Discussion

A Ramsey-style Problem on Hypergraphs

6thbit: > Subsequent to this solve, we finished developing our general scaffold for testing models on FrontierMath: Open Problems. In this scaffold, several other models were able to solve the problem as well: Opus 4.6 (max), Gemini 3.1 Pro, and GPT-5.4 (xhigh).Interesting. Whats that “scaffold”? A sort of unit test framework for proofs?

karmasimida: No denial at this point, AI could produce something novel, and they will be doing more of this moving forward.

inkysigma: I think in this context, scaffolds are generally the harness that surrounds the actual model. For example, any tools, ways to lay out tasks, or auto-critiquing methods.I think there's quite a bit of variance in model performance depending on the scaffold so comparisons are always a bit murky.

leptons: "A broken clock is right twice a day". Don't worry, "AI" will still mostly deliver slop.

renewiltord: Fantastic news! That means with the right support tooling existing models are already capable of solving novel mathematics. There’s probably a lot of good mathematics out there we are going to make progress on.

osti: Seems like the high compute parallel thinking models weren't even needed, both the normal 5.4 and gemini 3.1 pro solved it. Somehow Gemini 3 deepthink couldn't solve it.

readitalready: Usually involves a lot of agents and their custom contexts or system prompts.

an0malous: I feel like there’s a fork in our future approaching where we’ll either blossom into a paradise for all or live under the thumb of like 5 immortal VCs

XCSme: Change is always hard, even if it will be good in 20 years, the transitions are always tough.

johnfn: I like to imagine that the number of consumed tokens before a solution is found is a proxy for how difficult a problem is, and it looks like Opus 4.6 consumed around 250k tokens. That means that a tricky React refactor I did earlier today at work was about half as hard as an open problem in mathematics! :)

sublinear: You might be joking, but you're probably also not that far off from reality.I think more people should question all this nonsense about AI "solving" math problems. The details about human involvement are always hazy and the significance of the problems are opaque to most.We are very far away from the sensationalized and strongly implied idea that we are doing something miraculous here.

johnfn: I am kind of joking, but I actually don't know where the flaw in my logic is. It's like one of those math proofs that 1 + 1 = 3.If I were to hazard a guess, I think that tokens spent thinking through hard math problems probably correspond to harder human thought than tokens spend thinking through React issues. I mean, LLMs have to expend hundreds of tokens to count the number of r's in strawberry. You can't tell me that if I count the number of r's in strawberry 1000 times I have done the mental equivalent of solving an open math problem.

XCSme: Not sure if AI can have clever or new ideas, it still seems to be it combines existing knowledge and executes algoritms.I am not necessarily saying humans do something different either, but I have yet to see a novel solution from an AI that is not simply an extrapolation of current knowledge.

tombert: I was trying to get Claude and Codex to try and write a proof in Isabelle for the Collatz conjecture, but annoyingly it didn't solve it, and I don't feel like I'm any closer than I was when I started. AI is useless!In all seriousness, this is pretty cool. I suspect that there's a lot of theoretical math that haven't been solved simply because of the "size" of the proof. An AI feedback loop into something like Isabelle or Lean does seem like it could end up opening up a lot of proofs.

alberth: For those, like me, who find the prompt itself of interest …> A full transcript of the original conversation with GPT-5.4 Pro can be found here [0] and GPT-5.4 Pro’s write-up from the end of that transcript can be found here [1].[0] https://epoch.ai/files/open-problems/gpt-5-4-pro-hypergraph-...[1] https://epoch.ai/files/open-problems/hypergraph-ramsey-gpt-5...

pinkmuffinere: As someone with only passing exposure to serious math, this section was by far the most interesting to me:> The author assessed the problem as follows.> [number of mathematicians familiar, number trying, how long an expert would take, how notable, etc]How reliably can we know these things a-priori? Are these mostly guesses? I don't mean to diminish the value of guesses; I'm curious how reliable these kinds of guesses are.

daveguy: New goalpost, and I promise I'm not being facetious at all, genuinely curious:Can an AI pose an frontier math problem that is of any interest to mathematicians?I would guess 1) AI can solve frontier math problems and 2) can pose interesting/relevant math problems together would be an "oh shit" moment.

ramblingrain: Read about Paul Erdös... not all math is the Riemann Hypothesis, there is yeoman's work connecting things and whatever...

typs: I mean the details are in the post. You can see the conversation history and the mathematician survey on the problem

famouswaffles: >The details about human involvement are always hazy and the significance of the problems are opaque to most.Not really. You're just in denial and are not really all that interested in the details. This very post has the transcript of the chat of the solution.

pinkmuffinere: This is interesting, I like the thought about "what makes something difficult". Focusing just on that, my guess is that there are significant portions of work that we commonly miss in our evaluations:1. Knowing how to state the problem. Ie, go from the vague problem of "I don't like this, but I do like this", to the more specific problem of "I desire property A". In math a lot of open problems are already precisely stated, but then the user has to do the work of _understanding_ what the precise stating is.2. Verifying that the proposed solution actually is a full solution.This math problem actually illustrates them both really well to me. I read the post, but I still couldn't do _either_ of the steps above, because there's a ton of background work to be done. Even if I was very familiar with the problem space, verifying the solution requires work -- manually looking at it, writing it up in coq, something like that. I think this is similar to the saying "it takes 10 years to become an overnight success"

vlinx: This is a remarkable result if confirmed independently. The gap between solving competition problems and open research problems has always been significant - bridging that gap suggests something qualitatively different in the model capabilities.

throw310822: You can spend countless "tokens" solving minesweeper or sudoku. This doesn't mean that you solved difficult problems: just that the solutions are very long and, while each step requires reasoning, the difficulty of that reasoning is capped.

nkozyra: Clever/novel ideas are very often subtle deviations from known, existing work.Sometimes just having the time/compute to explore the available space with known knowledge is enough to produce something unique.