This is impressive, no question.
Without knowing all this model has been trained on though, it is pretty hard to ascertain the extent to which it arrived to this "on its own". The entire AI industry has been (not so secretly) paying a lot of experts in many fields to generate large amounts of novel training data. Novel training data that isn't found anywhere else--they hoard it--and which could actually contain original ideas.
It isn't likely that someone solved this and then just put it in the training data, although I honestly wouldn't put that past OpenAI. More interesting though is the extent to which they've generated training data that may have touched on most or all of the "original" tenets found in this proof.
We can't know, of course. But until these things are built in a non-clandestine manner, this question will always remain.
Exactly. Maybe OpenAI paid mathematicians to keep this discovery quiet, then added their proof to the training data, then manipulated a second team into prompting for this question such that the model could regurgitate the solution. This would plausibly explain why the model seems so capable at doing things like refuting fundamental theorems of mathematics while in things like competitive programming, biology, and physics it's merely only in the top 99.9%.
You're a bot! Hey everyone, over here! I found a bot!
Seems like a very tin-foil-hat-take to me
I’m quite certain that a few months ago, some problems were claimed to be solved by AI. However, those claims were actually false and were exactly that, solved erdos problems that were not marked as solved and the solution was "found" by AI.
edit: >> https://techcrunch.com/2025/10/19/openais-embarrassing-math/
The corollary is that this is a very valuable capability of AI!
The ability to find incredibly obscure facts and recall them to solve "officially unsolved" problems in minutes is like Google Search on steroids. In some sense, it is one core component of "deep expertise", and humans rely on the same methodology regularly to solve "hard" problems. Many mathematicians have said that they all just use a "bag of tricks" they've picked up and apply them to problems to see if they work. The LLMs have a huge bag of very obscure tricks, and are starting to reach the point that they can effectively apply them also.
I suspect the threshold of AGI will be crossed when the AIs can invent novel "tricks" on their own, and memorise their own new approach for future use without explicitly having to have their weights updated with "offline" training runs.
How is that a "tin-foil-hat" take? It's not a secret, and in fact widely reported, that these companies are spending billions on creating training data.
So you think that OpenAI paid some mathematicians to either solve this conjecture problem, or a bunch of related unpublished math related to it, then fed it into an LLM model so they could announce it as being solved by the model? How is that not a conspiracy theory?
It is just a theory, the conspiracy part is not really applicable. I don't see what is controversial about it. Are you implying the machine taught itself the mathematics to do all this?
> Are you implying the machine taught itself the mathematics to do all this?
Are you asking me how LLMs work?
The theory proposed by the original commenter was that there could have been some secret training data the model was trained on that made it possible to solve this problem set. So the only conclusion is they are implying it's a conspiracy by OpenAI to hide some novel math research they funded merely to do marketing about solving math problems (then convincing multiple math experts to verify and support it with papers). That is the definition of a conspiracy.
I'm not letting the government read my brainwaves.
In all seriousness though: My suggestion is that those shepherding the frontier of AI start acting with more transparency, and stop acting in ways that encourage conspiratorial thinking. Especially if the technology is as powerful as they market it as.