 After brief stints at the University of Göttingen, Princeton University, and Balliol College, Linfoot took a job in 1932 as assistant lecturer, and later lecturer, at the University of Bristol.During the 1930s Linfoot's interests slowly made the transition from pure mathematics to the application of mathematics to the study of optics, but not before proving an important result in number theory with Hans Heilbronn, that there are at most ten imaginary quadratic number fields with class number 1.The exact reasons that Linfoot chose to switch his research from pure mathematics to optics are complex and there is probably no single most important reason.