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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

#751

Post by ai_fry_ur_brain »

Im convinved they target these pure math problems because math is very occulted to the masses, and therefor can use math "discoveries" as a way to make an LLM seem more impressive than it is.

Everything is a grift.

What are the odds that if they ran the same prompt from scratch, with the same context and instructions that it would arrive at the same answer? Unlikely. I think its more likely that this is a 1:500000 chance and OpenAI can afford to brute force this result and justify the expense for marketing.

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

#752

Post by SyzygyRhythm »

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…

That's already how civilization works. There's no one person that knows everything about (say) modern food production, from top to bottom. If it ever stopped working (because too much knowledge was lost somehow), most people would die. And yet the system seems fairly resilient. Mostly, only local knowledge ever seems to be necessary to keep the whole thing running. Super-intelligence (or even just super-normal-intelligence) might expand the scope of what constitutes local knowledge but it will still run into limits somewhere.

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

#753

Post by famouswaffles »

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…

>It's clearly not yet a tool that can deliver new math at a scale.

What is at scale here exactly ? This is the most impressive so far, but it is one of several such advances in the last few months, all of which were with publicly accessible models.

https://news.ycombinator.com/item?id=48213189

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

#754

Post by worldsayshi »

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…

Why can't we (or AI) invent ways to explain information that makes it much more digestible? And the solutions simpler?

Why is it necessary to continue to increase complexity when we get better intelligence? Can't we find more simple solutions? Or at least more explainable.

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

#755

Post by worldsayshi »

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…

And more intelligence should give an opportunity to increase explain-ability rather than just complexity. It can potentially explain the proof at the level of the listener. Make visualizations. Etc.

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

#756

Post by darkwater »

tsunamifury wrote: post #748
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…

“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.

> as well as microprocessors

I mean, microprocessors have been on the "impossible to bootstrap from scratch in a short period of time" for 20 years already.

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

#757

Post by xamuel »

teiferer wrote: post #744
xamuel wrote: post #568

Earlier quoted context omitted.

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?

Before birth. ...Hey, don't point that pitchfork at me, point it at Socrates. In his defense, that kind of does describe when LLMs acquired their knowledge (if we consider "birth" to be the moment when the already-trained weights are sent to the GPU) https://en.wikipedia.org/wiki/Anamnesis_(philosophy)

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

#758

Post by alt227 »

kamaal wrote: post #728
bananaflag wrote: post #709

Earlier quoted context omitted.

As a mathematician, new, conceptual math is when I'll become interested in reading LLM output. I appreciate very much the work done so far, but this sort of asymptotic/quantitative result didn't interest me much even when it was done by humans. (This is not snobbery, just a personal preference.)

Well that's coming. As a matter of fact more logic and structure to your work, the more easy it is for AI to conquer it. Due to this programming was the first thing that got solved, but pure sciences are next. If what you do, and how you do can be written down on a piece of paper, then AI can do it. I do believe programming getting solved will be double assault on these fields. >>This is not snobbery This is good for…

> Well that's coming.

So is AGI, but we may be hundreds of years off still.

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

#759

Post by amunozo »

ori_b wrote: post #373
vatsachak wrote: post #212

Earlier quoted context omitted.

Math is a very specialized subset of art and science more amenable to automation.

The first thing we automated passably was art, even before programming. Were you not paying attention? This future still sucks. The tech industry is making the world a worse place.

Calling AI-generated images art is a stretch. Same thing with creative writing. It can make some low-cost illustrations and writing, but it is very far from decent art. Compare those results with their amazing coding or math capabilities.

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

#760

Post by mmnfrdmcx »

diordiderot wrote: post #732
virgildotcodes wrote: post #698

Earlier quoted context omitted.

I’m not in academia myself, and I think AI solving all our problems ASAP is ideal, even if it means no humans get attribution. What I’m saying is that the ultimate goal of those in power are not these sorts of altruistic or even scientific pursuits, and that the massive labor disruption and hyper concentration of power in the hands of those who are proving time and again that advancement of science and benefiting the…

Oh good. But I think you're over estimating the 'concentration of power', and under estimating 'benefiting the whole of humanity' Most homeless people have smartphones, and consistent access to food and clean water. Your average 'poor person' in America has HVAC. An unimaginable luxury in the EU

Unimaginable luxury, what are you in about. Have you ever even been outside of US?
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