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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

#781

Post by fauigerzigerk »

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…

I think explanation is itself a rather complex concept. At what point do we consider something as explained? Usually it has to do with identifying some causal factors and their relationships so that we can intervene and explore counterfactuals. But in many cases we are forced to act on the basis of incomplete explanations (e.g. in medicine).

I think there will be regulation that requires some users of AI to provide an explanation upon request. For instance, banks could be required to "explain" why you didn't get that loan. What if the decision is based on a credit score that includes some AI prediction that ultimately relies on the entire training corpus?

The bank can give you a list of factors that play into the decision but they may not be able to explain deterministically why a very similar customer did get that loan. At that point I think we're going to resort to statistics that prove a lack of bias against certain protected characteristics, but that's not really an explanation, is it?

I think we will never get useful and complete explanations for everything that AI does. Society will just accept some explanation-like thing or proxy and move on.

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

#782

Post by gizmondo »

voxl wrote: post #688
dellamonica wrote: post #534

Earlier quoted context omitted.

It is extremely well known. Lots of people have tried to solve it and it stood basically stuck for 80 years. It is getting harder every day to downplay these models. Given its elementary nature (very easy to state), you can bet that a lot of very bright people have worked on it (I know of one MIT graduate who specialized in Geometry had a lot of interest in it).

I don't believe the result at all. I think it contains faulty logic. Perhaps the mathematicians involved can read the tea leaves and decide something interesting happened, but all this AI psychosis bullshit still refuses to accept that AIs do not, and cannot, have a mental model of the world. Moreover, model output is incredibly good at looking credible but being wrong. It has NEVER produced something correct for me…

At this point the term "AI psychosis" is the more apt label for AI skeptics. Here we have literal Fields medalists vouching for correctness and relative importance of the result, but who cares, "I don't believe the result at all". Just pure denial of reality.

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

#783

Post by wartywhoa23 »

ocimbote wrote: post #778
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. "

That is fascinating how the more knowledge and reasoning we can get our hands on and actually produce, the higher the risk of us, as a species, to become actually much dumber. It's hard to describe the feeling of seeing intelligence being delegated increasingly to AI. If that's not a pivotal moment, a revolution, I don't know what is.

If you're not familiar with it, I recommend looking up the Taoist concept of overdevelopment. Sums it all up perfectly.

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

#784

Post by lesostep »

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 attribute discoveries to companies instead of people who put the work in

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

#785

Post by turzmo »

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.)

Not denying that these advances are impressive, but it is important to consider that this is a cherry-picked result. This doesn’t mean that AI can now be expected to do problems of similar or lower difficulty, but that it happened to work well on one problem. What you won’t see is how many others they had to try to get this result.

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

#786

Post by latexr »

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…

> Or we solve global warming but it requires giant cooling machines running 24/7

That’s not “solving it”, that’s putting a bandaid on it. Solving it would mean correcting the underlying issue to the point it’s no longer a problem which requires maintenance.

Managing symptoms is not curing the disease.

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

#787

Post by dwroberts »

OkWing99 wrote: post #371
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

Says in the papers. "...which was first mathematically generated in one shot by an internal model at OpenAI, and then expositionally refined through human interactions with Codex." Doesn't really matter the prep-work, what they say is it's a one-shot result, achieved by AI. The blog doesn't claim it was done by a currently public Model.

The model doing it one shot does not mean they only attempted it once though. They could have tried and retried a ‘one-shot’ answer hundreds of times before it produced a workable result

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

#788

Post by latexr »

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…

> I’m sure they were able to understand the solution 100% and could even drill down and ask more clarifying questions to the model.

If they understood it 100%, what clarification is needed?

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

#789

Post by aaron695 »

cpard wrote: post #224

The proof brings unexpected, sophisticated ideas from algebraic number theory to bear on an elementary geometric question. The more I read about these achievements the more I get a feeling that a lot of the power of these models comes from having prior knowledge on every possible field and having zero problems transferring to new domains. To me the potential beauty of this is that these tools might help us break thro…

[dead]

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

#790

Post by lefra »

SyzygyRhythm wrote: post #752
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…

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-intell…

> There's no one person that knows everything about (say) modern food production

True, but it is possible to assemble a team of people that does, with backup for each person. There's also teachers and written knowledge to educate new team members. That's what makes it resilient.

I think that's a very different situation from what's decribed.

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