Famously, someone in the last year claimed a proof of the Collatz conjecture verified in Lean, which turned out to be wrong.
Not the same as releasing a bad proof, but apparently result #311 may have been plagiarized from work someone uploaded to chatgpt on September 6.
True, if a non-expert outside the walls of OpenAI did the same then that would be just as bad. But I just don't think that that justifies the non-experts inside OpenAI doing it.
OpenAI posted 372 families of AI math results, including a claimed Unique Games proof. A computer has checked about 42%, but mathematicians say almost nobody understands them yet.
But we don't need OpenAI to publish this, no? Probably the same results were already being prompted by other more responsible researchers. Those people would have written a good paper immediately, without first putting out sloppy or faulty manuscripts. Example:
Everybody complains about the abysmal quality of the writeups. So OpenAI is making the state of the literature actively worse. I would not call contributing.
Consider: they say it took them 3 hours of compute per problem. Why publish that? Its not like nobody else would have found it soon anyway
Turns out 3 of the papers have been retracted based on a sign error in one of them.
github.com/openai/math/...
turns out openai might have vibed out a slop drive by millenium prize proof that makes basic mistakes like
"We show that the formalised Lean proof does not correspond to the [written paper] proof of blow-up of solutions to the Navier-Stokes equations."
arxiv.org/abs/2610.08144
its kind of funny that something named clippy also casually moonlights as a very useful formal verification tool (in so far as intent can be encoded into disallowed methods)
the OAI proof dump makea me mad even though there are like, a couple dozen Fields medals lurking in there
reverse-centauring an entire field of deep thinkers and turning them into quality checkers
we are not ready for our weird, human peer reviewless future
The other case is when no human understand the AI proof (in all its detail). This is the case for essentially all recent OpenAI proofs. Here they have several detailed suggestions:
alongside it is largely garbage, openai still has generated a lean proof of finite-time NS blowup. that's not nothing, that's still a marvelous result. the complicated artifact can be picked apart to try to reverse-engineer the proof, that would be interesting research in and of itself
AI companies approach mathematical proof the way people who only care about their own orgasm approach sex
#NaviesStokes lost in translations: #Lean can verify a formal proof perfectly well, while the #AI may have changed the actual #mathematical argument during translation
📝 arxiv.org/abs/2610.08144
#mathematics
1/N
It may be "the most significant moment in mathematical history." AI is solving hundreds of enduring math mysteries.
“If a human did this, it would be an instant Fields Medal, no questions asked,” said one math professor.
Also also, throwing computing power at math isn't necessarily going to give you more insight. The leaps of logic required to solve problems have typically required human creativity and the Millennium Prize problems are no exception.
It doesn't prove theorems, though. It outputs proof-shaped objects and they have more chance of resembling a real proof than when it outputs most other objects, because of the very specific nature of that training data.
Clearly there’s a distinction between knowledge associated with intimate understanding of every line of a proof and knowledge based on testimony, but I don’t see any general motive for ruling out this style of social trust, esp if e.g. there’re widespread successful efforts on kernel soundness.
Proofs are fine if after being read, the meaning overlaps with the appropriate usage. Then if an AI generated a proof, congrats! You can write a paper knowing the argument contained is correct. But you can't call something a proof if you don't read it!
Since no axiomatic system can prove its own consistency (thanks Gödel), it just feels stupid to let AI keep generating unintuitive, obscure proofs that only pass formal verification and can’t be demonstrated in practise.
As threatened, OpenAI dropped a shitload of math papers. 722 to be precise: https://github.com/openai/math/blob/main/overview.pdf None solve Millennium Prize Problems or other ultra-famous conjectures. Paper number 312 proves a version of the Homotopy Hypothesis, one of my favorite math problems. I guess I was the first to call it the homotopy hypothesis. It says homotopy types are "the same&…
Will “The Lean proof that OpenAI provided isn’t the same as their printed proof, so who knows if any of it is actually right” get as much publicity as the original PR, I wonder.
The final 20% is 80% of the work. Whether it’s a website, a Photoshop knock-off, or a Millennium prize problem
Well, how else are you going to get your hands on those Millennium Prize winnings?
I think the entire "dump" itself is irresponsible, to be quite honest. If, instead, they had taken the time to (a) use their model to produce a proof / solve a problem and (b) had it peer reviewed and validated before then publishing it, I think there would be a lot more good will.
Hmmm... Publicity stunt? Attention grab? Anyway, peer review pending... #OpenAI has posted hundreds of solutions and progress toward 372 major #math problems in a release of 722 manuscripts on #GitHub https://www.engadget.com/2279815/openai-just-posted-hundreds-more-results-on-major-math-problems/ #zeitgeist
When I'm thinking about AI in mathematics I end up thinking about the moon landings. It's not a perfect analogy. But there are some parallels. We tend to look back at them as a somewhat collective achievement of humanity; we're right to, I think. But the concentration of wealth in one place due to an arms race is what got us over the line. LLMs don't just stand on the shoulders of…
They are doing their verification in Lean, and with certain. caveats, most syntactically valid expressions in Lean are a proof of something, however trivial. So you churn out vast volumes of valid proofs, in there somewhere you are going to have some interesting ones. 2/3
Of course a lot of mathematicians will be fired by AI pilled middle managers because hey, with AI you can just do it
...With 'just' being 'comprehending the applicability of said proof' and 'it' being 'implementing the result within practical reality'
So I wish them all a happy being-rehired
importantly, most theorems in pure mathematics are exhaust fumes from other things (training, trying to build collective understanding, maintaining systems of employment and recognition, etc), so this is a different kind of exhaust but it's not unrelated
So long, math. We’ve had a good run.
OpenAI Releases 722 Papers Tied To Unsolved Math Problems
OpenAI's 722 math papers ship with Lean formalizations, which means the claims can be machine-checked rather than peer-reviewed by people. Verification by compiler is a different kind of proof than consensus.
But pumping the gas doesn't just solve famous problems that get newspaper headlines--like the Navier Stokes millennium prize problem--they solve a bunch of other problems collaterally too.
I think I’ve always felt like this for art, but its definitely made me realise I also feel like this about math and it changed my half formed philosophical views on proofs. Oh an AI was so good it solved a millennium prize problem? I genuinely don’t care
Terry Tao @teorth.bsky.social: Indiscriminate brute-force application of AI to mathematics is depleting the field of good questions without renewing this resource or providing commensurate value.
OpenAI: We hear you. Here's a .zip file with 377 hasty AI solutions to important open problems.
Yea in this case we probably wouldn't learn much from what the LLM tried that didn't work but I think we could start to grasp the contours of what they can and can't do in math.
We could begin to hypothesize the shape of theorems and proof techniques LLMs may or may not be good at.
welcome to the era of good enough. as long as the proof works right, that's all that matters? there is no point in discovery anymore; it's just about finding the end point. smiles.
I am shocked to learn that the Abundance Conjecture has been solved by OpenAI but they couldn't solve Termination of Flips. I always thought it'd be the other way around. I'm even more shocked to learn that the proofs are for compact Kähler varieties and not just for projective ones. #math #algebraicgeometry #mmp #openai #maths
Paper is the most AI written monstrosity ever. Just straight into the proof, no motivation, no connection to other areas, no implications for what this means and why its important.
The "single prompt" part hides the checking. A proof for those math problems can be verified line by line, so a wrong answer gets caught. Most tasks I hand to ChatGPT or Claude have no checker like that, which is why I still read every line
Okay, OpenAI just dropped news that their frontier model is solving open math problems. And get this: they're sharing the Lean proof formalizations and research details on GitHub! Not just results, but how they got there. That's a huge deal for advancing AI in complex fields. 🤯 #AI #Mathematics