I'm an engineering student an I can say with property that, although I don't know much about Sage, a good symbolic math project (in particular Open Source) is sorely needed. It would be far from a curiosity. Most students use Matlab/Octave where I study, and all it does is allow for numeric computation. We've had huge advances in computing and it's been long since numerical integration was our best aid! More math heavy engineering subjects will often encounter large symbolic manipulations needed to arrive at some result, and common sense is that there's no good tool to help with that. Common sense is there is some limited symbolic manipulation in some HP calculators, and Wolfram Alpha, although it often refuses to work once you start playing with larger expressions.

I also know that some fields like ANNs (AI) research rely heavily on automatic symbolic differentiation, although I'm not sure the tools they use.

Check out SymPy:

    >>> x, a, b, c = symbols('x a b c')
    >>> solve(a*x**2+b*x+c, x)     # solve(expr_eqal_to_zero, var)
    [ (-b + sqrt(-4*a*c + b**2))/(2*a),
      (-b - sqrt(-4*a*c + b**2))/(2*a)  ]

More info: https://minireference.com/static/tutorials/sympy_tutorial.pd...

I will, thank you vm :)