I hope someone will finally mathematically prove that it's impossible with current algorithms, so we can finally be done with this bullshiting.
They did! Here's a paper that proves basically that:
van Rooij, I., Guest, O., Adolfi, F. et al. Reclaiming AI as a Theoretical Tool for Cognitive Science. Comput Brain Behav 7, 616–636 (2024). https://doi.org/10.1007/s42113-024-00217-5
Basically it formalizes the proof that any black box algorithm that is trained on a finite universe of human outputs to prompts, and capable of taking in any finite input and puts out an output that seems plausibly human-like, is an NP-hard problem. And NP-hard problems of that scale are intractable, and can't be solved using the resources available in the universe, even with perfect/idealized algorithms that haven't yet been invented.
This isn't a proof that AI is impossible, just that the method to develop an AI will need more than just inferential learning from training data.
But if you read the article, then you saw that the author specifically concludes that the answer to the question in the headline is "yes."
This is a dead end and the only way forward is to abandon the current track.