The transition from university to professional working life is important to individual students, employers, universities and more generally to national economies. A better understanding of the match between skills required by industry and skills learnt at university is therefore paramount. This study examines the transition from the perspectives of those undergoing the shift--graduates! There are many studies from the viewpoint of employers but these often end up as an extensive list of requirements that are not possible to achieve in a degree programme. There is a significant expectation gap between employers and graduates. Using a small in-depth study, we show that the mathematics graduates interviewed required more computing power than was taught at university and more "soft" skills such as communication. An understanding of the transition from learning to work for mathematics graduates points the way to how curricula may be reformed to better prepare graduates for professional work. (Contains 3 tables.)