If we can’t solve every mathematical problem, there’s gonna be things in science that aren’t solvable either.

Not at all, math and science are very different things. Math is a fixed system of rules that we constructed. Within these rules, there are possible statements which cannot be proven or disproved using only those same rules.

Science is different, we don’t know the rules but we observe, measure, and make predictions. It’s not possible to “solve” physics but that’s because we can’t make infinitely accurate measurements, there’s nothing systemic to prevent us from making a complete theory.