OpenAI has published 722 mathematical articles on GitHub obtained thanks to an internal AI model not yet available to the general public. The catalogue, published on 6 October 2026, currently includes 719 articles, a smaller number than the initial 722. 3 results have already been “disproved” and, in all likelihood, the number is destined to fall further. The articles are grouped into 372 “families” of results.
According to what the company declared, the results were obtained with very limited computing times and resources. If the data were confirmed, it would mean that anyone could soon have access to unprecedented mathematical power. Let’s see what results these are, how OpenAI obtained them and why this news “scares” the world of mathematics.
The mathematical results published by OpenAI
OpenAI has published on its blog and on GitHub, an online platform used by developers to store, manage and share the code of their programs, a huge catalog of mathematical results produced by an AI model within the company.
The catalog is continuously updated and currently includes 719 articles organized into 372 result families. Each family may include a main result, alternative demonstrations, consequences, or related work. The problems touch on many different areas of mathematics and also include three “millennium problems”, that is, three of the seven problems considered among the most relevant for modern mathematics, chosen in 2000 by the Clay Mathematics Institute, which offers one million dollars for the solution of each.
The three millennium problems addressed are the Hodge conjecture, the Birch and Swinnerton-Dyer conjecture, and the Riemann hypothesis. For all three, however, the model obtained only partial results: none have yet been completely solved.
To make verifying its results easier and more automatic, OpenAI also published proofs in Lean, a programming language used to write mathematical proofs in a form that a computer can verify. This verification currently only covers about 40% of the results.
How he got them: The model is not available to the public
According to OpenAI, almost all the results were produced with the same procedure, using an internal model that is not available to the public. During an evaluation of its capabilities, the model was subjected to approximately 4,000 open problems. The company then collected those it considered relevant and grouped them into the 372 families in the catalogue.
This news comes one month after the controversial announcement of the resolution of another millennium problem, that of the Navier Stokes equations, by OpenAI. In that case, 10,000 agents were used, i.e. 10,000 AI systems that carry out tasks autonomously and can coordinate with each other, for 88 hours of calculations, with computational costs of millions of dollars.
This time, however, an OpenAI spokesperson stated that almost every result was obtained with a single agent and a single request. This would therefore be a notable improvement compared to the previous result. The company also said that, on average, each result required a computational cost equivalent to a roughly three-hour session of ChatGPT Pro with “reasoning.”
If this data were confirmed, the new model would have shown much higher mathematical capabilities than those used by OpenAI just a month earlier. The leap in the mathematical capabilities of the models, however, does not only concern the performance of AI: the way in which mathematical research is carried out and evaluated is also starting to change.
The impact of AI in the world of mathematical research
Artificial intelligence is having an ever-increasing impact on mathematical research, but the way in which companies in the sector are achieving and presenting these results is also fueling several concerns. OpenAI’s announcement of the solution to one of the millennium problems, which took place just over a month ago, was accompanied by numerous criticisms and accusations of plagiarism. Those involved in mathematical research therefore look with growing distrust at the results produced by large AI laboratories. Even Terence Tao, Fields Medalist and one of the best-known mathematicians in the world, has repeatedly criticized the pace at which these laboratories are producing results and the lack of transparency with which they are obtained.
To make more transparent how these types of results are produced and communicated, an independent group of mathematicians working with OpenAI published recommendations on September 29. These include requiring companies to make public the AI models they use, the exact demands made on the model, and the computation time spent on each of the problems solved. OpenAI, however, decided to reveal only the average computation time per problem and some statistics, without providing the requests made to the AI. However, so far he has published ten examples of how the model has “reasoned” to solve as many problems. Furthermore, the AI model remains inaccessible: the company has declared that it is working to release it “responsibly”, without however indicating when.
Meanwhile, the artificial intelligence sector seems to be focusing more and more on mathematics. The idea is that being able to obtain mathematical results that are verifiable and considered “objective” can help convince investors and the public that companies are on the right path towards superintelligence. For this reason, numerous companies in the sector have made mathematical research one of their priorities.
