> where an abundance of complicated mathematical formulae are necessary

I think what you mean to say is, a lot of linear algebra is involved. So multi-dimensional structures like matrices and vectors are expected to have linear arithmetic operators defined over them, because they're used quite a lot.

You don't need operator overloading for that. Your language should be providing them as primitive structures and extending operators over them. Think like how C has a polymorphic addition, where '+' doesn't discriminate between integers, pointers and floats.

There are a lot of problems with user-facing operator overloading, but I think Haskell is actually a really great example of how to do it sanely. At the point in which you have type-families, you can properly restrict the semantic domain of a polymorphic function but still keep it an open set. The addition operator being restricted over types belonging to the Num type-family as an example trivially allows you to use '+' for matrix addition.

https://hackage-content.haskell.org/package/matrix-0.3.6.4/d...

Now you've avoided the worst part of user-facing operator overloading (juniors creating incoherent DSLs by abusing the mechanism) while still providing the mechanism where it's useful.