News for hackers. Stuff that matters.

A comment on AI unlocks Gödel's notebooks, said to contain hundreds of proved theorems. Parent comment

Re:AI unlocks Gödel's notebooks, said to contain hundreds of... by LdBaringSwallow on Friday November 13, 2026 @01:33PM (#50487767)
Why? His incompleteness work explains why software and math suck so he would already expect them to; they're rhetorical and can never fully be a closed loop body of knowledge as we can never rhetorically define the far future or far past; merely simulate rhetorically

Ergo all defined axiomatic systems have sentences about the far past and future that cannot be defined with certainty; most do not make the connection to physics. Gödel did and would 100% aware the limits exist and will always exist

Scaling laws aren't just for computers; humans lived experience does not scale infinitely through time, just approximately 2-3 generations

As I understand immutable physical truth like this played a huge role in his early research and ultimately were the forcing function that led him to incompleteness

[ Parent | on HN ]
Re:AI unlocks Gödel's notebooks, said to contain hundreds of... by kevin42 on Friday November 13, 2026 @02:24PM (#50488468)
"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.

[ Parent | on HN ]
Re:AI unlocks Gödel's notebooks, said to contain hundreds of... by LdBaringSwallow on Friday November 13, 2026 @04:54PM (#50490442)
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.

[ Parent | on HN ]