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Epoch confirms GPT5.4 Pro solved a frontier math open problem

epoch.ai

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Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#261

I am thinking there’s a large category of problems that can be solved by resampling existing proofs. It’s the kind of brute force expedition machine can attempt relentlessly where humans would go mad trying. It probably doesn’t really advance the field, but it can turn conjectures into theorems.

Indeed, can't find my old comment on the topic but that's indeed the point, it's not how feasible it is to "find" new proof, but rather how meaningful those proofs are. Are they yet another iteration of the same kind, perfectly fitting the current paradigm and thus bringing very little to the table or are they radical and thus potentially (but not always) opening up the field?

With brute force, or slightly better than brute force, it's most likely the first, thus not totally pointless but probably not very useful. In fact it might not even be worth the tokens spent.

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#262

Earlier quoted context omitted.

I’d hope this isn’t a goal post move - an open math problem of any sort being solved by a language model is absolute science fiction.

That's been achieved already with a few Erdös problems, though those tended to be ambiguously stated in a way that made them less obviously compelling to humans. This problem is obscure, even the linked writeup admits that perhaps ~10 mathematicians worldwide are genuinely familiar with it. But it's not unfeasibly hard for a few weeks' or months' work by a human mathematician.

FWIW https://github.com/teorth/erdosproblems/wiki/AI-contribution... in particular the disclaimers are very interesting.

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#263

I have long said I am an AI doubter until AI could print out the answers to hard problems or ones requiring tons of innovation. Assuming this is verified to be correct (not by AI) then I just became a believer. I would like to see a few more AI inventions to know for sure, but wow, it really is a new and exciting world. I really hope we use this intelligence resource to make the world better.

Math and coding competition problems are easier to train because of strict rules and cheap verification. But once you go beyond that to less defined things such as code quality, where even humans have hard time putting down concrete axioms, they start to hallucinate more and become less useful. We are missing the value function that allowed AlphaGo to go from mid range player trained on human moves to superhuman by p…

LLMs already do unsupervised learning to get better at creative things. This is possible since LLMs can judge the quality of what is being produced.

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#264
post #238

I have long said I am an AI doubter until AI could print out the answers to hard problems or ones requiring tons of innovation. Assuming this is verified to be correct (not by AI) then I just became a believer. I would like to see a few more AI inventions to know for sure, but wow, it really is a new and exciting world. I really hope we use this intelligence resource to make the world better.

>it really is a new and exciting world... The point is that from now on, there will be nothing really new, nothing really original, nothing really exciting. Just endless stream of re-hashed old stuff that is just okayish.. Like an AI spotify playlist, it will keep you in chains (aka engaged) without actually making you like really happy or good. It would be like living in a virtual world, but without having anything…

>We have given up everything nice that human beings used to make and give to each other and to make it worse, we have also multiplied everything bad, that human being used to give each other..

Source?

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#265

Earlier quoted context omitted.

> all LLM output is based on likelihood of one word coming after the next word based on the prompt. Right but it has to reason about what that next word should be. It has to model the problem and then consider ways to approach it.

No, it does not reason anything. LLM "reasoning" is just an illusion. When an LLM is "reasoning" it's just feeding its own output back into itself and giving it another go.

Is that so different from brains?

Even if it is, this sounds like "this submarine doesn't actually swim" reasoning.

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#266
post #55

Earlier quoted context omitted.

AI is a remixer; it remixes all known ideas together. It won't come up with new ideas though; the LLMs just predict the most likely next token based on the context. That means the group of characters it outputs must have been quite common in the past. It won't add a new group of characters it has never seen before on its own.

The ability for some people to perpetually move the goalpost will never cease to amaze me. I guess that's one way to tell us apart from AIs.

The main reason for my top post is that I felt I should admit the AI scored a goal today and the last one or two weeks. I said I'd be impressed if it could solve an open problem. It just did. People can argue about how it's not that impressive because if every mathematician were trying to solve this problem they probably would have. However, we all know that humans have extremely finite time and attention, whereas computers not so much. The fact that AI can be used at the cutting edge and relatively frequently produce the right answer in some contexts is amazing.

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#267

Earlier quoted context omitted.

This is like saying chess engines don't actually "play" chess, even though they trounce grandmasters. It's a meaningless distinction, about words (think, reason, ..) that have no firm definitions.

Chess engines are not a comparable thing. Chess is a solved game. There is always a mathematically perfect move.

We know that chess can be solved, in theory. It absolutely isn't and probably will never be in practice. The necessary time and storage space doesn't exist.

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#268
post #182

Earlier quoted context omitted.

I’d hope this isn’t a goal post move - an open math problem of any sort being solved by a language model is absolute science fiction.

It is not. You're operating under the assumption that all open math problems are difficult and novel. This particular problem was about improving the lower bound for a function tracking a property of hypergraphs (undirected graphs where edges can contain more than two vertices). Both constructing hypergraphs (sets) and lower bounds are very regular, chore type tasks that are common in maths. In other words, there's p…

> nice that the LLMs solved something for once.

That sentence alone needs unpacking IMHO, namely that no LLM suddenly decided that today was the day it would solve a math problem. Instead a couple of people who love mathematics, doing it either for fun or professionally, directly ask a model to solve a very specific task that they estimated was solvable. The LLM itself was fed countless related proofs. They then guided the model and verified until they found something they considered good enough.

My point is that the system itself is not the LLM alone, as that would be radically more impressive.

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#269
post #13

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! :)

I think it's more of a data vs intelligence thing.

They are separate dimensions. There are problems that don't require any data, just "thinking" (many parts of math sit here), and there are others where data is the significant part (e.g. some simple causality for which we have a bunch of data).

Certain problems are in-between the two (probably a react refactor sits there). So no, tokens are probably no good proxy for complexity, data heavy problems will trivially outgrow the former category.

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#270

It's deeply surprising to me that LLMs have had more success proving higher math theorems than making successful consumer software

They haven't, not at all as far as I can tell. This math problem appears to be a nice chore to be solved, the equivalent to "Claude, optimize this code" or "Write a parser", which is being done 100000x a day.

But the title claims it is a "frontier" math problem, so which is it really.
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