OpenAI releases 722 math manuscripts from unreleased frontier model

The Verge AI10-05 19:28OfficialCross-checked by 17 sources

AI summary

OpenAI published 722 mathematics manuscripts on GitHub on October 6, grouped into 372 result families, all produced by an unreleased internal frontier model. The company says the set covers hundreds of open questions, including a quasi-Riemann hypothesis result (a zero-free region up to real part 7/8), three-dimensional Kakeya maximal and four-dimensional Kakeya conjectures, the Unique Games Conjecture, BSD formulas, Hilbert's tenth problem over the rationals and the Hodge conjecture for CM abelian varieties. OpenAI says the average result used compute equivalent to roughly three hours of ChatGPT Pro thinking and provides Lean formalizations for about 235 of the 372 families, while acknowledging that not all manuscripts are formalized. The release follows advice from the independent AGMAI group and continues to stir unease among mathematicians.

Why it matters: If confirmed through peer review, the results would mark a step change in how AI contributes to mathematical research; for now they remain unreviewed company claims.

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Source textThe Verge AI · 8 min read

Updated Oct 6, 2026, 11:26 PM UTC

All the drama around AI’s takeover of mathematics

by Robert Hart

This past year, OpenAI, Anthropic, and other labs have announced breakthroughs on numerous long-standing mathematical problems, in some cases pushing well beyond what researchers expected current systems to be capable of — including resolving one of the famous Millennium Prize problems. But in classic Silicon Valley style, AI labs are moving fast and breaking things, barreling through the discipline with all the grace of a runaway bulldozer. Results that might normally have been celebrated have instead sparked backlash. AI labs say they are learning from earlier mistakes. Whether those promises bear fruit remains to be seen.

Read on below for the latest updates in the AI takeover of mathematics.

Highlights

Oct 6
Robert Hart
OpenAI drops another batch of mathematical breakthroughs
Image: Getty Images
OpenAI has revealed solutions to a number of long-standing mathematics problems produced by an unreleased frontier model in a batch of 722 manuscripts, covering 372 result families that group related papers. It extends a run of breakthroughs that have both impressed and unsettled parts of the mathematical community while raising questions about research ethics and academic conduct. According to AGMAI, the newly formed independent advisory group of elite mathematicians put together to work on communicating the results responsibly, the release includes solutions to “hundreds” of open questions.
The results have been expected for weeks, although until now OpenAI had not provided details about which problems the model had solved or exactly when they would be published. In September, the company said its model had “resolved more than 100 long-standing open problems across most areas of mathematics.” The released papers and other details also include some summaries of the model’s reasoning, estimates of the compute used, and stats about the number of problems attempted. OpenAI claims the “average result” used the equivalent of three hours of ChatGPT Pro thinking.
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Sep 28
Robert Hart
OpenAI keeps bulldozing mathematicians
Image: The Verge, Shutterstock
In a chaotic few months, OpenAI has demonstrated it can do two things with remarkable consistency: make impressive breakthroughs in mathematics, then colossally screw up announcing them. OpenAI is now trying to do better. Somehow, it has botched that too.
OpenAI’s latest attempt to repair fractured relations with a mathematical community it has repeatedly alienated is to consult a new independent advisory group of elite practitioners. But mathematicians speaking to The Verge, including one of the group’s members, describe a messy and confusing affair bearing many of the hallmarks of OpenAI’s previous rushed forays into mathematics, suggesting the company has learned little from its mistakes. And then there’s the daunting task the group has been handed first: helping coordinate the release of scores more results OpenAI says its unreleased model has produced, the prospect of which is already stirring dread among researchers over what this looming tidal wave of breakthroughs could do to their field.
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Sep 23
Robert Hart
OpenAI wants to consult elite mathematicians about how to not fumble again
Bloomberg via Getty Images
After turning a string of spectacular mathematical results into a reputational crisis, OpenAI is consulting human mathematicians to help it figure out a less disastrous path forward.
On Monday, the company announced a new independent panel of mathematicians tasked with advising it and other AI companies on their interactions with mathematical research and the wider mathematics community, including how new results are presented and released. Its abrupt arrival caught many mathematicians by surprise. Researchers told The Verge the group is a good first step, but many said they were left with basic questions about what it will actually do, how much influence it will have, and whether OpenAI will actually listen to it, as well as concerns over whether such a small group of prominent researchers can represent the wider mathematical community.
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Sep 12
Robert Hart
OpenAI just wants to win
Image: Cath Virginia / The Verge, Getty Images
OpenAI has spent the last few years planting flags across the increasingly difficult terrain in mathematics. This week, it claimed one of its biggest prizes yet: a solution to a legendary Millennium Prize problem. In normal circumstances, this would have been celebrated as a historic achievement.
Instead, many mathematicians have watched OpenAI’s relentless advance with growing unease. To them, the company appears less like an enthusiastic newcomer than an impossibly well-resourced interloper, charging into problems they have dedicated their lives to studying with little apparent regard for long-standing norms or the consequences for those left in its wake. At the heart of that unease is a sense that OpenAI is doing mathematics for different reasons. Mathematicians want to advance the field. OpenAI wants to win.
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Sep 10
Robert Hart
Mathematicians want proof OpenAI didn’t use their work
Sam Altman, chief executive officer of OpenAI, during a media tour of the Stargate AI data center.
Bloomberg via Getty Images
Another researcher is challenging OpenAI about the data driving its increasingly impressive array of mathematical discoveries. Just days after a bitter row erupted over whether the company’s models benefited from unpublished work, a second mathematician has come forward accusing the AI giant of unethical and “dishonest” behavior and a lack of transparency about the origins of its training data.
In a series of posts on Mastodon, mathematician Andreas Thom raised concerns that interactions he and his colleagues had had with the ChatGPT chatbot before OpenAI’s triumphant announcement may have contributed to its success in the field. One of the 10 results OpenAI announced with great fanfare last month involved Thom’s area of expertise, so-called non-sofic groups, and OpenAI acknowledged that their result built heavily on previous work by Thom and fellow mathematician Gábor Kun.
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Sep 9
Robert Hart
OpenAI’s sly mathematical breakthrough sends a chill through academia
Open AI CEO Sam Altman speaks during the G20 Innovation Ministerial.
(Photo by Matt RAMEY / AFP via Getty Images)
OpenAI’s announcement Tuesday that it has solved one of mathematics’ legendary Millennium Prize problems should have been a moment of triumph. The result is both an undeniable achievement and a striking demonstration of just how rapidly AI is transforming mathematics. But before it was even formally announced, the breakthrough had been complicated by the unusual circumstances that prompted OpenAI to pursue the problem: After hearing other researchers were making progress, it seems to have thrown its considerable resources into a last-minute effort to beat them to the punch. The ensuing controversy has surfaced allegations of scooping, spying, and flagrant violations of long-standing academic norms that researchers fear could have a chilling effect on the field.
As Abhishek Saha, a mathematics professor at Queen Mary University of London, explains it, OpenAI has engaged in the “kind of things that mathematicians will generally not do.”
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Sep 8
Emma Roth
Drama swirls around OpenAI’s legendary mathematical milestone
Image: Cath Virginia / The Verge
OpenAI says it found a solution to a major math problem that has remained unsolved for around 90 years, as reported earlier by The New York Times and Wired. In a blog post on Tuesday, OpenAI announced that it discovered a solution to the Navier-Stokes problem — which relates to the flow of liquid and gas — using an internal AI model more powerful than the newly released GPT-6 Astra alongside 10,000 concurrent agents. The Navier-Stokes problem is one of seven Millennium Prize Problems, each of which comes with a $1 million reward for solving.
OpenAI says it started training the internal AI model on August 28th, which has “exhibited unprecedented performance in our benchmarks, including mathematics.” The solution is a big breakthrough for the mathematics community, but it doesn’t come without controversy.
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Aug 20
Nilay Patel
Welcome to the AI crisis in math
Today on Decoder, I’m talking with Robert Hart, The Verge’s London-based AI reporter, about what AI is doing to the field of mathematics and the existential crisis many lead mathematicians are having about it.
OpenAI just published a set of solutions to longstanding problems in math that went off like a bombshell in the field. It caused a huge debate in the math community, and Rob spent some time talking to some of the most accomplished mathematicians of our time about it.
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Aug 11
Robert Hart
The AI takeover of mathematics has begun
Image: Cath Virginia / The Verge, Getty Images
Mathematician James Maynard has spent a lot of time this past year “soul searching.” A professor at the University of Oxford and winner of the prestigious Fields Medal, Maynard told The Verge he’s been grappling with the future of his field as the traditionally slow-moving discipline hurries to adapt to AI.
Days before we spoke, OpenAI revealed it had produced the solutions to 10 long-standing mathematics problems, some of which had confounded academics for decades. Like generative AI used to produce text and images or propose ideas in science and medicine, the technology learns patterns and connections from the vast amount of material it’s trained on and uses them to create something new. Applied to mathematics, that can mean combining known results, methods, and tools in new ways to attack a problem, sometimes drawing links between disparate fields or resurfacing concepts buried in academic literature.
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