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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

#81
post #66

Can someone explain to me what is their "prompting-scaffolding" to make it work ?

"This is a general-purpose LLM. It wasn’t targeted at this problem or even at mathematics. Also, it’s not a scaffold. We have not pushed this model to the limit on open problems. Our focus is to get it out quickly so that everyone can use it for themselves." - Noam Brown (OpenAI reasoning researcher) on X

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

#82

Earlier quoted context omitted.

Managing a McDonalds is a question of integration and modalities at this point. I don't think anyone still doubts that these models lack the reasoning capability or world knowledge needed for the job. So it's less of a fundamental technical problem and more of a process engineering issue.

The capability they lack is being able to be sued.

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 I'm not sure the problem with qualified immunity making police unaccountable applies.

There already exist a lot of similar conventions in corporate law. Generally, a main advantage of incorporation is protecting the people making the decisions from personal lawsuits.

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

#83
post #22

While the result is impressive, this blog post is extremely disappointing. - It does not show an example of the new best solution, nor explain why they couldn't show an example (e.g. if the proof was not constructive) - It does not even explain the previous best solution. The diagram of the rescaled unit grid doesn't indicate what the "points" are beyond the normal non-scaled unit grid. I have no idea what to take aw…

apparently the proof is not constructive in the sense of not giving an easy to compute recipe for generating a set of points that you can plot on a 2d plane

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

#84

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…

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

#85

Earlier quoted context omitted.

I absolutely believe that AI will supercharge science. I do not believe it will replace humans.

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

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

#86
post #30

Is there a reason why we only hear of Erdos problems being solved? I would imagine there are a myriad of other unsolved problems in math, but every single ChatGPT "breakthrough in math" I come across on r/singularity and r/accelerate are Erdos problems.

It's a large set of problems that are both interesting and difficult, but not seen as foundational enough or important enough that they have already had sustained attention on them by mathematicians for decades or centuries, and so they might actually be solvable by an LLM.

Also fewer prerequisites to understand the statement than the average research problem.

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

#87

I dunno, I'm skeptical without proof. I've had the MAX+ plan for a while and I'm sorry, the quality between GPT vs Claude is night and day difference. Claude understands. GPT stumbles over every request I give it.

Weird thing to say about a report which literally has the attached mathematical proof.

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

#88

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.

The proof is not written in Lean, though. It’s written in English and requires validation by human experts to confirm that it’s not gibberish.

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

#90
post #57

Earlier quoted context omitted.

I absolutely believe that AI will supercharge science. I do not believe it will replace humans.

replace, no. obsolete, yes

lol

(That's the first time I used that expression on HN.)

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