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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

#211

Post by dyauspitr »

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.

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.

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

#212

Post by vatsachak »

ori_b wrote: post #205
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.

We're automating art and science so that we can flip burgers. This future sucks.

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

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

#213

Post by hammock »

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…

Recombining existing material is exactly right, and in this case LLMs were uniquely positioned to make the connection quicker than any group of humans.

The proof relies on extremely deep algebraic number theory machinery applied to a combinatorial geometry problem.

Two humans expert enough in either of those totally separate domains would have to spend a LONG time teaching each other what they know before they would be able to come together on this solution.

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

#214

Post by block_dagger »

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…

This is the second reference to Wittgenstein I’ve seen today in totally different contexts. Reminded me how much I vibe with his Tractatus.

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

#216

Post by baq »

omnimus wrote: post #189
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?

That has been the question since the beginning of humans. Maybe computers can help understand better because by now it's pretty clear brains aren't just LLMs.

The optimists believe brains are very special and we’re far from replicating what they do in silicon.

The pessimists just see a 20W meat computer.

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

#217

Post by estetlinus »

zozbot234 wrote: post #38

The summarized chain of thought for this task (linked in the blogpost) is 125 pages. That's an insane scale of reasoning, quite akin to what Anthropic has been teasing with Mythos.

Today I generated the equivalent of two LOTR books just to fix three missing rows in my SQL models (and open a PR), so +1

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

#218

Post by vatsachak »

dyauspitr wrote: post #211
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.

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.

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

#219

Post by TheOtherHobbes »

stonogo wrote: post #85
unsupp0rted wrote: post #70

Earlier quoted context omitted.

I absolutely believe that AI will supercharge science and replace humans. Why shouldn't it? Humans are poorly optimized for almost anything, and built on a substrate that's barely hanging together

Not like large language models, which only required tens of megawatts of power and use highly efficient monte carlo methods, eh

Individual humans are processing nodes on human culture as a whole, which runs on rather more than tens of megawatts.

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

#220

Post by pear01 »

logicchains wrote: post #159
pear01 wrote: post #82

Earlier quoted context omitted.

Police officers are human. In the United States in the vast majority of cases you can't sue the police, only the community responsible for them. https://en.wikipedia.org/wiki/Qualified_immunity Assuming you can still sue McDonalds I am not sure if this is a problem in the robotic llm case. I'm also trying to imagine a case where you would want to sue the llm and not the company. Given robots/llm don't have free will…

>Police officers are human. In the United States in the vast majority of cases you can't sue the police, only the community responsible for them. Police are a monopoly; nobody has a choice about which police company to use. McDonalds are not a monopoly, and many customers would prefer to eat at competitors run by entities that could be sued or jailed if they did anything particularly egregious.

You are missing the point. The point is you can still sue the McDonalds. With the police there is a human intuition to also want to sue the officer, given the officer is a human being who has free will and thus made a choice to violate your rights.

The same intuition applies if you walk into McDonald's and a person there mistreats you. You want that person held responsible.

But the LLM is not a person. What is there to even sue? It just seems like it would simply pass through to the corporate entity without the same tension of feeling like we let a human get away with something. Because there is no human, just a corporation and the robot servicing the place.

Put another way - if the LLM is not a person, what is the advantage of a personal lawsuit?

Just sue the McDonalds. Even in a case where the LLM is extremely misaligned and acts in a way where you might normally personally sue the McDonald's employee, I'm just not sure the human intuition about "holding someone accountable" would have its normal force because again - the LLM is not a person.

So given we already have the notions of incorporation and indemnification it doesn't make sense to say what is precluding LLMs from running McDonald's is they can't be sued. If McDonald's can still be sued, then not only is there no problem, there is very likely not even a change in the status quo.

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