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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

#261

Post by KalMann »

vatsachak wrote: post #11

As I have stated before, AI will win a fields medal before it can manage a McDonald's A difficult part was constructing a chess board on which to play math (Lean). Now it's just pattern recognition and computation. LLMs are just the beginning, we'll see more specialized math AI resembling StockFish soon.

I think your analogy is good but I don't believe modern LLMs use Lean or any lean-like structure in their proofs. At least recent open source ones like DeepSeek can do advanced math without it (maybe the most cutting edge ones are doing it I can't say).

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

#262

Post by paulddraper »

gpugreg wrote: post #195
paulddraper wrote: post #150

Earlier quoted context omitted.

"LLMs just interpolate their training data" Cracks me up. What exactly do we think that human brains do?

Maybe the human brain also does other things besides interpolation?

There is pre-training, and then empirical observations.

Yes?

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

#263

Post by dist-epoch »

truncate wrote: post #124
Tenobrus wrote: post #96

Earlier quoted context omitted.

what basis do you have for assuming an LLM is fundamentally incapable of doing this?

What's your basis for assuming LLM is capable of doing this? I honestly don't know personally either way. Based on my limited understanding of how LLMs work, I don't see them be making the next great song or next great book and based on that reasoning I'm betting that it probably wont be able to do whatever next "Descartes, Newton, Leibnitz, Gauss, Euler, Ramanujan, Galois" are going to do. Of course AI as a wider fi…

LLMs are already making the next great songs. Just check out the Billboard charts.

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

#264

Post by trostaft »

ComplexSystems wrote: post #258
trostaft wrote: post #114

Earlier quoted context omitted.

> A difficult part was constructing a chess board on which to play math (Lean). Now it's just pattern recognition and computation. However, this was not verified in Lean. This was purely plain language in and out. I think, in many ways, this is a quite exciting demonstration of exactly the opposite of the point you're making. Verification comes in when you want to offload checking proofs to computers as well. As it s…

That may be true for now, but it seems clear enough that letting the model use Lean in its internal reasoning process would be a great idea

That I'd agree with! I really need to get around to learning Lean myself. It might be interesting to try and formalize some missing theoretical pieces from my field (or likely start smaller).

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

#265

Post by BoredPositron »

m-hodges wrote: post #40

To the “LLMs just interpolate their training data” crowd: Ayer, and in a different way early Wittgenstein, held that mathematical truths don’t report new facts about the world. Proofs unfold what is already implicit in axioms, definitions, symbols, and rules. I think that idea is deeply fascinating, AND have no problem that we still credit mathematicians with discoveries. So either “recombining existing material” isn…

Post hoc ergo propter hoc

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

#266

Post by cyanydeez »

m-hodges wrote: post #40

To the “LLMs just interpolate their training data” crowd: Ayer, and in a different way early Wittgenstein, held that mathematical truths don’t report new facts about the world. Proofs unfold what is already implicit in axioms, definitions, symbols, and rules. I think that idea is deeply fascinating, AND have no problem that we still credit mathematicians with discoveries. So either “recombining existing material” isn…

I think someone should be talking to Godel.

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

#267

Post by dyauspitr »

vatsachak wrote: post #218
dyauspitr wrote: post #211

Earlier quoted context omitted.

Nonsense. Have you been watching the figure live stream? Or the Unitree video from yesterday with real time novel action generation? We’re less than a year away. If you can cook a burger, assemble a sandwich and clean up surfaces you’re all of the way there.

Fair. Let's see in a year. I'm willing to bet that nothing happens.

Yeah, it’s gonna be an exciting year. I still think you’ll need one human in there, but that’s about it.

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

#268

Post by ActorNightly »

paulddraper wrote: post #150
m-hodges wrote: post #40

To the “LLMs just interpolate their training data” crowd: Ayer, and in a different way early Wittgenstein, held that mathematical truths don’t report new facts about the world. Proofs unfold what is already implicit in axioms, definitions, symbols, and rules. I think that idea is deeply fascinating, AND have no problem that we still credit mathematicians with discoveries. So either “recombining existing material” isn…

"LLMs just interpolate their training data" Cracks me up. What exactly do we think that human brains do?

I love this comment because it so clearly highlights the difference between intelligence and reasoning.

A lot of people across all fields seem to operate in a mode of information lookup as intelligence. They have the memory of solving particular problems, and when faced with a new problem, they basically do a "nearest search" in their brain to find the most similar problem, and apply the same principles to it.

While that works for a large number of tasks this intelligence is not the same as reasoning.

Reasoning is the ability to discover new information that you haven't seen before (i.e growing a new branch on the knowledge tree instead of interpolating).

Think of it like filling a space on the floor of arbitrary shape with smaller arbitrary shapes, trying to fill as much space as possible.

With interpolation, your smaller shapes are medium size, each with a non rectangular shape. You may have a large library of them, but in the end, there are just certain floor spaces that you won't be able to fill fully.

Reasoning on the flip side is having access to very fine shape, and knowing the procedure of how to stack shapes depending on what shapes are next to it and whether you are on a boundary of the floor space or not. Using these rules, you can fill pretty much any floor space fully.

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

#269

Post by _heimdall »

As this becomes more common it makes me wonder where the LLM ends and the harness begins.

The underlying model may still effectively be a stochastic parrot, but used properly that can do impressive things and the various harnesses have been getting better and better at automating the use of said parrot.

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

#270

Post by KalMann »

tracerbulletx wrote: post #44
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?

Hasn't AlphaFold been used to make real discoveries for a few years now?

I think he's talking about reasoning models.
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