Top
Best
New

Posted by tedsanders 8 hours ago

An OpenAI model has disproved a central conjecture in discrete geometry(openai.com)
765 points | 556 commentspage 5
phkahler 7 hours ago|
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.
comboy 7 hours ago||
Yes, not providing visualization of the solution seems criminal.
red_admiral 6 hours ago|||
Unless it's a non-constructive proof.
kmeisthax 6 hours ago|||
Knowing OpenAI, the solution's probably being withheld as a trade secret, lest it fall victim to distillation attacks (i.e. exactly the same shit they did to the open Internet).
bustermellotron 6 hours ago|||
The grid of squares actually gets > Cn for any C. (More in fact… C can grow like n^a/loglog(n).) The AI proved > n^{1 + b} for some small b > 0, which a human (Will Sawin) has now proved can be about b = 0.014. The grid can be rescaled so the edges are not necessarily length 1, but other pairs will have length 1; that is necessary to get more than 2n unit distances.
kilotaras 6 hours ago||
Both 3n and 2n are linear, the broken conjecture is that you can't do better than linear.
yusufozkan 7 hours ago||
"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."
horhay 3 hours ago||
The accomplishment is cool. But all Erdos problems and other complicated mathematical problems they solved were accomplished with general-purpose models too. In fact for some of those problems, including bountied ones, they were public models. So I don't get saying this
seydor 7 hours ago|||
all reasoning is .. well problem reasoning. restricting black-box AIs to specific human-defined domains because we believe that's better is such a human-ist thing to do.
Kwantuum 7 hours ago||
I trust openAI's marketing team 100%
krackers 7 hours ago||
It seems plausible given that people have been using off the shelf 5.5 xhigh to decent success with some erdos problems. There is likely still some scaffolding around it though (like parallel sampling or separate verifier step) since it's not clear if you can just "one shot" problems like this.
solomatov 7 hours ago||
How central is it in the discrete geometry? Could anyone with the knowledge in the field reply?
sigmar 7 hours ago||
The blog post links a pdf that OpenAI put together of nine mathematicians that commented on the proof. Each is quite brief and written in accessible terms (or more accessible terms, at least). https://cdn.openai.com/pdf/74c24085-19b0-4534-9c90-465b8e29a...
horhay 3 hours ago|||
There may be years of investigation as to how far you can generalize these methods. As to how central it is, it's a longstanding problem that Erdos loves to cite for that branch of math.

The thing is is that it seems a lot of the effort through the years (which is unquantifiable in scale as to how much time was spent and how many people focused their entire worklives on it if any) has gone for trying to look for the proof, and the search for the disproof seems minimal.

energy123 7 hours ago||
There's pages of comments from like 8 mathematicians in the attached pdf
auggierose 5 hours ago||
Which model did this? Is it available to the public?
dev1ycan 2 hours ago||
Wouldn't surprise me if they're just paying math geniuses to do math research and attribute it to AI models.
catigula 7 hours ago||
Every time I interact even with OpenAI's pro model, I am forced to come to the conclusion that anything outside the domain of specific technical problems is almost completely hopeless outside of a simple enhanced search and summary engine.

For example, these machines, if scaling intellect so fiercely that they are solving bespoke mathematics problems, should be able to generate mundane insights or unique conjectures far below the level of intellect required for highly advanced mathematics - and they simply do not.

Ask a model to give you the rundown and theory on a specific pharmacological substance, for example. It will cite the textbook and meta-analyses it pulls, but be completely incapable of any bespoke thinking on the topic. A random person pursuing a bachelor's in chemistry can do this.

Anything at all outside of the absolute facts, even the faintest conjecture, feels completely outside of their reach.

dvfjsdhgfv 7 hours ago|
Yeah, I remember it was one of my biggest disappointments with LLMs.
_heimdall 5 hours ago||
As this becomes more common it makes me wonder where the LLM ends and the harness begins.

The underlying model may still effectively be a stochastic parrot, but used properly that can do impressive things and the various harnesses have been getting better and better at automating the use of said parrot.

alsetmusic 5 hours ago||
> AI is about to start taking a very serious role in the creative parts of research, and most importantly AI research itself. While this progress is not unexpected, it reinforces the urgency we feel about understanding this next phase of AI development, the challenges of aligning very intelligent systems, and the future of human-AI collaboration.

I find this hyperbolic, but ya gotta juice up the upcoming IPO. I hate that they took an interesting announcement and reminded me why I hate tech and our society at the end.

pizzao 7 hours ago||
Can someone explain to me what is their "prompting-scaffolding" to make it work ?
yusufozkan 7 hours ago|
"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
seydor 7 hours ago|
can the AI please tell us what to do now that all knowledge work will become unemployment?
bmacho 6 hours ago||
Physical labour?
layer8 4 hours ago||
Revolt against the AI overlords.
More comments...