--- title: OpenAI claims progress on the Navier-Stokes Millennium... description: OpenAI claims to have made substantial progress toward solving the Navier-Stokes Millennium Prize Problem, a decades-old unsolved question in fluid dynamics... canonical: https://daily.dev/posts/openai-claims-progress-on-the-navier-stokes-millennium-prize-problem-jbi0dji6e twitter:card: summary_large_image twitter:site: @dailydotdev og:type: website og:site_name: daily.dev og:title: OpenAI claims progress on the Navier-Stokes Millennium Prize Problem | daily.dev og:description: OpenAI claims to have made substantial progress toward solving the Navier-Stokes Millennium Prize Problem, a decades-old unsolved question in fluid dynamics... og:url: https://daily.dev/posts/openai-claims-progress-on-the-navier-stokes-millennium-prize-problem-jbi0dji6e og:image: https://api.daily.dev/og/posts/JBI0dJI6E.png og:image:alt: OpenAI claims progress on the Navier-Stokes Millennium Prize Problem og:image:width: 1200 og:image:height: 630 og:locale: en --- > ## Documentation Index > Fetch the complete documentation index at: https://daily.dev/llms.txt > Use this file to discover all available pages before exploring further. # OpenAI claims progress on the Navier-Stokes Millennium Prize Problem **[Collections](https://daily.dev/sources/collections)** · 4 min read · 1 upvotes · 1 comments ## Summary OpenAI claims to have made substantial progress toward solving the Navier-Stokes Millennium Prize Problem, a decades-old unsolved question in fluid dynamics mathematics designated by the Clay Mathematics Institute. The company confirmed the claim to the New York Times and published its own post detailing the proposed solution. OpenAI hinted it is working on other Millennium Prize problems as well, though independent verification from mathematicians is still required before any solution can be accepted. ## Content ## What happened OpenAI announced it had made "substantial progress" on the Navier-Stokes Millennium Prize Problem, one of seven unsolved problems in mathematics that carry a $1 million prize each. The claim landed with a thud in the mathematical community, which had already been growing uneasy about how AI labs were using famous open problems as marketing benchmarks. Around the same time, OpenAI withdrew its $1 million sponsorship of Caltech's student-run Mathathon AI math contest after 771 mathematicians signed an open letter calling the output "slop mathematics" and accusing AI companies of offloading verification labor onto unpaid academics. Anthropic kept its $1 million in the contest and has been taking a different approach, working with mathematicians directly - including using Claude to formalize Fermat's Last Theorem in Lean. The Mathathon is still running at Caltech from October 30 to November 1. Organizers made some concessions (adding an arXiv requirement, expanding an educational track) but declined to cancel it. ## The Fields Medalists weigh in Twenty-five Fields Medalists, including Terence Tao, signed a declaration warning that AI companies' race to solve famous problems as benchmarks is misaligned with what mathematics actually is. The core argument: solving a problem is only a proxy for conceptual understanding, and a poor one when the solution bypasses peer review, attribution, and the slow human process of turning a proof into shared knowledge. Nearly five thousand mathematicians signed a related statement. The concern isn't just about credit - it's about what gets destroyed in the process. Mathematical problems were legible proxies for valuable idea-generation. If AI can game those proxies without advancing real understanding, the proxies stop working, and the field loses something harder to replace than any single theorem. The declaration stops short of rejecting AI outright. Signatories acknowledge AI could accelerate genuine mathematical understanding if guided responsibly. What they're objecting to is the benchmark-chasing, the rushed unattributed outputs, and the implicit claim that true/false verification is the same thing as mathematical progress. ## The Goodhart's Law problem This is a version of a pattern showing up across fields. Puzzles were useful signals because solving them required the kind of thinking that produces new ideas. Once an AI can solve the puzzle without that thinking, the signal breaks. Chess went through this. Speedrunning went through this. Both ended up with human-only categories because the original competition was never really about the output - it was about what the output revealed. Software engineering is hitting the same wall. Impressive GitHub side projects used to signal skill. AI agents are devaluing that signal fast, and nobody has agreed on what replaces it. ## Why the Navier-Stokes claim is complicated The Lean proof angle matters here. Pure mathematics formalized in Lean/Mathlib is arguably the best-case scenario for agentic AI work - the specification is already rigorous, machine-checkable, and audited. If AI is going to do reliable autonomous work anywhere, it should be here. And yet even this setup has had problems. Lean's kernel has had soundness bugs that were exploited. The verification layer that's supposed to make everything trustworthy isn't perfectly trustworthy. Human review doesn't scale as a substitute, and the humans doing the reviewing aren't being compensated for it. The broader argument from skeptics: models generalize narrowly, reward hacking is real, and the only reliable counter is rigorous formal specification - which is scarce and expensive to produce. The firms that can safely use fully autonomous LLMs are a short list: those tolerant of cheap failure, those with narrow well-defined tasks, and those already paying for rigorous specification and validation (chip design, drug discovery are the usual examples). Most adoption will probably favor cheap open models running in wide swarms rather than frontier models doing deep autonomous work. ## Sam Altman's counter-narrative Meanwhile, Sam Altman told Salesforce's Mark Benioff that an internal model beyond their current Astra release can do things the world's best mathematicians cannot. His framing of the progression: GPT-5.5 was roughly at the level of an average math professor, 5.6 was top one or two percentile, Astra was a bit better, and the next internal model is past all of that. It's a striking claim, and it's the kind of claim that's hard to evaluate without seeing the work - which is exactly what the mathematicians are asking for. ## The actual disagreement The gap between the AI labs and the mathematical community isn't really about whether AI can produce correct proofs. It's about what "solving" a problem means. For the labs, a verified proof is a solved problem. For the mathematicians, a solved problem is one that's been understood, written up, reviewed, disseminated, and absorbed into the field's shared knowledge. Those are very different things, and conflating them is what's generating most of the friction. ## Questions this post answers ### What is the Navier-Stokes Millennium Prize Problem that OpenAI claims to have made progress on? It is one of seven unsolved mathematics problems designated by the Clay Mathematics Institute, concerning whether smooth, physically reasonable solutions to the Navier-Stokes fluid dynamics equations always exist in three dimensions. The problem has remained open for decades. OpenAI confirmed to the New York Times it made substantial progress and published its own account of the claimed solution, though independent verification by mathematicians is still needed. _daily.dev surfaces how the math community responds as verification of this claim unfolds._ ## Community take How the wider developer community reacted, aggregated from 3 discussions and 2811 comments across hackernews, lobsters (as of 2026-09-17). **TL;DR:** A Severe Misalignment of AI in Mathematics: Reaction is split between those who see AI-generated proofs as a chess-engine-like disruption that could still spark productive community activity, and those who share the declaration's worry that fast, unaccountable 'proof dumps' from well-funded labs will produce slop, concentrate power, and hollow out the incentives for human mathematical understanding. Why i'm still bearish on LLMs after Navier-Stokes: The discussion barely engages with the Navier-Stokes/Lean argument itself and instead spirals into a long, heated tangent about frontier models' poor chess performance (frequent illegal moves) as evidence against claims of near-AGI generality, with a vocal minority pushing back that chess is an unfair or irrelevant benchmark. A Severe Misalignment of AI in Mathematics: Reactions split between sympathy for the concern that AI-generated proofs strip away the human process of mathematical understanding, and skepticism that this framing is naive, gatekeeping, or simply the same disruption software already went through. **Sentiment:** 12% positive · 35% mixed · 53% skeptical **The case for** - Some argue AI-generated proofs, even if controversial, could spark the same kind of community activity (talks, discussions, verification efforts) that a human proof like Mochizuki's did. - Some argue the labs simply haven't optimized for chess and that with RL training or better harnesses models could play at a much higher level. - The concern is seen as sympathetic because the 'journey' of discovery historically built understanding, not just the answer. - Formal/Lean verification is seen by some as a way to sidestep trust and attribution problems raised in the declaration. - A few point out models can still write chess engines or use tools/harnesses to play well even if the raw model can't. **The pushback** - Concern that labs can flood the field with proofs faster than the community can verify or digest them, creating 'slop fatigue' or a denial-of-service on researchers' time. - Frequent illegal moves and forgotten pieces even in a simple, rule-bound, well-documented domain are seen as damning evidence against claims of general intelligence or reasoning. - Some argue the analogy to gatekeeping mountain summits is flawed since nothing stops anyone from still 'climbing' (doing math the traditional way). - Worry that a small number of well-funded AI labs/compute owners will concentrate power and control over mathematical progress. - Chess ELO comparisons on tested benchmarks are criticized as relative-only and not comparable to real human ratings, undermining claims of 'GM level' play. **By community** - hackernews (heated): A long, contentious thread ranging from cautious optimism (comparisons to chess engines and Mochizuki-style community scrutiny) to sharp skepticism about slop, power concentration, and the erosion of human mathematical understanding. - lobsters (mixed): No comments were available to characterize the discussion. **Hottest debate:** A Severe Misalignment of AI in Mathematics: Whether AI-driven mathematics will resemble the chess-engine era \u2014 disruptive but ultimately enriching for human understanding \u2014 or instead produce unverifiable 'slop' that overwhelms and displaces the human community process. **Open questions** - If AI proofs become too complex for humans to fully understand or verify, does that undermine the point of doing mathematics at all? - Would current-generation frontier models perform meaningfully better at chess than the somewhat dated models tested in the cited paper? - Will AI-solved problems and their reasoning actually get fed back into future model training, or will that context be lost? - Will frontier labs continue producing headline-grabbing proofs, or was this a one-off publicity effort? - Is chess a fair generality test given labs don't specifically optimize for it, or does that itself prove a lack of cross-domain transfer? **Highlights** > One question I have is whether/how AI "solutions" make it back into future models. I've sort of naively assumed that AI companies basically scrape the web in large swaths, do a bit curating, and train. In a case where an AI solves math problems, I conjecture, that lots of text is created documenting that the discovery happened (only because its new), but very little where mathematicians are spending the time to really document and discuss it in detail where future training runs will have lots of human produced content to ingest. Are Anthropic/Google/OpenAI specifically feeding back these refined gems into future training runs with a "this really matters, but since we took away the thunder of mathematicians online geeking out about it, you should still consider this as as significant as other great discoveries from the past"? > — [travisgriggs on lobsters · 1 points, 1 comments](https://lobste.rs/s/xsbz3l/severe_misalignment_ai_mathematics#c_anqyvn) > The quote at the top is inspiring but not realistic. Humans have long produced proofs that are difficult to follow and there are many proofs that only a few understand after long and specialized study. It seems out of place to me to complain about mathematical discoveries made by computers simply because they might be hard to understand by humans. I even thing it will go in the opposite direction: we will be able to train LLMs to break down mathematical proofs tailored to each of our indvidual levels and ways of understanding, thereby improving mathematical education. > — [kghose on lobsters · 1 points](https://lobste.rs/s/xsbz3l/severe_misalignment_ai_mathematics#c_fvfbfc) > The situation seems analogous indeed. However, cynically, I do wonder whether the outcome will differ across the CS and math industry once the dust settles. One could argue that software production is funded in large part for the end product, not the process, whereas mathematics is far more exploratory. More concretely, it seems to me that an agent that outputs unreadable code implementing software that works perfectly from a user perspective is substantially more useful and disruptive than an agent that outputs a unreadable proof of a mathematical result that is formally verified. > — [jo3\_l on lobsters · 1 points, 1 comments](https://lobste.rs/s/xsbz3l/severe_misalignment_ai_mathematics#c_ak3mhj) > As a mathematician maybe I am a little more optimistic than this declaration. I am thinking of Mochizuki's abc conjecture: He worked in relative isolation, and dumped a huge incomprehensible proof on the community (to oversimplify a bit). That's not totally unlike what might happen if AI generates a huge, incomprehensible proof of let's say RH. Well, what is the result? In the Mochizuki case, it was a lot of skepticism, but it also generated conferences, papers, talks in the hallway, discussions with students, and so on--a flurry of exactly that kind of community process that the declaration says is the main driver of mathematics. Ultimately we think a fatal flaw was found in Mochizuki's proof, so it didn't lead anywhere in particular. But in our hypothetical "AI lean-verified proof of RH" situation, it would presumably generate substantially more of that community activity we saw in the Mochizuki situation. And if it's correct, that community activity would be productive (expository talks, students given problems to flesh out or generalize, etc). Maybe mathematics just becomes a little more like other fields--relying on labs with lots of money for compute, digging through a corpus of AI-generated proofs, etc. > — [tmhn2 on hackernews · 15 comments](https://news.ycombinator.com/item?id=49664047) > Even before AI we used to say if you write code that you only barely understand, then it will be to complicated to debug. (and/or maintain) Mochizuki was still one human and it required legions of other humans to unpack and untangle to confirm that it didn't lead to anywhere in particular. AI is now capable of constructions so complex that no human or human team can unpack. And its ability to increase that complexity is growing while our human ability is stagnant. meta-AI analysis cannot help. We (software professionals who use AI regularly) already know that if you run into a situation where a Fable/Astra-generated analysis reaches the limits of our comprehension/complexity due to their subjectivity, throwing more AI at the problem doesn't always converge. There are many reasons to feel optimistic about AI, and ultimately its general ability to help science and mathematics. I see no reason to feel optimistic about the future of mathematics and AI based on the current path of frontier labs, unless the misalignment Tao is writing about can be reconciled. > — [deanCommie on hackernews · 3 comments](https://news.ycombinator.com/item?id=49664942) **Source threads** - [hackernews](https://news.ycombinator.com/item?id=49662371) · 715 points · 1544 comments - [hackernews](https://news.ycombinator.com/item?id=49715927) · 453 points · 1224 comments - [hackernews](https://news.ycombinator.com/item?id=49662116) · 144 points · 24 comments - [lobsters](https://lobste.rs/s/cianny/why_i_m_still_bearish_on_llms_after_navier) · 42 points · 11 comments - [lobsters](https://lobste.rs/s/xsbz3l/severe_misalignment_ai_mathematics) · 40 points · 7 comments - [lobsters](https://lobste.rs/s/oossfd/severe_misalignment_ai_mathematics) · 4 points · 1 comments ## Community discussion Top comments from developers on daily.dev. **@zx8086** · 1 upvotes > AI can solve cancer, if you put the solution in the prompt. --- Tags: [#openai](https://daily.dev/tags/openai), [#math](https://daily.dev/tags/math) [View this post on daily.dev](https://daily.dev/posts/openai-claims-progress-on-the-navier-stokes-millennium-prize-problem-jbi0dji6e) ```json {"@context":"https://schema.org","@graph":[{"@type":"Organization","@id":"https://daily.dev/#organization","name":"daily.dev","url":"https://daily.dev","logo":{"@type":"ImageObject","url":"https://daily.dev/apple-touch-icon.png","width":180,"height":180},"sameAs":["https://twitter.com/dailydotdev","https://github.com/dailydotdev","https://www.linkedin.com/company/daily-dev-ltd"]},{"@type":"WebSite","@id":"https://daily.dev/#website","url":"https://daily.dev","name":"daily.dev","publisher":{"@id":"https://daily.dev/#organization"},"potentialAction":{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https://daily.dev/search?q={search_term_string}"},"query-input":"required name=search_term_string"}}]} 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