Controversy Surrounds OpenAI's Claimed Breakthrough on Navier-Stokes Equations

OpenAI announced it has solved the Navier-Stokes existence and smoothness problem, a complex mathematical puzzle that has remained unsolved for roughly 90 years. The company stated that the breakthrough was achieved using an unreleased internal AI model with capabilities exceeding its GPT-6 Astra system, working concurrently alongside 10,000 AI agents. Training for this specialized internal model began on August 28th, yielding performance leaps across mathematical benchmarks. The announcement sparked significant controversy within the mathematics and AI research communities. Just one day prior to OpenAI's post, NYU mathematics professor Tristan Buckmaster and Anthropic researcher Levent Alpöge published research addressing a related aspect of the problem. Buckmaster voiced concerns that OpenAI may have leveraged private research drafts uploaded to OpenAI's Codex during their collaborative research sessions. Buckmaster noted that after contacting OpenAI about overlapping methodologies, he questioned whether OpenAI's internal system had been trained on or granted access to their private Codex sessions. OpenAI refuted claims of improper data handling, asserting that no specific user data was accessed to generate the Navier-Stokes proof, though the company acknowledged it could not entirely rule out the presence of de-identified data in broad processing.