A recent survey of Canadian mathematicians found that while 43% of the participants use computer programming in their research, only 18% integrate this activity into their teaching. The first statistic highlights the significant place that programming may have in professional mathematics practice. The second suggests that such significance may not yet be acknowledged in undergraduate curricula across Canada. Our exploratory study involving 14 Canadian mathematicians sought to gain a deeper understanding of the place of programming in both contexts and therefore describe the gap from a more qualitative perspective. The views of our participants highlight some important issues that may require attention in order to bridge the identified gaps, should that be deemed the favourable direction to take.