The floodgates are open. Right on the heels of OpenAI’s new large language model producing the biggest math breakthrough in two decades, the company just released no less than 372 results from the same model. Each resolves or makes substantial progress on a major open question in mathematics or theoretical computer science, the company says.
OpenAI revealed the results in a GitHub repository at 6 P.M. EDT. The deluge will take mathematicians months to parse through and understand—including to determine whether the proofs contain novel and important ideas or are mostly mash-ups of existing techniques. But many of the results have already been verified in Lean—a programming language that validates a proof’s logic—and are therefore all but certain to be correct.
Among the results claimed are a solution to the four-dimensional Kakeya conjecture, improvements on some of the world’s most important computer algorithms, and actual progress toward math’s scariest problem, the Riemann hypothesis.
On supporting science journalism
If you’re enjoying this article, consider supporting our award-winning journalism by subscribing. By purchasing a subscription you are helping to ensure the future of impactful stories about the discoveries and ideas shaping our world today.
A spokesperson for OpenAI told Scientific American that 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. This would be a striking difference from OpenAI’s earlier blockbuster solution to the Navier-Stokes problem, which was produced through the collective efforts of a 10,000-strong agentic swarm that cost millions of dollars in computing power. If true, it would mean that unprecedented mathematical power could soon be accessible to anyone. But OpenAI’s reputation, among mathematicians, for bold claims and little transparency is causing considerable skepticism.
“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,” says Andrew Sutherland, a mathematician at the Massachusetts Institute of Technology. “We should ask for receipts.” (The OpenAI spokesperson also told Scientific American that some results might have taken multiple attempts.)
OpenAI’s handling of the Navier-Stokes solution’s release has proved so controversial that, on September 21, the company announced it was assembling an independent advisory group of mathematicians to provide recommendations on responsibly publishing AI-generated results. The recommendations that the group developed call for a company that releases such results to make public the model, exact prompt and compute time behind each one. In spite of the group’s recommendations, though, OpenAI is choosing only to reveal the average compute time for a problem, with some additional statistics—and no prompts.
The OpenAI spokesperson told Scientific American that the team is taking the advisory group’s guidelines seriously and doing its best to comply but added that the company is not bound by these recommendations.
The recommendations are particularly critical of AI companies using “proprietary internal models” that aren’t broadly accessible to mathematicians. OpenAI told Scientific American that the company is working to release the model as quickly and responsibly as possible.
As the Navier-Stokes dispute unfolded, comments from OpenAI personnel led some mathematicians to believe the company’s model had produced additional results but that it was hesitating to publicize them. This raises a vital question: Is it more harmful to unload heaps of unexplained proofs on the community or withhold them entirely?
“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,” says Daniel Litt, a mathematician at the University of Toronto. “To me, it’s going to be a good thing for mathematics.”
On the other hand, the famed mathematician Terence Tao has vocally criticized OpenAI and other “frontier” AI labs for the “insane” pace of their AI-generated results.
Such results may even be coming too fast for the labs themselves—the OpenAI spokesperson told Scientific American that many of the company’s newly released results are not yet understood by its own mathematicians. Still, they don’t plan on slowing down. The company wants to put as powerful a tool as possible in mathematicians’ hands.
Moreover, OpenAI maintains that it can’t slow down because these math problems are an indispensable test to show that their AI really is getting smarter.
But for the practitioners who see mathematical truth as an end rather than a means, the consequences of this race are becoming harder and harder to predict.
Editor’s Note (10/6/26): This is a breaking news story and will be updated.
Subscribe to Support Independent Journalism
Great science journalism requires human expertise, time, effort and creativity. And it costs money. That’s why I and the journalists here at Scientific American hope you’ll join our community.
When you subscribe, you are supporting staff and freelance journalists who are passionate about telling science stories that are true, important and compelling. Our editors and reporters are often experts in their fields, which means they understand the nuances of big discoveries and can untangle the breakthroughs from the hype. With a subscription, you are also supporting rigorous fact-checking to ensure the words we publish are precise and accurate. And you’re supporting original illustrations, graphics and photos that bring you closer to an advanced laboratory, an ice sheet in Antarctica or a space mission in orbit. You’re helping us craft other types of high-quality journalism as well: Our newsletters are carefully written, edited and curated by staffers you have or will come to know and love. Our Science Quickly podcast is based on original reporting, collaboration with editors and scientists and exacting production.
Subscriptions keep this engine running so we can continue to deliver thoughtful, rigorous and independent science journalism to you. In an era of viral misinformation, this work is crucial. If you value what we do, I hope you’ll consider joining us as a subscriber
