Mathematicians grapple with AI solving 10 long-standing problems
OpenAI says its unreleased Astra model solved 10 long-standing mathematics problems, prompting excitement and concern among mathematicians about the field's future and proper credit for human researchers.
James Maynard, an Oxford University professor and Fields Medal winner, has spent the past year reflecting on how the traditionally slow-moving field of mathematics is being forced to adapt to artificial intelligence. Shortly before speaking with The Verge, OpenAI announced that an unreleased internal model called Astra had produced solutions to 10 long-standing mathematics problems, ranging from how spheres can be packed in high-dimensional spaces to error-correcting codes and questions in quantum game theory, some with implications for post-quantum cybersecurity.
A dispute over credit
One of the most notable results concerned the existence of non-sofic groups, a question that had remained open for decades. Cambridge mathematician Francesco Fournier-Facio and Alfréd Rényi Institute researcher Gábor Kun said OpenAI's initial announcement understated how much the result relied on earlier work by Kun and fellow researcher Andreas Thom. Kun said OpenAI contacted him before publishing, but found the sweeping language of the original post misleading. After publication and further correspondence, OpenAI revised the wording without noting the change, and spokesperson Laurance Fauconnet confirmed the update was made to better credit prior research.
Excitement mixed with concern
Many mathematicians told The Verge the problems Astra solved were genuinely difficult — the kind that could launch an academic career. This follows other recent AI breakthroughs, including an OpenAI model resolving a decades-old Erdős conjecture in May and an Anthropic model disproving the Jacobian conjecture in July. Still, concerns are growing. University of St Andrews professor Colva Roney-Dougal warned that universities may struggle to afford AI-driven research tools, and that access to the most capable models remains largely controlled by a handful of companies. In June, more than 3,400 people signed the Leiden Declaration, urging caution against companies overstating AI's mathematical capabilities.
