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.