Is a brute force method considered a proof? Say we have some finite set, and some theory about a set, say "All elements of the finite set $X$ satisfy condition $Y$".
If we let a computer check every single member of $X$ and conclude that the condition $Y$ holds for all of them, can we call this a proof? Or is it possibly something else?

Exhaustive checking is certainly a valid method proof, that is, everyone agrees that it is a proof.
It is usually considered a not very satisfying proof, though, because it usually fails to produce any insight why such-and-such is true. It just observes that it is true, but mathematicians are generally interested in understanding rather than mere facts, and that is something you don't get from an exhaustive search.
In contrast an "elegant" proof will generally tell you not only that such-and-such is true but will also give you an understanding why it has to be true.
