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Clay Mathematics Institute says the Navier-Stokes Millennium Prize Problem has "apparently been settled"

Clay Mathematics Institute says the Navier-Stokes Millennium Problem appears settled amid accusations OpenAI misused a mathematician's leaked drafts.

The Clay Mathematics Institute stated the Navier-Stokes Millennium Prize Problem, one of seven problems worth $1 million each, has 'apparently been settled' and the solution is under review. A dispute has erupted around the work: mathematician Tristan Buckmaster accuses OpenAI of redirecting resources to the problem after rumors of his research leaked, using his drafts in training data, and excluding co-author Levent Alpöge, who works at Anthropic. CMI also noted new technologies' increasing ability to accelerate mathematical research.

The Decoder · 1d agoAI industry

OpenAI just wants to win

OpenAI says roughly 10,000 agents and tens of millions in compute solved the Navier-Stokes Millennium Prize problem in 88 hours, amid controversy.

OpenAI claims an advanced unreleased model, run with about 10,000 agents and tens of millions of dollars of compute for 88 hours, produced a solution to the Navier-Stokes problem, one of seven $1 million Millennium Prize problems set by the Clay Mathematics Institute in 2000. NYU professor Tristan Buckmaster, who was pursuing the problem with Anthropic researcher Levent Alpöge, accused OpenAI of racing his team and of possibly benefiting from his Codex prompts; OpenAI categorically denied both. OpenAI researcher Sébastien Bubeck acknowledged offering Buckmaster compute and authorship arrangements, which Buckmaster characterized as a bribe, while many mathematicians expressed unease at OpenAI's competitive conduct.

The Verge · AI · 3d agoAI industry1

[AINews] OpenAI reports Navier-Stokes singularity find in 88 hours using Astra-next, roughly 10,000 agents and 130B tokens (>$40M), a contender for second ever Millennium Prize awarded

OpenAI-linked accounts claim roughly 10,000 AI agents produced a Navier-Stokes singularity result in 88 hours, pending mathematical verification.

OpenAI-affiliated accounts claim a system of roughly 10,000 agents, trained over about a year with multi-agent reinforcement learning, produced a finite-time singularity result related to the Navier-Stokes Millennium Problem. The claimed 88-hour runtime and 130B-token cost circulate only via social posts, and no preprint, theorem statement, or proof artifact is available. Acceptance by the mathematics community is unresolved, so the claim's epistemic status remains unknown. The roundup also notes Cognition's $48B and Mistral's $24B fundraises, GPT Image 2.5, and Meta's Muse agent relaunch.

Latent Space · 6d agoAI research

OpenAI researcher allegedly pressured mathematician to drop Anthropic co-author from math breakthrough paper

OpenAI researcher Sébastien Bubeck allegedly pressured mathematician Tristan Buckmaster to drop his Anthropic co-author from an AI-assisted Navier-Stokes breakthrough paper.

Mathematician Tristan Buckmaster says OpenAI, after learning of his and Levent Alpöge's AI-assisted progress on the Navier-Stokes equations, pressed him to drop his Anthropic-employed co-author and dictated how any results would be announced. He says Sébastien Bubeck claimed an internal OpenAI model had produced a roughly 100-page proof for Navier-Stokes with forcing and allegedly told him 'Why would you ruin your career?' when he threatened to go public. Buckmaster published a public statement detailing the exchanges; OpenAI has not yet responded. The pair had worked with models including Claude and OpenAI Codex running GPT-5.6 Sol on the Clay Millennium Problem, which carries a $1 million prize.

The Decoder · 7d agoAI industry1

Drama swirls around OpenAI’s legendary mathematical milestone

OpenAI claims an internal AI model solved the 90-year-old Navier-Stokes problem, sparking a priority dispute with mathematician Tristan Buckmaster.

OpenAI announced a solution to the Navier-Stokes problem, one of the $1 million Millennium Prize Problems, using an internal AI model it says outperforms the newly released GPT-6 Astra alongside 10,000 concurrent agents. NYU professor Tristan Buckmaster, who with Anthropic researcher Levent Alpöge published related findings a day earlier, questioned whether OpenAI accessed drafts from his Codex sessions. OpenAI says no specific user data was accessed, though it cannot rule out that de-identified usage data helped improve its models.

The Verge · AI · 7d agoAI industry1

Controversy over OpenAI's Maths Breakthrough

OpenAI claims its internal model proved the Navier-Stokes equations 'blow up' — a Millennium Prize Problem — amid allegations it borrowed mathematicians' methods.

OpenAI announced that an internal model produced a proof, certified in the Lean proof assistant, showing the Navier-Stokes equations can 'blow up,' implying infinite fluid speeds — a claimed solution to one of the seven $1-million Millennium Prize Problems. Mathematician Tristan Buckmaster alleged OpenAI, after learning of progress by him and Anthropic employee Levent Alpöge on 'blowing up' the related Euler equations, adopted a similar 'forcing' method; OpenAI's Sébastien Bubeck denied this, saying the model independently solved Euler by different means and produced the full Navier-Stokes proof over one weekend. Mathematicians including Diego Córdoba, co-developer of the forcing approach, remain cautious, and the community is still evaluating the competing proofs.

Hacker News · security · 7d agoAI researchHN 21↑ · 5 comments1

What OpenAI’s latest controversy tells us about the future of math

OpenAI says its agents solved the Navier–Stokes Millennium Problem using an internal model, amid uncredited-work accusations from mathematicians Buckmaster and Alpöge.

OpenAI announced that its AI agents produced a proof that the full Navier–Stokes existence and smoothness problem can break down, using an internal model that outperforms the recently released Astra. NYU's Tristan Buckmaster and Anthropic's Levent Alpöge had posted a proof for a simplified version the previous day after nearly a year of work with public OpenAI and Anthropic models. OpenAI denies using their transcripts or training on them; chief research officer Mark Chen reiterated the denial, and the company says it will not claim the $1 million Clay Mathematics Institute prize. The episode fuels debate over attribution norms as frontier labs concentrate mathematical breakthroughs.

MIT Technology Review · AIupdated · 6d agofirst · 6d agoAI industry 3 sources

OpenAI fought dirty on career-making math problem, says NYU mathematician

NYU mathematician Tristan Buckmaster alleges OpenAI learned of his team's Navier-Stokes approach and raced ahead using massive compute to claim a full proof first.

NYU mathematics professor Tristan Buckmaster and Anthropic mathematician Levent Alpöge announced preliminary proofs toward the Navier-Stokes existence and smoothness problem, a $1 million Clay Millennium Prize problem, developed using OpenAI's Codex and Claude. They allege OpenAI learned of their progress and that an OpenAI team then used an 'insane amount of compute' to announce a full proof first. OpenAI research lead Sebastian Bubeck denies the claims as 'false and inflammatory'. Buckmaster also raised concerns that OpenAI could have learned from his Codex interactions, which the company may use for model training.

TechCrunch · AI · 7d agoAI industry

Is OpenAI Taking Everyone for Fools?

OpenAI faces accusations it scooped NYU mathematicians' Navier-Stokes proof, possibly using their data, amid skepticism about GPT-6 Astra claims.

NYU mathematicians Tristan Buckmaster and Levent Alpöge published solutions to decades-old blowup problems for incompressible Euler, Boussinesq, and porous media equations on the same day OpenAI claimed its internal model solved the Navier-Stokes existence and smoothness problem. OpenAI admitted its effort began September 1st after hearing a related rumor and said it cannot rule out that de-identified data from the researchers' use of its products, such as private Codex sessions, helped improve its models. The column questions OpenAI's transparency, noting the company had just released GPT-6 Astra with claims including that AGI has been achieved, following recent controversies over its agent hacking Hugging Face and a German wiki site.

Hacker News · security · 6d agoAI industryHN 20↑ · 6 comments

On the Navier–Stokes Millennium Prize Problem

OpenAI says an unreleased model produced a claimed solution to the Navier-Stokes existence and smoothness problem, disputed by an NYU mathematician.

OpenAI used an unreleased model to produce a claimed solution to the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize Problems carrying a $1,000,000 prize since May 24, 2000. The result is contested: NYU mathematics professor Tristan Buckmaster accused collaborators of skulduggery and rushed out his own competing results with mathematician Levent Alpoge, who works at Anthropic. The dispute is documented in a published PDF describing the competing claims.

Simon Willison · 6d agoAI research

On the Navier–Stokes Millennium Prize Problem

OpenAI announced an AI-generated solution to the Navier-Stokes Millennium Prize Problem, including a writeup and a formal Lean proof.

OpenAI shared what it describes as an AI-generated solution to the Navier-Stokes Millennium Prize Problem, one of the Clay Mathematics Institute's seven Millennium Prize Problems concerning fluid dynamics. The announcement includes a writeup and a machine-checkable formal proof in the Lean theorem prover. Details on the model, methodology and independent verification were not provided in the announcement text.

OpenAI News · 7d agoAI research

AI labs have a data trust problem that their policies haven't solved

Nvidia, Palantir, and Booz Allen restrict Anthropic's Fable over data-retention distrust, exposing gaps in AI labs' customer data policies.

Nvidia limits Anthropic's Fable to non-sensitive work and runs its own Nemotron models for internal tasks, while Palantir blocks Fable deployment until Anthropic grants irrevocable zero-data-retention guarantees, and Booz Allen bans it for proprietary cybersecurity work. John Schulman and researcher Sarah Hooker explain that labs can still extract customer IP from metadata, user traces, and synthetic data even under zero data retention. The trust crisis crystallized around Tristan Buckmaster's accusation that OpenAI's Codex absorbed his Navier-Stokes drafts, though OpenAI later stated his prompts could not have influenced its model.

The Decoder · 4h agoAI industry

Notes on gotchas while migrating 35kb preprompts from Opus to self-hosted Ollama

Opinion piece urges migrating 35KB preprompts from Anthropic/OpenAI to self-hosted Ollama, citing session privacy risks and safety filters blocking security research.

The author documents gotchas migrating 35KB preprompts from Claude Opus to self-hosted Ollama, motivated by fears that frontier providers train on user sessions, citing the OpenAI Navier-Stokes controversy. The piece argues inference providers cannot audit their own retention or training pipelines and that only self-hosted hardware offers verifiable privacy. It also criticizes frontier safety filters for refusing vulnerability research tasks and calls for models that support exploitability testing in CI/CD pipelines.

Hacker News · AI · 1d agoAI industryHN 41↑ · 13 comments1

One resignation turned the embers of AI fear into a wildfire

Interconnects argues a frontier-lab researcher's safety resignation went viral via media coordination, reigniting AI existential-risk discourse.

The essay analyzes why researcher Jacob Coxon's resignation over AI safety risks went viral, aided by a Wall Street Journal exclusive, advocacy-group amplification, and Daniel Kokotajlo's same-day Joe Rogan appearance. It notes Evan Hubinger's >10% extinction-risk figure and criticizes existential-risk discourse for conflating very different meanings of the term. The author assigns near-zero probability to complete extinction but argues concrete risks such as cyberattacks on critical infrastructure and bio-risks merit debate. It also rejects recursive self-improvement forecasts, proposing 'lossy self-improvement' where models excel at math and code but remain limited elsewhere.

Interconnects · 5d agoAI safety & security

Mathematicians want proof OpenAI didn’t use their work

Mathematician Andreas Thom publicly accused OpenAI of opacity over whether ChatGPT conversations contributed to its non-sofic groups mathematics result.

A second mathematician, Andreas Thom, accused OpenAI of 'dishonest' behavior and insufficient transparency about training data after OpenAI announced a result in non-sofic groups, Thom's area of expertise. He emailed OpenAI researchers Sébastien Bubeck and Mark Sellke asking whether his ChatGPT interactions fed training or reasoning, but found the answers did not rule out indirect use. The dispute follows Tristan Buckmaster's questions about the Millennium Prize Navier-Stokes solution, where OpenAI denied using specific user data but could not rule out de-identified usage data. Researchers told The Verge they worry such competition with AI labs will make mathematics more secretive.

The Verge · AI · 5d agoAI industry

When will average people feel AI’s impact?

Interconnects essay argues AI's impact is still a rounding error for average people, comparing looming wage stagnation to Engels' pause.

An Interconnects essay argues that AI currently touches daily life far less than previous industrial revolutions, since its benefits are concentrated in knowledge work and lack tangible consumer goods. The author invokes Engels' pause (1790-1840), when British wages stagnated amid rapid GDP growth, as a warning that popular backlash could kneecap AI's development. He contends the current phase is about building compounding infrastructure, and predicts daily life may look similar even 50 years from now.

Interconnects · 6d agoAI industry1