>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.

Indeed. To be clear, I'm not saying I think any current system is remotely close to AGI. I just think that saying that no one is thinking about or making progress on a math research AI is inaccurate.