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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

#741

Post by ai_fry_ur_brain »

lacewing wrote: post #326
dwroberts wrote: post #99

Would be interesting to know what kind of preparatory work actually went into this - how long did it take to construct an input that produced a real result, and how much input did they get from actual mathematicians to guide refining it

Why? It's clearly not yet a tool that can deliver new math at a scale. I say this because otherwise, the headline would be that they proved / disproved a hundred conjectures, not one. This is what happened with Mythos. You want to be the AI company that "solved" math, just like Anthropic got the headlines for "solving" (or breaking?) security. The fact they're announcing a single success story almost certainly means…

Its a marketing stunt thats probably wholey exaggerated or concocted. Not sure why anyone would take these companies at their word, especially Altman.

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

#742

Post by kamaal »

lubujackson wrote: post #60

For anyone using LLMs heavily for coding, this shouldn't be too surprising. It was just a matter of time. Mathematicians make new discoveries by building and applying mathematical tools in new ways. It is tons of iterative work, following hunches and exploring connections. While true that LLMs can't truly "make discoveries" since they have no sense of what that would mean, they can Monte Carlo every mathematical tool…

>>But the result has no meaning without the human intent behind the objective, human understanding to value the new pathway the AI used (more valuable than the result itself, by far) and the mathematical language (built by humans) to explore the concept.

Future of code is pretty much a bunch of guys shepherding a bunch of agents to get them to your goal.

I don't see how math might not go that way as well.

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

#743

Post by melagonster »

zamadatix wrote: post #624
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.)

My only complaint is the claims always start spreading 6-12 months before the delivery. A little patience goes a long way in what's possible with AI and we all just have to wait and see what parts actually grow this next cycle or not. Guessing at it based on trend lines only leads to people getting excited when it matches their particular guess and ignoring it when it doesn't.

They said that their specific version of model had has this ability one year ago.

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

#744

Post by teiferer »

xamuel wrote: post #568
ted_dunning wrote: post #505

Earlier quoted context omitted.

In Erdös idiosyncratic nomenclature, all the best proofs are "in the book" and it was always a joyful thing to not only find a proof, but to find the proof that is in the book. Who cares if it is God's book or the machine's Xeroxed copy?

Long before Erdös, we had Plato and Socrates develop the theory of anamnesis, that there is no such thing as learning, but rather, whatever we supposedly learn, we actually remember (we knew it already and had forgotten it). Presumably this should be understood only of universal facts (like mathematics), not contingent facts (like who was the president of the U.S. in 1950).

Remember from ...when?

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

#745

Post by ai_fry_ur_brain »

karmasimida wrote: post #31
aurareturn wrote: post #2

One thing seems for certain is that OpenAI models hold a distinct lead in academics over Anthropic and Google models. For those in academics, is OpenAI the vendor of choice?

I think the mathematicians on X are all using GPT 5.5 Pro

And they all think its garbage. This is a publicity stunt.

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

#746

Post by fergie »

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…

> 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 original ideas.

Really? Any references to read more?

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

#747

Post by f055 »

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…

So I guess sci-fi movies were right all along. Nobody in Star Wars knows how hyperspace travel works, it just works. The little robots know everything but almost no human bothers to care. People just carry on with their bickering lives while the bots whiz in the background, and these robots are astonished at human inefficiency every single time, but rarely do anything about it. And people are still people.

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

#748

Post by tsunamifury »

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…

“Few-shun drive. Mmmm. Yes.”

https://youtu.be/pfNS2kWf5cY?si=SH6_QC0bCspV-ngz

There are comments that truly reveal a future horrifying and true. Few of them. But I count yours among them.

But I’d argue also that airplanes already achieve this complexity to some degree as well as microprocessors.

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

#749

Post by suncemoje »

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…

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 much effort it takes to surface the explanation.
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