OpenAI publishes 377 math solutions, mathematicians protest

OpenAI published 377 new mathematical results on Tuesday, obtained from an internal artificial intelligence model not yet available to the public. The results span different fields, from algebra to number theory, from geometry to differential equations, as well as mathematical logic, topology and theoretical computer science. According to the company, each result required on average about three hours of computation, and almost all were produced by a single AI agent from a single prompt. Many of the proofs were later checked with Lean, a computer language that verifies the logical correctness of each step.

The independent advisory committee hosted by the Institute for Advanced Study in Princeton has asked artificial intelligence labs to guarantee fair access to their most advanced models for the entire global mathematical community. The group described the publication as "the beginning, not the end" of the work needed for researchers to understand these results and integrate them into mathematical knowledge.

Mathematicians protest

The Association for Human Mathematics, founded to defend mathematics as a human endeavour, reacted more harshly. In a statement released the day after the publication, the association accuses OpenAI of ignoring the Princeton committee's central request: to stop testing the most advanced mathematical problems on its own internal models. It also rejects the idea, put forward by OpenAI, that these results advance mathematics, and calls for scepticism toward them. According to the association, publishing more than 700 files all at once is "a demonstration of power, not of scientific rigor." The mathematicians write that OpenAI has shown disregard for the norms of scientific research, the same norms that keep the discipline reliable, ethically sound and in the public interest, and they call on colleagues to stop all collaboration with the company.

Among the most discussed results is progress on a modified version of the Riemann hypothesis, one of the great open problems in number theory. Mathematician Alex Kontorovich, of Rutgers University, told the Washington Post that colleagues had long talked about the embarrassment of being unable to achieve anything comparable, adding that this particular problem was solved in a single evening.

The episode recalls the controversy that arose last month over the claimed solution of the Navier-Stokes equations, one of the seven Millennium Problems set by the Clay Mathematics Institute. In that case, the result had been achieved by a swarm of 10,000 AI agents, at a cost of millions of dollars in computing power. Tristan Buckmaster, a mathematician at New York University, told the New York Times that with so many proofs published together, he did not believe proper checks had been carried out.

On September 29, the Princeton committee had already asked companies to stop testing their proprietary models on open mathematical problems, and to make public the prompts and reasoning chains used by the artificial intelligence. OpenAI published a summary of the reasoning behind ten of the new solutions, but according to the New York Times, it continues to fall short of the main request: to stop testing its own models on open research problems.