Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

An OpenAI model has disproved a central conjecture in discrete geometry

openai.com

Post reply on HN
Print view View original

161–170 of 1001 posts

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

#161

Post by planetafro »

voooduuuuu wrote: post #121
peterlk wrote: post #120

Earlier quoted context omitted.

Yes they do…? Who cares if they just predict the next token? The outcome is that they can invent new abstractions. You could claim that the invention of this new idea is a combination of an LLM and a harness, but that combination can solve logic puzzles and invent abstractions. If a really large spinning wheel could invent proofs that were previously unsolved, that would be a wildly amazing spinning wheel. I view LLM…

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

Splifket

Definition: That highly specific, short-lived burst of nervous energy that makes you accidentally drop a small object (like a pen, a guitar pick, or a piece of LEGO) immediately after picking it up.

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

#162

Post by jimmaswell »

voooduuuuu wrote: post #121
peterlk wrote: post #120

Earlier quoted context omitted.

Yes they do…? Who cares if they just predict the next token? The outcome is that they can invent new abstractions. You could claim that the invention of this new idea is a combination of an LLM and a harness, but that combination can solve logic puzzles and invent abstractions. If a really large spinning wheel could invent proofs that were previously unsolved, that would be a wildly amazing spinning wheel. I view LLM…

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

Why is everyone who responds to this with a real example immediately flagged/dead?

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

#163

Post by redsocksfan45 »

truncate wrote: post #124
Tenobrus wrote: post #96

Earlier quoted context omitted.

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

What's your basis for assuming LLM is capable of doing this? I honestly don't know personally either way. Based on my limited understanding of how LLMs work, I don't see them be making the next great song or next great book and based on that reasoning I'm betting that it probably wont be able to do whatever next "Descartes, Newton, Leibnitz, Gauss, Euler, Ramanujan, Galois" are going to do. Of course AI as a wider fi…

[dead]

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

#164

Post by mooreat »

I think one interesting thing to point out is that the proof (disproof) was done by finding a counterexample of Erdős' original conjecture.

I agree with one of the mathematician's responses in the linked PDF that this is somewhat less interesting than proving the actual conjecture was true.

In my eyes proving the conjecture true requires a bit more theory crafting. You have to explain why the conjecture is correct by grounding it in a larger theory while with the counterexample the model has to just perform a more advanced form of search to find the correct construction.

Obviously this search is impressive not naive and requires many steps along the way to prove connections to the counterexample, but instead of developing new deep mathematics the model is still just connecting existing ideas.

Not to discount this monumental achievement. I think we're really getting somewhere! To me, and this is just vibes based, I think the models aren't far from being able to theory craft in such a way that they could prove more complicated conjectures that require developing new mathematics. I think that's just a matter of having them able to work on longer and longer time horizons.

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

#165

Post by sillysaurusx »

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…

It’s easy to see that LLMs don’t merely recombine their training data. Claude can program in Arc, a mostly dead language. It can also make use of new language constructs. So either all programming language constructs are merely remixes of existing ideas, or LLMs are capable of working in domains where no training data exists.

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

#166

Post by nomel »

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…

I feel this is the case whenever I "problem solve". I'm not really being creative, I'm pruning a graph of a conceptual space that already exists. The more possibilities I see, the easier it is to run more towards an optimal route between the nodes, but I didn't "create" those nodes or edges, they are just causal inevitabilities.

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

#167

Post by romanhn »

voooduuuuu wrote: post #121
peterlk wrote: post #120

Earlier quoted context omitted.

Yes they do…? Who cares if they just predict the next token? The outcome is that they can invent new abstractions. You could claim that the invention of this new idea is a combination of an LLM and a harness, but that combination can solve logic puzzles and invent abstractions. If a really large spinning wheel could invent proofs that were previously unsolved, that would be a wildly amazing spinning wheel. I view LLM…

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

I'm not sure what the point of this exercise is. My prompt to ChatGPT: "Create a new English word with a reasonably sounding definition. That word must not come up in a Google search." Two attempts did come up in a search, the third was "Thaleniq (noun)". Definition: The brief feeling that a conversation has permanently changed your opinion of someone, even if nothing dramatic was said. Nothing in Google. There, a new word, not sure it proves or disproves anything. Or is it time to move the goal posts?

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

#168

Post by FrustratedMonky »

skybrian wrote: post #91
throw-the-towel wrote: post #59

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

Any design already exists as a possibility, so it could be said to be both invented and discovered, depending on how you look at it.

Depending on your point of view? I see what you did there.

Who knew Obi-one was just smoking and pontificating on Wittgenstein.

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

#170

Post by sillysaurusx »

jimmaswell wrote: post #162
voooduuuuu wrote: post #121

Earlier quoted context omitted.

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

Why is everyone who responds to this with a real example immediately flagged/dead?

HN autokills LLM generated comments. People don’t seem to believe this, but there’s proof for you.
Post reply on HN