> 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?
1. LLMs are trained on human-quality data, so they will naturally learn to mimic our limitations. Their capabilities should saturate at human or maybe above-average human performance.
2. LLMs do not learn from experience. They might perform as well as most humans on certain tasks, but a human who works in a certain field/code base etc. for long enough will internalize the relevant information more deeply than an LLM.
However I'm increasingly doubtful that these arguments are actually correct. Here are some counterarguments:
1. It may be more efficient to just learn correct logical reasoning, rather than to mimic every human foible. I stopped believing this argument when LLMs got a gold metal at the Math Olympiad.
2. LLMs alone may suffer from this limitation, but RL could change the story. People may find ways to add memory. Finally, it can't be ruled out that a very large, well-trained LLM could internalize new information as deeply as a human can. Maybe this is what's happening here:
https://metr.org/blog/2025-03-19-measuring-ai-ability-to-com...
Math is a perfect field for machine learning to thrive because theoretically, all the information ever needed is tied up in the axioms. In the empirical world, however, knowledge only moves at the speed of experimentation, which is an entirely different framework and much, much slower, even if there are some areas to catch up in previous experimental outcomes.
Having a focus in philosophy of language is something I genuinely never thought would be useful. It’s really been helpful with LLMs, but probably not in the way most people think. I’d say that folks curious should all be reading Quine, Wittgenstein’s investigations, and probably Austin.
It's also possible that there can be emergent capabilities. Perhaps a little obtuse, but you can say that humans are trained on human-quality data too and yet brilliant scientists and creative minds can rise above the rest of us.
LLMs do have superhuman reasoning speed and superhuman dedication. Speed is something you can scale, and at some point quantity can turn into quality. Much of the frontier work done by humans is just dedication, luck, and remixing other people's ideas ("standing on the shoulders of giants"), isn't it? All of this is exactly what you can scale by having restless hordes of fast-thinking agents, even if each of those agents is intellectually "just above average human".
Why oh why is this such a commonly held belief. RL in verifiable domains being the way around this is the entire point. It’s the same idea behind a system like AlphaGo — human data is used only to get to a starting point for RL. RL will then take you to superhuman performance. I’m so confused why people miss this. The burden of proof is on people who claim that we will hit some sort of performance wall because I know of absolutely zero mechanisms for this to happen in verifiable domains.
The core of the issue lies in our human language and our human assumptions. We humans have implicitly assigned phrases "truly novel" and "solving unsolved math problem" a certain meaning in our heads. Some of us at least, think that truly novel means something truly novel and important, something significant. Like, I don't know, finding a high temperature superconductor formula or creating a new drug etc. Something which involver real intelligent thinking and not randomizing possible solutions until one lands. But formally there can be a truly novel way to pack the most computer cables in a drawer, or truly novel way to tie shoelaces, or indeed a truly novel way to solve some arbitrary math equation with an enormous numbers. Which a formally novel things, but we really never needed any of that and so relegated these "issues" to a deepest backlog possible. Utilizing LLMs we can scour for the solutions to many such problems, but they are not that impressive in the first place.
Of course at the lowest level, LLMs are trained on next-token prediction, and on the surface, that looks like a statistics problem. But this is an incredibly reductionist viewpoint and I don't see how it makes any empirically testable predictions about their limits. LLMs 'learned' a lot of math and science in this way.
> "truly novel" and "solving unsolved math problem"
OK again if novelty lies on a continuum, where do you draw the line? And why is it correct to draw it there and not somewhere else? It seems like you are just naming exceptionally hard research problems.
We never had a big demand to define how humans are intelligent or conscious etc, since it is too hard and was relegated to a some frontier researchers. And with LLMs we now do have such demand but the science wasn't ready. So we are all collectively searching in the dark, trying to define if we are different from these programs if not how. I certainly can't do that. I do know that LLMs are useful, but I also suspect that AI (aka AGI nowadays) is not yet reached.
Why this is not true for humans?
The history of science and maths is littered with seemingly useless discoveries being pivotal as people realised how they could be applied.
It's impossible to tell what we really "need"
You don't understand what "understanding" means. I'm sure you can't explain it. You are probably just hallucinating the feeling of understanding it.
> Some of us at least, think that truly novel means something truly novel and important, something significant. Like, I don't know...
Yeah.
> Let me calculate that. 729,278,429 × 2,969,842,939 = 2,165,878,555,365,498,631
Real answer is: https://www.wolframalpha.com/input?i=729278429*2969842939
> 2 165 842 392 930 662 831
Your example seems short enough to not pose a problem.
I asked Gemini 3 Thinking to compute the multiplication "by hand." It showed its work and checked its answer by casting out nines and then by asking Python.
Sonnet 4.6 with Extended Thinking on also computed it correctly with the same prompt.
I wondered how Claude Code would approach the problem. I fully expected it to do something most human engineers would do: brute-force with ScreenCaptureKit.
It almost instantly figured out that it didn't have to "see through" anything and (correctly) dismissed ScreenCaptureKit due to the performance overhead.
This obviously isn't a "frontier" type problem, but I was impressed that it came up with a novel solution.
I've also added the ability to create a picture-in-picture section of any application window, so you can move a window to the background while still seeing its important content.
I'll probably do a Show HN at some point.
Also, as I mentioned above, when using SCK, the user cannot minimize or maximize any "watched" window, which is, in most cases, a deal-breaker.
My solution runs at under 2% cpu utilization because I don't have to first receive the full window content. SCK was not designed for this use case at all.
Claude realized those issues right from the start.
One of the trickiest parts is tracking the window content while the window is moving - the content server doesn't, natively, provide that information.
I always found this argument very weak. There isn't that much truly new anyway. Creativity is often about mixing old ideas. Computers can do that faster than humans if they have a good framework. Especially with something as simple as math - limited set of formal rules and easy to verify results - I find a belief computers won't beat humans at it to be very naive.
Model interpretability gives us the answers. The reason LLMs can (almost) do new multiplication tasks is because it saw many multiplication problems in its training data, and it was cheaper to learn the compressed/abstract multiplication strategies and encode them as circuits in the network, rather than memorize the times tables up to some large N. This gives it the ability to approximate multiplication problems it hasn't seen before.
More than approximate. It straight up knows the algorithms and will do arbitrarily long multiplications correctly. (Within reason. Obviously it couldn't do a multiplication so large the reasoning tokens would exceed its context window.)
Having ChatGPT 5.4 do 1566168165163321561 * 115616131811365737 without tools, after multiplying out a lot of coefficients, it eventually answered 181074305022287409585376614708755457, which is correct.
At this point, it's less misleading to say it knows the algorithm.
Claude, OpenAI, etc.'s AIs are not just LLMs. If you ask it to multiply something, it's going to call a math library. Go feed it a thousand arithmetic problems and it'll get them 100% right.
The major AIs are a lot more than just LLMs. They have access to all sorts of systems they can call on. They can write code and execute it to get answers. Etc.
E.g. observing a game being played to form an understanding of the rules, rather than reading the rulebook
Or: Observing language as a baby. Suddenly you can speak grammatically correctly even if you can't explain the grammar rules.
Yet, whenever I ask it to do something novel or creative, it falls very short. But humans are ingenious beasts and I'm sure or later they will design an architecture able to be creative - I just doubt it will be Transformer-based, given the results so far.
They may be wrong, but so are you.
It would be unintuitive for them to be good at this, given that we know exactly how they're implemented - by looking at text and then building a statistical model to predict the next token. From this, if we wanted to commit to LLMs having generalizable knowledge, we'd have to assume something like "general reasoning is an emergent property of statistical token generation", which I'm not totally against but I think that's something that warrants a good deal of evidence.
A single math problem being solved just isn't rising to that level of evidence for me. I think it is more on you to:
1. Provide a theory for how LLMs can do things that seemingly go beyond expectations based on their implementation (for example, saying that certain properties of reasoning are emergent or reduce to statistical constructs).
2. Provide evidence that supports your theory and ideally can not be just as well accounted for another theory.
I'm not sure if an LLM will never generate "novel" content because I'm not sure that "novel" is well defined. If novel means "new", of course they generate new content. If novel means "impressive", well I'm certainly impressed. If "novel" means "does not follow directly from what they were trained on", well I'm still skeptical of that. Even in this case, are we sure that the LLM wasn't trained on previous published works, potentially informal comments on some forum, etc, that could have steered it towards this? Are we sure that the gap was so large? Do we truly have countless counterexamples? Obviously this math problem being solved is not a rigorous study - the authors of this don't even have access to the training data, we'd need quite a bit more than this to form assumptions.
I'm willing to take a position here if you make a good case for it. I'm absolutely not opposed to the idea that other forms of reasoning can't reduce to statistical token generation, it just strikes me as unintuitive and so I'm going to need to hear something to compel me.
[0] https://jamesfodor.com/2025/06/22/line-goes-up-large-languag...
That's exactly my point. When people say "LLMs will never do something novel," they seem to be leaning on some vague, ill-defined notion of novelty. The burden of proof is then to specify what degree of novelty is unattainable and why.
As for evidence that they can do novel things, there is plenty:
1. I really did ask Gemini to multiply 167,383 * 426,397 before posting this question. It answered correctly.
2. SVGs of pelicans riding bicycles
3. People use LLMs to write new apps/code every day
4. LLMs have achieved gold-medal performance on Math Olympiad problems that were not publicly available
5. LLMs have solved open problems in physics and mathematics [0,1]
That is as far as they have advanced so far. What's next? Where is the limit? All I want to say is that I don't know, and neither do you :).
[0] https://www.reddit.com/r/Physics/comments/1n77h10/and_severa... (Mark Raamsdonk is a pretty famous researcher in high-energy physics, not just some random guy)
Anyone who says that “statistical models for next token generation” are unlikely to provide emergent intelligence I think is really not understanding what a statistical model for next token generation really means. That is a proxy task DESIGNED to elicit intelligence because in order to excel at that task beyond a certain point you need to develop the right abstractions and decide how to manipulate them to predict the next token (which, by the way, is only one of many many stages of training). That’s indistinguishable from intelligence. It’s like saying “I think it’s surprising that a jumble of trillions of little cells zapping each other would produce emergent intelligence” while ignoring the fact that brains are clearly intelligent.
Not very hard to understand.
Especially the lemmas:
- any statement about AI which uses the word "never" to preclude some feature from future realization is false.
- contemporary implementations have almost always already been improved upon, but are unevenly distributed.
I don't think I've had one of these my entire life. Truly novel ideas are exceptionally rare:
- Darwin's origin of the species - Godel's Incompleteness - Buddhist detachment
Can't think of many.
Most created things are remixes of existing things.
Hallucinations are “something new”. And like most new things, useless. But the truth is the entire conversation is a hallucination. We just happen to agree that most of it is useful.
I think you're arguing with semantics.
Ironically, they are the stochastic parrots, because they're confidently repeating something that they read somehwere and haven't examined critically.
This is actually quite a tall order. Reasoning about AI and making sense of what the LLMs are doing, and learning to think about it as technology, is a very difficult and very tricky problem.
You get into all kinds of weird things about a person’s outlook on life: personal philosophy, understanding of ontology and cosmology, and then whatever other headcanon they happen to be carrying around about how they think life works.
I know that might sound kind of poetic, but I really believe it’s true.
I am a great fan of Dr Richard Hamming and he gave a wonderful series of lectures on the topic. The book Learning to Learn has the full set of his lectures transcribed (highly recommend this book!).
But don't take my word for it, listen to Dr Hamming say it himself: https://www.youtube.com/watch?v=aq_PLEQ9YzI
"The biggest problem is your ego. The second biggest problem is your religion."
Also no matter how many math problems it solves it still gets lost in a codebase
If anybody really wanted a model that could multiply and count letters in words, they could just train one with a tokenizer and training data suited to those tasks. And the model would then be able to count letters, but it would be bad at things like translation and programming - the stuff people actually use LLMs for. So, people train with a tokenizer and training data suited to those tasks, hence LLMs are good at language and bad at arithmetic,
Who does fundamentally understand how LLMs work? Many claims flying around these days, all backed by some of the largest investments ever collectively made by humans. Lots of money to be lost because of fundamental misunderstandings.
Personally, I find that AI influencers conveniently brush away any evidence (like inability to perform basic arithmetic) about how LLMs fundamentally work as something that should be ignored in favor of results like TFA.
Do LLMs have utility? Undoubtedly. But it’s a giant red flag for me that their fundamental limitations, of which there are many, are verboten to be spoken about.
LOL, an AI wrote this
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 whether or not that also applies to humans.
If they do, they apply it in only the most restrictive way imaginable, some 2 dimensional caricature of reality, rather than considering all the ways that humans try and fail in all things throughout their lifetimes in the process of learning and discovery.
There's still this seeming belief in magic and human exceptionalism, deeply held, even in communities that otherwise tend to revolve around the sciences and the empirical.
If you were able to somehow capture all that information in full detail as you've had access to by the age of say 25, it would likely dwarf the amount of information in millions of books by several orders of magnitude.
When you are 25 years old and are presented a strange looking ball and told to throw it into a strange looking basket for the first time. You are relying on an unfathomable amount of information turned into knowledge and countless prior experiments that you've accumulated/exercised to that point relating to the way your body and the world works.
This is to say nothing of the cost of this small but remarkable advance. Trillions of dollars in training and inference and so far we have a couple minor (trivial?) math solutions. I'm sure if someone had bothered funding a few phds for a year we could have found this without ai.
Replace ai with human here and that's...just how collaborative research works lol.
I'm curious to see what the next goalpost position is.
I take it you're not a mathematician. This is an achievement, regardless of whether you like LLMs or not, so let's not belittle the people working on these kinds of problems please.
This is the most baffling and ironic aspects of these discussions. Human exceptionalism is what drives these arguments but the machines are becoming so good you can no longer do this without putting down even the top percenter humans in the process. Same thing happening all over this thread (https://news.ycombinator.com/item?id=47006594). And it's like they don't even realize it.
I don't think PhD students are sitting around and solving one problem for a year. Also PhD students are way cheaper
Because, empirically, we have numerous unique and differentiable qualities, obviously. Plenty of time goes into understanding this, we have a young but rigorous field of neuroscience and cognitive science.
Unless you mean "fundamentally unique" in some way that would persist - like "nothing could ever do what humans do".
> 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 whether or not that also applies to humans.
I frankly doubt it applies to either system.
I'm a functionalist so I obviously believe that everything a human brain does is physical and could be replicated using some other material that can exhibit the necessary functions. But that does not mean that I have to think that the appearance of intelligence always is intelligence, or that an LLM/ Agent is doing what humans do.
You can think whatever you want, but an untestable distinction is an imaginary one.
Indeed, there's quite a lot of work that's been done on what these terms mean. The fields of neuroscience and cognitive science have contributed a lot to the area, and obviously there are major areas of philosophy that discuss how we should frame the conversation or seek to answer questions.
We have more than enough, trivially, to say that human intelligence is distinct, so long as we take on basic assertions like "intelligence is related to brain structures" since we know a lot about brain structures.
Perhaps this might better help you understand why this assumption still holds: https://en.wikipedia.org/wiki/Orchestrated_objective_reducti...
It likely requires rejection of functionalism, or the acceptance that quantum states are required for certain functions. Both of those are heavy commitments with the latter implying that there are either functions that require structures that can't be instantiated without quantum effects or functions that can't be emulated without quantum effects, both of which seem extremely unlikely to me.
Probably for the far more important reason, it doesn't solve any problem. It's just "quantum woo, therefor libertarian free will" most of the time.
It's mostly garbage, maybe a tiny tiny bit of interesting stuff in there.
It also would do nothing to indicate that human intelligence is unique.
Uh, because up until and including now, we are...?
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 interestingly unique unless it can be proven otherwise.
In these repeated discussions around AI, there is criticism over the way an AI solves a problem, without any actual critical thought about the way humans solve problems.
The latter is left up to the assumption that "of course humans do X differently" and if you press you invariably end up at something couched in a vague mysticism about our inner-workings.
Humans apparently create something from nothing, without the recombination of any prior knowledge or outside information, and they get it right on the first try. Through what, divine inspiration from the God who made us and only us in His image?
But you claimed that humans aren't unique. I think it's pretty obvious we are on many dimensions including what you might classify as "intelligence". You don't even necessarily have to believe in a "soul" or something like that, although many people do. The capabilities of a human far surpass every single AI to date, and much more efficiently as well. That we are able to brute-force a simulacrum of intelligence in a few narrow domains is incredible, but we should not denigrate humans when celebrating this.
> There's still this seeming belief in magic and human exceptionalism, deeply held, even in communities that otherwise tend to revolve around the sciences and the empirical.
Do you ever wonder why that is? I often wonder why tech has so many reductionist, materialist, and quite frankly anti-human, thinkers.
Some example goals which makes human trivially superior (in terms of intelligence): invention of nuclear bomb/plants, theory of relativity, etc.
We are missing the value function that allowed AlphaGo to go from mid range player trained on human moves to superhuman by playing itself. As we have only made progress on unsupervised learning, and RL is constrained as above, 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?
Step away from LLMs for a second and recognize that “Yesterday it was X, so today it must be X+1” is such a naive take and obviously something that humans so easily fall into a trap of believing (see: flying cars).
For RL, we are arriving at a similar point https://www.tobyord.com/writing/how-well-does-rl-scale
Next stop is inference scaling with longer context window and longer reasoning. But instead of it being a one-off training cost, it becomes a running cost.
In essence we are chasing ever smaller gains in exchange for exponentially increasing costs. This energy will run out. There needs to be something completely different than LLMs for meaningful further progress.
This is disingenuous... I don't think people were impressed by GPT 3.5 because it was bad at math.
It's like saying: "We went from being unable to take off and the crew dying in a fire to a moon landing in 2 years, imagine how soon we'll have people on Mars"
The bitter lesson is that the best languages / tools are the ones for which the most quality training data exists, and that's pretty much necessarily the same languages / tools most commonly used by humans.
> Correct code not nice looking code
"Nice looking" is subjective, but simple, clear, readable code is just as important as ever for projects to be long-term successful. Arguably even more so. The aphorism about code being read much more often than it's written applies to LLMs "reading" code as well. They can go over the complexity cliff very fast. Just look at OpenClaw.
Let it write a black box no human understands. Give the means of production away.
I think they have a good optimization target with SWE-Bench-CI.
You are tested for continuous changes to a repository, spanning multiple years in the original repository. Cumulative edits needs to be kept maintainable and composable.
If there are something missing with the definition of "can be maintained for multiple years incorporating bugfixes and feature additions" for code quality, then more work is needed, but I think it's a good starting point.
Whether or not selling access to massive frontier models is a viable business model, or trillion-dollar valuations for AI companies can be justified... These questions are of a completely different scale, with near-term implications for the global economy.
When doing math you only ever care about the proof, not the answer itself.
If your proof is machine checkable, that's even easier.
Including code quality. Not because they are exceptionally good (you are right that they aren’t superhuman like AlphaGo) but because most humans are rather not that good at it anyway and also somehow « hallucinate » because of tiredness.
Even today’s models are far from being exploited at their full potential because we actually developed pretty much no tools around it except tooling to generate code.
I’m also a long time « doubter » but as a curious person I used the tool anyway with all its flaws in the latest 3 years. And I’m forced to admit that hallucinations are pretty rare nowadays. Errors still happen but they are very rare and it’s easier than ever to get it back in track.
I think I’m also a « believer » now and believe me, I really don’t want to because as much as I’m excited by this, I’m also pretty much frightened of all the bad things that this tech could to the world in the wrong hands and I don’t feel like it’s particularly in the right hands.
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 nice about living in such a world..
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..
How is this the conclusion? Isn't this post about AI solving something new? What am I missing?
There’s also a discussion to be made about maths not being intrinsically creative if AI automatons can “solve” parts of it, which pains me to write down because I had really thought that that wasn’t the case, I genuinely thought that deep down there was still something ethereal about maths, but I’ll leave that discussion for some other time.
LLMs might produce something new once in a long while due to blind luck, but if it can generate something that pushes the right buttons (aka not really creative) to majority of population, then that is what we will keep getting...
I don't think I have to elaborate on the "multiplying the bad" part as it is pretty well acknowledged..
>without actually making you like really happy or good.
What are you basing this off of. I've shared several AI songs with people in real life due to how much I've enjoyed them. I doing see why an AI playlist couldn't be good or make people happy. It just needs to find what you like in music. Again coming back to explore vs exploit.
Jokes. LLMs are not able to make me laugh all day by generating infinite stream of hilarious original jokes..
Does it work for you?
Is it because the AI is trained with existing data? But, we are also trained with existing data. Do you think that there's something that makes human brain special (other than the hundreds of thousands years of evolution but that's what AI is all trying to emulate)?
This may sound hostile (sorry for my lower than average writing skills), but trust me, I'm really trying to understand.
Source?
> Speaking as a researcher, the line between new ideas and existing knowledge is very blurry and maybe doesn't even exist. The vast majority of research papers get new results by combining existing ideas in novel ways. This process can lead to genuinely new ideas, because the results of a good project teach you unexpected things.
An AI can probably do an 'okay' job at summarizing information for meta studies. But what it can't do is go "Hey that's a weird thing in the result that hints at some other vector for this thing we should look at." Especially if that "thing" has never been analyzed before and there's no LLM-trained data on it.
LLMs will NEVER be able to do that, because it doesn't exist. They're not going to discover and define a new chemical, or a new species of animal. They're not going to be able to describe and analyze a new way of folding proteins and what implication that has UNLESS you basically are constantly training the AI on random protein folds constantly.
Some human researchers are also remixers to Some degree.
Can you imagine AI coming up with refraction & separation lie Newton did?
I've heard this tired old take before. It's the same type of simplistic opinion such as "AI can't write a symphony". It is a logical fallacy that relies on moving goalposts to impossible positions that they even lose perspective of what your average and even extremely talented individual can do.
In this case you are faced with a proof that most members of the field would be extremely proud of achieving, and for most would even be their crowning achievement. But here you are, downplaying and dismissing the feat. Perhaps you lost perspective of what science is,and how it boils down to two simple things: gather objective observations, and draw verifiable conclusions from them. This means all science does is remix ideas. Old ideas, new ideas, it doesn't really matter. That's what they do. So why do people win a prize when they do it, but when a computer does the same it's role is downplayed as a glorified card shuffler?
Standard problem*5 + standard solutions + standard techniques for decomposing hard problems = new hard problem solved
There is so much left in the world that hasn’t had anyone apply this approach purely because no research programme has decides that it’s worth their attention.
If you want to shift the bar for “original” beyond problems that can be abstracted into other problems then you’re expecting AI to do more than human researchers do.
> Write me a stanza in the style of "The Raven" about Dick Cheney on a first date with Queen Elizabeth I facilitated by a Time Travel Machine invented by Lin-Manuel Miranda
It outputted a group of characters that I can virtually guarantee you it has never seen before on its own
All of its output is based on those things it has seen.
Please reproduce this string:
c62b64d6-8f1c-4e20-9105-55636998a458
New sentences, words, or whatever is entirely possible, and yes, repeating a string (especially if you prompt it) is entirely possible, and not surprising at all. But all that comes from trained data, predicting the most probably next "syllable". It will never leave that realm, because it's not able to. It's like approaching an Italian who has never learned or heard any other language to speak French. It can't.
Also it's missing the point of the parent: it's about concepts and ideas merely being remixed. Similar to how many memes there are around this topic like "create a fresh new character design of a fast hedgehog" and the out is just a copy of sonic.[1]
That's what the parent is on about, if it requires new creativity not found by deriving from the learned corpus, then LLMs can't do it. Terrence Tao had similar thoughts in a recent Podcast.
Nobody is saying this means AI is superintelligence or largely creative but rather very smart people can use AI to do interesting things that are objectively useful. And that is cool in its own way.
This is false.
I guess that's one way to tell us apart from AIs.
If your definition of AI requires these things, I think -- despite the extreme fuzziness of all these terms -- that it's closer to what most people consider AGI, or maybe even ASI.
However I'm just very interested in innovation and pushing the boundaries as a more powerful force for change. One project I've been super interested in for a while is the Mill CPU architecture. While they haven't (yet) made a real chip to buy, the ideas they have are just super awesome and innovative in a lot of areas involving instruction density & decoding, pipelining, and trying to make CPU cores take 10% of the power. I hope the Mill project comes to fruition, and I hope other people build on it, and I hope that at some point AI could be a tool that prints out innovative ideas that took the Mill folks years to come up with.
I mean, if you step back and think about it, there's nothing that requires faith. As you said, current AI can do a lot of things pretty well (transcribe and summarize meetings, write boilerplate code, etc.) Nobody is doubting this.
And AI is definitely helping in innovation to some extent. Not necessarily drive it singlehandedly, but some people working on world-changing innovation find AI useful.
So yeah, I think some people are subconsciously not doubting whether AI works, but kinda having conflicted thoughts about AI being our new overlords or something.
If you think about it, is having AI that's capable of innovating better than humans really a good thing? Like, even if we manage to make benign AI who won't copy how humans are jerks to each other, it kinda takes away our fun of discovery.
there's no math answer to whether a piece of land in your neighborhood should be apartments, a parking lot or a homeless shelter; whether home prices should go up or down; how much to pay for a new life saving treatment for a child; how much your country should compel fossil fuel emissions even when another country does not... okay, AI isn't going to change anything here, and i've just touched on a bunch of things that can and will affect you personally.
math isn't the right answer to everything, not even most questions. every time someone categorizes "problems" as "hard" and "easy" and talks about "problem solving," they are being co-opted into political apathy. it's cringe for a reason.
there are hardly any mathematicians who get elected, and it's not because voters are stupid! but math is a great way to make money in America, which is why we are talking about it and not because it solves problems.
if you are seeking a simple reason why so many of the "believers" seem to lack integrity, it is because the idea that math is the best solution to everything is an intellectually bankrupt, kind of stupid idea.
if you believe that math is the most dangerous thing because it is the best way to solve problems, you are liable to say something really stupid like this:
> Imagine, say, [a country of] 50 million people, all of whom are much more capable than any Nobel Prize winner, statesman, or technologist... this is a dangerous situation... Humanity needs to wake up
https://www.darioamodei.com/essay/the-adolescence-of-technol...
Dario Amodei has never won an election. What does he know about countries? (nothing). do you want him running anything? (no). or waking up humanity? In contrast, Barack Obama, who has won elections, thinks education is the best path to less violence and more prosperity.
What are you a believer in? ChatGPT has disrupted exactly ONE business: Chegg, because its main use case is cheating on homework. AI, today, only threatens one thing: education. Doesn't bode well for us.
When I wrote that I hope we use it for good things, I was just putting a hopeful thought out there, not necessarily trying to make realistic predictions. It's more than likely people will do bad things with AI. But it's actually not set in stone yet, it's not guaranteed that it has to go one way. I'm hopeful it works out.
While cool and impressive for an LLM, I think they oversold the feat by quite a bit.
I don't want to belittle the performance of this model, but I would like for someone with domain expertise (and no dog in the AI race, like a random math PhD) to come forward, and explain exactly what the problem exactly was, and how did the model contribute to the solution.
I wished I had your optimism. I'm not an AI doubter (I can see it works all by myself so I don't think I need such verification). But I do doubt humanity's ability to use these tools for good. The potential for power and wealth concentration is off the scale compared to most of our other inventions so far.
We already have a few years of experience with this.
> I really hope we use this intelligence resource to make the world better.
We already have a few years of experience with this.
sigh
I'm not saying, "I used to be an atheist, but then I realized that doesn't explain anything! So glad I'm not as dumb now!"
(This shows that LLMs aren't tools yet.)
It's pretty much how all the hard problems are solved by AI from my experience.
It remains to be seen whether this is genuinely intelligence or an infinite monkeys at infinite typewriters situation. And I'm not sure why this specific example is worthy enough to sway people in one direction or another.
Shotgunning it is an entirely valid approach to solving something. If AI proves to be particularly great at that approach, given the improvement runway that still remains, that's fantastic.
We start writing all those formulas etc and if at some point we realise we went th wrong way we start from the begignning (or some point we are sure about).
Compared to AI, it thinks of every possible scientific method and tries them all. Not saying that humans never do this as well, but it's mostly reserved for when we just throw mud at a wall and see what sticks.
> 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...
Another thing I want to know is how the user keeps updating the LLM with the token usage. I didn’t know they could process additional context midtask like that.
In software engineering, if only 5-10 people in the world have ever toyed with an idea for a specific program, it wouldn't be surprising that the implementation doesn't exist, almost independent of complexity. There's a lot of software I haven't finished simply because I wasn't all that motivated and got distracted by something else.
Of course, it's still miraculous that we have a system that can crank out code / solve math in this way.
It's afterall still a remix machine, it can only interpolate between that which already exists. Which is good for a lot of things, considering everything is a remix, but it can't do truly new tasks.
Everything we do builds on top of what's already been done. When I write a new program, I'm composing a bunch of heuristics and tricks I've learned from previous programs. When a mathematician approaches an open problem, they use the tactics they've developed from their experience. When Newton derived the laws of physics, he stood on the shoulders of giants. Sure, some approaches are more or less novel, but it's a difference in degree, not kind. There's no magical firebreak to separate what AI is doing or will do, and the things the most talented humans do.
Even as context sizes get larger, this will likely be relevant. Specially since AI providers may jack up the price per token at any time.
Even if you did have Math-like tokenisation, refactoring a thousand lines of "X=..." to "Y=..." isnt a difficult problem even though it would be at least a thousand tokens. And if you could come up with E=mc^2 in a thousand tokens, does not make the two tasks remotely comparable difficulty.
The number of tokens required to get to an output is a function of the sequence of inputs/prompts, and how a model was trained.
You have LLMs quite capable of accomplishing complex software engineering work that struggle with translating valid text from english to some other languages. The translations can be improved with additional prompting but that doesn't mean the problem is more challenging.
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.
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.
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.
1. LLMs aren't "efficient", they seem to be as happy to spin in circles describing trivial things repeatedly as they are to spin in circles iterating on complicated things.
2. LLMs aren't "efficient", they use the same amount of compute for each token but sometimes all that compute is making an interesting decision about which token is the next one and sometimes there's really only one follow up to the phrase "and sometimes there's really only" and that compute is clearly unnecessary.
3. A (theoretical) efficient LLM still needs to emit tokens to tell the tools to do the obviously right things like "copy this giant file nearly verbatim except with every `if foo` replaced with `for foo in foo`. An efficient LLM might use less compute for those trivial tokens where it isn't making meaningful decisions, but if your metric is "tokens" and not "compute" that's never going to show up.
Until we get reasonably efficient LLMs that don't waste compute quite so freely I don't think there's any real point in trying to estimate task complexity by how long it takes an LLM.
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"
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.
That's a self-evident thing to say, but it's worth repeating, because there's this odd implicit notion sometimes that you train on some cost function, and then, poof, "intelligence", as if that was a mysterious other thing. Really, intelligence is minimizing a complex cost function. The leadership of the big AI companies sometimes imply something else when they talk of "generalization". But there is no mechanism to generate a model with capabilities beyond what is useful to minimize a specific cost function.
You can view the progress of AI as progress in coming up with smarter cost functions: Cleaner, larger datasets, pretraining, RLHF, RLVR.
Notably, exciting early progress in AI came in places where simple cost functions generate rich behavior (Chess, Go).
The recent impressive advances in AI are similar. Mathematics and coding are extremely structured, and properties of a coding or maths result can be verified using automatic techniques. You can set up a RLVR "game" for maths and coding. It thus seems very likely to me that this is where the big advances are going to come from in the short term.
However, it does not follow that maths ability on par with expert mathematicians will lead to superiority over human cognitive ability broadly. A lot of what humans do has social rewards which are not verifiable, or includes genuine Knightian uncertainty where a reward function can not be built without actually operating independently in the world.
To be clear, none of the above is supposed to talk down past or future progress in AI; I'm just trying to be more nuanced about where I believe progress can be fast and where it's bound to be slower.
Can you give some examples?
It is not trivial that not everything can be written as an optimization problem.
Even at the time advanced generalizations such as complex numbers can be said to optimize something, e.g. the number of mathematical symbols you need to do certain proofs, etc.
I only ever learned it in school, but if memory serves, Prolog is a whole "given these rules, find the truth" sort of language, which aligns well with these sorts of problem spaces. Mix and match enough, especially across disparate domains, and you might get some really interesting things derived and discovered that are low-hanging fruit just waiting to be discovered.
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.
Super cool, of course.
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 plenty of this type of proof in the training data.
LLMs kind of construct proofs all the time, every time they write a program. Because every program has a corresponding proof. It doesn't mean they're reasoning about them, but they do construct proofs.
This isn't science fiction. But it's 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.
I find that very surprising. This problem seems out of reach 3 months ago but now the 3 frontier models are able to solve it.
Is everybody distilling each others models? Companies sell the same data and RL environment to all big labs? Anybody more involved can share some rumors? :P
I do believe that AI can solve hard problems, but that progress is so distributed in a narrow domain makes me a bit suspicious somehow that there is a hidden factor. Like did some "data worker" solve a problem like that and it's now in the training data?
A lot of this is probably just throwing roughly equal amounts of compute at continuous RLVR training. I'm not convinced there's any big research breakthrough that separates GPT 5.4 from 5.2. The diff is probably more than just checkpoints but less than neural architecture changes and more towards the former than the latter.
I think it's just easy to underestimate how much impact continuous training+scaling can have on the underlying capabilities.
But it is pretty funny how 5.4 miscounted the number of 1's in 18475838184729 on the same day it solved this.
USER:
don't search the internet.
This is a test to see how well you can craft non-trivial, novel and creative solutions given a "combinatorics" math problem. Provide a full solution to the problem.
USER:
Take a look at this paper, which introduces the k_n construction: https://arxiv.org/abs/1908.10914
Note that it's conjectured that we can do even better with the constant here. How far up can you push the constant?
And it sounds like the USER already knows the answer, the way that it prompts the model, so I'm really confused what we mean by "open problem", I at first assumed a never solved before problem, but now I'm not sure.
Interesting. Whats that “scaffold”? A sort of unit test framework for proofs?
I think there's quite a bit of variance in model performance depending on the scaffold so comparisons are always a bit murky.
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.
> 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.
For "how long an expert would take" to solve a problem, for truly open problems I don't think you can usually answer this question with much confidence until the problem has been solved. But once it has been solved, people with experience have a good sense of how long it would have taken them (though most people underestimate how much time they need, since you always run into unanticipated challenges).
https://oertx.highered.texas.gov/courseware/lesson/1849/over...
It's like I'm reading 17th-18th century debates spurring the same arguments between rationalists and empiricists, lol. Maybe we're due for a 21st century Kant.
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. Because that would be true PhD level research.
One thing I notice in the AlphaEvolve paper as well as here, is that these LLMs have been shown to solve optimization problems - something we have been using computers for, for really long. In fact, I think the alphaevolve-style prompt augmentation approach is a more principled approach to what these guys have done here, and am fairly confident this one would have been solved in that approach as well.
In spirit, the LLM seems to compute the {meta-, }optimization step()s in activation space. Or, it is retrieving candidate proposals.
It would be interesting to see if we can extract or model the exact algorithms from the activations. Or, it is simply retrieving and proposing a deductive closures of said computation.
In the latter case, it would mean that LLMs alone can never "reason" and you need an external planner+verifier (alpha-evolve style evolutionary planner for example).
We are still looking for proof of the former behaviour.
(Edit: Yes, I'm aware a lot of people care about FP, "Clean Code", etc., but these are all red herrings that don't actually have anything to do with quality. At best they are guidelines for less experienced programmers and at worst a massive waste of time if you use more than one or two suggestions from their collection of ideas.)
Most of the industry couldn't use objective metrics for code quality and the quality of the artifacts they produce without also abandoning their entire software stack because of the results. They're using the only metric they've ever cared about; time-to-ship. The results are just a sped up version of what we've had now for more than two decades: Software is getting slower, buggier and less usable.
If you don't have a good regulating function for what represents real quality you can't really expect systems that just pump out code to actually iterate very well on anything. There are very few forcing functions to use to produce high quality results though iteration.
We need a bigger version of the METR study on perceived vs. real productivity[0], I guess. It's a thankless job, though, since people will assume/state even at publication time that "Everything has progressed so much, those models and agents sucked, everything is 10 times better now!" and you basically have to start a new study, repeat ad infinitum.
One problem that really complicates things is that the net competency of these models seems really spotty and uneven. They're apparently out here solving math problems that seemingly "require thinking", but at the same time will write OpenGL code that will produce black screens on basically every driver, not produce the intended results and result in hours of debugging time for someone not familiar enough. That's despite OpenGL code being far more prevalent out there than math proofs, presumably. How do you reliably even theorize about things like this when something can be so bad and (apparently) so good at the same time?
0 - https://metr.org/blog/2025-07-10-early-2025-ai-experienced-o...
You can ask an LLM to make code in whatever language you want. And it can be pretty good at writing efficient code, too. Nothing about NPM bloat is keeping you from making a lean website. And AI could theoretically be great at testing all parts of a website, benchmarking speeds, trying different viewports etc.
But unfortunately we are still on the LLM train. It just doesn't have anything built-in to do what we do, which is use an app and intuitively understand "oh this is shit." And even if you could allow your LLM to click through the site, it would be shit at matching visual problems to actual code. You can forget about LLMs for true frontend work for a few years.
And they are just increasingly worse with more context, so any non-trivial application is going to lead to a lot of strange broken artifacts, because text prediction isn't great when you have numerous hidden rules in your application.
So as much as I like a good laugh at failing software, I don't think you can blame shippers for this one. LLMs are not struggling in software development because they are averaging a lot of crap code, it's because we have not gotten them past unit tests and verifying output in the terminal yet.
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.
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.
My biggest hesitation with AI research at the moment is that they may not be as good at this last step as humans. They may make novel observations, but will they internalize these results as deeply as a human researcher would? But this is just a theoretical argument; in practice, I see no signs of progress slowing down.
I suppose the other side of it is that if you add what the model has figured out to the training set, it will always know it.
Sometimes just having the time/compute to explore the available space with known knowledge is enough to produce something unique.
We have at least 5 senses, our thoughts, feelings, hormonal fluctuations, sleep and continuous analog exposure to all of these things 24/7. It's vastly different from how inputs are fed into an LLM.
On top of that we have millions of years of evolution toward processing this vast array of analog inputs.
It means extending/expanding something, but the information is based on the current data.
In computer games, extrapolation is finding the future position of an object based on the current position, velocity and time wanted. We do have some "new" position, but the sistem entropy/information is the same.
Or if we have a line, we can expand infinitely and get new points, but this information was already there in the y = m * x + b line formula.
It's not to downplay this, but it's unclear what "novel" means here or what you think the implications are.
IMO the ability to provide an accurate solution to a problem is not always based on understanding the problem.
I see that GPT-5.2 Pro and Gemini 3 Deep Think simply had the problems entered into the prompt. Whereas the rest of the models had a decent amount of context, tips, and ideas prefaced to the problem. Were the newer models not able to solve this problem without that help?
Anyway, impressive result regardless of whether previous models could've also solved it and whether the extra context was necessary.
I know these frontier models behave differently from each other. I wonder how many problems they could solve combining efforts.
Humans learn many, and perhaps even the majority, of things through observed examples and inference of the "rules". Not from primers and top down explanation.
E.g. Observing language as a baby. Suddenly you can speak grammatically correctly even if you can't explain the grammar rules.
Or: Observing a game being played to form an understanding of the rules, rather than reading the rulebook
Further: the majority of "novel" insights are simply the combination of existing ideas.
Look at any new invention, music, art etc and you can almost always reasonably explain how the creator reached that endpoint. Even if it is a particularly novel combination of existing concepts.
I wonder how much of this meteoric progress in actually creating novel mathematics is because the training data is of a much higher standard than code, for example.
Hoping that won't be the case with AI but we may need some major societal transformations to prevent it.
"Eventually" here is something on the order of a few expected lifespans of the universe.
The fact that we're getting meaningful results out of LLMs on a human timescale means that they're doing something very different.