I find it unbelievable that this question can't be settled themselves without posting this simply by asking the AI enough novel questions. I myself have little doubt that at least they can solve some novel questions (of course similarity of proofs is a spectrum so it's hard to draw the line at how original they are)
I settle this question for myself every month: I try asking ChatGPT and Gemini for help, but in my domains it fails miserably at anything that looks new. But, YMMV, that's just the experience of one professional mathematician.
