I recall reading that it's important to separate mathematics and metamathematics. What exactly does this mean, and why is it so?
I understand that this question may make no sense without more context, but I've been curious about this for a while and can't seem to find where I originally read that.
Metamathematics is a branch of mathematics, so the assertion does not really make sense. It is certainly important not to confuse a formal system with the mathematical tools and ideas used to look into properties of the formal system, or formal systems in general.