> It's intended to understand the nature and theoretical limits of computation.

Not in a general sense, at least for standard complexity theory. It only deals with a very specific model of computation. Anyone with a sufficiently solid grasp of metamathematics intuitively understands that the distinction between solve and verify is nothing but a description of how badly matched our foundations are for the structure we're trying to view.

... This is the second time today I've posted about foundations like this.