"Discovering/inventing and proving new theorems" is qualitatively different to the things you list. Computers have been able to calculate since they were invent

"Discovering/inventing and proving new theorems" is qualitatively different to the things you list. Computers have been able to calculate since they were invented, and there has certainly been plenty of progress on getting them to solve problems, but calculating and solving problems isn't what mathematics research is. Ever since computers were invented there has been a hope that you could set up a system that would just churn out interesting new theorems. Indeed it was one of the primary motivations for the invention of the computer, but it hasn't materialised yet. You clearly consider the progress on solving problems to be progress towards being able to do mathematical research. I don't think it is, any more than progress in, say, graphics is. But maybe I will turn out to be wrong and you will turn out to be right. We won't have the answer until the problem is solved and we have our wonderful machine churning out theorems. But I think you will probably be able to agree that since mathematical research is something human minds are capable of it's something that an AGI should be capable of, i.e. if an AI approach is inherently incapable of it, it's not AGI. You may consider it an unnecessarily stringent requirement, in that there may be other, easier challenges that AIs can perform that will convince you that they are AGI. That's fine - you think about the problem differently to me, so you find different things persuasive. If you are convinced that a given AI is AGI, though, you shouldn't be too concerned about my particular goalpost given that your AGI should be able to achieve it (and convince me) pretty soon. We'll see what happens. I'm just explaining what I would find convincing, and pointing out that contrary to the oft-repeated accusation that started this discussion, I for one have never once "moved the goalposts".