In early October, during a videoconference organized by the Société mathématique de France, Fields Medalist Hugo Duminil-Copin revealed, according to Le Monde, that he cried after OpenAI’s announcement. On Tuesday, October 6, the company published 719 manuscripts dedicated to solving still open mathematical problems. This publication concluded six weeks of consecutive announcements on the subject.
- AI companies announced major results, including a Lean-formalized proof of Fermat’s Last Theorem.
- Mathematicians fear AI solves problems while erasing the exploratory work that made research valuable.
- Researchers now hesitate to share ideas, fearing theft, and young researchers face shrinking career prospects.
- Matthieu Alfaro finds AI-generated proofs unreadable, which raises the question of how to judge them.
“Tuesday night, I cried and it woke my daughter,” the newspaper reported. In early September, Anthropic had indicated that Claude had formalized in eleven days the proof of Fermat’s Last Theorem in Lean, a language that allows a computer to verify each step of a proof. Four days later, OpenAI claimed a result on the Navier-Stokes equations, related to one of the Clay Institute’s seven Millennium Prize Problems. These announcements led 25 Fields Medal winners to denounce, in an op-ed, the gap between the goals of AI companies and those of the mathematical community.
To assess what these announcements mean for researchers, we interviewed Matthieu Alfaro, professor of applied mathematics at the Laboratoire de mathématiques Raphaël Salem (Université de Rouen Normandie and CNRS). His work focuses notably on reaction-diffusion equations, used to model species evolution or epidemic spread.
The problem is solved, but the path disappears
According to Le Monde, OpenAI alone devoted thirteen articles to one of the problems that interested Hugo Duminil-Copin, enough to cover an entire research project. For the researcher, the mathematician’s tears can be understood on two levels. The first concerns the organization of scientific work, which progresses through multi-year projects funding travel, conferences, and doctoral positions. “What happened to Hugo Duminil-Copin is that his projects for the next ten years have been crushed […]. On a personal level, it’s a disaster, it’s very unsettling,” he explains.
The second level goes beyond the individual case. “I think he also cried for humanity… or at least the human in mathematics,” says Matthieu Alfaro, for whom, until now, mathematics “were done by humans.” He now describes “an infinite firepower that may not destroy, but will disrupt a large part of mathematics as it exists.”
The researcher especially emphasizes what these results short-circuit. Previously, an open problem served as a goal: “The act of working toward this goal allowed exploring other fields, proposing other ideas, connecting reflections.” Not reaching the result was therefore not so bad, “since other things had been created along the way.” With AI, he summarizes, “it’s solved, finished, go home.” Mathematical research proceeds by conjectures, often considered true long before being proven. “The day a conjecture is proven true is no surprise. What’s interesting is how it was proven. The proof is vital,” he stresses.
Yet these proofs remain difficult to read. In the October deposit, about 42% of OpenAI’s main results were formalized in Lean, according to the company, and three manuscripts were withdrawn the next day after errors were discovered. “In what was deposited by the AI, I admit I understand nothing, absolutely nothing. It’s unreadable. The machine tells you it’s true. What do we do with that?” asks Matthieu Alfaro.
Between fear of theft and the race for showcase
OpenAI’s announcement on Navier-Stokes also sparked controversy. Mathematician Tristan Buckmaster, who was working on the same problem with a coauthor, suspected that their unpublished work might have been used by the company, which denied it. No proof was provided either way, but the affair sowed doubt. “It’s going to make me a little paranoid, it already does. We no longer want to share our ideas, our research leads, because we’re afraid of having them stolen,” confides Matthieu Alfaro. He reports that after a doctoral student’s presentation, a preprint signed by someone present in the room appeared on arXiv two days later, “48 hours after, there are 30 pages proving what the doctoral student had mentioned.”
On the laboratory side, the official discourse emphasizes science. OpenAI says it wants to advance knowledge and has set up a consulting group of mathematicians, who recommended not making these results a showcase for their models. For Matthieu Alfaro, the speed of progress has nevertheless surprised: “Two years ago, we didn’t believe it for a second. When I tested ChatGPT 18 months ago, the basic version made mistakes on undergraduate exercises.” He also fears “a two-speed research” and “a slight anxiety that math research is now very American or Chinese.”
Young researchers, meanwhile, are on the front line. “People like me have a position. However, it’s extremely stressful for young people looking for a position. What do we do with our PhD students?” he asks. He adds that journals receive twice as many articles as a few months ago, while it is researchers who edit and review them. “I’m a bit afraid that will completely collapse,” he warns.
