I'm not a mathematician but last year iPython saved my bacon big style when I suddenly needed to convert a dozen pages of dense math to an API with no notice.

I checked it all into iPython and then poked around playing with the equations to get a grasp of how they worked and what sane outputs would be, it was an incredibly powerful experience as it allowed me to visualise what was happening in a way I'd never been able to before, it also made me think there is a huge gap in the way math is taught in the UK, if I'd have had iPython when I was 15 I might not have needed to resit.