interesting if true, but this isn't the first time we heard of something like this
quanta published an article that talked about a physics lab asking chatGPT to help come up with a way to perform an experiment, and chatGPT _magically_ came up with an answer worth pursuing. but what actually happened was chatGPT was referencing papers that basically went unread from lesser famous labs/researchers
this is amazing that chatGPT can do something like that, but `referencing data` != `deriving theorems` and the person posting this shouldn't just claim "chatGPT derived a better bound" in a proof, and should first do a really thorough check if it's possible this information could've just ended up in the training data
> what actually happened was chatGPT was referencing papers that basically went unread from lesser famous labs/researchers
Which is actually huge. Reviewing and surfacing all the relevant research out there that we are just not aware of would likely have at least as much impact as some truly novel thing that it can come up with.
Any mathematicians who have actually called it "new interesting mathematics", or just an OpenAI employee?
The paper in question is an arxiv preprint whose first author seems to be an undergraduate. The theorem in it which GPT improves upon is perfectly nice, there are thousands of mathematicians who could have proved it had they been inclined to. AI has already solved much harder math problems than this.
1. This is one example. How many other attempts did the person try that failed to be useful, accurate, coherent? The author is an OpenAI employee IIUC, so it begs this question. Sora's demos were amazing until you tried it, and realized it took 50 attempts to get a usable clip.
2. The author noted that humans had updated their own research in April 2025 with an improved solution. For cases where we detect signs of superior behavior, we need to start publishing the thought process (reasoning steps, inference cycles, tools used, etc.). Otherwise it's impossible to know whether this used a specialty model, had access to the more recent paper, or in other ways got lucky. Without detailed proof it's becoming harder to separate legitimate findings from marketing posts (not suggesting this specific case was a pure marketing post)
3. Points 1 and 2 would help with reproducibility, which is important for scientific rigor. If we give Claude the same tools and inputs, will it perform just as well? This would help the community understand if GPT-5 is novel, or if the novelty is in how the user is prompting it
I don't mean to be cynical, but I don't think these points matter as much as you think, at least not in practice. The hardest part of a proof is working out the intermediate steps; joining them up is often trivial, even for a student. So even if it works out a few good steps or finds an effective theorem to apply, and does so only every one in a hundred prompts, the time savings can be significant.
I should know, I've been using LLM thinking models to help brainstorm ideas for stickier proofs. It's been more successful at discovering esoteric entry points than I would like to admit.
I don’t get why so many people are resistant to the concept that AI can prove new mathematical theorems.
The entire field of math is fractal-like. There are many, many low hanging fruits everywhere. Much of it is rote and not life changing. A big part of doing “interesting” math is picking what to work on.
A more important test is to give an AI access to the entire history of math and have it _decide_ what to work on, and then judge it for both picking an interesting problem and finding a novel solution.
1. There's this huge misconception that LLMs are literally just memorizing stuff and repeating patterns from their training data
2. People glamorize math and feel like advancements in it would "be AGI"
They don't realize that having it generate "new math" is not much harder than having it generate "new programs." Instead of writing something in Python, it's writing something in Lean.
A monkey hammering gibberish on a keyboard can prove new math given sufficient time. That's a low bar to set. The question is if the signal-to-noise ratio is high enough for it to be worthwhile.
I used to work at a drug discovery startup. A simple model generating directly from latent space 'discovered' some novel interactions that none of our medicinal chemists noticed e.g. it started biasing for a distribution of molecules that was totally unexpected for us.
Our chemists were split: some argued it was an artifact, others dug deep and provided some reasoning as to why the generations were sound. Keep in mind, that was a non-reasoning, very early stage model with simple feedback mechanisms for structure and molecular properties.
In the wet lab, the model turned out to be right. That was five years ago. My point is, the same moment that arrived for our chemists will be arriving soon for theoreticians.
I wanted to know how to set the environment variables for CGI in IIS.
The GPT 5 thoughts made a totally unrelated picture and then gave the wrong answer.
If you think of this as a search, retrieval and “application” problem on the space of convex optimization proof techniques, it’s not a particularly striking result to a mathematician. Partly because: the space of results/techniques and crucially applications of those results and proof techniques is very rich (it’s an active field with many follow up papers).
On the other hand, I have a collection of unpublished results in less active fields that I’ve tested every frontier model on (publicly accessible and otherwise) and each time the models have failed to solve them. Some of these are simply reformulations of results in the literature that the models are unable to find/connect which is what leads me to formulate this as a search problem with the space not being densely populated enough in this case (in terms of activity in these subfields).
I'm not sure why this is surprising or newsworthy; it has been this way ever since o3. I guess few people noticed.
There are a few masters-level publishable research problems that I have tried with LLMs on thinking mode, and it had produced a nearly complete proof before we had a chance to publish it. Like the problem stated here, these won't set the world on fire, but they do chip away at more meaningful things.
It often doesn't produce a completely correct proof (it's a matter of luck whether it nails a perfect proof), but it very often does enough that even a less competent student can fill in the blanks and fix up the errors. After all, the hardest part of a proof is knowing which tools to employ, especially when those tools can be esoteric.
Hypothesis: If you had ~1M dollar to burn, I think we should try setting up an AI agent to explore and try to invent new mathematics. It turns out agents can get an IMO gold with Gemini 2.5 Pro production model only. Therefore I suspect a swarm of agents burning through tokens like there's no tomorrow can invent new math.
Alternative: If Gemini Deep Think or GPT5-Pro people are listening, I think they should give free access to their models with potential scaffolding (ie. agentic workflow) to say some ~100 researchers to see if any of them can prove new math with their technology.
48 comments
[ 117 ms ] story [ 1214 ms ] threadquanta published an article that talked about a physics lab asking chatGPT to help come up with a way to perform an experiment, and chatGPT _magically_ came up with an answer worth pursuing. but what actually happened was chatGPT was referencing papers that basically went unread from lesser famous labs/researchers
this is amazing that chatGPT can do something like that, but `referencing data` != `deriving theorems` and the person posting this shouldn't just claim "chatGPT derived a better bound" in a proof, and should first do a really thorough check if it's possible this information could've just ended up in the training data
Which is actually huge. Reviewing and surfacing all the relevant research out there that we are just not aware of would likely have at least as much impact as some truly novel thing that it can come up with.
now let's invalidate probably 70% of all patents
Context: https://x.com/GeoffLewisOrg/status/1945864963374887401
The paper in question is an arxiv preprint whose first author seems to be an undergraduate. The theorem in it which GPT improves upon is perfectly nice, there are thousands of mathematicians who could have proved it had they been inclined to. AI has already solved much harder math problems than this.
https://x.com/ErnestRyu/status/1958408925864403068?t=QmTqOcx...
Bad at arithmetic, promising at math: https://www.lesswrong.com/posts/qy5dF7bQcFjSKaW58/bad-at-ari...
A few things to consider:
1. This is one example. How many other attempts did the person try that failed to be useful, accurate, coherent? The author is an OpenAI employee IIUC, so it begs this question. Sora's demos were amazing until you tried it, and realized it took 50 attempts to get a usable clip.
2. The author noted that humans had updated their own research in April 2025 with an improved solution. For cases where we detect signs of superior behavior, we need to start publishing the thought process (reasoning steps, inference cycles, tools used, etc.). Otherwise it's impossible to know whether this used a specialty model, had access to the more recent paper, or in other ways got lucky. Without detailed proof it's becoming harder to separate legitimate findings from marketing posts (not suggesting this specific case was a pure marketing post)
3. Points 1 and 2 would help with reproducibility, which is important for scientific rigor. If we give Claude the same tools and inputs, will it perform just as well? This would help the community understand if GPT-5 is novel, or if the novelty is in how the user is prompting it
I should know, I've been using LLM thinking models to help brainstorm ideas for stickier proofs. It's been more successful at discovering esoteric entry points than I would like to admit.
The entire field of math is fractal-like. There are many, many low hanging fruits everywhere. Much of it is rote and not life changing. A big part of doing “interesting” math is picking what to work on.
A more important test is to give an AI access to the entire history of math and have it _decide_ what to work on, and then judge it for both picking an interesting problem and finding a novel solution.
1. There's this huge misconception that LLMs are literally just memorizing stuff and repeating patterns from their training data 2. People glamorize math and feel like advancements in it would "be AGI"
They don't realize that having it generate "new math" is not much harder than having it generate "new programs." Instead of writing something in Python, it's writing something in Lean.
So then, what are they doing?
I'm seeing people creating full apps with GPT-5-pro, but nothing is novel.
Just discussed the "impressiveness" of it creating a gameboy emulator from scratch.
(There's over 3500 gameboy emulators on github. I would be suprised if it failed to produce a solution with that much training data).
Where's the novel break-throughs?
As it stands today, I'm sure it can produce a new ssl implementation or whatever it has been trained on, but to what benefit???
https://mathstodon.xyz/@tao/114881418225852441
https://mashable.com/article/openai-claims-gold-medal-perfor...
Note that no one expressed skepticism of what google said when they claimed they achieved gold medal. But no one is willing to believe OpenAI.
Our chemists were split: some argued it was an artifact, others dug deep and provided some reasoning as to why the generations were sound. Keep in mind, that was a non-reasoning, very early stage model with simple feedback mechanisms for structure and molecular properties.
In the wet lab, the model turned out to be right. That was five years ago. My point is, the same moment that arrived for our chemists will be arriving soon for theoreticians.
But yes, it's getting better and better.
On the other hand, I have a collection of unpublished results in less active fields that I’ve tested every frontier model on (publicly accessible and otherwise) and each time the models have failed to solve them. Some of these are simply reformulations of results in the literature that the models are unable to find/connect which is what leads me to formulate this as a search problem with the space not being densely populated enough in this case (in terms of activity in these subfields).
There are a few masters-level publishable research problems that I have tried with LLMs on thinking mode, and it had produced a nearly complete proof before we had a chance to publish it. Like the problem stated here, these won't set the world on fire, but they do chip away at more meaningful things.
It often doesn't produce a completely correct proof (it's a matter of luck whether it nails a perfect proof), but it very often does enough that even a less competent student can fill in the blanks and fix up the errors. After all, the hardest part of a proof is knowing which tools to employ, especially when those tools can be esoteric.
Reference: https://arxiv.org/abs/2507.15855
Alternative: If Gemini Deep Think or GPT5-Pro people are listening, I think they should give free access to their models with potential scaffolding (ie. agentic workflow) to say some ~100 researchers to see if any of them can prove new math with their technology.