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OpenAI announced that its most advanced AI model produced a mathematical proof that the Navier–Stokes equations, which describe fluid flow, can generate a singularity — a point of physically impossible infinite speed. Mathematician George Karniadakis calculated that for air this breakdown occurs at a vortex width of about 70 nanometres, roughly the distance a molecule travels before colliding with another.
OpenAI announced on 8 September that one of its AI models had solved a major open problem in fluid dynamics, the Navier-Stokes puzzle. The claim provoked backlash after researchers, including Tristan Buckmaster and Levent Alpöge, said they had already been working on the same problem using AI tools from OpenAI and Anthropic and were tipped off before the announcement. Twenty-five Fields Medal winners have since signed an open letter warning that AI involvement in mathematics raises serious plagiarism and credit-attribution concerns.
OpenAI announced it had solved part of the Navier–Stokes Millennium Prize Problem using an AI system, but the announcement via press release drew criticism for lacking transparency about verification and prior human contributions. Hours earlier, mathematicians Tristan Buckmaster and Levent Alpöge said they had reached a partial solution using AI tools from both OpenAI and Anthropic, raising questions about who deserves credit for the breakthrough.
A discussion thread examines how medieval mathematicians like Scipione del Ferro hid discoveries such as cubic-equation solutions to protect their livelihoods, using secrecy as leverage in public problem-solving contests. The post traces this culture of concealment through the Newton–Leibniz calculus dispute, contrasting it with today's norm of open publication despite paywalls and peer-review issues.
Almost 5,000 mathematicians, including 25 Fields medalists, signed a declaration titled 'A Severe Misalignment of AI in Mathematics,' arguing that AI's success at solving famous problems is being mistaken for genuine mathematical progress. They contend that solving problems is merely a proxy for the real goal of conceptual insight, and that rapid AI-generated 'true/false' outputs could crowd out the slower work of idea generation rather than advance it.
A new essay from Proofs and Prompts traces how AI systems went from struggling with basic arithmetic three years ago to earning IMO gold-medal-level scores last year, and are now autonomously cracking open research problems. The author, who previously gave a talk called 'The End of Mathematics,' argues this trajectory will force a fundamental restructuring of how the mathematics profession operates, even though outright 'solving' math isn't the point.
Twenty-five Fields Medal winners signed a letter titled 'A Severe Misalignment of AI in Mathematics,' arguing that AI companies rush out proof announcements—reportedly including a claimed solution to the Navier-Stokes problem attributed to OpenAI—without proper writeups, credit to prior work, or space for conceptual understanding. The commentary piece agrees with the medalists' critique of AI companies but turns the argument back on the mathematics community itself, noting the irony that the letter was also released hastily without consultation, and questioning whether academia has truly nurtured students and ideas as it claims to value.
OpenAI says it has solved a Millennium Prize-level math problem, extending a string of high-profile claims in mathematics. Researchers including Tristan Buckmaster and Andreas Thom say the company has been vague about whether their own prior work, done through OpenAI's Codex tool, fed into its results. OpenAI denies this, insisting Buckmaster's recent prompts could not have influenced the system's training.
The Clay Mathematics Institute issued a statement noting growing momentum toward solving the Navier-Stokes Millennium Prize Problem, which concerns whether smooth, well-defined solutions always exist for the equations governing 3D fluid motion. CMI pointed to recent breakthroughs in related research, some already honored with its Clay Research Award, as evidence that a resolution could be near.
A group of mathematicians argues that while large language models have rapidly gained the ability to solve major outstanding problems, AI companies' drive to treat these solutions as benchmarks conflicts with how mathematics actually operates as a discipline. They describe this as a broader misalignment between AI industry goals and the values of the mathematical community, which relies on slow, collective processes of verification, teaching, and simplification rather than one-off problem-solving feats.
A group of 25 Fields Medal-winning mathematicians has issued a joint declaration warning that AI companies' rush to use famous unsolved math problems as benchmarks for large language models is harming the discipline. They argue that while LLMs have rapidly gained the ability to crack major open problems, this benchmark-driven approach conflicts with how mathematical knowledge has traditionally been built and validated over generations.
OpenAI announced Tuesday that a swarm of 10,000 AI agents, run for 88 hours at a cost of millions of dollars, had found a scenario where the Navier-Stokes equations describe fluids reaching infinite velocity, effectively breaking the famous equations. NYU mathematician Tristan Buckmaster then publicly accused the company of producing a solution suspiciously similar to unpublished work he had been developing for years and was close to finishing.