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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

#281

Earlier quoted context omitted.

I never said that humans are better than LLM's along every axis. Rather, a reasonable definition of intelligence would necessarily encompass domains that LLM's are either incapable of or inferior to us. Here might be some definitions of intelligence for example: > The aggregate or global capacity of the individual to act purposefully, to think rationally, and to deal effectively with his environment. > "...the result…

>I never said that humans are better than LLM's along every axis. Rather, a reasonable definition of intelligence would necessarily encompass domains that LLM's are either incapable of or inferior to us. So all humans are overwhelmingly more intelligent but cannot even manage to be as capable in a significant number of domains ? That's not what overwhelming means. >I would consider statistical reasoning systems that…

> So all humans are overwhelmingly more intelligent but cannot even manage to be as capable in a significant number of domains

When the amount of domains in which humans are more capable than LLM's vastly exceeds the amount of domains in which LLM's are more capable than humans, yes.

I also agree that we don't have a great understanding of either human or LLM intelligence, but we can at least observe major differences and conclude that there are, in fact, major differences. In the same way we can conclude that both birds and planes have major differences, and saying that "there's nothing unique about birds, look at planes" is just a really weird thing to say.

> If we were to be more accurate to the brain in silicon, it would be even less efficient than LLMs

Do you think perhaps this massive difference points to there being a significant and foundational structural and functional difference between these types of intelligences?

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

#282
post #159
post #152

Earlier quoted context omitted.

> LLMs will NEVER be able to do that, because it doesn't exist. I mean, TFA literally claims that an AI has solved an open Frontier Math problem, descibed as "A collection of unsolved mathematics problems that have resisted serious attempts by professional mathematicians. AI solutions would meaningfully advance the state of human mathematical knowledge." That is, if true, it reasoned out a proof that does not exist i…

It generated a proof that was close enough to something in its training data to be generated.

That may be, and we can debate the level of novelty, but it is novel, because this exact proof didn't exist before, something which many claim was not possible with AI. In fact, just a few years ago, based on some dabbling in NLP a decade ago, I myself would not have believed any of this was remotely possible within the next 3 - 5 decades at least.

I'm curious though, how many novel Math proofs are not close enough to something in the prior art? My understanding is that all new proofs are compositions and/or extensions of existing proofs, and based on reading pop-sci articles, the big breakthroughs come from combining techniques that are counter-intuitive and/or others did not think of. So roughly how often is the contribution of a proof considered "incremental" vs "significant"?

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

#283

I don't know why I am still perpetually shocked that the default assumption is that humans are somehow unique. It's this pervasive belief that underlies so much discussion around what it means to be intelligent. The null hypothesis goes out the window. People constantly make comments like "well it's just trying a bunch of stuff until something works" and it seems that they do not pause for a moment to consider whethe…

The ability to learn and infer without absorbing millions of books and all text on internet really does make us special. And only at 20 watts!

To be fair, the knowledge embedded in an LLM is also, at this point, a couple orders of magnitude (at least) larger than what the average human being can retain. So it's not like all those books and text in the internet are used just to bring them to our level, they go way beyond.

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

#284

Earlier quoted context omitted.

That is a pretty bold assertion for a meatball of chemical and electrical potentials to make.

Do you know what "LLM" stands for? They are large language models, built on predicting language. They are not capable of mathematics because mathematics and language are fundamentally separated from each other. They can give you an answer that looks like a calculation, but they cannot perform a calculation. The most convincing of LLMs have even been programmed to recognize that they have been asked to perform a calcu…

Mathematics is a language. Everything we can express mathematically, we can also express in natural language. The real interesting, underlying question is: Is there anything worth knowing that cannot be expressed by language? - That's the theoretical boundary of LLM capability.

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

#285

Earlier quoted context omitted.

> I don't know why I am still perpetually shocked that the default assumption is that humans are somehow unique. Uh, because up until and including now, we are...?

Every living thing on Earth is unique. Every rock is unique in virtually infinite ways from the next otherwise identical rock. There are also a tremendous number of similarities between all living things and between rocks (and between rocks and living things). Most ways in which things are unique are arguably uninteresting. The default mode, the null hypothesis should be to assume that human intelligence isn't intere…

Humans are obviously unique in an interesting way. People only "move the goalpost" because it's not an interesting question that humans can do some great stuff, the interesting question is where the boundary is. (Whether against animals or AI).

Some example goals which makes human trivially superior (in terms of intelligence): invention of nuclear bomb/plants, theory of relativity, etc.

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

#286
post #99

I don't know why I am still perpetually shocked that the default assumption is that humans are somehow unique. It's this pervasive belief that underlies so much discussion around what it means to be intelligent. The null hypothesis goes out the window. People constantly make comments like "well it's just trying a bunch of stuff until something works" and it seems that they do not pause for a moment to consider whethe…

Re: "I don't know why I am still perpetually shocked that the default assumption is that humans are somehow unique." Perhaps this might better help you understand why this assumption still holds: https://en.wikipedia.org/wiki/Orchestrated_objective_reducti...

"Controversial theory justifies assumption". Because humans never hallucinate.

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

#287

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.

[deleted]

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

#288
I am kind of amazed at how many commenters respond to this result by confidently asserting that LLMs will never generate 'truly novel' ideas or problem solutions.

> AI is a remixer; it remixes all known ideas together. It won't come up with new ideas

> it's not because the model is figuring out something new

> LLMs will NEVER be able to do that, because it doesn't exist

It's not enough to say 'it will never be able to do X because it's not in the training data,' because we have countless counterexamples to this statement (e.g. 167,383 * 426,397 = 71,371,609,051, or the above announcement). You need to say why it can do some novel tasks but could never do others. And it should be clear why this post or others like it don't contradict your argument.

If you have been making these kinds of arguments against LLMs and acknowledge that novelty lies on a continuum, I am really curious why you draw the line where you do. And most importantly, what evidence would change your mind?

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

#289

Earlier quoted context omitted.

The original researchers who proposed this problem tried and failed multiple times to solve it. Does that sound like a 'nice chore to be solved' to you ?

That's interesting context, where do you see that? I'm going off of the label "Moderately interesting". edit: I see in the full write up that the contributor says that they'd estimate an expert would take 1-3 months to do this. They also note that they came up with this solution independently but hadn't confirmed it.

https://epochai.substack.com/p/first-ai-solution-on-frontier...

>The newly-solved problem came from Will Brian, who had placed it in the Moderately Interesting category. It is a conjecture from a paper he wrote with Paul Larson in 2019. They were unable to solve it at the time, or in several attempts since. Brian had this to say.

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

#290

Earlier quoted context omitted.

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…

> I don't see this getting better. We went from 2 + 7 = 11 to "solved a frontier math problem" in 3 years, yet people don't think this will improve?

LLMs in some form will likely be a key component in the first AGI system we (help) build. We might still lack something essential. However, people who keep doubting AGI is even possible should learn more about The Church-Turing Thesis.

https://plato.stanford.edu/entries/church-turing/

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