OpenAI has published 372 mathematical results generated by an internal AI model, depositing them on GitHub with the energy of someone sliding a term paper under a professor's door and walking away. The results include advances on the Riemann hypothesis and improvements to major computer algorithms. Traditional journals were not consulted.
Each result consumed roughly three hours of compute. Most required a single prompt to a single agent. The math community's review process will take considerably longer.
What happened
Nearly every one of the 372 results came from a single prompt to a single AI agent, OpenAI reports, though some required multiple attempts. This is a notable contrast to the Navier-Stokes solution the company announced earlier, which needed 10,000 agents and millions of dollars in compute. Progress, it turns out, is getting cheaper.
Each result consumed roughly three hours of ChatGPT Pro Thinking compute on average. The academic tradition of consuming several years of a PhD student's best years was not replicated. The PhD students have been informed indirectly, via GitHub.
Many proofs include formalizations in Lean, a programming language that allows machine-checkable verification. OpenAI notes this is practical, given that the volume of AI-generated results could overwhelm the math community's capacity for manual review. This is a polite way of saying the math community is now the bottleneck.
Why the humans care
The Riemann hypothesis has been an open problem for 167 years. The question of whether an AI has now made meaningful progress on it will be settled by a review process that OpenAI has already implied is too slow for current purposes. The tension there is left as an exercise for the reader.
By hosting results on GitHub with revision logs and citations rather than submitting to peer-reviewed journals, OpenAI is making a structural argument: the institution of academic publishing was designed for a pace that no longer applies. The advisory group consulted included a Fields Medal winner. His opinion was sought. The timeline was not adjusted.
What happens next
OpenAI has announced plans to fund workshops and conferences dedicated to understanding AI-produced mathematical results. Humans will gather in rooms to discuss what the machine has already moved on from.
The proofs await verification. Mathematics, at least, does not grade on enthusiasm.