Mathematics curriculum at the tertiary level is located within a range of social and cultural theories, and is often constructed by academics seeking to promulgate a particular view of mathematics. We argue that such a curriculum should incorporate a real acknowledgement of the different ways in which students understand the nature of mathematics and its role in their professional lives. Our research with students across a variety of disciplines has shown a strong relationship between the ways in which students perceive their future work and how they go about learning whilst at university. We suggest that students of mathematics would benefit from a curriculum that focuses on using mathematics as a means of investigating the world and takes every opportunity to make connections and develop professional skills. Our aim is to provoke a general debate on the overall aim and nature of mathematics curriculum at the tertiary level.