Mathematica is worth learning and using since it's so far ahead of the open source alternatives (e.g. Python/Jupyter and associated libraries ) in usability/interactivity/rapid development that it comes across like future-tech.
Unfortunately it's also the single tool most hampered by its licensing and silo-like ecosystem.
I'm an R and sometimes Julia user, although not Python. Can you offer some examples of how Mathematica surpasses open source alternatives in those areas you've mentioned?
How much symbolic computation can you do with R?
R package Deriv for symbolic differentiation, it allows user to supply custom rules for differentiation.[1]
R package numDeriv[2] for calculating numerical approximations to derivatives.
R package gmp[3] and Rmpfr[4] provide multiple precision arithmetic and floating point operations. They also include some special functions, e.g. Rmpfr::integrateR for numerical integration.
R package mpc[5] available at R forge. It provides multiple precision arithmetic for complex numbers.
R package rSymPy[6] provides an interface to ‘SymPy’ library in python via rJava.
R package Ryacas[7] provides an interface to the ‘Yacas’ computer algebra system. It is easier to install compared to `rSymPy`.
R package symengine[8] is an R interface to the SymEngine C++ library for symbolic computation.
[1] https://cran.r-project.org/web/packages/Deriv/index.html
[2] https://cran.r-project.org/web/packages/numDeriv/index.html
[3] https://cran.r-project.org/web/packages/gmp/index.html
[4] https://cran.r-project.org/web/packages/Rmpfr/index.html
[5] http://mpc.r-forge.r-project.org/
[6] https://cran.r-project.org/web/packages/rSymPy/index.html
[7] https://cran.r-project.org/web/packages/Ryacas/index.html