> Mathematicians don't really use "vectors" in the traditional sense like in physics but deal with abstract vector spaces
This is not at all true in general: many mathematicians use non-abstract vectors too. My (maths) PhD, for example, uses vectors throughout but doesn't mention vector spaces once.
This is not at all true in general: many mathematicians use non-abstract vectors too. My (maths) PhD, for example, uses vectors throughout but doesn't mention vector spaces once.