After a very short period of school teaching in Maybole, Miller was appointed in 1897 to a George A Clark scholarship in the University, where he was then obliged to conduct tutorial classes both in Mathematics and in Natural Philosophy. In 1899 be was appointed Assistant to George A Gibson, Professor of Mathematics in the Glasgow and West of Scotland Technical College (later known as the Royal Technical College, Glasgow, and now known as the Royal College of Science and Technology, Glasgow), and in 1909, when Gibson moved to the University, succeeded him in the chair. In the same year he was awarded the degree of D.Sc. for a thesis dealing with the geometry of the triangle and the conic sections.
Miller remained in the Technical College, where he was held in high regard as a clear, concise and methodical lecturer, until 1934, when he retired at the age of 63. He retired before the usual age in order to be able to extend his study of the Classics, for which he had a deep and abiding love, and to visit some of the places of importance in Latin and Greek lore.
Miller died on 14th July 1956, having been predeceased by his wife in 1928. There were no children of the marriage.