An OpenAI model has disproved a central conjecture in discrete geometry

aurareturn

One thing seems for certain is that OpenAI models hold a distinct lead in academics over Anthropic and Google models. For those in academics, is OpenAI the vendor of choice?

empath75

Important note: this was not done with a special mathematics harness or specialized workflow.

Jeff_Brown

Can anyone find (or draw) a picture of the construction?

alansaber

AI isn't going to supercharge science but I wouldn't be as dismissive as other posters here.

vatsachak

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.

yusufozkan

"The proof came from a general-purpose reasoning model, not a system built specifically to solve math problems or this problem in particular, and represents an important milestone for the math and AI communities."

endymi0n

To paraphrase Gwynne Shotwell: “Not too bad for just a large Markov chain, eh?”

phkahler

I would have thought a triangular grid works better than a grid of squares. You get ~3n links vs ~2n for the square grid. Curious what the AI came up with.

dadrian

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 away from it. - It's description of the new proof just cites some terms of art with no effort made to actually explain the result. If this post were not on the OpenAI blog, I would assume it was slop. I understand advanced pure mathematics is complicated, but it is entirely possible to explain complicated topics to non-experts.

solomatov

How central is it in the discrete geometry? Could anyone with the knowledge in the field reply?

reactordev

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.

0x5FC3

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.

bradleykingz

ok. so what are the implications of for math

Fraterkes

I guess if this stuff is going to make my employment more precarious, it’d be nice if it also makes some scientific breakthroughs. We’ll see

zozbot234

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.

m-hodges

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’t disqualifying, or a lot of Fields Medals need to be returned.

taimurshasan

I wonder how much this cost vs a Math Professor or a team of Math Professors.

seydor

can the AI please tell us what to do now that all knowledge work will become unemployment?

throw-the-towel

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

lubujackson

For anyone using LLMs heavily for coding, this shouldn't be too surprising. It was just a matter of time. Mathematicians make new discoveries by building and applying mathematical tools in new ways. It is tons of iterative work, following hunches and exploring connections. While true that LLMs can't truly "make discoveries" since they have no sense of what that would mean, they can Monte Carlo every mathematical tool at a narrow objective and see what sticks, then build on that or combine improvements. Reading the article, that seems exactly how the discovery was made, an LLM used a "surprising connection" to go beyond the expected result. But the result has no meaning without the human intent behind the objective, human understanding to value the new pathway the AI used (more valuable than the result itself, by far) and the mathematical language (built by humans) to explore the concept.