Comment by Davidzheng
19 days ago
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.
New doesn't have to mean "the hardest thing yet", but as humans mastering our subdomain, they are often the same.
Trust, but verify, no? No one benefits from refusing to experiment and test.