The "do it on your own right" is actually the weaker part of it. It's somewhat ill-defined, and I could imagine some future instance where it's highly debatable

The "do it on your own right" is actually the weaker part of it. It's somewhat ill-defined, and I could imagine some future instance where it's highly debatable whether the AI was working on its own or being used as a tool by a human. There aren't yet any cases where that's in question, though, so it's a hypothetical future debate. In any case, it's certainly not the meat of the test. It has to be maths for a specific reason. I think it's in some sense the purest form of an ability distinctive to human minds and pervasive in how they work. As I mentioned, it's an ability that can be demonstrated in the absence of any particular physical capability, and yet despite it being perhaps the oldest goal of AI it may be the one we have made least progress towards. Anyway that's my goalpost, and it's not moving. AGI, being "general", surely should be capable of this hitherto uniquely human activity. If our attempts so far are not capable of it, then clearly they are not "general". If you know of any evidence that my goalpost has been achieved, please let me know. I'm very eager to see it happen.