Summary: In this paper, we report on an international study of undergraduate mathematics students’ conceptions of mathematics. Almost 1,200 students in five countries completed a short survey including three open-ended questions asking about their views of mathematics and its role in their future studies and planned professions. Responses were analysed starting from a previously-developed phenomenographic framework (Reid et al.: Mathematics students’ conceptions of mathematics, New Zealand Journal of Mathematics, 32 (Supplement), 2003, [ME 2005d.01405]) which required only minor modification. Students’ conceptions of mathematics ranged from the narrowest view as a focus on calculations with numbers, through a notion of mathematics as a focus on models or abstract structures, to the broadest view of mathematics as an approach to life and a way of thinking. Broader conceptions of mathematics were more likely to be found in later-year students ($p<0.001$) and there were significant differences between universities ($p<0.001$). The information obtained from the study not only confirms previous research, but also provides a basis for future development of a monitoring questionnaire.