[vjk800]

I used to be a university researcher in theoretical physics and, in that field, everyone uses it, but I suppose that would count as "very specific math research" Any kind of complex integrals, systems of equations, etc. and Mathematica is invaluable, and, as I said, so much ahead of Sympy.

You could do stuff other than theoretical physics research with Mathematica, though. I has a lot of functionality and I always felt that I used only a tiny fraction of it.