In response to a recent Canada-wide survey, where it was found that mathematicians use computer programming much less in their teaching than in their research, an exploratory study involving 14 Canadian mathematicians sought to gain a deeper understanding of the place of programming in both contexts. To capture the differences in the degree of interaction with programming in various mathematical practices, a scale of six levels has been defined and used. While providing visibility to an aspect of mathematical practice that is often absent from published work, the views of our participants also highlight some important issues that would require attention in order to reduce the identified gap, should that be deemed the favourable direction to take.