The type systems underlying computer algebra systems like Sage, GAP, etc. are immensely more complex than this. Read the source of Sage (lots of python/cython) and the source of GAP (pure c; everything is basically a void *). Operator overloading is immensely helpful for entire classes of objects -- groups, rings, fields, categories, combinatorial objects... some of them are kinda number-like, but for example groups can support multiplication and division but not addition/subtraction (unless it's an abelian group and you'd rather represent it that way). I've been writing C for nearly 30 years, and GAP is a slog to read. Sage makes this stuff way easier.

In short... math isn't just arithmetic, isn't even arithmetic of complex tensors. Math is way bigger than most programmers seem to comprehend. I'm on the other side of the DK curve; I know that I've only scratched the surface despite a decade of dedicated study