Claim: GPT-5-pro can prove new interesting mathematics
66 comments
·August 20, 2025whymauri
svantana
Interesting! Depending on your definition, "automated invention" has been a thing since at least the 1990's. An early success was the evolved antenna [1].
hhh
IBM has done this with pharmaceuticals for ages no? That’s why they have patents on what would be the next generation of ADHD medications e.g. 4F-MPH?
wenc
A lot of interesting possibilities lie in latent space. For those unfamiliar, this means the underlying set of variables that drive everything else.
For instance, you can put a thousand temperature sensors in a room, which give you 1000 temperature readouts. But all these temperature sensors are correlated, and if you project them down to latent space (using PCA or PLS if linear, projection to manifolds if nonlinear) you’ll create maybe 4 new latent variables (which are usually linear combinations of all other variables) that describe all the sensor readings (it’s a kind of compression). All you have to do then is control those 4 variables, not 1000.
In the chemical space, there are thousands of possible combinations of process conditions and mixtures that produce certain characteristics, but when you project them down to latent variables, there are usually less than 10 variables that give you the properties you want. So if you want to create a new chemical, all you have to do is target those few variables. You want a new product with particular characteristics? Figure out how to get < 10 variables (not 1000s) to their targets, and you have a new product.
timClicks
It's been a while since I've played in the area, but is PCA still the go to method for dimensionality reduction?
wenc
PCA (essentially SVD) the one that makes the fewest assumptions. It still works really well if your data is (locally) linear and more or less Gaussian. PLS is the regression version of PCA.
There are also nonlinear techniques. I’ve used UMAP and it’s excellent (particularly if your data approximately lies on a manifold).
https://umap-learn.readthedocs.io/en/latest/
The most general purpose deep learning dimensionality reduction technique is of course the autoencoder (easy to code in PyTorch). Unlike the above, it makes very few assumptions, but this also means you need a ton more data to train it.
baq
PCA is nice if you know relationships are linear. You also want to be aware of TSNE and UMAP.
pojzon
If AI comes up with new drugs or treatments - does it mean its a public knowledge and cant be copyrighted ?
Wouldnt that mean a fall of US pharmaceutical conglomate based on current laws about copyright and AI content?
selkin
Drugs discovered by humans are not under the protections of copyright as well.
ACCount37
Hallucinations or inhuman intuition? An obvious mistake made by a flawed machine that doesn't know the limits of its knowledge? Or a subtle pattern, a hundred scattered dots that were never connected by a human mind?
You never quite know.
Right now, it's mostly the former. I fully expect the latter to become more and more common as the performance of AI systems improves.
kmarc
Reminds me of this story on the Babbage podcast a month ago:
https://www.economist.com/science-and-technology/2025/07/02/...
My understanding is, iterating on possible sequences (of codons, base pairs, etc) is exactly what LLMs, these feedback-looped predictor machines, are especially great at. With the newest models, those that "reason about" (check) their own output, are even better at it.
freshtake
An interesting debate!
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
bawolff
> 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.
If you could combine this with automated theorem proving, it wouldn't matter if it was right only 1 out of a 1000 times.
energy123
4. How many times has this happened already but the human took credit for the output because they don't have the incentive to give credit to the LLM
OtomotO
Yeah, how many times?
How many times did a stochastic parrot by pure chance bring words into an order that made up a new proof?
And why should a stochastic parrot get any credit?
AaronAPU
Are you referring to the person or the LLM?
DonHopkins
How many times have you stochastically parroted that term?
foobarqux
> This is one example. How many other attempts did the person try that failed to be useful, accurate, coherent?
High chance given that this is the same guy that came up with SVG unicorn (sparks of AGI) which raises the same question even more obviously.
aabhay
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.
SkyPuncher
For me it comes down to signal vs noise.
I’m absolutely confident that AI/LLM can solve things, but you have to shift through a lot of crap to get there. Even further, it seems AI/LLM tend to solve novel problems in very unconventional ways. It can be very hard to know if an attempt is doomed, or just one step away from magic.
null
teeray
At that point, is it really solving or is it just monkeys with typewriters?
fwip
"Monkeys with typewriters," is in one sense, a uniform sampling of the probability space. A brute-force search, even when using structured proof assistants, take a very long time to find any hard proof, because the possibility space is roughly (number of terms) raised to the power of (length of the proof).
But similarly to how a computer plays chess, using heuristics to narrow down a vast search space into tractable options, LLMs have the potential to be a smarter way to narrow that search space to find proofs. The big question is whether these heuristics are useful enough, and the proofs they can find valuable enough, to make it worth the effort.
tcshit
I like the idea of letting AI try to formulate new math problems that are interesting, i.e. worthy research level. I guess we are still a number of iterations away till AI get there though..
xenotux
I think a simple way to take emotion out of this is to ask if a computer can beat humans at math. The answer to that is pretty much "duh". Symbolic solvers and numerical methods outperform humans by a wide margin and allow us to reach fundamentally new frontiers in mathematics.
But it's a separate question of whether this is a good example of that. I think there is a certain dishonesty in the tagline. "I asked a computer to improve on the state-of-the-art and it did!". With a buried footnote that the benchmark wasn't actually state-of-the-art, and that an improved solution was already known (albeit structured a bit differently).
When you're solving already-solved problems, it's hard to avoid bias, even just in how you ask the question and otherwise nudge the model. I see it a lot in my field: researchers publish revolutionary results that, upon closer inspection, work only for their known-outcome test cases and not much else.
Another piece of info we're not getting: why this particular, seemingly obscure problem? Is there something special about it, or is it data dredging (i.e., we tried 1,000 papers and this is the only one where it worked)?
foobarqux
As others have said computers already help prove theorems like the four color theorem. It’s not that shocking that LLMs can prove a relative handful of obscure theorems. An alpha-theorem (neural net directed “brute force” search) type system will probably also be able to prove some theorems. There is no evidence today that there will be a massive breakthrough in math due to those systems let alone through LLM type systems.
If LLMs were already a breakthrough in proving theorems, even for obscure minor theorems, there would be a massive increase in published papers due to publish or perish academic incentives.
drudolph914
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
martinpw
> 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.
DennisP
Maybe we should think of current AIs as not so much artificial intelligence, as collective intelligence. Which itself can be extremely valuable.
xigoi
It turns out that if you use a fancy search engine to search instead of pretending that it’s intelligent, it will actually be good at its job. Who would have guessed?
mhh__
How would we know it was referencing an old paper versus almost everything trivial already having a derivation somewhere?
fwip
One signal is to check the journal. Most reputable journals won't publish a paper claiming a new technique if it's actually trivial and well-known.
leeoniya
> but what actually happened was chatGPT was referencing papers that basically went unread from lesser famous labs/researchers
now let's invalidate probably 70% of all patents
jsw97
I know this was a throwaway, but finding prior art for a large group of existing patents would be a cool application.
nybsjytm
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.
marcuschong
More comments from another mathematician:
https://x.com/ErnestRyu/status/1958408925864403068?t=QmTqOcx...
EcommerceFlow
The coolest part about this IMO is they used the same model we all have access to (GPT5-Pro), and not some secret invite only model.
dinobones
Are we sure this guy is not someone being mirrored by a recursive non-governmental system?
Context: https://x.com/GeoffLewisOrg/status/1945864963374887401
aeve890
What does this even mean? This read like a SCP thing.
semi-extrinsic
It is exactly SCP regurgitated by the LLM, and this guy thinks it's all true.
IceDane
This is either satire that's over my head or mental illness.
StilesCrisis
This is one of 4o’s biggest flaws. If you are a conspiracy theorist, it’ll confirm any outlandish theory you can come up with, and provide invented receipts to go with it. Of course, it’s just model hallucinations, but for those who are already primed to believe that secrets are being kept, it gives the “evidence” they were always looking for.
osti
In here https://blog.google/products/gemini/gemini-2-5-deep-think/, the professor google worked with also claimed proving some previously unproven conjecture.
42lux
I guess arithmetic is just harder for an LLM than higher math.
bubblyworld
Arithmetic is harder for mathematicians than higher maths too =P not even joking. It was a meme in my university's maths dept for a reason.
PartiallyTyped
In a group, you’d usually let the freshest handle splitting the bill because everyone else forgot arithmetic.
therobots927
it might take a while but their answer would always be correct. the same cannot be said for LLMs.
soulofmischief
Mathematicians make calculations in their errors all the time.
bubblyworld
Yeah, of course I agree with that =)
mikert89
I cannot wait that all we hold to be holy and sacred about the human mind, to be slowly unravelled by ai. It will remove the chains of the status associated with these fields, and allow people to move into higher modes of being
sunrunner
What are these higher modes? I'm very excited to hear about them.
bgwalter
Yes, that is why the chess world championship allows Stockfish assistance in order to democratize chess.
strangescript
It can't reason -> It can't make new discoveries -> It can only tie together bespoke missed data -> It can make some basic discoveries -> ??????
ACCount37
It doesn't outsmart the entirety of humankind combined, so it's not actually intelligent. Duh.
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.