Let's not pretend math notation has remained constant for millennia.
Of course it has evolved. But some landmarks of it (e.g., using single letters for "variables") have been used since 2500 years ago. Now I laugh when programmers tell me to be "civilized" and name my matrices with full words.
Exactly, it has been refined over millennia.
Right, and it's important to remember that mathematics is sharply optimized for human understanding, whereas programming languages strike a careful compromise between human understanding and efficient execution by machines. I don't think anyone could seriously argue that programming languages are "more expressive" than mathematical notation, which has the powers of ambiguity and hand-drawn graphics.
You are not wrong. Replace 'efficient execution by machines' with 'efficient processing by a compiler' and you will be even more correct.
To be fair, the mathematical notation that is familiar to us today is just a few hundred years old.