Thousands of years ago children figured out how to troll adults. Whatever the adult says, the child just responds, "Why?" The child will always win.
I too assume that there is no end to such question. But sometimes and end (I'm not saying "an answer") comes in the most unexpected way. At one time people wondered, whether the earth is infinite, or there is an edge somewhere. No one could think of a third option. And you still can't be sure to have considered every possible option.
Likewise, it requires only finitely many elementary computations to verify that they have the property that we claim.
And what if you fail to find such numbers? Until you find a solution, Fermat's equation, in Turing's terms, is an undecidable problem, because you are not guaranteed to get an answer (assuming for a second that the answer can't be found analytically).
we should create a Chuck Norris of figure skating.
Speaking of figure skating (I know, it's a weird topic for a philosophical forum, but still). I see figure skating jumps as elementary particles. Toe loop, Salchow, loop, flip and Lutz are bosons, because they have an integer spin (±1, ±2, ±3, etc), while Axel and the waltz jump are fermions, because they have a half-integer spin (±½, ±1½, ±2½, etc).