The first time I heard of the unsolvability of general quintic equations, my response was "Wait, there's unsolvable polynomials?" followed immediately by "Why five? It seems so arbitrary!". Then I looked it up, and realized that it would take a lot more background knowledge before I could come even close to being able to understand the proof. Even so, my initial reaction was very similar to the one Jonah mentioned from Scott in the post, so I think he's on the right track with what he's saying.