The Navier–Stokes Millennium Prize Problem (simonwillison.net)

OpenAI recently announced a breakthrough resolution to the Navier–Stokes Millennium Prize Problem, utilizing a yet-to-be-released model to achieve impressive results in just days. This mathematical challenge has eluded experts for decades and carries a $1 million prize for a correct solution. The announcement, however, has been marred by controversy, as Tristan Buckmaster, a mathematics professor at NYU, raised concerns about the timing and potential overlap with his own collaborative work with Levent Alpöge of Anthropic. Their team used OpenAI's models for nearly a year before achieving a breakthrough, only to find OpenAI launching a parallel effort shortly afterward. The significance of OpenAI's accomplishment lies in the significant capabilities of LLMs (large language models) to tackle complex theoretical problems, potentially reshaping the landscape of mathematical research. OpenAI’s agents reportedly sent 4.9 million messages and processed around 300 billion output tokens within 88 hours to reach their resolution. While OpenAI claims no user data from Buckmaster and Alpöge was accessed, the incident raises ethical questions about how AI models train and potentially influence future research outcomes. As AI begins to intersect with cutting-edge mathematics, this dynamic reflects broader implications for intellectual property and collaborative innovation in the AI/ML community.