Because validity doesn't depend on meaning. Take the classic example: "What is north of the North Pole?". This is a valid phrasing of a question, but is meaningless without extra context about spherical geometry. The trick question in reference is similar in that its intended meaning is contained entirely in the LLM output.
I was not replying to your remark, but rather, a later comment regarding the "validity" vs "sensibility". I don't see where I made any distinction concerning wanting to wash cars.
But now I suppose I'll engage your remark. The question is clearly a trick in any interpretive frame I can imagine. You are treating the prompt as a coherent reality which it isn't. The query is essentially a logical null-set. Any answer the AI provides is merely an attempt to bridge that void through hallucinated context and certainly has nothing to do with a genuine desire to wash your car.
Because to 99.9% people it’s obvious and fair to assume that person asking this question knows that you need a car to wash it. No one ever could ask this question not knowing this, so it implies some trick layer.
"GPT did this". Authored by Guevara (Institute for Advanced Study), Lupsasca (Vanderbilt University), Skinner (University of Cambridge), and Strominger (Harvard University).
Probably not something that the average GI Joe would be able to prompt their way to...
I am skeptical until they show the chat log leading up to the conjecture and proof.
I'm a big LLM sceptic but that's… moving the goalposts a little too far. How could an average Joe even understand the conjecture enough to write the initial prompt? Or do you mean that experts would give him the prompt to copy-paste, and hope that the proverbial monkey can come up with a Henry V? At the very least posit someone like a grad student in particle physics as the human user.
I would interpret it as implying that the result was due to a lot more hand-holding that what is let on.
Was the initial conjecture based on leading info from the other authors or was it simply the authors presenting all information and asking for a conjecture?
Did the authors know that there was a simpler means of expressing the conjecture and lead GPT to its conclusion, or did it spontaneously do so on its own after seeing the hand-written expressions.
These aren't my personal views, but there is some handwaving about the process in such a way that reads as if this was all spontaneous involvement on GPTs end.
But regardless, a result is a result so I'm content with it.
Hi I am an author of the paper. We believed that a simple formula should exist but had not been able to find it despite significant effort. It was a collaborative effort but GPT definitely solved the problem for us.
Oh that's really cool, I am not versed in physics by any means, can you explain how you believed there to be a simple formula but were unable to find it? What would lead you to believe that instead of just accepting it at face value?
There are closely related "MHV amplitudes" which naively obey a really complicated formula, but for which there famously also exists a much simpler "Parke-Taylor formula". Alfredo had derived a complicated expression for these new "single-minus amplitudes" and we were hoping we could find an analogue of the simpler "Parke-Taylor formula" for them.
In this case there certainly were experts doing hand-holding. But simply being able to ask the right question isn't too much to ask, is it? If it had been merely a grad student or even a PhD student who had asked ChatGPT to figure out the result, and ChatGPT had done that, even interactively with the student, this would be huge news. But an average person? Expecting LLMs to transcend the GIGO principle is a bit too much.
The Average Joe reads at an 8th grade level. 21% are illiterate in the US.
LLMs surpassed the average human a long time ago IMO. When LLMs fail to measure up to humans, it's that they fail to measure up against human experts in a given field, not the Average Joe.
they probably also acknowledge pytorch, numpy, R ... but we don't attribute those tools as the agent who did the work.
I know we've been primed by sci-fi movies and comic books, but like pytorch, gpt-5.2 is just a piece of software running on a computer instrumented by humans.
I don't see the authors of those libraries getting a credit on the paper, do you ?
>I know we've been primed by sci-fi movies and comic books, but like pytorch, gpt-5.2 is just a piece of software running on a computer instrumented by humans.
And we are just a system running on carbon-based biology in our physics computer run by whomever. What makes us special, to say that we are different than GPT-5.2?
> And we are just a system running on carbon-based biology in our physics computer run by whomever. What makes us special, to say that we are different than GPT-5.2?
Do you really want to be treated like an old PC (dismembered, stripped for parts, and discarded) when your boss is done with you (i.e. not treated specially compared to a computer system)?
But I think if you want a fuller answer, you've got a lot of reading to do. It's not like you're the first person in the world to ask that question.
You misunderstood, I am prohumanism. My comment was about challenging the believe that models cant be as intelligent as we are, which cant be answered definitely, though a lot of empirical evidence seems to point to the fact, that we are not fundamentally different intelligence wise. Just closing our eyes will not help in preserving humanism, so we have to shape the world with models in a human friendly way, aka alignment.
It's always a value decision. You can say shiny rocks are more important than people and worth murdering over.
Not an uncommon belief.
Here you are saying you personally value a computer program more than people
It exposes a value that you personally hold and that's it
That is separate from the material reality that all this AI stuff is ultimately just computer software... It's an epistemological tautology in the same way that say, a plane, car and refrigerator are all just machines - they can break, need maintenance, take expertise, can be dangerous...
LLMs haven't broken the categorical constraints - you've just been primed to think such a thing is supposed to be different through movies and entertainment.
I hate to tell you but most movie AIs are just allegories for institutional power. They're narrative devices about how callous and indifferent power structures are to our underlying shared humanity
Their point is, would you be able to prompt your way to this result? No. Already trained physicists working at world-leading institutions could. So what progress have we really made here?
No it’s like saying: New expert drives new results with existing experts.
The humans put in significant effort and couldn’t do it. They didn’t then crank it out with some search/match algorithm.
They tried a new technology, modeled (literally) on us as reasoners, that is only just being able to reason at their level and it did what they couldn’t.
The fact that the experts were a critical context for the model, doesn’t make the models performance any less significant. Collaborators always provide important context for each other.
My understanding is there's been around 10 erdos problems solved by GPT by now. Most of them have been found to be either in literature or a very similar problem was solved in literature. But one or two solutions are quite novel.
I am not aware of any unsolved Erdos problem that was solved via an LLM. I am aware of LLMs contributing to variations on known proofs of previously solved Erdos problems. But the issue with having an LLM combine existing solutions or modify existing published solutions is that the previous solutions are in the training data of the LLM, and in general there are many options to make variations on known proofs. Most proofs go through many iterations and simplifications over time, most of which are not sufficiently novel to even warrant publication. The proof you read in a textbook is likely a highly revised and simplified proof of what was first published.
If I'm wrong, please let me know which previously unsolved problem was solved, I would be genuinely curious to see an example of that.
"We tentatively believe Aletheia’s solution to Erdős-1051 represents an early example of an AI system autonomously resolving a slightly non-trivial open Erdős problem of somewhat broader (mild) mathematical interest, for which there exists past literature on closely-related problems [KN16], but none fully resolves Erdős-1051. Moreover, it does not appear to us that Aletheia’s solution is directly inspired by any previous human argument (unlike in
many previously discussed cases), but it does appear to involve a classical idea of moving to the series tail and applying Mahler’s criterion. The solution to Erdős-1051 was generalized further, in a collaborative effort by Aletheia together with human mathematicians and Gemini Deep Think, to produce the research paper [BKK+26]."
"The erdosproblems website shows 851 was proved in 1934." I disagree with this characterization of the Erdos problem. The statement proven in 1934 was weaker. As evidence for this, you can see that Erdos posed this problem after 1934.
You recommended I look at the erdosproblems website.
But evidence that it was posed after 1934 is not really evidence it was not solved, because one of the things we learned from LLMs was that many of these problems were already solved in the literature, or are relatively straightforward applications of known, yet obscure, results. Particularly in the world of Erdos problems, the majority of which can be described as "off the beaten path" and are basically musings in papers that Erdos was asking -- many of these are in fact solved in more obscure articles and no one made the connection until LLMs allowed us to do systematic literature searches. This was the primary source of "solutions" of these problems by LLMs in the cited paper.
The Erdos Problem site also does not say it was solved in 1934. If you read the full sentence there, it refers to a different statement proven which is related.
Yeah that was also my take-away when I was following the developments on it. But then again I don't follow it very closely so _maybe_ some novel solutions are discovered. But given how LLMs work, I'm skeptical about that.
I honestly don't see the point of the red data points. By now all the erdos problems have been attempted by AIs--so every unsolved one can be a red data point.
Order - transitive verb - 1. to put in order : arrange - "The books are ordered alphabetically by author."
noun - 4. b(1) the arrangement, organization, or sequence of objects or of events - "alphabetical/chronological/historical order" "listed the items in order of importance"
Sort - transitive verb - 1. to put in a certain place or rank according to characteristics - "sort the mail" "sorted the winners from the losers" "sorting the data alphabetically"
noun - 5. an instance of sorting - "a numeric sort of a data file"
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