OpenAI's AI solves 10 math problems, sparking credit disputes and field anxieties

In the past year, mathematician James Maynard, a professor at the University of Oxford and Fields Medal winner, has spent considerable time "soul searching" about the future of his discipline. Days before speaking to The Verge, his concerns crystallized when OpenAI revealed that its unreleased model Astra had produced solutions to ten long-standing mathematics problems, some of which had confounded academics for decades. The breakthrough applies to mathematics the pattern-learning and recombination approach familiar from generative AI in text and images—the technology absorbs vast amounts of mathematical material, identifies connections, and combines known results, methods, and tools in novel ways to attack open problems.

The ten results span diverse mathematical fields. One concerns sphere packing in more than three dimensions, directly relevant to data encoding efficiency. Another advanced error-correcting codes used to recover information from noisy signals. A third resolved two long-standing questions about structural patterns in complex connected networks. Additional results addressed quantum game theory and the search for targets in high-dimensional grids, with implications for post-quantum cybersecurity. Among the most attention-grabbing was the resolution of whether non-sofic groups—infinite mathematical structures that cannot be approximated by finite ones—actually exist. This question had remained open for decades. OpenAI released more than 250 pages of papers detailing the solutions and 60 additional pages explaining "how the ideas came together," and verified each result using Lean, software designed for checking mathematical proofs.

Yet almost immediately, a credit dispute emerged. Francesco Fournier-Facio, a mathematician at the University of Cambridge, and others working in that area believed OpenAI's original announcement minimized the contributions of researchers Andreas Thom and Gábor Kun, whose recent work had laid crucial groundwork. OpenAI's initial text claimed it was sharing "results to problems that have been open and have seen no progress on the main result for at least a decade, and in most cases much longer." This language was later changed to say it was sharing "results, each of which resolves or makes substantial progress on a long-standing open problem." The page contained no correction note. Gábor Kun, a researcher at the Alfréd Rényi Institute of Mathematics in Hungary, told The Verge he found the sweeping language "rather comical," especially since the detailed research paper "clearly said that it builds on my results from 2016 and 2019," the latter coauthored with Thom. "It's rather sloppy," Kun said. After publication, OpenAI contacted him again. According to an excerpt Kun shared, an OpenAI mathematician wrote that "the language had been intended to refer to other results in the collection. It was not intended to suggest that there had been no progress on this problem. We certainly agree that the argument relies crucially on your work." OpenAI spokesperson Laurance Fauconnet confirmed the post was updated: "We updated the language to better reflect the prior research these results build upon."

Mathematicians broadly acknowledge the genuine weight of OpenAI's achievement. Yang-Hui He, a fellow at the London Institute for Mathematical Sciences, noted that "solving one of these 10 problems would get you a job in academia." He had just returned from a four-week AI and mathematics research conference in South Korea, where many felt there had been a "phase transition" over the past six months, with AI producing genuine and meaningful advances. Earlier in 2024, in May, OpenAI had announced an unnamed internal model cracking a conjecture by Paul Erdős that had eluded mathematicians for nearly a century. In July, Harvard mathematician Levent Alpöge tweeted that Anthropic's Claude Fable 5 had disproved the Jacobian conjecture, a problem that had occupied decades of efforts to prove it true. Yet this acceleration masks anxiety about the field's survival. Maynard noted that until recently, most AI breakthroughs in mathematics involved problems attracting little serious attention from researchers. The speed of change has caught the field off guard.

The economic realities are acute. Colva Roney-Dougal, a professor at the University of St Andrews, noted: "It's not quite clear whether our universities are going to be willing to pay that much for our theorems. Maths is a cheap discipline typically. Most of the time I don't even bother getting a research grant." OpenAI estimates that generating Astra's ten solutions cost around $2,000 in tokens at current API prices for its Sol model, though researchers believe the true cost was considerably higher depending on failed attempts. For a field used to shoestring budgets, even the advertised price is prohibitive. Roney-Dougal fears researchers at smaller and less wealthy institutions could be locked out of entire research domains. Beyond cost lies a structural concern: the most capable models from OpenAI and Anthropic are proprietary and access is tightly controlled. While both companies offer free academic access, that access is far from universal, and few researchers The Verge spoke to had been able to use the most sophisticated systems. Maynard and Roney-Dougal expressed hope that open-weight models could eventually close the gap, letting mathematicians access tools without relying on a handful of big AI companies.

Several researchers also questioned whether corporate values align with mathematical values. With products to sell and enormous valuations for upcoming IPOs to justify, companies have every incentive to hype and exaggerate, while underselling the human scholarship underlying results. In June, mathematicians published the Leiden Declaration, endorsed by the International Mathematical Union and signed by more than 3,400 people, urging policymakers, governments, and media not to buy into the hype created by companies that overstate capabilities. The fear is that exaggerated claims will convince funders and governments that human mathematicians are less necessary than they are. Gábor Kun summed up his ambivalence: it was gratifying to see his work prove useful in resolving a significant problem and to receive unexpected attention and congratulations, but he joked to well-wishers that he will be a "very famous unemployed" person. Francesco Fournier-Facio felt considerably less ambivalent, arguing that most people reading the OpenAI announcement will take it at face value without the time, expertise, or inclination to dig through hundreds of pages of technical papers. "They're just choosing the narrative that benefits them most," he said. "It's a lot more impressive to say that an AI system came up independently."