As a random computer engineer, I find using mathematica to be extremely convenient when trying to grok a problem or lay out a first attempt at a solution. Of course it isn't really helpful when dealing with glue issues (i.e. making software work together) but it is really good at letting you experiment at a high level and put together an algorithm to process/interpret/transform/generate some data.

I say it's good for high level experimentation because basically every function/transform/operation/solver you could ever need is present in the standard library [1] and stuff "just works". IMHO it's not really something you'd want in production but it lets you get an MVP for a given problem/solution working faster than any other tool I've used and all while rarely needing to even consider a 3rd party library. You can then focus on just mapping that MVP to whatever language/library/ecosystem you are actually working in.

1. https://reference.wolfram.com/language/

It's extremely versatile which makes it able to solve some neat problems. My favorite example is this was a CodeGolf to find if a goat in an image is upside down. - https://codegolf.stackexchange.com/questions/71631/upgoat-or...

It used to be the big differentiator was the ability to do symbolic math and actually solve equations. Maple could also do it, as could the TI89, so I never really got into it. It was just a huge difference from Matlab.

But if I have an actually nasty equation to solve, like a system of differential equations with erf functions or something, I do actually go to wolfram alpha for help. It happens more often than I'd like, it's especially nice that no matter how nasty the equations you can still use units.

Mathematica usage appears widespread in my own domain of theoretical physics, but it is probably used in elsewhere as well.

A good niche for mathematica is finance: type in your equations, tell it what "type" your variables are, let it solve them. Let the machine get it right.