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AI unlocks Gödel's notebooks, said to contain hundreds of proved theorems

theguardian.com

176 points by bookofjoe · 42 comments

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14 threads
tiffanyh

I’m been trying to use various frontier models to decipher lost ancient languages (like Linear A).

I wonder what tactics this used, so that I can leverage in my own work.

iltennico

From what historians of science tell us, Gödel was in any case an absolute perfectionist who mostly published work that was bulletproof. His enormous body of notes surely contained some very sharp insights, but it is unlikely that he would have produced illuminating, conclusive new theorems by chance and without realizing it. He was a very harsh reviewer of his own work.

hobo123

The stuff about Gabelsberger shorthand sounds ludicrous to me. My father would write notes in a custom version of it until his death 2020.

Officially (i.e. in schools teaching stenography, back in the day) it was long ago replaced by "unified German shorthand" (Deutsche Einheitskurzschrift IIRC), but he always considered Gabelsberger to be superior.

Well, maybe he too was one of the 6 people in the world who could read it (or yes, maybe that was hyperbole, I'm not sure) :D

imbiased

I can't remember the exact quote but I believe I read that Gödel confided to Einstein (in their walks in Princeton) on his deep worry of his work being forgotten. If only he knew.

ducttapecrown

It'd be interesting to hear about these new 14 themes of logic Gödel pursued!

  • bahbahbahbah

    Yeah, these notes need to be just openly published. Then I could ask my own Claude for an explanation. (Not /s)

    • rsoto2

      You could likely "unlock" the manuscript yourself with a competent computer vision algorithm. It's nothing that fancy.

semolinapudding

This is incredibly exciting! Gödel is unquestionably the most important logician in history, but unfortunately he published very little. For instance, the Dialectica interpretation was published approximately 20 years after his first ideas on the subject.

Plus, Jan von Plato is the world's leading expert on Gödel -- the number of people who can read Gödel's handwriting can be counted on the fingers of one hand, and I think that every single one is part of Jan von Plato's research group. If he is excited about the output, this is a huge deal.

jdelman

I wonder how much expertise was actually needed to translate these notebooks. In other words, could a general purpose model one-shot these translations, or did we really need a subject matter expert to do the work? BTW - I'm not saying having a subject matter expert tackle the problem with Claude isn't useful - just wondering what the limits are!

  • rsoto2

    Uh, a decades old properly trained OCR algorithm could probably "unlock" these manuscripts

sheikhnbake

This might be an actual concrete example of someone making themselves obsolete with AI.

> Von Plato said he had started his Gödel project in 2017 because he was facing mandatory retirement from Helsinki University. “What should I do to make myself indispensable? Oh yes, I’ll start reading Gödel’s enigmatic shorthand pages!” He received a €2.5m (£2.1m) grant from the European Research Council, taught himself Gabelsberger shorthand – “I am one of only six people who can read it in the world” – and assembled a small team.

  • arbot360

    Okay let me know when AI gets itself a 2.1M Euro grant from ERC as the PI.

    • sheikhnbake

      I think you're missing my point. It's that once the workbooks are completely interpreted, which is happening at an accelerated pace thanks to AI, von Plato's value as an interpreter of the short hand becomes severely reduced, presumably as does his ability to get future grants.

      I'd think there would be more competition to lead studies and receive grants now that the workbooks are accessible to a wider audience of logicians

  • snk

    And via earthshaking victory, at that, wow.

  • alterom

    It's literally an example of someone keeping themselves from becoming obsolete with AI.

    • sheikhnbake

      The professor's value was/is in being one of a few people with the capability of interpreting the shorthand. By translating it with AI, his value as an interpreter begins evaporating as the translated workbooks become accessible to more logicians.

      • Bayart

        He might see his value in his role of carrying the knowledge itself rather than being its gatekeeper.

    • ShinyLeftPad

      That's what he thinks, surely.

      • bdamm

        It's clear though. Even if an AI had connected all the dots on the obsolete shorthand, it would never have recognized the human value. I doubt that any AI process would choose to spend the energy on interpreting this particular obsolete handwriting and then understand that it was from the hand of a genius.

      • jvanderbot

        Using AI to do your job does not mean that AI suddenly walks in the door and escorts you out and starts collecting your paycheck.

        Someone is still driving these studies, and probably will be for a while. Or maybe not. But still we can reward this guy for opening up this can of theorems that had before.

        Silliest case: Imagine a dusty basement terminal screen open to claude code with "There we go! Cancer is cured as you requested, let me know and I'll send off the results" and nobody is around to approve it.

empath75

https://aitp-conference.org/2026/slides/JvP.pdf this seems to be slide deck with some of the results.

alterom

"You don't get credit for the work you don't tell anybody about"

This has been a problem long before Godel: famously, Newton tried to get credit for inventing Calculus only after Leibniz published his work, leading to a bitter dispute that lasted long after they both died.

I wonder if this problem is now going to be significantly exacerbated by AI, as mathematicians are getting more incentives to keep their works secret —

— or, to the contrary, the community will get a push to publish incomplete ideas, scratch work, etc. early to establish a record of thinking about a problem before others did.

In the end, as always, it's a social problem created by " publish or perish " institutional incentives which reward (and require!) published results, but not the work that led to to them.

This, I hope, will finally change.

  • soulofmischief

    Maybe we'll see a solid societal use case for zero-knowledge proofs here, establishing one had a set of documents at a given date without revealing them.

    • _bent

      you can just write a doc with your proof/idea, hash it and post that hash on twitter

  • ShinyLeftPad

    so what would the new incentives be? don't publish... and get paid anyway?

    • hobo123

      At least that's how traditional Western universities used to work. The profs sometimes published something, and they taught students. Looking at science back then, it seemed to work out rather well.

insane_dreamer

> Increasingly paranoid in his later years, he refused to eat food that was not cooked by his wife, and died of starvation in 1978

genius often comes with side effects

rsoto2

"Unlocks" cool so Claude the trillion dollar technology did what any funded researcher with a computer vision algorithm could have done years ago. Wow so impressive.

2aFds

Nice timing for the IPO. Cooked Nvidia numbers on the 17th are still missing, and the 19th will go well!

The AI was of course trained on existing pre-AI transcriptions of Goedel's shorthand, which he was taught in school around 1920 and which was widespread and only technically "obsolete".

https://link.springer.com/book/10.1007/978-3-030-67606-3

  • letmevoteplease

    In the first paragraph, we have an evidence-free insinuation that the foremost expert on this subject is some kind of shill running a campaign for Anthropic. What does this campaign involve? Is he just making it all up? Let me hear your theory of what is happening here and how it invalidates the claimed abilities of the model (or why the abilities do not matter).

    In the second paragraph, we have what appears to be a claim that the model knows how to read Gödel's shorthand because it has been exposed to past examples of that shorthand. What is your point here? I think the model learning to generalize by training on a few examples is a point in its favor.

cyanydeez

I think we'll find godel's most pungent critiques of modern logic & mathmatics to be the maddening limits of LLMs.

  • LdBaringSwallow

    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 with rhetoric concretely observe/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 in those languages 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 cultures do 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

    • kevin42

      "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.

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