This paper examines the thoughts and early career of the astrophysicist and cosmologist E. A. Milne. Although Milne only turned to cosmology in 1932, many of the ideas that characterised his heterodox system of world physics can be traced back to his works from the 1920s. Contrary to what has been stated in the literature, we argue that Milne was familiar with and interested in cosmology even before 1932. The relationship between mathematics and physics, an important topic in Milne's cosmophysics, was the subject of an unpublished paper he gave in 1922. We place the paper in its historical context and comment on its relevance for Milne's later work. An annotated transcript of the address is included as an accompanying paper under the title 'The Relations of Mathematics to Science'.