We report on an international study of students’ ideas about mathematics and how they view its relevance to their further studies and their careers. About 1200 students enrolled in mathematics subjects at five universities in different countries responded to three open-ended questions. The responses were coded using phenomenographic methods and grouped into a hierarchy of conceptions. We used a qualitative methodology in preference to a closed form survey in order to draw out the students’ ideas rather than imposing those of the researchers. We present the categorisations found and implications for learning and teaching.