Just after going through a few examples in my head, the difficulty becomes somewhat more apparent. let’s start with 3. This is odd, so 3(3)+1 = 10. 10 is even so we have 10/2=5.

By this point my intuition tells me that we don’t have a very obvious pattern that we can use to decide whether the function will output 4, 2, or 1 by recursively applying the function to its own output, other than the fact that every other number that we try appears to result in this pattern. We could possibly reduce the problem to whether we can guess that the function will eventually output a power of 2, but that doesn’t sound to me like it makes things much easier.

If I had no idea whether a proof existed, I would guess that it may, but that it is non-trivial. Or at least my college math courses did not prepare me to find one. Since it looks like plenty of professional mathematicians have struggled with it, I have no doubt that if a proof exists it is non-trivial.

Take 'im away, toys.

Might be right but in my experience a lack of skill in conversing with AI is a much greater factor in determining it’s usefulness. It’s almost always going to defer to the user. It’s like when someone is dealing with tech support and they tell them to try turning it off and on again. If that really is the solution, and the user insists that it is not, CGPT is going to make something up just to appease the user’s request.

Users have to know that CGPT isn’t magic. How they behave affects how it behaves. Kind of like talking to actual people, which is what it’s essentially trying to simulate.