An OpenAI model has disproved a central conjecture in discrete geometry • Hacker News Board

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

#811

Post by andy12_ » Thu, May 21, 2026, 9:00 AM UTC

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…

> Was the question asked by a mathematician?

As per the report, the prompt used to solve the problem is AI-written and the solution was initially graded by an AI grading pipeline. They don't say this explicitly, but it seems like OpenAI has an automatic pipeline where they prompt models for solutions to famous math problems (which wouldn't be unexpected given how flashy a solution to a famous math problem looks)

> Was the paper right from a get-go or was there someone who pointed out mistakes?

Also as per the report, the output of the model isn't really a "paper"; it's a very terse 2 page solution which is apparently correct. The paper was later written based on this solution to make it more presentable.

> How much attempts were made before solution was found?

Given that this appears to be from an automated pipeline, I would say that it had many attempts. But either way, the blogpost says that with enough test-time compute, the model finds this same solution 50% of the time.

[1] https://cdn.openai.com/pdf/74c24085-19b0-4534-9c90-465b8e29a...

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

#812

Post by wartywhoa23 » Thu, May 21, 2026, 9:02 AM UTC

ffaccount2 wrote: post #803

wartywhoa23 wrote: post #766

Earlier quoted context omitted.

Noble " save the humankind using the tech nobody fucking understands " textbook goals like curing cancer, solving global warming and achieving interstellar travel would always turn up when owners of trillions of dollars place orders on positive AI narratives, but in reality all of that will wither down to " It's what plants crave! It's got electrolytes. "

>ve AI narratives, but in reality all of that WILL wither down to... Looks like you're pretty sure of that. Every time I see argument like this delivered with confidence I wonder how is it different from, say, digital calculators. Or better yet, books - Greek philosophers moaned that young people will stop understanding anything and just check books when they want to know anything.

> Looks like you're pretty sure of that.

Knowing the history of the humankind is what makes me pretty sure of that.

The extent of misery and destruction is directly proportional to the level of technological advancements, and I don't like the idea of sacrificing millions of lives in the name of the figurative HVAC, smartphone and other benefits of civilization. Or billions in the name of whatever benefits the next VC money stake should bring.

> I wonder how is it different from, say, digital calculators.

Did a single digital calculator ever stop any war, or liquidate a psychopath who orders people to go kill and die?

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

#813

Post by Quentak » Thu, May 21, 2026, 9:05 AM UTC

I'd like to know how many tokens in total went into solving this problem. Have they talked about this? It matters whether they got this result in 10 million tokens or 10 billion. Whether it's closer to 1 human working on this for 1 year or 1000 humans for 1 year. The news feels different when the probability of one AI run solving this is 1 in a thousand vs 1 a million. Approximately I'm asking about the amount of money it cost to solve it, which has to include the failed parallel runs.

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

#814

Post by juvoly » Thu, May 21, 2026, 9:06 AM UTC

biztos wrote: post #731

teiferer wrote: post #727

Earlier quoted context omitted.

> Every day, it grows harder and harder to contain a mental map of recent relevant progress by simple virtue of the amount being produced. And by opening the door to LLM-generated results, you'll see greater and greater amounts without any hope of ever navigating this field again without machine help. It's a little like a software project which more and more gets extended by a AI agents with less and less review by h…

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…

Like the discovery of penicillin by Alexander Fleming in 1928?

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

#815

Post by ben_w » Thu, May 21, 2026, 9:07 AM UTC

pishpash wrote: post #804

loandbehold wrote: post #796

Earlier quoted context omitted.

This is pretty much what underlies AI doomer argument of people like EY. Humans will gradually hand over civilization to black box AI they can't understand. As AI becomes more complex and powerful it will be harder and harder to control.

That assumes everyone will do so. Some people won't, and it's not clear you need a large number of such, a priesthood if you like, to survive as a species without AI.

There's a lot of un-contacted (or voluntarily self-isolating, it's hard to tell which) tribes around the world; things go poorly for them when businesses with power tools decide they want the resources of the land they live in, even when they're theoretically protected by law of the nation whose borders both the tribes and the businesses both find themselves within.

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

#816

Post by ptrl600 » Thu, May 21, 2026, 9:09 AM UTC

staticman2 wrote: post #603

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.)

What's laughable is an OpenAI employee invented the term "PHD level intelligence" and you think that " PHD Level intelligence" is a real term that describes a real thing and you are repeating it here.

It's clearly smarter than any PhD and dumber than any ant.

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

#817

Post by cindyllm » Thu, May 21, 2026, 9:09 AM UTC

wartywhoa23 wrote: post #792

piloto_ciego wrote: post #581

Earlier quoted context omitted.

So, I've seen this mindset a lot lately... The answer is that we simply need to decouple the "right to exist" from "worth." You should have the right to exist and explore the world simply because you're human, not because you can use your skills to provide some sort of transactional value to someone else. Deprogramming so many people is going to be hard...

All sane and noble in theory, but in practice, how do you see that happening? Let's start with the first practical step: how do you dethrone the psychopaths in charge of the world who own about everything on Earth and have all the world's lethal force in their pockets?

[dead]

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

#818

Post by 0xDEAFBEAD » Thu, May 21, 2026, 9:13 AM UTC

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

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

#819

Post by ApolloRising » Thu, May 21, 2026, 9:14 AM UTC

Quentak wrote: post #813

I'd like to know how many tokens in total went into solving this problem. Have they talked about this? It matters whether they got this result in 10 million tokens or 10 billion. Whether it's closer to 1 human working on this for 1 year or 1000 humans for 1 year. The news feels different when the probability of one AI run solving this is 1 in a thousand vs 1 a million. Approximately I'm asking about the amount of mon…

I would like to know this as well, including how long was it working on this problem?

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

#820

Post by rowanG077 » Thu, May 21, 2026, 9:17 AM UTC

wartywhoa23 wrote: post #812

ffaccount2 wrote: post #803

Earlier quoted context omitted.

>ve AI narratives, but in reality all of that WILL wither down to... Looks like you're pretty sure of that. Every time I see argument like this delivered with confidence I wonder how is it different from, say, digital calculators. Or better yet, books - Greek philosophers moaned that young people will stop understanding anything and just check books when they want to know anything.

> Looks like you're pretty sure of that. Knowing the history of the humankind is what makes me pretty sure of that. The extent of misery and destruction is directly proportional to the level of technological advancements, and I don't like the idea of sacrificing millions of lives in the name of the figurative HVAC, smartphone and other benefits of civilization . Or billions in the name of whatever benefits the next V…

> The extent of misery and destruction is directly proportional to the level of technological advancements.

By statistics of war, poverty rates etc this is trivially false. I think you are really, really underestimating how hard life was pre-industrial revolution.