There are at leastttwo reasons to learn Maple or Mathematica, or maybe some open source alternatives such as Sage. These two reasons I’m thinking about are i) To actually be able to calculate difficult stuff, such as integrals with difficult integrands or horrible determinants. ii) To have a reliable way to verify your computations.
Obviously both of these are important. So why aren’t these programs more widely used? There might be a reason I am not aware of — but I actually think there are some low-hanging fruits here.
Consider automating verifications — this should be doable!. If you have plenty of lemmas containing only calculations, which is quite common, it should be possible to make automatic tests of these by connecting Tex to Maple or Mathematica. Then both you and your audience could put greater trust in your result. (And let’s face it, no one’s going to bother checking your results anytime soon, at least not in statistics. And at least not if what you’re doing is a little bit boring.)
The other part, using Maple to calculate stuff, requires knowledge about the language and program, which of course requires a time investment, preferably as a course. And courses should only be taken during your Bachelor or Master’s degree (taking a course as faculty or PhD student is hard since it feels you can’t justify it.) So why wasn’t I ever offered a course in Maple? I would much rather have known Maple (and some of the theory it’s based on such as Groebner basis and computational algebra) than, say, wasting hours calculating divergences in a GLM course!