I don't know the history of mathematical theories, but in physics it has often been the case that something took years (or decades) for people to wrap their hea

I don't know the history of mathematical theories, but in physics it has often been the case that something took years (or decades) for people to wrap their heads around as they were poking at the edges of understanding. But as they continued to do so, new ideas and concepts emerged which made a better mental framework for understanding them. Hence, for example, the work-energy theorem can now be proved by a high school senior, but in the day there was big debate over the factor of 1/2 in the term for kinetic energy. So it may be with mathematics. Things like Fermat's Last Theorem and P != NP may be difficult to grasp simply within our current frameworks, but new ideas may give rise to new frameworks that makes them more digestible. If you can just get it proved somehow then you can proceed with confidence towards these new ideas.