On Tuesday, October 6, American company OpenAI published 722 manuscripts generated by an internal artificial intelligence model on the GitHub platform. These manuscripts, organized into 372 "families," include mathematical results, their implications, and sometimes alternative proofs. Some of the texts are accompanied by versions written in Lean, a programming language that allows computers to verify proofs step by step. OpenAI warned that some unformalized results "could be problematic" and promised to "correct them quickly." The manuscripts were prepared and discussed in advance with an independent advisory group on mathematics and AI at the Institute for Advanced Study (IAS) in Princeton, established on September 21. The group includes nine experts intended to help OpenAI approach its work in mathematics more cautiously, following tensions caused by previous AI research in the field. According to OpenAI, the model was presented with approximately 4,000 open problems during internal evaluations, from which the 372 published families were derived. Each selected result required on average the equivalent of three hours of thinking by ChatGPT Pro, the highest-tier offering of the assistant. OpenAI has also published brief summaries of the model's reasoning for ten cases from several families, including topics such as the irrationality exponent of pi, the Mézard–Parisi formula for diluted spin glasses, and the three-dimensional relativistic Vlasov–Maxwell system. Among the results, OpenAI claims advances on questions that have resisted mathematicians for decades, though the company admits that these results have not (yet) all been verified and that some could contain errors. The most attention has been drawn to a result related to the Riemann hypothesis, one of the seven "millennium problems" listed by the Clay Institute. The hypothesis concerns the zeta function, whose zeros govern the distribution of prime numbers. According to the hypothesis, all the "interesting" zeros are on a single vertical line with an abscissa of 1/2. OpenAI's model claims a fixed width margin: no zeros beyond 7/8, regardless of the height. A second manuscript demonstrates a slightly weaker version with a limit at 11/12. Alex Kontorovich, a professor at Rutgers University and a specialist in number theory, stated that if a human had achieved this result, it would be an immediate Fields Medal. He noted that the model's result excludes "Siegel zeros," which serve as potential counterexamples to the generalized Riemann hypothesis. If the result holds, there would be none of these zeros, according to Kontorovich. The GitHub repository notes that nearly all the manuscripts come from a single automated procedure, with two exceptions: the work on the zeta function and a proof related to the Hodge conjecture (another millennium problem). The writing of the zeta result was edited by humans "for readability." Levent Alpöge, a mathematician at Anthropic, who had previously disputed with OpenAI the credit for its breakthrough on Navier-Stokes, praised these two results, calling them "the most significant moment in the history of mathematics." Sam Altman, CEO of OpenAI, praised "a new era of discovery." Some believe OpenAI is downplaying the event "for communication reasons," and that mathematicians should feel as if a nuclear bomb has just fallen on them.