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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

#381

See the longstanding debate on whether new math is "invented" or "discovered". Most mathematicians I knew thought it's discovered.

This is like saying a sculpture always existed, the sculptor just had to remove the superfluous material. Or like a musical octave has only 12 semitones, so all music is just a selection from a finite set that already existed. Sure the insane computation we're throwing at this changes our perspective, but still there is an important distinction.

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

#382

Earlier quoted context omitted.

What is the difference between what LLM's do and "true" understanding? I feel like people grasping straws on the shrinking limitations of AI systems are just copying the "god of the gaps" fallacy

> What is the difference between what LLM's do and "true" understanding? The thing where you can understand the meaning of this sentence without first compiling a statistical representation of a 10 trillion line corpus of training data. Unless you're an NPC of course.

I mean brains get a lot of training data too in order to understand language. I don't think you provided a relevant difference.

Or rather, maybe I don't understand what you mean :)

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

#383

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 an excellent point, new ground isn't necessarily novel, it's a rearrangement of existing pieces

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

#384

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?

We don't know what human brains do.

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

#386
post #67

Earlier quoted context omitted.

> manage a McDonald's Dystopia vibes from the fictional "Manna" management system [0] used at a hamburger franchise, which involved a lot of "reverse centaur" automation. > At any given moment Manna had a list of things that it needed to do. There were orders coming in from the cash registers, so Manna directed employees to prepare those meals. There were also toilets to be scrubbed on a regular basis, floors to mop,…

Casual reminder that the author's proposed solution to the labor-automation dystopia is to invent a second identity-verification dystopia. Also casual reminder that the author wanted the death penalty to anyone over the age of 65.

I was curious about this book but now you've absolutely sold me on it, sounds like I'm in for a ride!

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

#389

Earlier quoted context omitted.

Why would it excite you, rather than terrifying you? The better LLMs get at math, the closer the expertise you spent your whole life building is to being worthless. Along with all the rest of what humans find meaningful and fulfilling.

What's happening is the verbal/linguistic equivalent of the invention of calculus. No intellectual field will ever be the same again. Who wouldn't find that exciting, and want to experience it?

People who enjoy thinking. Ya know, the "intellectual" part.

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

#390
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.

The models can't actually so good work on practical problems so openai tasks them on stuff nobody cares about
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