> 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.
Remember, the basis of these models is unsupervised training, which, at sufficient scale, gives it the ability to to detect pattern anomalies out of context.
For example, LLMs have struggled with generalized abstract problem solving, such as "mystery blocks world" that classical AI planners dating back 20+ years or more are better at solving. Well, that's rapidly changing: https://arxiv.org/html/2511.09378v1
That is, even if there are cool things that LLM make now more affordable, the level of bullshit marketing attached to it is also very high which makes far harder to make a noise filter.
Kinda funny because that looked _very_ close to what my Opus 4.6 said yesterday when it was debugging compile errors for me. It did proceed to explore the other vector.
This is the crucial part of the comment. LLMs are not able to solve stuff that hasn't been solve in that exact or a very similar way already, because they are prediction machines trained on existing data. It is very able to spot outliers where they have been found by humans before, though, which is important, and is what you've been seeing.
This is very common already in AI.
Just look at the internal reasoning of any high thinking model, the trace is full of those chains of thought.
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 in its training data.
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"?
What really happened here was that the LLM produced a python script that generated examples of hypergraphs that served as proof by example.
And the only thing that has been verified are these examples. The LLM also produced a lot of mathematical text that has not been analyzed.
- Edit: I can't reply, probably because the comment thread isn't allowed to go too deep, but this is a good argument. In my mind the argument isn't that coding is harder than math, but that the problems had resisted solution by human researchers.
So really this is no different from generating any python program. There are also many examples of combinatoric construction in python training sets.
It's still a nice result, but it's not quite the breakthrough it's made out to be. I think that people somehow see math as a "harder" domain, and are therefore attributing more value to this. But this is a quite simple program in the end.
Some human researchers are also remixers to Some degree.
Can you imagine AI coming up with refraction & separation lie Newton did?
That being said, I think this is a great question. Did Einstein and Newton use a qualitatively different process of thought when they made their discoveries? Or were they just exceedingly good at what most scientists do? I honestly don't know. But if LLMs reach super-human abilities in math and science but don't make qualitative leaps of insight, then that could suggest that the answer is 'yes.'
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?
You can make that claim about anything: "The human isn't being creative when they write a novel, they're just summoning patterns at typing time".
AlphaGo taught itself that move, then recalled it later. That's the bar for human creativity and you're holding AlphaGo to a higher standard without realizing it.
AlphaGo didn't teach itself that move. The verifier taught AlphaGo that move. AlphaGo then recalled the same features during inference when faced with similar inputs.
No. AlphaGo developed a heuristic by playing itself repeatedly, the heuristic then noticed the quality of that move in the moment.
Heuristics are the core of intelligence in terms of discovering novelty, but this is accessible to LLMs in principle.
Ok so it sounds like you want to give the rules of Go credit for that move, lol.
I don't really play Go but I play chess, and it seems to me that most of what humans consider creativity in GM level play comes not in prep (studying opening lines/training) but in novel lines in real games (at inference time?). But that creativity absolutely comes from recalling patterns, which is exactly what OP criticizes as not creative(?!)
I guess I'm just having trouble finding a way to move the goalpost away from artificial creativity that doesn't also move it away from human creativity?
Mixing the two (training and construction) is rhetorically convenient (anthropomorphization), but holds us back in critically assessing a model’s capabilities.
The opposite is true as well. Emergent complexity isn’t limitless. Just like early physicists tried to explain the emergent complexity of the universe through experimentation and theory, so should we try to explain the emergent complexity of LLMs through experimentation and theory.
Specifically not pseudoscience, though.
Physicists had the real world to verify theories and explanations against.
So far anyone 'explaining the emergent complexity of LLMs through experimentation and theory' is essentially just making stuff up nobody can verify.
- OP asked for someone to make a logical argument for the separation of “training” from “model”
- I made the argument
- You cherry picked an argument against my specific example and made an appeal to emergent complexity
- I pointed out that emergent complexity isn’t limitless
- “the only people making unsupported claims in this thread are those trying to deflate LLM capabilities”What does linear regression have to do with the limitations of a stacked transfer ? Absolutely nothing. This is the problem here. You don't know shit and just make up whatever. You can see people doing the same thing in GPT-1, 2, 3, 4 threads all telling us why LLMs will never be able to do thing it manages to do later.
lol. Why so emotionally charged? Are you perhaps worried that you’ve invested too much time and effort into a technology that may not deliver what influencers have been promising for years? Like a proverbial bagholder?
> What does linear regression have to do with the limitations of a stacked transfer ? Absolutely nothing. This is the problem here.
We’re talking about fundamental concepts of modeling in this subthread. LLMs, despite what influencers may tell you, are simply models. I’ll even throw you a bone and admit they are models for intelligence. But they are still models, and therefore all of the things that we have learned about “models” since Plato are still relevant. Most importantly, since Plato we’ve known that “models” have fundamental limits vs. what they try to represent, otherwise they would be a facsimile, not a model.
> You can see people doing the same thing in GPT-1, 2, 3, 4 threads all telling us why LLMs will never be able to do thing it manages to do later.
I hope you enjoy winning these imaginary arguments against these imaginary comments. The fundamental limitations of LLMs discussed since GPT-1 have never been addressed by changing the architecture of the underlying model. All of the improvements we’ve experienced have been due to (1) improvements in training regime and (2) harnesses / heuristics (e.g. Agents).
Now, care to provide a counterargument that shows you know a little more than “shit”?
Okay, but the brain is also “just a model” of the world in any meaningful sense, so that framing does not really get you anywhere. Calling something a model does not, by itself, establish a useful limit on what it can or cannot do. Invoking Plato here just sounds like pseudo-profundity rather than an actual argument.
>I hope you enjoy winning these imaginary arguments against these imaginary comments. The fundamental limitations of LLMs discussed since GPT-1 have never been addressed by changing the architecture of the underlying model. All of the improvements we’ve experienced have been due to (1) improvements in training regime and (2) harnesses / heuristics (e.g. Agents).
If a capability appears once training improves, scale increases, or better inference-time scaffolding is added, then it was not demonstrated to be a 'fundamental impossibility'.
That is the core issue with your argument: you keep presenting provisional limits as permanent ones, and then dressing that up as theory. A lot of people have done that before, and they have repeatedly been wrong.
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.
It's not "thinking." It's not "solving." It's simply stringing words together in a way that appears most likely.
ChatGPT cannot do math. It can only string together words and numbers in a way that can convince an outsider that it can do math.
It's a parlor trick, like Clever Hans [1]. A very impressive parlor trick that is very convincing to people who are not familiar with what it's doing, but a parlor trick nontheless.
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.
When an LLM is "reasoning" it's just feeding its own output back into itself and giving it another go.
And by the way, I don't think it's surprising that so many people are being unreasonable on this issue, there is a lot at stake and it's implications are transformative.
This is a good example of being confidently misinformed.
The best move is always a result of calculation. And the calculation can always go deeper or run on a stronger engine.
Even if it is, this sounds like "this submarine doesn't actually swim" reasoning.
What am I as a human doing when I "Do math" ?
1.I am looking at the problem at hand, identifying what I have and what I need to get
2.I am then doing a prediction using my pretrained neural net to find possible courses of action to go in a direction that "feels" right
3.I am using my pretrained neural net to find pairs of values that I can substitute with each other (Think multiplication tables, standard results, etc...)
4.Repeat till I arrive at the answer or give up.
As a simple example, when I try to find 600×74+42 I remember the steps for multiplication. I recall the associated pairs of numbers from my tables and complete the multiplication step by step. I then recall the associated pairs of numbers for addition of single digits and add from left to right.
We need to remember that just because we are fast at doing this and are able to do it subconsciously it doesn't mean that we can natively do math, we just do association of information using the neural networks we have trained.
It can produce outputs that resemble calculations.
It can prompt an agent to input some numbers into a separate program that will do calculations for it and then return them as a prompt.
Neither of these are calculations.
You are wrong. Especially that we are talking about models with 50T parameters.
Can they do arbitrary computations for arbitrarily long numbers? Nope. But that's not remotely the same statement, and they can trivially call out to tools to do that in those cases.
Edit: the implication comes from demanding that the OP’s definition must be rigorous enough to cover all models of “computation”, and by failing to do so, it means that LLMs must be more like humans than computers.
I think there are differences, and I think we can make good guesses, but I'm not sure we can reliably classify a P-zombie from a normal human from their behaviour with 100% accuracy..
“What are you doing?”, asked Minsky.
“I am training a randomly wired neural net to play Tic-Tac-Toe” Sussman replied.
“Why is the net wired randomly?”, asked Minsky.
“I do not want it to have any preconceptions of how to play”, Sussman said.
Minsky then shut his eyes.
“Why do you close your eyes?”, Sussman asked his teacher.
“So that the room will be empty.”
At that moment, Sussman was enlightened.
-- from the jargon file
Virtually all output from people is based in things the person has experienced.
People aren't designed to objectively track each and every event or observation they come across. Thus it's harder to verify. But we only output what has been inputted to us before.
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.
Interesting similitude, because I expect an Italian to be able to communicate somewhat successfully with a French person (and vice versa) even if they do not share a language.
The two languages are likely fairly similar in latent space.
Please reproduce this string, reversed:
c62b64d6-8f1c-4e20-9105-55636998a458
I think there are examples of what you’re looking for, but this isn’t one.
LLMs can use data in their prompt. They can also use data in their context window. They can even augment their context with persisted data.
You can also roll out LLM agents, each one with their role and persona, and offload specialized tasks with their own prompts, context windows, and persisted data, and even tools to gather data themselves, which then provide their output to orchestrating LLM agents that can reuse this information as their own prompts.
This is perfectly composable. You can have a never-ending graph of specialized agents, too.
Dismissing features because "all of the data is in the prompt" completely misses the key traits of these systems.
> how could anything it produces not fall under the "already in the model" umbrella
It doesn't. That is the point of my comment.
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.
This is specious reasoning. If you look at each and every single realization attributed to "creativity", each and every single realization resulted from a source of inspiration where one or more traits were singled out to be remixed by the "creator". All ideas spawn from prior ideas and observations which are remixed. Even from analogues.
> 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.
My only claim is that precisely this is incorrect.
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.
A bog standard random number generator or even a flipping coin can produce novel output at will. That's a weird thing to fault LLMs for? Novelty is easy!
See also how genetic algorithms and re-inforcement learning constantly solve problems in novel and unexpected ways. Compare also antibiotics resistances in the real world.
You don't need smarts for novelty.
Where I see the problem is producing output that's both high quality _and_ novel. On command to solve the user's problem.
This is false.
I guess that's one way to tell us apart from AIs.
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 calculation and hand the task off to a calculator, and then receive the calculator's output as a prompt even.
But it is fundamentally impossible for an LLM to perform a calculation entirely on its own, the same way it is fundamentally impossible for an image recognition AI to suddenly write an essay or a calculator to generate a photo of a giraffe in space.
People like to think of "AI" as one thing but it's several things.
In either case, this "it's a language model" is a pretty dumb argument to make. You may want to reason about the fundamental architecture, but even that quickly breaks down. A sufficiently large neural network can execute many kinds of calculations. In "one shot" mode it can't be Turing complete, but in a weird technicality neither does your computer have an infinite tape. It just simply doesn't matter from a practical perspective, unless you actually go "out of bounds" during execution.
50T parameters give plenty of state space to do all kinds of calculations, and you really can't reason about it in a simplistic way like "this is just a DFA".
Let alone when you run it in a loop.
Either one. An LLM cannot solve 3+5 by adding 3 and 5. It can only "solve" 3+5 by knowing that within its training data, many people have written that 3+5=8, so it will produce 8 as an answer.
An LLM, similarly, cannot simulate a Turing machine. It can produce a text output that resembles a Turing machine based on others' descriptions of one, but it is not actually reading and writing bits to and from a tape.
This is why LLMs still struggle at telling you how many r's are in the word "strawberry". They can't count. They can't do calculations. They can only reproduce text based on having examined the human corpus's mathematical examples.
The reason "strawberry" is hard for LLMs is that it sees $str-$aw-$berry, 3 identifiers it can't see into. Can you write down a random word your just heard in a language you don't speak?
Nor our brains, in fact.
By your definition, humans can't perform calculation either. Only a calculator can.
You can already do this today with every frontier modal. You can give it an image and have it write an essay from it. Both patches (parts of images) and text get turned into tokens for the language the LLM is learning.
You're also correlating "mathematics" and "calculation". Who cares about calculation, as you say, we have calculators to do that.
Mathematics is all just logical reasoning and exploration using language, just a very specific, dense, concise, and low level language. But you can always take any mathematical formula and express it as "language" it will just take far more "symbols"
This might be the worse take on this entire comment section. And I'm not even an overly hyped vibe coder, just someone who understands mathematics