In 1964 he went to the London School of Economics as a student to study Logic and Scientific Method. Soon afterwards he became one of Karl Popper's research assistants. In a series of papers in the 1970s, Miller and others uncovered defects in Popper's formal definition of verisimilitude, previously a mostly ignored aspect of Popper's theory. A substantial literature developed in the two decades following, including papers by Miller, to assess the remediability of Popper's approach.
Miller's Critical Rationalism (1994) is an attempt to expound, defend, and extend an approach to scientific knowledge identified with Popper. A central, "not quite original", thesis is that rationality does not depend on good reasons. Rather, it is better off without them, especially as they are unobtainable and unusable.