October 6, 2026, a public GitHub repository
OpenAI uploads a folder of 721 math papers. All of them were written by an unreleased internal model, with no human researcher's name on them. According to the company, they tackle about 372 open problems, some open for more than a century.
The next day, OpenAI is already withdrawing three papers over a sign error and revising 14 more. And within two weeks, some of the world's top mathematicians check one of the proofs, cut it down to three pages and say: it's correct.
Both things are true at once. And that's the whole story.
On October 6, 2026, OpenAI's AI published what the company describes as solutions and progress on about 372 open math problems. I went through the announcement, what mathematicians have checked since and the criticism, and ran a few numbers of my own that haven't been published anywhere. One term that keeps coming up: Lean, software that checks a math proof step by step, like a calculator checking arithmetic. A proof that passes Lean doesn't depend on anyone's opinion of it, as long as someone made sure the computer checked the right question.
In short
- OpenAI's AI wrote 721 papers on about 372 open math problems. About 42% of the main results were also checked by computer.
- Two big results have expert backing: a proof that Siegel zeros don't exist (checked and shortened), and the quasi-Riemann hypothesis (experts largely agree, checking continues). The Navier–Stokes claim from September is disputed.
- By my calculation, only about 9% of the problems the model attempted ended in a claimed solution or progress. Checking, not writing, is now the slow part.
- The pace is speeding up: from gold at the student olympiad in July 2025 to hundreds of claims on open problems took about 15 months. For a business, the lesson is simple: AI is most reliable where it can be checked.
My take, at a glance
My take: AI is already solving open math problems, and the checkers can't keep up
This isn't another "almost". Exactly a year ago, OpenAI was publicly embarrassed: a senior executive, Kevin Weil, wrote that GPT-5 had solved ten open Erdős problems, and it turned out the model had only found old papers that had already solved them. This time there are new proofs. Leading mathematicians have read them, and even shortened one to three pages.
But picture a student handing in 721 exam booklets in one night. Even if most are good, the teachers need months to grade them, and he's already writing the next batch. That's what happened here. OpenAI itself calls the papers "raw research data, rather than polished academic papers". About half haven't been checked by computer. The limit is no longer the ability to solve, but the ability to check.
And that, I think, is also the lesson for anyone working with AI, including a business owner with an agent. We'll come back to it at the end.
What OpenAI published in math, by the numbers
Source: the README in the github.com/openai/math repository, October 6, 2026 (721 papers in 373 families). Retraction Watch counts 722 papers on 372 problems.
The model isn't available to the public, and neither are the prompts it was given. OpenAI published summaries of the reasoning process for only ten families of results. The next day it pulled three papers in an area called Hodge theory over a sign error, and revised 14 more.
The three results everyone's talking about, in plain English
What's claimed, and where checking stands
Green: confirmed by outside experts. Orange: experts largely agree, checking continues. Red: disputed. Sources: Quanta Magazine, Terence Tao's blog and The Next Web.
The quasi-Riemann hypothesis ("almost Riemann"). The prime numbers (2, 3, 5, 7, 11...) look randomly scattered. In 1859, Bernhard Riemann showed that their distribution is governed by a list of special points, the "zeros" of a single function. His hypothesis: all these points sit exactly on one line, down the middle of a strip. Back in 1896 it was proved that no point lies on the edges of the strip. But for 160 years, nobody could show they keep a fixed distance from the edges.
Picture a three-lane highway. Riemann claimed every car drives exactly down the middle. Until now, all we knew was that no car drives right on the shoulder, but the farther down the road you go, they could get as close to it as you like. OpenAI's model proved for the first time that every car keeps a fixed distance from the shoulders along the entire road: all the points lie between 1/12 and 11/12 of the width. The experts checking the proof, including Maksym Radziwill of NYU, largely agree it's correct. Radziwill added that the papers are poorly written. And Peter Sarnak of Princeton says he won't call it a "theorem" until humans check every detail.
Siegel zeros. For about a century, mathematicians couldn't rule out a single "bad zero". If it exists, it throws off many calculations about primes, such as how many primes fall in each arithmetic progression. Like a suspect who was never caught, but never cleared either. The model wrote a 9-page proof that it doesn't exist. Within two weeks, several mathematicians, including Ben Green of Oxford, wrote shorter versions, and Tao posted a sketch on his blog. One mathematician, Hector Pasten, wrote that the proof "settles the question".
Navier–Stokes. Equations that describe how fluids flow, from coffee in a cup to air around a wing. The question, one of the Clay Mathematics Institute's seven "Millennium Prize Problems": can a smooth flow suddenly reach infinite velocity? In September, a month before the 721, OpenAI announced: yes, if someone keeps "stirring the cup" from outside. It argues this answers one of the official formulations of the problem, which allows such an external force. But most mathematicians see the question without outside stirring as the heart of the problem, and the Clay Institute hasn't ruled yet. OpenAI itself wrote that it won't claim the million-dollar prize. On top of that, Tristan Buckmaster of NYU says OpenAI took a direction from work he hadn't yet published with a coauthor. OpenAI denies it, but added credit to both for parallel work.
And there are more big claims no expert has confirmed yet. One: a theoretical method for matrix multiplication, the operation AI chips are built on, with an exponent of 2.25 instead of the previous record of about 2.37. Theoretical gains like this usually don't speed up a real computer, because they only win on problem sizes that don't exist in practice.
My calculation: from 4,000 attempts to a handful of confirmed results
You won't find these numbers in OpenAI's announcement. I calculated them from the data it published:
The checking funnel: what's left at each stage
Platin Digital's calculation from OpenAI's README: 373 families of results out of about 4,000 problems is about 9.3%; 42% of 373 is about 157. Last row: Siegel zeros and the quasi-Riemann hypothesis, per reports through October 27. Other results may have been checked without being reported.
How much work went into Navier–Stokes alone
10,000 agents, 88 hours and 130 billion tokens: according to OpenAI, via The Next Web. "Computer-years" and "cost" are my calculation: 10,000 × 88 divided by 8,760 hours in a year; 130 billion × $10 to $50 per million tokens. The internal model isn't sold and its real price is unknown.
What this means: these results didn't come out of a $20 subscription. Each of the 721 results got an average of about 3 hours of reasoning from OpenAI's strongest model, after 4,000 attempts, and Navier–Stokes alone consumed hundreds of thousands of agent-hours. What does reach businesses: models from the same family, in cheaper versions, can already work for hours on a single task and check their own work.
What's changed since the 2025 embarrassment
October 2025
- "GPT-5 solved 10 Erdős problems"
- In reality: it found old papers that had already solved them
- DeepMind's CEO: "This is so embarrassing"
- Zero new solutions
October 2026
- New proofs to famous problems
- About 42% passed a computer check
- Top experts checked, and one was cut to three pages
- An independent advisory group of 9 mathematicians, at the Institute for Advanced Study in Princeton
Sources: The Decoder (October 2025), Quanta Magazine, Fortune and agmai.org (2026).
Still, not everything has changed. Volume again outran checking, papers were pulled after a day, and the model and prompts weren't released, so no one outside OpenAI can reproduce the results.
What mathematicians are saying
For
- Dan Litt, Toronto: "this is great for mathematics"
- James Maynard, Fields Medal winner: ideas "not terribly mainstream", combined "in an exceptionally clever way"
- Hector Pasten: the Siegel zeros proof "settles the question"
Against, or wary
- Terence Tao: "excessive emphasis on automated solving of open problems by AI"
- Hugo Duminil-Copin, Fields Medal winner: "They have annihilated my field of research"
- 28 Fields Medal winners signed a letter against turning open problems into an AI benchmark
Litt: Fortune. Pasten: Scientific American. Tao: his blog. Maynard, Duminil-Copin and the letter: via Wikipedia's summary of reporting by Science and Le Monde, and the letter itself on Zenodo.
The sharpest criticism isn't about whether the proofs are correct. It's about understanding. Math isn't just knowing that something is true, but understanding why. Melanie Wood, a member of the advisory group, described the results as "the beginning, not the completion, of the process of human understanding". Tao calls the direction he wants "Math 2.0": AI that helps the community understand, not just ticks off problems.
The pace: from the olympiad to open problems in about 15 months
AI milestones in math
- DeepMind's AlphaGeometrySolves olympiad geometry problems at nearly gold-medal level
- Silver at the International Math OlympiadDeepMind, 28 of 42 points
- Olympiad goldOpenAI and Google DeepMind, 35 of 4212 months after silver
- The "ten Erdős problems" fiascoNot one new solution
- A 1946 Erdős conjecture disprovedNine outside mathematicians checked it. Timothy Gowers: worthy of the field's top journal10 months after gold
- The Navier–Stokes claimFollowed by more than 100 open problems3.5 months
- 721 papers, ~372 problemsTwo big results already have expert backingOne month
Sources: DeepMind's blog, Quanta Magazine, The Decoder, The Next Web and OpenAI. Gaps between dates: my calculation.
The gaps keep shrinking: 12 months, 10, then 3.5. The last month is mostly the announcement cadence of the same OpenAI program, not a new leap. This isn't a law of nature, and the pace may slow, but it's been the direction for the past two years.
And there's an important gap between benchmarks and real work. FrontierMath is a test of hard math problems that already have solutions. On its hardest tier, the best models scored about 5% in July 2025, and according to OpenAI, its model reached 97.6% in September 2026. But on a test of 68 genuinely open Erdős problems, published by Epoch in September, the best model solved 3%, and all the rest zero:
A test with answers vs. genuinely open problems
Sources: Epoch AI (FrontierMath Erdős, September 1, 2026); OpenAI, via reports, for 97.6%. Different versions of the test aren't fully comparable. 5% is the score when the hardest tier launched in July 2025.
A benchmark nearly saturated within about a year, at least by OpenAI's numbers. An open problem, where nobody knows whether a solution even exists, is still a different story. OpenAI's 721 are a leap there, but they came from an enormous compute budget, and from 4,000 attempts.
Where AI in math is heading in 2027
What's been announced, and what I predict
The goals: MIT Technology Review and reports from September 2026. The advisory group: agmai.org. The prediction is my opinion, not data.
One more sign of which way the wind is blowing: according to Quanta, Jacob Tsimerman announced in July 2026, the same day he won the Fields Medal, that he's leaving academia for OpenAI. And the Israeli mathematician Noga Alon told Quanta that AI is "changing dramatically the way mathematical research is being done".
What I didn't find: any serious source linking these results to breaking encryption, new drugs or actually faster chips. You'll probably see headlines like that. Right now, they have no basis.
What AI solving math problems means for your business
The lesson here has nothing to do with prime numbers. It's about checking. The model did best where something could check it: software like Lean, or an expert who can read a proof. And even a brilliant model got one sign wrong, and three papers fell. What caught the mistake was checking, not more thinking.
- Is the website up
- Do the totals in the report add up
- Do the links work
- Does the code pass its tests
- A post to publish
- A reply to a customer
- A change to an ad
- A price quote
- "We solved it" with no proof
- A figure with no link
- Legal or medical advice
That's how the agents I set up are built, too. What can be checked automatically, the agent does and checks on its own. What can't comes to you for approval before it goes out. Why models sometimes make things up with total confidence, we explain in What is an AI hallucination, and how an agent works, in What is an AI agent.
I usually build agents on Hermes Agent, an open-source framework, and pick the model that fits each business: OpenAI, Anthropic, Google and others. Platin Digital is an OpenAI Select Partner, and that doesn't change the choice. Which model leads right now, you can see in our ranking, the Sigma AI Ranking. And on OpenAI's new model for everyday work, we wrote a full review of GPT-6.1 Terra.
Frequently asked questions
What did OpenAI discover in math?
On October 6, 2026, OpenAI published 721 math papers written by an unreleased internal model, on about 372 open problems. The headline results: a proof that the zeros of the Riemann zeta function keep a fixed distance from the edges of the critical strip (the "quasi-Riemann hypothesis"), and a proof that Siegel zeros don't exist. About 42% of the main results were checked in the Lean proof assistant. A month earlier, in September, OpenAI also claimed to have solved a version of the Navier–Stokes problem.
Did AI solve the Riemann hypothesis?
No. The model proved a weaker version, the "quasi-Riemann hypothesis": that all the important zeros lie between 1/12 and 11/12 of the strip, at every height. That had never been proved before. The full Riemann hypothesis says they all lie exactly on one line, down the middle, and it's still open. A first version of the proof, with a strip from 1/8 to 7/8, has already been checked in Lean. The stronger version hasn't yet, and experts largely agree it's correct.
Will OpenAI get the million-dollar Navier–Stokes prize?
No. OpenAI wrote that it won't claim the prize. Its result concerns a flow with an external force applied. One of the official formulations allows such a force, but most mathematicians see the version without an external force as the heart of the problem, and the Clay Mathematics Institute hasn't ruled on whether it counts. Under its rules, a solution must be published, wait two years and gain acceptance in the community.
How is this different from OpenAI's October 2025 claim?
In 2025, a senior OpenAI executive wrote that GPT-5 had solved ten Erdős problems, and it turned out the model had only found existing papers. The post was deleted. In 2026 there are new proofs, some checked in Lean, and leading mathematicians have checked the two big results. One has already been cut to three pages. On the other hand, about half weren't checked by computer, and three papers were pulled the next day.
What is Lean and why does it matter?
Lean is software that checks math proofs step by step. If a proof is written in Lean and passes, you don't need to trust whoever wrote it, human or model. You only need to make sure the question fed into the software is the right one. That's why AI results that pass Lean are far more reliable than results that were only written out as text.
What does this mean for a small business?
That powerful models can already handle long, complex reasoning, but they're truly reliable only when there's a way to check them. For a business agent, that means automatic checks for everything possible (website, totals, links), and your approval for anything that goes out in the business's name.
Sources
- https://github.com/openai/math/blob/main/README.md
- https://www.quantamagazine.org/ai-proved-the-quasi-riemann-hypothesis-what-happens-now-20261019/
- https://terrytao.wordpress.com/2026/10/19/a-sketch-of-the-proof-of-non-existence-of-siegel-zeroes/
- https://terrytao.wordpress.com/2026/10/10/math-2-0/
- https://www.scientificamerican.com/article/the-most-exciting-claims-from-openais-heap-of-new-proofs/
- https://retractionwatch.com/2026/10/08/openai-withdraws-preprints-722-manuscripts-unsolved-math-problems/
- https://fortune.com/2026/10/07/openai-math-controversy-solutions-370-outstanding-challenges-published-criticisms-celebration/
- https://thenextweb.com/news/openai-navier-stokes-proof-published-millennium-prize
- https://rits.shanghai.nyu.edu/ai/openai-navier-stokes-proof-credit-dispute/
- https://www.claymath.org/millennium/navier-stokes-equation/
- https://www.techtimes.com/articles/329332/20261021/four-independent-math-proofs-2-weeks-back-ai-claim-tied-twin-primes.htm
- https://www.quantamagazine.org/how-ai-tore-through-a-mathematical-community-20260803/
- https://agmai.org/
- https://doi.org/10.5281/zenodo.22737750
- https://en.wikipedia.org/wiki/OpenAI_bulk_release_of_mathematical_papers
- https://epoch.ai/latest/announcing-frontiermath-erdos
- https://the-decoder.com/leading-openai-researcher-announced-a-gpt-5-math-breakthrough-that-never-happened/
- https://deepmind.google/discover/blog/alphageometry-an-olympiad-level-ai-system-for-geometry/
- https://deepmind.google/discover/blog/ai-solves-imo-problems-at-silver-medal-level/
- https://www.technologyreview.com/2026/03/20/1134438/openai-is-throwing-everything-into-building-a-fully-automated-researcher/
- https://developers.openai.com/api/docs/pricing
- https://platindigital.net/ai-index/
