I guess the nomenclature behind "AGI" and "ASI" is still debatable and i just watched an interview with Sundar Pichai (on Lex Fridman) where he brilliantly almost mocked the term, essentially describing it as a recent invention, neologism mostly used to mean "our ai will soon be very advanced".

Even so my question is: what problems as of 2025 September are impossible for even the best AI? I can think of many, though since they are currently unsolved, they may as well be impossible regardless for any human or human tool anyway:

*here are some problems ordered randomly, "on top of my head":

1. P =|!= NP; 2.Unification of gen. relativity+quantum mechanics; 3. prove/disprove the Riemann hypothesis; 4. "lonely runner conjecture" proof/disproof; 5. cure for 4th stage cancer that works most of the time; 6. orders of magnitudes colder fusion; 7. reactionless drive - proof/disproof; 8. prove(show)/disprove 'quantum supremacy'; 9. install user-friendly main purpose OS on quantum computer; 10. humanoid defeats ufc fighter in a fight; 11. humanoid performs parkour better than Storror; 12. AI designs orders of magnitude faster textgen/mediagen algorithms than transformers without sacrificing quality (or 5-10% worse deviation); 13. AI builds self-replicating robots that build city on Mars (i stole this idea from Grok month ago or so...); 14. discovers way to make cheap invitro meat; 15. synthesizes ununennium; 16. correct interpretation of quantum mechanics; 17. solve the 'problem of time'; 18. make glueballs; 19. prove/reject the Collatz conjecture;

and many more...what in your opinion are agi-like problems?

I know my phrasing of the problems above isn't perfect, for example "cheap" as in invitro meat is open to interpretation and 1 million degrees fusion is still ~2 'orders of magnitude' colder but likely useless to have impact on mainstream fusion etc. But it's an internet forum after all not Ph.d thesis, regardless any of the problems if solved despite the horrible wording will signal an immense paradigma shift in AI or whatever it "signals" someone/some people will be doing something very right surpassing even Demis Hassabis, or even Einstein, Da Vinci, Tesla, Ada and the likes.

I'm curious what many people want to see from AI, since the IQ of this forum is high, I guess it won't be a beavis-and-butthead level of answers like "photorealistic fps" or "teslas that sound like shelby" or "tastier burgers", "badass jetpacks" , "fully immersive VR where you can interview andrew tate", "cabrio boeing", etc etc.