The relationship between mathematicians and researchers in mathematics education has often been fragile. Yet it is crucial. We conducted a series of themed Focus Group interviews with mathematicians from six UK universities. Pre-distributed samples of mathematical problems, typical written student responses, observation protocols, interview transcripts and outlines of relevant bibliography were used to trigger an exploration of pedagogical issues. Here we elaborate the theme "the relationship, and its potential, between mathematicians and researchers in mathematics education" that emerged from the data analysis. We do so by presenting the participants views on this relationship in terms of: obstacles, desired characteristics and potential benefits. [For complete proceedings, see ED489538.]