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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

#181

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

> Humans are poorly optimized for almost anything, and built on a substrate that's barely hanging together

Goodness gracious!

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

#182

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.

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.

I disagree. Even frontier models still achieve way worse results than the human baseline in VendingBench. As long as models can't manage optimally something as simple as a vending machine, they have no hope of managing a McDonalds.

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

#183

Ask an LLM to invent a new word and post it here. You will see that it simply combines words already in the training data.

Funny that the replies are dead. It's true that generally we shouldn't have AI output on HN but this case is an exception as we are explicitly asking for it, so it's interesting that people still flag the replies.

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

#184

Ask an LLM to invent a new word and post it here. You will see that it simply combines words already in the training data.

Mathematics can be mostly boiled down to a few sentences with very lengthy possible combinations, so yeah that is not a problem

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

#185
post #105

Earlier quoted context omitted.

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 exper…

You're proving the GP's argument - LLMs aren't creative you say as much, it's the driving that is the creative force

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

#186
post #105

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.)

What is creativity if not permutation? A brain has some model of the world and recombines concepts to create new concepts.

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

#187
post #61

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 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…

"new kind of math"

Well I think the point is there is no "new kind of math". There's just types of math we've discovered and what we haven't. No new math is created, just found.

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

#189

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?

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.

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

#190

Earlier quoted context omitted.

> 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.

Good on you for spelling out this reasoning, but it is manifestly unsound. For a wide variety of values of X, people a few years ago had no reason to expect that LLMs would be capable of X. Yet here we are.

In 1989, Gary Kasparov said that it was "ridiculous!" to suggest a computer would ever beat him at chess.

"Never shall I be beaten by a machine!”

In 1997 he lost to Deep Blue.

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