OpenAI releases a range of new mathematical results produced by an internal model, with details like estimations of compute spent in terms of ChatGPT Pro usage

We're releasing a broad range of new mathematical results produced by an internal frontier model.

OpenAI 2026-10-07

Context & Ripple Effects

OpenAI had already presented its next-model research effort through 10 results spanning mathematics, quantum complexity, and theoretical computer science. The broader release shifts the evidence from a small set of claims toward manuscripts and proof artifacts that mathematicians can inspect.

Expressing the work in ChatGPT Pro usage gives the release an economic dimension alongside its research claims. That matters against OpenAI's own report that its compute expanded sharply between 2023 and 2025, as covered in its capacity and revenue disclosure.

First-order effects

Mathematicians gain access to manuscripts and supporting proof artifacts, making verification of the internal model's results the immediate test of OpenAI's claims.
OpenAI's ChatGPT Pro-based estimates make the inference demand behind the released work legible in a customer-facing unit rather than as an undifferentiated model demonstration.

Second-order effects

Researchers and evaluators can assess AI-generated mathematics on two linked dimensions: whether the artifacts substantiate the result and how much compute the work consumed.
Rival frontier labs face a more concrete comparison point for research-capability disclosures: inspectable proof material paired with task-level compute framing.

Third-order effects

If proof artifacts become standard for AI-generated research, scientific capability claims will be judged less by benchmark scores alone and more by reproducibility and verification workflows.
As frontier capacity is allocated between customer products and internal research agents, compute budgeting becomes part of deciding which scientific questions receive machine attention.

The trend: Frontier AI labs are moving from reporting mathematical performance to exposing the verification artifacts and inference economics behind machine-generated research.

Discussion

@openai @openai on x
We're releasing a broad range of new mathematical results produced by an internal frontier model. We've been consulting with the independent Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study, and we have drawn on their advice and public…
@ccatalini Christian Catalini on x
In the limit, humans become directors of intent and agent swarms do the work. A nice promotion for our species. One catch: whoever allocates the compute gets to decide whose intent counts. And we haven't worked out how to make sure that stays us.
@garymarcus Gary Marcus on x
since problem are asking, for the math stuff openAI - uses symbolic AI (Lean, etc) in addition to LLMs which is what i said for years we would need to do; this confirms what i actually said (as opposed to various fictitious misrepresentations that run rampant around here ) - stil…
@gdb Greg Brockman on x
towards acceleration of scientific discovery and improving quality of life for everyone
@natolambert Nathan Lambert on x
Naming the github repo for this “math” is hilarious [embedded post]
@hesamation @hesamation on x
mathematicians: frontier labs need to publish real proofs so we can check them, not blog posts OpenAI: fine. here's 722 papers [image] [embedded post]
@daniel_mac8 Dan McAteer on x
OpenAI is downplaying this for PR reasons. If you're a mathematician, you must feel like a nuclear bomb hit, and you're at ground zero. Reasoning models are two years-old. In that time they went from incapable of basic arithmetic to solving problems humans couldn't solve for deca…
@jdlichtman Jared Duker Lichtman on x
While reading their proof, important note: The cubic family of L-functions appear to be essential for the proof, even for the corollary to the Riemann zeta function
@cgtwts @cgtwts on x
math is solved it's so over
@moultano Ryan Moulton on x
Downside of dumping it all at once is that the feed isn't going to spend a week nicely explaining to me what each result is and why it's important.
@kenono691 Ken Ono on x
Our 2025 Nature Physics note aged quickly. OpenAI's release today makes clear that AI-assisted mathematical discovery at the highest level is no longer hypothetical.
@aisafetymemes @aisafetymemes on x
Suddenly, AI has solved 90 of the 500 most important open problems in mathematics Highest ranked problems: #2 Riemann Hypothesis — PARTIAL #4 Hodge Conjecture — PARTIAL #5 Birch and Swinnerton-Dyer Conjecture — PARTIAL #10 Extended Riemann hypothesis for Dedekind zeta functions —…
@nasqret Bartosz Naskręcki on x
I am browsing these results in awe. It's only going to get faster from here. Getting back to work. I have some big news to announce soon and they are not on that list, and we have a team of people interested to talk about them!
@cremieuxrecueil @cremieuxrecueil on x
This OpenAI math drop is nuts. This 7/8 quasi-Riemann hypothesis proof looks like one of the most important advances in analytical number theory in decades. And they also resolved one of the most famous decidability problems in number theory! Plus 3,998 more things! Oh my god.
@petergostev Peter Gostev on x
I probably spent 300 billion tokens on Hadwiger-Nelson problem (GPT-5.6 and Astra) and got absolutely nothing - and here it is, five-colours is no go, lower bound has moved to 6 or 7. Not a full solution yet, but it's a biggie.
@alexkontorovich Alex Kontorovich on x
Quasi-RH?!?!???! Are you kidding me? If a human did this, it would be an instant Fields Medal, no questions asked. RH says zeta has no zeros in Re(s)>1/2. The best we had until a second ago was a region that got thinner and thinner the higher up the imaginary axis you go. I …
@astrodanish Danish Hussain on x
how many fields will it eat before you realize it will eat every field?
@emostaque Emad on x
got 722 problems but the hodge conjecture ain't one
@mathemagic1an Jay Hack on x
Partial progress on 3 millenium prize problems: Riemann, Hodge and BSD
@acerfur @acerfur on x
oh yeah btw guys we can do integer multiplication faster than n log n lol I was definitely very surprised when this one came in lol https://github.com/...
@__alpoge__ Levent on x
Big, big, big, big props for quasiriemann and no Siegel zeroes (with many other beauties in there), I'm kicking myself for talking all over about it being within reach but not actually having pushed. There are some sad stories related to their users getting scooped / conflicts of…
@isaac__kim Isaac Kim on x
This contains a shocking list of problems in quantum information, many-body physics and quantum computing, the field that are dear to my heart. There are too many, but let me pick the following. 1. Proof of area law in 2D. 2. Spin-one Haldane gap 3. Parity is not in QAC^0 4. Cons…
@stevenstrogatz Steven Strogatz on x
Many staggering results here. But this is a particularly amazing one: the exponent for matrix multiplication is no more than 2.25. The previous world record had been something like 2.37. This leap in progress is like Bob Beamon's long jump. https://github.com/...
@jdlichtman Jared Duker Lichtman on x
This output is absolutely historic by any objective metric. However, it is not the Millenium problem rumor that was buzzing around in past weeks. Worth bearing in mind...
@willdepue Will Depue on x
i asked GPT 6 Pro and Fable 5.1 to rank all discoveries in the last three years 🔵 for Human discovered 🔴 for AI discovered (before October 6th) 🟢 for AI discovered from OpenAI/math repo 81% of them have been released today. wtf
@teortaxestex @teortaxestex on x
The cool thing is that they didn't really care that much about pure math, it's just a good hard eval. They want superhumanity in *applied* math very much; but most likely, no algorithmic discovery on the path to ASI requires of us to have solutions to Millennium Prize problems.
@thezvi Zvi Mowshowitz on x
Today is simultaneously the biggest day in mathematical history, and also felt kind of slow, okay, sure, 90 of the top 500 open problems in math, but what's news?
@jakehalloran1 Jake Halloran on x
Laughing that they had the math bomb uploaded to GitHub as anon so no one gets threats like alpoge did lol
@imjustnewatai @imjustnewatai on x
OpenAI just released 722 AI-written math papers. Here are the 4 biggest claims in plain English. None have been confirmed by outside mathematicians yet. 1/ Quasi-Riemann hypothesis. Zeta has no zeros with real part above 7/8. It's not the Riemann hypothesis (that needs 1/2), but …
@lechmazur Lech Mazur on x
A quick check shows that this list claims to fully solve 90 of the top 500 open problems in math ( https://proofatlas.ai/...). The highest ranked would be:
@fchollet François Chollet on x
What if the jagged frontier is mainly math + code (which you can push arbitrarily far with RLVR), and everything else starts to plateau because it is still bottlenecked by human generated data? Model performance in non-verifiable areas has kept improving steadily, albeit much slo…
@joeintheory Joe Bebel, PhD on x
This includes a claimed proof and Lean formalization of the Unique Games Conjecture, which I have been personally working on for the last year and a half.
@jdlichtman Jared Duker Lichtman on x
Another one: The Kakeya problem in 4-D! Just this summer, Hong Wang won the Fields medal for the Kakeya proof in 3-D (Wang-Zahl, 2026) https://github.com/...
@jdlichtman Jared Duker Lichtman on x
OpenAI has just released floodgates for 300+ solutions to math problems. Among them include a proof of: — a zero-free strip for the Riemann Zeta function — a proof of the Hodge conjecture for CM abelian varieties https://github.com/...
@kimmonismus @kimmonismus on x
HOLY, the rumors were true: OpenAI has published 722 mathematical manuscripts produced by an *unreleased* internal model. …
@khoomeik Rohan Pandey on x
kakeya conjecture in R^3 has been resolved (fields medal for hong wang this yr was for progress on this problem)
@jdlichtman Jared Duker Lichtman on x
Also related work on Birch-Swinnerton-Dyer https://github.com/...
@thsottiaux Tibo on x
Completely unrelated to the rest of the ships today, but our models did solve some important math problems and the team documented it in the following blogpost. Remarkable new era of scientific progress. https://openai.com/...
@littmath Daniel Litt on x
Fun! Looks like mathematicians have a lot of exciting work to do. If I understand correctly one of the results is a (very special) case of a conjecture of mine, which is also a consequence of stronger work in progress by a student of mine.
@sama Sam Altman on x
We are entering a new era of discovery now: https://openai.com/...
@deryatr_ Derya Unutmaz on x
Amazing! OpenAI just released solutions to hundreds of math problems: a GitHub repo with 722 manuscripts organized into 372 families. This incredible achievement was done with their internal Pro AI model, averaging 3 hours per problem. As @alexwg already said: math is cooked!
Bojan Tunguz Bojan Tunguz on linkedin
OpenAII just released hundreds of high end proofs and solutions using their internal model: — https://lnkd.in/... Here is the repo: — https://lnkd.in/... …
@emollick Ethan Mollick on bluesky
Context, OpenAI cracked or made important progress in hundreds of critical problems today — : openai.com/index/sharin...
@esqueer.net Alejandra Caraballo on bluesky
Oh my god, OpenAI just made the single largest advancement in mathematics and number theory in modern history. They released a quasi reimann hypothesis. This is just one of 722 proofs and advancements they released all at once. — github.com/openai/math [image]
@timkellogg.me Mr. Tim on bluesky
OpenAI has released 100 math results along with reasoning summaries, proofs, and descriptions of how they did it — this was done in coordination with the advisory group on mathematics and artificial intelligence — github.com/openai/math — openai.com/index/sharin...
@kjhealy.co Kieran Healy on bluesky
Hey how about 722 advanced math papers dumped on everyone's head. Don't worry, there's a forty page catalog summarizing all the claimed results. github.com/openai/math
r/theprimeagen r on reddit
The bubble is gonna pop trust
r/accelerate r on reddit
THE MATHEMATICS INDUSTRY HAS BEEN HIT BY AN UNKNOWN NUCLEAR WEAPON! (722 proofs released including an incomplete proof of the Riemann Hypothesis) …
r/slatestarcodex r on reddit
OpenAI - Sharing AI progress in mathematics
r/singularity r on reddit
OpenAI publishes 722 mathematical proofs & manuscripts
r/aiwars r on reddit
OpenAI: Sharing AI progress in mathematics
r/mathmemes r on reddit
Proof that AI is trained on brainrot
r/technology r on reddit
OpenAI: Sharing AI progress in mathematics
r/antiai r on reddit
Are we cooked?
r/mathematics r on reddit
OpenAI: Sharing AI progress in mathematics
r/OpenAI r on reddit
OpenAI: Sharing AI progress in mathematics
r/technology r on reddit
OpenAI unleashes hundreds more math results upon a field already in shock
r/EverythingScience r on reddit
OpenAI unleashes hundreds more math results upon a field already in shock
r/Btechtards r on reddit
Open AI releases the solutions to over 400 “big” open problems on GitHub
r/ArtificialInteligence r on reddit
OpenAI: Sharing AI progress in mathematics
@jehovahscript Jacob on x
imagine being a math PhD student with $400k in student loans and seeing this today
@kevinnbass Kevin Bass on x
AI is the biggest human advance since the discovery of fire. We are living and experiencing the most consequential few years in more than ten thousand years of human civilization. (Vote straight-red in the midterms.)
@sama Sam Altman on x
thank you to the machines, and the structure of reality, for letting us understand a little more.
@beffjezos @beffjezos on x
This is what Ilya saw.
@sama Sam Altman on x
looking up at the stars with extra awe tonight. “thy sea is so great and my boat is so small.”
@nickadobos Nick Dobos on x
Humans are officially done Ai is better at math than all humans combined This also means Ai is better at algorithm design, which means it can code things no human can Tipping point achieved. The only question left is how fast AI can recursively improve itself
@nellieblight Nellie on x
they're trying to make terrence tao kill himself
@cryptopunk7213 @cryptopunk7213 on x
2 years ago ai models were “incapable of basic arithmetic
@josusanmartin Josu San Martin on x
This is incredible
@matansf Matan Grinberg on x
In case you're further from the math community and wondering how to react to the latest news, Alex's reaction is a good bellwether
@hamandcheese Samuel Hammond on x
My partner is a theoretical computer scientist (essentially a mathematician). She has mixed feelings about AI's impact on math research overall, but her feeling about today's release is one of overwhelming awe and excitement. Literal tears of joy. Quote:
@petergostev Peter Gostev on x
“On average, each result used three hours of ChatGPT Pro thinking compute with [the unreleased internal OpenAI] model.” So these unsolved problems were solved in 3 hours each of next gen chatty pro? 💀
@quantian1 @quantian1 on x
You can do Fourier transforms in O(N log(N)^0.9999999999999) time. Fuck this gay chud universe
@hsu_steve Steve Hsu on x
A number of these results are in theoretical or mathematical physics! For example: A proof of spontaneous magnetization in quantum Heisenberg ferromagnets (Lean-verified) If it survives scrutiny, it would be the first rigorous proof of quantum ferromagnetic order and a landmark i…
@nicbstme Nicolas Bustamante on x
Looking at OpenAI releasing hundreds of mathematical results, I think we really have to lead with empathy here. When you've spent years learning a craft, whether it's writing code, creating illustrations or doing mathematics, and suddenly a lot of what you do seems to be a prompt…
@sreeramkannan Sreeram Kannan on x
THE MATH SINGULARITY IS HERE and it is screaming at us to pay attention. OpenAI solved 722 really hard math problems. Solving even ONE of these problems is a big deal. I have been on the bandwagon that AI will reinvent theoretical algorithms for 8 years (see figure). And still th…
@austen Austen Allred on x
It's really not that impressive though, all it's doing is stochastically predicting what a Fields Medal winner would say as they did their research
@nrehiew_ @nrehiew_ on x
wh (@nrehiew_) on X
@dwlz Dan Loewenherz on x
Why do people act like mathematicians aren't the happiest people on earth right now? Who's going to check that all this stuff is right? Some random 20-something software engineer at a big lab who didn't know what a field was until yesterday? Gimme a break.
@scaling01 @scaling01 on x
I find it hard to believe that any scientific breakthrough could prevent everyday people from turning more anti-AI over the next few years. And I don't think this depends on AI pushing up unemployment. I think it depends on the gap between when breakthroughs pay off for companies…
@amoylan @amoylan on x
I am begging frontier labs to devote their bleeding-edge internal models to something (anything) that would positively impact the life of a median American here, now, today. These math challenges feel like a tomorrow problem, given that today's problem is, roughly,
@emollick Ethan Mollick on x
After a brief but institution-eroding slop science era, it increasingly looks like we are going to have two revolutions from AI: 1) Everything ever published will be re-read and re-judged in ways that human scientists never anticipated 2) Novel discoveries will start to come fast
@pedrobeltrao Pedro Beltrao on bluesky
Open AI released 722 manuscripts (skipping preprint server) on 372 families of math problems. On average it took their internal model a few hours each. Despite the scientific advance this must be a difficult day for the thousands (?) of people that were working on these. github…
@deanwball Dean W. Ball on x
I really recommend you savor the renaissance-flavored part of this transformation. Even if you're not a mathematician, try to sit with one or two of these results and understand them conceptually. It is a beautiful day.
@tszzl Roon on x
we are breathing rarefied air
@ejenk Evan Jenkins on x
Every mathematician rn
@scottsantens Scott Santens on x
“The new model—which the company has not released to the public—produced almost every one of the results in response to a single prompt handed to a single AI agent.” That sentence is insane. https://www.scientificamerican.com/ ...
@wtgowers Timothy Gowers on bluesky
I'd like to add that we are very aware that we are not representative of the mathematical community, and for that reason we greatly value the approximately 500 views we have received via a form linked to here. — agmai.org
Ritendra Datta Ritendra Datta on linkedin
Today is one of the most important days for Mathematics. We shared proofs of 372 of the hardest open problems in Math solved by an internal model. …
Todd Austin Todd Austin on linkedin
Watching the reaction to OpenAI's latest math announcement, I keep thinking about the Valley of Sorrow that many Computer Vision (CV) researchers went through in the early 2010s. …
r/france r on reddit
OpenAI Releases Findings on 377 Math Problems, Further Roiling Field
r/Destiny r on reddit
Open AI just solved 90 of the world's most difficult maths problems in one go
r/neoliberal r on reddit
OpenAI Releases Findings on 377 Math Problems, Further Roiling Field
r/technology r on reddit
OpenAI Releases Findings on 377 Math Problems, Further Roiling Field
@krishnanrohit Rohit on x
Truly a country of genuises in a data center is here. Extraordinary!
Juan Meza Juan Meza on linkedin
Hard to beat this quote for insight from Kai Shaikh, one of the graduate students interviewed for this article: …
@_nathancalvin Nathan Calvin on x
“If I were OpenAI, I would be asking this model to immediately target major unsolved problems in AI R&D.” It seems safe to assume OAI and their peer companies are applying these internal models to AI R&D and this should inspire a feeling somewhat resembling severe vertigo
@deedydas Deedy on x
OpenAI's math release is, in the words of Opus, “the single most consequential mathematical release ever
@drakefjustin Justin Drake on x
Today I call upon the blockchain industry to calmly begin planning for “bunker mode
@deredleritt3r Prinz on x
OpenAI's internal model clearly has “research taste” in math - i.e., the final component we need to get to RSI. - jboggan (post on Hacker News) on Barnette's Conjecture:
r/Futurology r on reddit
OpenAI Releases Findings on 377 Math Problems, Further Roiling Field
Preston Bradham Preston Bradham on linkedin
My background is in applied mathematics so I've been nerding out over this one. — OpenAI just released hundreds of new mathematical results …
r/ArtificialInteligence r on reddit
OpenAI unleashes hundreds more math results upon a field already in shock
@robinhanson Robin Hanson on x
It seems that few expect big impact in non-math areas from these big new math results. Which suggests that math has long been in its own little world mostly detached from issues that matter to others. Prestige props to AI, but sad when prestige so detached from impact.
r/artificial r on reddit
OpenAI unleashes hundreds more math results upon a field already in shock

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