OpenAI has published 722 mathematical papers addressing 372 open problems, covering fields from algebra and geometry to theoretical computer science. The company said the work, produced largely by an AI model it has not yet disclosed, could help expand the boundaries of human knowledge. The release has prompted both excitement and concern among mathematicians over the results’ reliability and the way they were presented.
Some papers claim progress on prominent, longstanding questions, including the Riemann hypothesis and the Birch and Swinnerton-Dyer conjecture. Each is one of the seven Millennium Prize Problems, with a US$1 million award for a solution. Several papers from the collection have since been withdrawn or revised.
OpenAI says it released the results to promote progress in mathematics. But some researchers have questioned whether the papers are clear enough to assess. One mathematician told the article’s author that a paper on a problem he knew well was so difficult to understand that, in his view, it would not have been suitable for journal review. The author also reported that ChatGPT expressed strong doubts about at least one high-profile result, saying it should not be treated as a proof without a full expert audit.
The release followed a separate controversy over OpenAI’s September work on a case of the Navier-Stokes problem, another Millennium Prize Problem. Mathematicians Tristan Buckmaster and Levent Alpöge alleged that OpenAI had accessed their data and used their ideas before devoting computing resources to a solution. OpenAI denied the allegations.
The scale of the new collection has also raised questions about the checks applied before publication. OpenAI has withdrawn three papers over an elementary error and corrected several others after mistakes invalidated their results. In mathematics, new work is generally assessed by specialists before it becomes part of the accepted literature, a process that can take years for lengthy technical papers. The community’s review will therefore be central to determining whether the claims hold up.
OpenAI says it has formalized 300 of the leading results, using software such as Lean to translate mathematical arguments into proofs that can be checked step by step by a computer. AI systems are increasingly being used to automate this process. However, formalizations can also be implemented incorrectly, and previous AI-generated work, including on Navier-Stokes, has faced questions. It remains unclear whether mathematicians will accept OpenAI’s formalizations.
Reactions to the publication have ranged from describing it as a landmark moment to criticizing the volume of material and the burden placed on researchers asked to assess it. The results have energized specialists investigating possible advances, while also prompting concerns about how rapid AI-assisted research could affect the work of mathematicians, particularly students and early-career researchers.
Sources: Folha Ciência.