What are best examples of questions in mathematics that are not interesting until one knows the answers, whose answers themselves are what is interesting?
The thing that prompts me to post this is just one example. I've seen others, but they escape me at the moment. Here it is:
A torus is embedded in just the usual way in $\mathbb R^3$. It has parallels of latitude and meridians of longitude. A curve that meets every parallel of latitude at the same angle, or, equivalently, meets every meridian of longitude at the same angle, is a loxodrome. Suppose that angle is so chosen, given the shape of the particular torus, that the loxodrome goes through all $360^\circ$ of longitude in just the length it takes to go through all $360^\circ$ of latitude, returning there to its starting point. (There must be some conventional terminology for describing these windings, but I don't know it.) The question is: What are the curvature and torsion at the various points along this curve? Doubtless some will consider this question interesting, but to me, and, I suspect, to many, the answer, because it is so unexpected, is where this starts to get interesting. The answer is that the curvature is constant --- the same at all points on the curve --- and the torsion is everywhere $0$. (And it's really easy to deduce from that the precise value of the curvature.) I believe this was discovered in the 1890s and is stronger than the celebrated theorem of Villarceau, published in 1848. Villarceau's theorem says that a plane bitangent to a torus intersects the torus in two circles. This proposition does not assume as a hypothesis, but rather has as a (trivial corollary of its) conclusion, that the curve lies in a plane.