Mathematicians around the world are struggling to come to terms with a breakthrough that has challenged their understanding of their profession and its future. On 6 October, OpenAI released 722 manuscripts generated by an advanced internal artificial intelligence model, later withdrawing three of them. The remaining collection contained proofs for 372 mathematical problems that had resisted solutions for decades or, in some cases, centuries, including problems that researchers had spent much of their careers trying to resolve.
The scale of the achievement has provoked an unusually emotional response from a community whose work is traditionally associated with logic, precision and abstraction. Hugo Duminil-Copin, a French probability theorist and recipient of the Fields Medal, mathematics’ highest award, said he had sobbed so loudly after learning about the proofs that he woke his daughter. Comparing the development to an experienced mountaineer discovering that future climbers would reach summits by helicopter, he said: “They have annihilated my field of research.”
Steven Strogatz, a prominent American mathematician, also struggled to contain his emotions while discussing the implications on a New York Times podcast. He described colleagues moving through different stages of grief as they confronted the possibility that the work defining their careers might no longer be necessary. “You know what’s actually being lost is we like to think of ourselves as heroes, and maybe that’s over,” he said. “It’s hard to be a hero if you can’t be the first to solve a problem or… explain it to the world.”
The reaction follows an earlier announcement by OpenAI that its internal model had solved the Navier-Stokes problem, a notoriously difficult question concerning fluid motion that had eluded mathematicians for almost a century. The company said the model produced a solution in 88 hours. The problem is one of seven Millennium Prize problems identified in 2000 by the Clay Mathematics Institute, each carrying a $1m award. The evaluation process remains under way, although the institute has acknowledged that OpenAI appears to have solved it.
Initially, critics dismissed the proof’s presentation as “AI slop”, arguing that the output was difficult to understand and lacked mathematical elegance. Similar objections were raised about the subsequent collection of manuscripts. But the sheer volume of results has made it harder for mathematicians to treat the achievement as an isolated incident or a technical curiosity. The concern is no longer simply whether AI can produce an individual proof, but how quickly it might transform a discipline built around the discovery and demonstration of mathematical truths.
Kevin Buzzard, professor of pure mathematics at Imperial College, said the speed of progress had been particularly difficult to anticipate. “In 2022, you could ask ChatGPT to multiply two five-digit numbers together and it would get it wrong,” he said. Buzzard had begun preparing for the possibility of machine-led mathematics seven years earlier, when he decided to stop concentrating on proving theorems himself and instead devote his time to investigating whether machines could become better than he was.
In a blog responding to the distress among his colleagues, Buzzard called on OpenAI to release its work in full so mathematicians could examine exactly what the company claimed to have achieved. He also believes that the emergence of powerful AI systems need not eliminate the role of human researchers, arguing that collaboration between mathematicians and machines could produce new opportunities for discovery.
Marcus du Sautoy, professor of public understanding at the University of Oxford, shares that more optimistic assessment, despite acknowledging his unease. He recently used AI to disprove a conjecture made by his PhD supervisor in 1986, an experience he said had “completely reinvigorated” his research. AI’s capacity to process vast quantities of existing research, he argues, allows it to identify connections across human knowledge. The ideas being synthesised, however, remain the product of human mathematical work.
James Maynard, professor of number theory at Oxford’s Mathematical Institute and a Fields medallist, also sees potential for collaboration but is less confident about the long-term implications. “It’s certainly plausible, in the not too distant future, that AI will become capable of developing its own [big theories],” he said. He described himself as “quite down and depressed” about the prospect that the disruption to mathematics could be “exceptionally significant”.
Maynard was among more than 20 Fields medal winners who signed a letter criticising the misalignment between the interests of AI companies and those of mathematics itself. His concern is that commercial incentives are driving the deployment of technologies built on mathematical knowledge without sufficient regard for the discipline’s long-term intellectual development.
“Maths is all about developing long-term human understanding,” Maynard said. “AI has the potential to accelerate that understanding but because it is being developed by commercial labs that are lining up for IPOs with so much money on the line, they’re introducing these very powerful tools in an unnecessarily disruptive way.”
Leslie Ann Goldberg, head of computer science at Oxford, was also surprised by the speed of the advances. She said that, having understood the limitations of existing AI models, she had not expected them to improve so dramatically. In her assessment, the current upheaval represents the biggest crisis in mathematics since the collapse of David Hilbert’s programme, an early 20th-century attempt to establish a comprehensive foundation for mathematical theories through a consistent set of axioms.
Goldberg has decided not to use AI to obtain mathematical solutions. “I’m not a typist, so I don’t see any point in spending my time posing problems to AI and reporting the conclusions,” she said. Instead, she argues that mathematicians should defend the broader purpose of their discipline: advancing human understanding rather than merely producing answers.
That distinction offers some reassurance to researchers who believe creativity and conceptual insight will remain essential. Yet the immediate consequences for early-career mathematicians are less clear. Postgraduate students have entered a profession in which solving difficult problems has traditionally provided both an intellectual objective and a route towards academic employment. If machines can increasingly perform that work, the future responsibilities of human researchers may have to change.
Goldberg remains confident that creative mathematicians will continue to be needed. Her concern is what happens to the current generation of doctoral students, many of whom have spent years preparing for careers whose established goals are suddenly uncertain. “That’s the crisis,” she said.
