When I mentioned the unsolvability of quintic to Scott in passing, it grabbed his attention, and he was visibly very curious as to how it could be possible to show that a general quintic polynomial has no solutions in terms of radicals.
Why should this be so surprising to us? I guess I think it’s a bit interesting that it starts at the 5th degree rather than elsewhere, but I’m sort of used to seeing such discontinuities. Naive induction doesn’t really get much of my faith anymore. Is there anything else to the problem here that I’m not seeing?
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.
Why should this be so surprising to us? I guess I think it’s a bit interesting that it starts at the 5th degree rather than elsewhere, but I’m sort of used to seeing such discontinuities. Naive induction doesn’t really get much of my faith anymore. Is there anything else to the problem here that I’m not seeing?
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.
Not the fact that it’s true, the fact that it’s possible to prove that it’s true.