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OpenAI's 372 Math Results Leave Mathematicians Racing to Read the Proofs
Dana Moshkovitz, a complexity theorist at the University of Texas at Austin, was being taunted by her son on the night of Oct. 6. The 9-year-old had heard that “a robot solved the math problem you worked on for your whole career.” Her husband, fellow UT Austin researcher Scott Aaronson, recounted the exchange on his blog the next day.
The problem was the Unique Games Conjecture. OpenAI had just released a claimed proof.
At 6 p.m. EDT on Oct. 6, 2026, OpenAI posted 372 families of mathematical results from an unreleased internal model. As of Oct. 7, about 42% of the top-line results (300 of 719) had proofs a computer had checked in Lean, while the people reading them were only starting to understand them.
Key Takeaways
* OpenAI posted 372 families of math results from an unreleased internal model on Oct. 6, including a claimed proof of the Unique Games Conjecture.
* As of Oct. 7, 300 of 719 top-line results (about 42%) had Lean proofs; Scott Aaronson wrote that no human appears to have understood just about any of the proofs yet.
* OpenAI published average compute and 10 reasoning summaries but no prompts, short of the Sept. 29 guidelines from the Institute for Advanced Study's advisory group.
* MIT's Andrew Sutherland called single-agent claims unverified until the model is released; the Association for Human Mathematics urged mathematicians to stop working with OpenAI.
AI-generated summary, reviewed by an editor. More on our AI guidelines.
## Reading the proofs
Moshkovitz had worked toward proving the conjecture throughout the time Aaronson had known her and had never doubted it was true. It concerns the difficulty of finding good enough answers to optimization problems, where the task is to choose the best solution from many possibilities.
If the conjecture holds, a long list of optimization problems, including Max Cut, are NP-hard. That holds even when you ask only for an answer slightly better than the one semidefinite programming, the field's standard tool, already gives.
The new argument was difficult for Moshkovitz to read. “It feels like something written by someone who's on psychedelics,” she wrote in texts published by Aaronson. To read the AI-written proof, she asked an AI model to pull together claims scattered across the paper.
“Basically the paper is so horribly written that it's impossible to read it without AI help,” she wrote.
Researchers at UT Austin and the Simons Institute in Berkeley were rushing to study the manuscripts. Aaronson wrote on Oct. 7 that “it also appears that no human has understood just about any of these proofs yet; the race to do so has just started.” Many of the results were also not yet understood by OpenAI's own mathematicians, a company spokesperson said.
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The OpenAI math release, from the beginning
* On Sept. 8, 2026, OpenAI announced a result involving the Navier-Stokes equations, which describe fluid motion. The work used a swarm of 10,000 AI agents and millions of dollars in computing resources.
* On Oct. 6, OpenAI released 372 families of results, each said to resolve or substantially advance an open mathematical question. An OpenAI spokesperson said nearly every result came from a single prompt to a single agent, and that some results might have taken multiple attempts.
* A “family” groups papers about a related result. It can include the main proof, supporting arguments, consequences or alternative proofs, so the number of manuscripts exceeds the number of families.
* Lean is a programming language that lets a computer check every step of a mathematical proof. The catalogue lists 719 manuscripts; as of Oct. 7, 300 of the 719 top-line results, about 42%, had Lean proofs.
* Few people have yet understood the proofs, including ones a computer has checked. Dana Moshkovitz, who worked for years toward the Unique Games Conjecture, said its claimed proof was so badly written she could not read it without AI help, and OpenAI said many results are not yet understood by its own mathematicians.
* The list includes a claimed proof of the Unique Games Conjecture, which concerns limits on finding good enough answers to optimization problems. It also includes a claimed positive answer to unitary synthesis, which asks whether a suitable classical function can help a quantum computer efficiently perform any quantum operation.
* The advisory group's Sept. 29 guidelines requested the model name, prompts, reasoning summary, time and computation cost for each result. They also asked labs to stop testing advanced problems on proprietary models.
* OpenAI's October release supplied average computing figures and 10 reasoning summaries. It supplied no prompts and kept the model unreleased.
* On Oct. 7, OpenAI withdrew three manuscripts after a sign error affected their arguments; the catalogue now lists 719 manuscripts. It revised 14 other manuscripts and said some results without formal computer checks could have issues.
* MIT mathematician Andrew Sutherland said claims about solving problems with a single agent should be treated as unverified until outsiders can repeat the work. The Association for Human Mathematics urged mathematicians to stop working with OpenAI in its Oct. 7 statement.
* Cryptographers are watching because mathematical shortcuts could weaken systems used to protect information and cryptocurrency wallets. On Oct. 7, Justin Drake said in the worst case ECDSA could be broken “in months, not years”; OpenAI reported no attack on ECDSA or RSA, and Vitalik Buterin advised against hurried wallet moves.
## What was released
A family groups a principal result with related arguments, consequences or alternative proofs.
Alongside the Unique Games Conjecture, OpenAI's Oct. 6 list included L = BPL, a claim that randomness adds no computational power when a computer's working memory grows only logarithmically with its input. It also claimed faster integer multiplication, which Aaronson wrote broke a running-time barrier that had stood since the 1960s.
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For Aaronson, another entry was personal: a positive solution to the unitary synthesis problem he and Greg Kuperberg posed in 2007. The question asks whether access to the right ordinary computer function lets a quantum computer efficiently carry out any quantum operation. The claimed answer was “the opposite of what most of us expected,” Aaronson wrote. Aaronson noted that the paper does not give an efficient way to construct that function.
For the October collection, OpenAI said it posed approximately 4,000 problems to its internal model. Each result used an average of about three hours of ChatGPT Pro thinking compute.
OpenAI's September announcement had involved the Navier-Stokes equations, which describe fluid motion. That result, announced Sept. 8, used a swarm of 10,000 AI agents and millions of dollars in computing resources.
Nearly every result came from a single prompt to a single agent, the spokesperson said, although some may have required multiple attempts.
The Lean coverage figures were updated on Oct. 7. Lean is a programming language in which a computer checks each step of a proof. OpenAI said unformalized results “could have issues.” That day it withdrew three manuscripts after a sign error and revised 14 others.
## The release rules
Before publication, the Advisory Group on Mathematics and Artificial Intelligence had proposed disclosure rules. Hosted by the Institute for Advanced Study, the group includes Timothy Gowers and Edward Witten.
Its Sept. 29 guidelines, informed by more than 600 survey responses, asked labs to publish the model name and prompts for each result, along with a reasoning summary, elapsed time and computation cost. It also asked labs to stop testing advanced problems on proprietary models. The guidelines asked labs to avoid using mathematical releases as marketing vehicles.
OpenAI released average computing figures and 10 reasoning summaries for the October collection. It supplied no prompts, and the model remained unreleased. The spokesperson said the company was not bound by the recommendations.
Tasmin Chu, a Caltech doctoral student, helped form the Association for Human Mathematics. “What is happening is a huge damage to open science,” Chu said. In an Oct. 7 statement, the association called the release of more than 700 files a “demonstration of power” and urged mathematicians to “discontinue their work with OpenAI.” It cited the advisory group's request to stop testing advanced problems on proprietary models.
Daniel Litt, a University of Toronto mathematician, supported making the work available. “If we want to know the answers to these math questions, I see no reason why we should ask the company to keep them secret from us,” he said.
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The advisory group's Oct. 6 statement said its involvement should not be understood as an endorsement of OpenAI's process. OpenAI says it will fund workshops, conferences and special programs to help mathematicians understand the results, and is working to release the model.
On Oct. 5, Josh Alman and Virginia Vassilevska Williams posted a preprint refuting long-standing conjectures about the 3SUM and all-pairs shortest paths problems. Aaronson wrote that an Anthropic model supplied the central idea and Anthropic let the two write and announce a digested version in exchange for compensation. He wrote that this approach puts a company in the position of choosing which mathematicians explain its AI's work.
“Until and unless they release the model and people can replicate their results, I think you should treat any claims about one-shotting problems with a single agent as unverified,” said Andrew Sutherland, an MIT mathematician. “We should ask for receipts.”
## The cryptography question
Cryptography, the mathematics used to protect information and authorize transactions, is absent from OpenAI's list, Aaronson noted. Ethereum researcher Justin Drake nevertheless urged “bunker mode” on Oct. 7, including controlled moves of assets to fresh addresses. He said an effective break of ECDSA, a digital signature system used by cryptocurrency wallets, could arrive “in months, not years” in the worst case.
OpenAI reported no attack on ECDSA or RSA, another widely used cryptographic system. Drake framed the timeline as a worst case, and the release demonstrates no such capability.
Ethereum co-founder Vitalik Buterin urged caution about hurried transfers. “I don't recommend anyone scramble to move their funds to new wallets today,” he wrote. “But we should take the risks to cryptography from AI-accelerated math seriously.”
## A researcher reads her problem
Dakshita Khurana, a professor working on cryptography and quantum computing, had spent most of her research time over the past three years on unitary synthesis. She believed in a positive answer when that position was unpopular. Aaronson had written that the claimed answer was the opposite of what most researchers expected; Khurana was among the few who expected it.
Her student Kabir Tomer worked with her for years on approaches that reached dead ends. Over the past year, she also asked AI agents to explore ideas. She wrote that as she works through OpenAI's manuscript, much of it “feels familiar,” including approaches she tried.
“Part of me would like a little longer in the world where the problem is still open and I am still looking for its solution,” she wrote.
“But reaching a summit, even by someone else's route, comes with a view. From here I can see new mountains, and I look forward to climbing them with my students, collaborators and the machines.”
Frequently Asked Questions
What did OpenAI release on Oct. 6?
OpenAI posted 372 families of mathematical results produced by an unreleased internal model in a GitHub repository. Each was said to resolve or substantially advance an open question. The catalogue now lists 719 manuscripts after OpenAI withdrew three on Oct. 7 over a sign error.
What is the Unique Games Conjecture?
If it holds, a long list of optimization problems, including Max Cut, are NP-hard even when you only ask for an answer slightly better than semidefinite programming, the field's standard tool, already gives. OpenAI's release includes a claimed proof. Dana Moshkovitz, who worked toward it for years, said the paper was impossible to read without AI help.
How many of the results have been checked by computer?
As of Oct. 7, 300 of 719 top-line results, about 42%, had Lean formalizations. Lean is a programming language in which a computer checks each step of a proof. OpenAI said some unformalized results could have issues.
What did the advisory group ask OpenAI to disclose?
The Advisory Group on Mathematics and Artificial Intelligence asked labs on Sept. 29 to publish the model name, prompts, a reasoning summary, time and computation cost for each result. OpenAI released average compute figures and 10 reasoning summaries, supplied no prompts, and said it was not bound by the recommendations.
Why are cryptographers paying attention?
Ethereum researcher Justin Drake said on Oct. 7 that in the worst case an effective break of ECDSA could arrive in months. OpenAI reported no attack on ECDSA or RSA, and Vitalik Buterin advised against hurried wallet migrations.
AI-generated summary, reviewed by an editor. More on our AI guidelines.
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