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Can you be more explicit?

I absolutely do not understand what are you talking about.

The question whether the tautologies exists regardless of whether we know about them or not is absolutely not a problem that is studied by mathematics and can be proven by mathematics.

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Correct, these questions lie outside the internal practice of mathematics. If you want to see where that computational mindset breaks down, read Carnap's "Empiricism, Semantics, and Ontology" regarding internal versus external frameworks (or have an LLM summarize it...), or look into Brouwer's Intuitionism, or better yet into Lawvere and Topos theory, where the "underlying tautologies" literally change depending on the categorical environment you construct (but this may take some time to wrap your mind around so don't expect to understand much right away). Or, given the thread topic, you can just prompt an LLM to interactively walk you through how classical logic fails in a constructivist topos, or if you have interests outside of applied math or mathematics itself, you can ask it about foundational questions in science and mathematics, which unlike the prevailing opinion in many tech circles, aren't resolved.

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