at the University of Liverpool before assuming the position of Lecturer.In 1964, he took a position at the University of Hull, serving first as a Senior Lecturer and then as a Reader before becoming a Professor of pure mathematics at Bangor University, then a part of the University of Wales, in 1970.Brown served as Professor of Pure Mathematics for 30 years; he also served during the 1983–84 term as a Professor for one month at Louis Pasteur University in Strasbourg.