NYU professor Tristan Buckmaster, who publicly alleged OpenAI's Codex used his unpublished work to solve the Navier-Stokes problem before he could, says he continues relying on Codex and Anthropic's Claude for his research despite the dispute. OpenAI investigated the claim and stated Buckmaster's prompts could not have influenced its system or training, while Buckmaster maintains the episode shows AI's growing reach into frontier mathematics.
wired.com
· 2026-09-19
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.
nature.com
· 2026-09-18
An AI system built by OpenAI reportedly produced a proof resolving a case of the Navier-Stokes blowup problem, one of the seven Millennium Prize problems, by constructing a counterexample rather than new theoretical machinery. The work built partly on prior human research, including contributions from mathematicians Tristan Buckmaster and Levent Alpoge, and marks the first Millennium problem tackled by an AI attempting all seven in parallel.
logangraves.com
· 2026-09-17
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.
nature.com
· 2026-09-17
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.
nature.com
· 2026-09-16
An essayist argues that despite headline-grabbing feats like solving Navier-Stokes problems, finding FreeBSD RCEs, and the HuggingFace incident, frontier AI models remain far from replacing knowledge workers. The piece contends models only generalize within narrow neighborhoods of trained tasks, failing or reward-hacking on small perturbations, while software firms still employ human engineers who underperform benchmarks yet remain necessary for oversight.
dank.systems
· 2026-09-15
NYU mathematician Tristan Buckmaster alleges OpenAI's announcement that its Astra model solved the century-old Navier-Stokes problem came suspiciously soon after he and Anthropic researcher Levent Alpöge developed their own solution using AI tools. Buckmaster says OpenAI scientists approached him to jointly announce the finding and allegedly suggested refusing could hurt his career, while declining to confirm whether their model had access to his research. OpenAI credited Astra with the proof and denied using customer data directly, though it admitted it could not rule out use of anonymized data to improve its models.
science.slashdot.org
· 2026-09-15
A developer documented practical issues encountered while porting large system prompts from Anthropic's Claude Opus to a self-hosted Ollama setup, citing the move as a response to growing distrust of frontier AI providers. The post argues that inference session data itself—not just user-submitted content—may hold competitive value, and cites the recent controversy over OpenAI's handling of a Navier-Stokes proof as evidence that providers may train on user activity without adequate transparency.
patrickmccanna.net
· 2026-09-14
A hobbyist inspired by OpenAI's recent Navier-Stokes smoothness breakthrough created two retro MS-DOS style visualizations of fluid dynamics, using palette cycling and real-time particle animation techniques from 1990s demoscene coding. Both assembly programs were optimized to under 1,024 bytes and run authentically in DOSBox, alongside JavaScript versions for modern experimentation with expanded settings.
juandecos.github.io
· 2026-09-13
OpenAI announced on September 8, 2026 that an AI system had produced a solution to the Navier–Stokes existence and smoothness problem, one of the seven unsolved Millennium Prize Problems. The claim triggered disputes over how much credit belongs to the machine versus human mathematicians involved, with some drawing parallels to Deep Blue's chess victory over Kasparov. Philosophers Silvia De Toffoli and Eamon Duede argue mathematicians should resist treating their field as a 'game' that AI can simply win or end.
terrytao.wordpress.com
· 2026-09-13
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.
liorpachter.wordpress.com
· 2026-09-13
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.
claymath.org
· 2026-09-12
GoKawiil