I cannot speak to data science / statistics but can say that Wolfram Mathematica is vastly, vastly superior to other options in non-statistical arenas of applie

I cannot speak to data science / statistics but can say that Wolfram Mathematica is vastly, vastly superior to other options in non-statistical arenas of applied math and physics. I'd definitely encourage giving it a quick try just because you are working in a closely related field and so might occasionally run into cases where Wolfram is actually a better tool for the job. There are some very respected people that the company employs doing good work pushing the limits of different equation solvers and that sort of thing. Whatever one thinks of the man Wolfram himself, I think its an impressive company and probably a good example of a piece of software that is on the cutting edge and also wouldn't be viable as an open source project (too many PhDs required to support it for that tbh, and definitely not very accessible to contribute to). And yes, it is expensive, but not prohibitively so for interested hobbyists. I pay for a personal edition, but my work pays quite a bit more than that. If you are affiliated with a school, see if they have deals or computers with it they can make available. Most schools with big physics or engineering or applied math programs are going to have it licensed.