I mostly get what you’re saying, though I don’t have the requisite understanding to follow formal proofs, but if there is one thing I do know for certain, it’s that “understanding” is anthropomorphizing and shorthand for something that is very much not understanding in a human context at all.

I get that it can be hard to find the right words to explain a some of these emergent phenomena, but I think it’s misleading to use words that make AI appear to have a thought process akin to anything we could understand as such—at least in settings where folks might not understand the shorthand as such.

And maybe everyone here is aware of that, but it makes me uneasy, hence this comment to hopefully make that point.