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"all defined axiomatic systems have sentences about the far past and future that cannot be defined in those languages with certainty."

This is often misunderstood or misstated to mean that there are some things that are unknowable or unable to be solved. (I'm not saying that's what you were implying, I am referring to the common way I see his theorem being represented)

But what he really proved is that no single sufficiently powerful, consistent, effectively specified formal system can prove every arithmetic truth.

He didn't prove that there are mathematical truths that are unsolvable through any possible extension or alternative framework. It's just that one framework isn't enough to solve all problems.

by LdBaringSwallow2 hours ago|

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You're just restating Gödel verbatim without considering what that would entail physically; they're implicitly unsolvable as it would take forever to solve them all; the universe would experience heat death before they're all solved.

Scaling issues do not just matter when making bridges and when hosting LLMs.

Back in Gödel's day physicists were like rockstars and all Gödel's output was 100% influenced by Einstein and the rest. Given the group's expertise in the domain the implicitly forever incomplete/never computed did not need to be spelled out explicitly.