[jabl]

Background: I did a PhD in computational physics.

Starting as an undergrad, I extensively used mathematica to help or double check homework problems, plotting functions etc. For more "numerical" type of work, we extensively used matlab, so typically we used mathematica for more symbolical type problems. Later on, when working in physics, I often used mathematica, again mostly for doing things like symbolical integration, or things like quickly calculating symbolical gradients that I could copy-paste into some numerical software etc.

I no longer work in academia so I don't have access to a mathematica license, but similar free tools are Sympy, Maxima, which are good for basic stuff but in my experience are not nearly as good as Mathematica for more complicated stuff. Or just the online wolframalpha.