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An OpenAI model has disproved a central conjecture in discrete geometry

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Re: An OpenAI model has disproved a central conjecture in discrete geometry

#871

Post by yourapostasy »

xbmcuser wrote: post #625
trostaft wrote: post #232

Speaking as a postdoc in math, I must say that this is rather exciting. This is outside of my field, but the companion remarks document is quite digestible. It appears as though the proof here fairly inspired by results in literature, but the tweaks are non-trivial. Or, at least to me, they appear to be substantial to where I would consider the entire publication novel and exciting. Many of my colleagues and I have b…

This is the main thing that I keep harping about that human knowledge is too vast today for a person or even a group of people and llm will change that many discoveries that require serendipity in the past will be more likely than ever

I want to hear James Burke of Connections [1] and his writer team to have a free wheeling discussion for a few hours on what they see will happen with LLM’s making these connections with more conscious intent a lot easier. The awesome compression of knowledge aspect of LLM’s is a far undersold aspect of the technology.

[1] https://en.wikipedia.org/wiki/Connections_(British_TV_series...

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#872

Post by fc417fc802 »

pocksuppet wrote: post #849
edbaskerville wrote: post #92

Earlier quoted context omitted.

I just visited a McDonald's for the first time in a while. The self-order kiosk UI is quite bad. I think this is evidence in favor of the idea that an incompetent AI will soon be incompetently running a McDonald's.

Recently I tried to order at a Subway (which has decent quality food outside of the USA). They have kiosks. The kiosk only responded to touch about 60% of the time and took two seconds to respond. The employee who could've easily taken my order was just standing there bored. The future is here and it sucks.

> which has decent quality food outside of the USA

Is there something wrong with their food in the USA?

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#873

Post by wartywhoa23 »

ninjagoo wrote: post #847
wartywhoa23 wrote: post #808

Earlier quoted context omitted.

These all are valid, noble points I also used to brood about while being young and financially supported by my parents.

> These all are valid, noble points I also used to brood about while being young and financially supported by my parents. Ah, the proverbial silver spoon. Sadly, I never had that luxury. If you look through my comments, you'll notice I'm more at the get-off-my-lawn point. Also, what happened? Real world wear you down and turn you cynical? It is possible to be hopeful and cynical at the same time. This tech is somethi…

I wish I could share your optimism, but no recent event in the world affairs can help with that for me.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#874

Post by felipeerias »

mooreat wrote: post #164

I think one interesting thing to point out is that the proof (disproof) was done by finding a counterexample of Erdős' original conjecture. I agree with one of the mathematician's responses in the linked PDF that this is somewhat less interesting than proving the actual conjecture was true. In my eyes proving the conjecture true requires a bit more theory crafting. You have to explain why the conjecture is correct by…

One of the mathematicians in the video describes the process as:

> the AI has been able to explore all these possibilities much more comprehensibly, and doing that it found a path, it found a way to the solution.

Finding a counterexample of a mathematical conjecture strikes me as not that different from finding a vulnerability in a complex codebase.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#875

Post by fontain »

0xDEAFBEAD wrote: post #818
lesostep wrote: post #784

I am cautious about AI "discoveries" after Mythos paper. What was the process of a writing a paper? Was the question asked by a mathematician? Was the paper right from a get-go or was there someone who pointed out mistakes? How much attempts were made before solution was found? I will eat my words if an AI oneshotted that one without any external help, but for know I am left wandering whether it's a new way to attrib…

>I am cautious about AI "discoveries" after Mythos paper. Can you be more specific? I'm still under the impression that Mythos was a huge deal: https://xcancel.com/hlntnr/status/2052479493801975987

There is little evidence that Mythos is any better at finding bugs than any other system. Mythos appears to be impactful because people are, for the first time, using lots of resources (for free from Anthropic) to try and find security issues. The actual bugs found are mostly inconsequential, any chart showing a giant leap in fixes that doesn’t consider whether they were even using any tooling before and whether these are serious issues is junk. If you read the partner’s summaries of Mythos so far, it is a damp squib. Maybe that’ll change but at least for now there is no evidence Mythos is anything but marketing hype.

https://www.aisi.gov.uk/blog/our-evaluation-of-claude-mythos...

https://daniel.haxx.se/blog/2026/05/11/mythos-finds-a-curl-v...

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#876

Post by bigzyg33k »

gilgoomesh wrote: post #689
devttyeu wrote: post #228

Earlier quoted context omitted.

That's here for anyone wondering - https://cdn.openai.com/pdf/1625eff6-5ac1-40d8-b1db-5d5cf925d...

I'm disappointed only that the chain of thought needed to be rewritten. Need to train these LLMs to natively communicate in LaTeX research paper format.

I believe they rewrite the chain of thought to protect their IP, i.e. the chain of thought reveals information about how the model works in a manner that may aid replication

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#877

Post by Valakas_ »

raincole wrote: post #280

I like how everyone laughed when OpenAI said their models will have "PhD-Level Intelligence" and now the goalpost has been moved to if AI can create new math (i.e., not PhD-Level, but Leibniz/Euler/Galois level.)

And the goalposts will keep getting moved all the way to the singularity. And then those people will/would say "Oops. I was wrong."

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#878

Post by recitedropper »

JacobAsmuth wrote: post #531
recitedropper wrote: post #244

This is impressive, no question. Without knowing all this model has been trained on though, it is pretty hard to ascertain the extent to which it arrived to this "on its own". The entire AI industry has been (not so secretly) paying a lot of experts in many fields to generate large amounts of novel training data. Novel training data that isn't found anywhere else--they hoard it--and which could actually contain origi…

Exactly. Maybe OpenAI paid mathematicians to keep this discovery quiet, then added their proof to the training data, then manipulated a second team into prompting for this question such that the model could regurgitate the solution. This would plausibly explain why the model seems so capable at doing things like refuting fundamental theorems of mathematics while in things like competitive programming, biology, and ph…

Thank you for engaging with my comment in a kind and authentic way.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#879

Post by criddell »

suncemoje wrote: post #749
biztos wrote: post #731

Earlier quoted context omitted.

I'm no mathematician but it seems like if this happens, we get to a quite intriguing place as a species. Say we achieve interstellar travel, but nobody actually knows how it works. Or we cure cancer, but the "cure" requires a microrobotic implant, and it runs as a blackbox AI, and only the other AIs can make one, and there's no guarantee they will know how to make one tomorrow. Or we solve global warming but it requi…

I think anything is and will be explainable. Like in the OpenAI proof, I’m sure they were able to understand the solution 100% and could even drill down and ask more clarifying questions to the model. After all, the point of science is so that knowledge can be made logically transparent. If something can’t be explained, it isn’t really understood yet — and the same applies to model outputs. The only question is how m…

The explanation isn't the problem, it's the comprehension.

Your dog will never understand calculus or why Fourier transforms are interesting. There's almost certainly topics that are beyond human comprehension that an advanced artificial or alien intelligence can easily handle.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#880

Post by recitedropper »

muhneesh wrote: post #654
recitedropper wrote: post #244

This is impressive, no question. Without knowing all this model has been trained on though, it is pretty hard to ascertain the extent to which it arrived to this "on its own". The entire AI industry has been (not so secretly) paying a lot of experts in many fields to generate large amounts of novel training data. Novel training data that isn't found anywhere else--they hoard it--and which could actually contain origi…

This type of discourse is just inane and more reflective of the author's sensibilities than anything it claims. Congrats to the OpenAI team for one of the most significant breakthrough discoveries in AI history.

It is interesting to me how controversial this post is. It has the highest upvotes, and most disagreeing comments, of anything I've typed up on HN.

I'll gladly admit I think what these companies are doing is unethical, and I'm sure that biases my thinking toward skepticism.

That said, there remains way too much that is hidden to be able to effectively evaluate what is going on. You have the perfect storm:

  - AI companies do not share their custom internal harnesses.
  - AI companies do not share their custom internal training data. 
  - AI companies do not share how much compute they allocate to trying to solve problems of this nature. 
  - AI companies are primarily marketing their models to investors as human-replacing rather than human-augmenting. 
  - AI companies are under enormous financial pressure to make their business work.
The last two points incentivize them to find these types of "first proof" successes as aggressively as they can, and I'm sure they've thrown the whole book at it.

Is it likely that they literally had a mathematician discover this, put it into the training data, and then prompted it out? Of course not.

But it would make a world of difference--in evaluating the impressiveness of this discovery and LLM capabilities in general--if we were to know the extent to which the training data crosses over this problem, the harness with which this was ran, and how much compute was spent.

Until they bring more transparency to the whole process--something which some of the mathematicians commenting on this even asked for--I will personally take discoveries of this nature with a good dose of salt.

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