Knowing math and programming is important, knowing finance isn't.

The friends I have who have a degree in mathematical finance say that the finance portion of their degree was quite useless and only very weakly correlated with how 'finance' worked day to day at their job. Basically they learnt everything they had to know about finance on the job. The optimization and statistics they studied on the other hand is stuff they use every day, and if they could go back and do it again they would study less finance and more math at university.