This paper explores the inherent tension in the nature of research for art and design at doctoral level, and notes how these tensions have been accommodated in the Royal College of Art’s Research Methods course. Alex Seago outlines the traditional components of the course, including the need to map the background to one’s theory, and to demonstrate originality. The methodological section of the course has proved more problematic owing to the significant minority which is sceptical about the idea of methodology itself. Seago notes that debate polarizes around positions which have been described by Gerald Holton as ‘Dionysian’ (which regards traditional methodology as stultifying) and ‘Apollonian’ (which regards analysis as central, and dismisses unconventional approaches as pseudo-science). Seago argues that the process of discovery in much successful research is a combination of the two: pairing rigorous methodology with the following-up of intuitive hunches.