Sure, but each step was probably reached with the aid of intuition -- in other words, the mathematician suspected that it had to be true before they found the p

Sure, but each step was probably reached with the aid of intuition -- in other words, the mathematician suspected that it had to be true before they found the particular formal proof employed. So long as the original intuition is actually correct, then any bug will probably be patchable. (Obviously there's no guarantee!)