OpenAI releases hundreds of computer-generated papers tackling unsolved mathematics problems

OpenAI has uploaded 722 research manuscripts to the code-hosting site GitHub, presenting work generated by an unreleased artificial intelligence system. The documents address 372 distinct mathematical challenges spread across about twenty branches of the discipline. Some manuscripts offer complete proofs for longstanding questions, while others rule out false assumptions or set tighter limits on unsolved problems.

The release represents work that OpenAI began highlighting in September, when it announced that its software had tackled open mathematical puzzles. To support the work, the company shared details about the general computing power used, noting that an average finding took roughly three hours of system time. Company representatives stated that almost every manuscript came from giving a single instruction to a single automated agent.

One prominent focus of the release involves prime numbers, which are whole numbers that can only be divided by themselves and one. The company reported progress on the Riemann hypothesis, an idea older than a century and a half about how prime numbers are distributed. While the full problem remains unsolved, the system produced a proof for a related piece known as the quasi-Riemann hypothesis.

The manuscripts also address theoretical computer science, a category that received more than 80 papers. Three of these investigate matrix multiplications, which are mathematical procedures computers use to sort data and train machine learning tools. The AI mapped out clearer boundaries for how fast these calculations can theoretically run, alongside a separate algorithm designed to multiply whole numbers more efficiently.

Other papers focus on physics and engineering. More than a dozen manuscripts deal with partial differential equations, which describe how forces change across space and time. These equations are used to model fluid movements, design microchips, and study quantum systems. The system addressed questions tied to the Navier–Stokes equations, used to track fluid flow, and offered a proof related to De Giorgi's conjecture, a framework used in the study of metal mixtures.

The release also claims a solution to the four-dimensional Kakeya conjecture, another longstanding geometric puzzle about how shapes rotate within narrow spaces.

To help outside experts check the findings, OpenAI paired many papers with Lean code. Lean is a computer language that checks mathematical arguments step by step to confirm that each deduction follows strict logical rules. The company stated that it will release more machine-checked files later and plans to help pay for review workshops and academic gatherings.

The publication followed guidance from an independent advisory panel on mathematics and AI, though OpenAI did not adopt every recommendation. The company published on GitHub rather than a traditional academic server, established citation guidelines, and omitted both the specific prompts given to the model and the exact run times for individual problems.

The broader mathematical community has reacted with caution. Outside researchers point to past arguments over AI claims, including recent debates about Navier–Stokes equations, as reason to inspect the papers carefully. Independent experts, including Andrew Sutherland at the Massachusetts Institute of Technology, have noted that claims about single-prompt solutions cannot be treated as proven until the underlying model is made available and others can reproduce the findings.