Agree. I really dislike this terminology because like many analogies it tempts you into thinking it means more than it really does and thereby reasoning from it

Agree. I really dislike this terminology because like many analogies it tempts you into thinking it means more than it really does and thereby reasoning from it to things which are entirely unsupported by anything sound. NP-Hardness and NP-Completeness are rigorously-defined concepts. By proving a problem NP hard you establish some extremely important properties about its nature and its relationship with other problems. AGI-Hard sounds like the same sort of thing but really isn't. It's fundamentally just pure speculation. Of the three letters "AGI" it's arguable that we don't have a hard definition of what constitutes any of them. Then further to that we don't have any kind of idea what being in the set of AGI-Hard problems might mean other than you're in the set. Do these hypothetical AGI-Hard problems have some relationship with each other? Whereas we know P is in NP, do we have an equivalent class to P and what would that mean other than "The class of problems solvable by AGI"? You can see this weakness when you look at the proposed examples of what is purportedly AGI-hard. What do they have in common? Mostly just that they are weakly-defined themselves. For example. How would you judge if an AGI derived from first principles something that isn't calculus but is equivalently important/innovative? Well you'd first need to define what that equivalence would mean.