Many people have argued (perhaps most famously Richard Dawkins) that a supernatural god, even the God of the Bible, if one exists, could not convincingly prove its own existence to us. The reason for this is that there's literally no way to distinguish whether any phenomenon, information or other kind of proof is coming from a supernatural entity or from an extraterrestrial entity from within this universe that has technology advanced beyond all comprehension (after all, "any sufficiently advanced technology is indistinguishable from magic.") No matter what happens, no matter what kind of observable measurable physical phenomenon, no matter what kind of information is given to us, it's always possible that it has a fully natural source, and is coming from alien technology so advanced that we cannot even begin to comprehend it (any more than an ancient Sumerian could comprehend how an LCD display works, especially with zero explanation.)
I fully agree with that assertion. When we logically think about it, there indeed is no way to distinguish between the two for sure. Any "proof" you can think of, no matter what it is, could be coming from a natural source from within this universe, by some extraordinarily advanced extraterrestrial beings who are playing with you. What seems physically impossible to you may be trivial everyday technology to the extraterrestrial species. There just is no way to know for certain.
However, for decades I have maintained that there's one thing that can be proven with a great degree of certainty and reliability: And that's the existence of a non-human intelligence higher than us (either natural or supernatural.)
And what would that proof be? If this higher intelligence gave us several proofs (or counter-examples) to currently unsolved mathematical problems that the best mathematicians have been struggling with for decades and centuries, in a form that we can check and corroborate.
No random UFO believer or "channeler" or any of the sort could come up with such a mathematical proof of their own, so if they just came up with a couple of such proofs, claimed that the proofs came from an alien species, that would be quite convincing. Perhaps still not 100%, but very close.
Except now... that type of proof is being quickly destroyed by developments in artificial intelligence.
No longer is there a way to know if such a mathematical proof came from some higher intelligence or whether someone ran it through a modern LLM and got a proof that way. And, in fact, just in recent months top-of-the-line LLMs have been proving (and disproving) mathematical conjecture after mathematical conjecture that have puzzled mathematicians for decades.
So, unfortunately and sadly, my favorite "valid proof for the existence of a higher extraterrestrial or supernatural intelligence" has vanished. Somewhat ironically, technology made it vanish.
Now, I'm not sure what other such proof could be considered reliable and trustworthy.
Ironically, the more our technology advances, the less sure we can be that non-human higher intelligence actually exists.
