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An OpenAI model has disproved a central conjecture in discrete geometry

openai.com

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

#131

Post by lajamerr »

dvt wrote: post #105
Tenobrus wrote: post #96

Earlier quoted context omitted.

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

Because by definition LLMs are permutation machines, not creativity machines. (My premise, which you may disagree with, is that creativity/imagination/artistry is not merely permutation.)

LLMs by themselves are not able to but you are missing a piece here.

LLMs are prompted by humans and the right query may make it think/behave in a way to create a novel solution.

Then there's a third factor now with Agentic AI system loops with LLMs. Where it can research, try, experiment in its own loop that's tied to the real world for feedback.

Agentic + LLM + Initial Human Prompter by definition can have it experiment outside of its domain of expertise.

So that's extending the "LLM can't create novel ideas" but I don't think anyone can disagree the three elements above are enough ingredients for an AI to come up with novel ideas.

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

#132

Post by blueone »

Tenobrus wrote: post #96
dvt wrote: post #61

Earlier quoted context omitted.

> I think that idea is deeply fascinating, AND have no problem that we still credit mathematicians with discoveries. Most discoveries are indeed implied from axioms, but every now and then, new mathematics is (for lack of a better word) "created"—and you have people like Descartes, Newton, Leibniz, Gauss, Euler, Ramanujan, Galois, etc. that treat math more like an art than a science. For example, many belive that to…

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

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

because I have no basis for assuming an LLM is fundamentally capable of doing this.

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

#135

Post by [deleted] »

edbaskerville wrote: post #92
Lerc wrote: post #46

Earlier quoted context omitted.

I disagree. It will be able to perform work deserving if a fields medal before it is capable of running a McDonalds. I think it will be running a McDonalds well before either of those things happen, and a fields medal long after both have happened.

I just visited a McDonald's for the first time in a while. The self-order kiosk UI is quite bad. I think this is evidence in favor of the idea that an incompetent AI will soon be incompetently running a McDonald's.

[deleted]

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

#136

Post by kmeisthax »

comboy wrote: post #24
phkahler wrote: post #21

I would have thought a triangular grid works better than a grid of squares. You get ~3n links vs ~2n for the square grid. Curious what the AI came up with.

Yes, not providing visualization of the solution seems criminal.

Knowing OpenAI, the solution's probably being withheld as a trade secret, lest it fall victim to distillation attacks (i.e. exactly the same shit they did to the open Internet).

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

#139

Post by lukol »

dvt wrote: post #105
Tenobrus wrote: post #96

Earlier quoted context omitted.

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

Because by definition LLMs are permutation machines, not creativity machines. (My premise, which you may disagree with, is that creativity/imagination/artistry is not merely permutation.)

This "new math" might be a recombination of things that we already know - or an obvious pattern that emerges if you take a look at things from a far enough distance - or something that can be brute-forced into existence. All things LLMs are perfectly capable of.

In the end, creativity has always been a combination of chance and the application of known patterns in new contexts.

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

#140

Post by Silamoth »

edbaskerville wrote: post #92
Lerc wrote: post #46

Earlier quoted context omitted.

I disagree. It will be able to perform work deserving if a fields medal before it is capable of running a McDonalds. I think it will be running a McDonalds well before either of those things happen, and a fields medal long after both have happened.

I just visited a McDonald's for the first time in a while. The self-order kiosk UI is quite bad. I think this is evidence in favor of the idea that an incompetent AI will soon be incompetently running a McDonald's.

Out of curiosity, what issue did you have with the McDonald’s self-order kiosk? I actually think McDonald’s has the best kiosk I’ve ever encountered. The little animation that plays when you add an item to your cart is a little annoying (but I think they’ve sped that up). But otherwise, it’s everything I’d want. It shows you all the items, tells you every ingredient, and lets you add or remove ingredients. I have a better experience ordering through the kiosk than I do talking to a cashier.
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