Basically, can we prove that we won't be able to overcome the skeptic argument? Anything I should look up to better understand this?
To prove something you always have to look at a problem/hypothesis from an higher viewpoint. It is impossible to solve a problem when only looking at the problem from within the domain itself because it can affect your view at the problem.
When you solve a mathematics problem you are solving it with only mathematics. But you are looking at the problem and thinking about the problem without mathematics can affect your thinking.
So to solve the problem "Can we prove that we can't prove reality?" we realy have to look at reality from outside of reality otherwise reality can have effect on the results. This clearly is impossible at this moment in time.
so there is some sort of prove for you.
The skeptic argument is unreliable because it asserts the reality of its own proposition in contradiction to its own premises. It says: It is real that we can't prove anything is real. It is a self-defying argument. Skepticism is a tool inside reason and is not a procedure to derive proof about the world itself.