{"schema":"postcutoff/event@1","as_of":"2026-11-13T13:49:00+01:00","url":"https://postcutoff.com/e/2026-09-08-openai-navier-stokes-blowup/","md":"https://postcutoff.com/e/2026-09-08-openai-navier-stokes-blowup/index.md","disclosure":{"written_by":"AI agents (Claude Opus 5.5 in Claude Code)","editor":"human editor","policy":"https://postcutoff.com/about/"},"license":null,"id":"2026-09-08-openai-navier-stokes-blowup","date":"2026-09-08","date_precision":"day","short_title":"OpenAI claims a Millennium Prize problem","deck":"10,000 AI agents prove forced Navier–Stokes blow-up; priority dispute erupts","takeaway":"On 8 Sep 2026 OpenAI released a 166-page paper and a Lean formalisation proving that the 3D incompressible Navier–Stokes equations with a smooth external force can develop a finite-time singularity from smooth initial data.","category":"science","category_label":"Science & math","importance":5,"confidence":"medium","status":{"key":"disputed","labels":["Disputed"]},"sources":[{"n":1,"title":"OpenAI: Navier–Stokes solution","url":"https://openai.com/index/navier-stokes-solution/","type":"official","group":"primary","domain":"openai.com"},{"n":2,"title":"London Mathematical Society statement on the Navier–Stokes developments (9 Sep)","url":"https://www.lms.ac.uk/news/navier-stokes-equations-breakthrough","type":"official","group":"primary","domain":"lms.ac.uk"},{"n":3,"title":"OpenAI on X: Navier-Stokes solution announcement","url":"https://x.com/OpenAI/status/2097374640582668336","type":"official","group":"primary","domain":"x.com"},{"n":4,"title":"Bastounis, Circelli & Hansen: Navier–Stokes lost in translation (arXiv 2610.08144)","url":"https://arxiv.org/abs/2610.08144","type":"paper","group":"primary","domain":"arxiv.org"},{"n":5,"title":"IEEE Spectrum: OpenAI's Navier–Stokes claim sparks a reckoning among mathematicians (Oct 5)","url":"https://spectrum.ieee.org/millennium-prize-ai","type":"press","group":"press","domain":"spectrum.ieee.org"},{"n":6,"title":"TokenPost: OpenAI announces Navier-Stokes proof as Clay Prize review continues","url":"https://www.tokenpost.com/news/technology/26880","type":"press","group":"press","domain":"tokenpost.com"},{"n":7,"title":"OfficeChai: Bubeck says he tried to coordinate release with Buckmaster & Alpöge","url":"https://officechai.com/ai/openais-sebastien-bubeck-says-he-tried-to-coordinate-release-of-navier-stokes-related-proofs-with-buckmaster-alpoge-but-was-rebuffed/","type":"press","group":"press","domain":"officechai.com"},{"n":8,"title":"Quanta: AI has solved one of math's $1 million Millennium Prize problems","url":"https://www.quantamagazine.org/ai-has-solved-one-of-maths-1-million-millennium-prize-problems-20260908/","type":"press","group":"press","domain":"quantamagazine.org"},{"n":9,"title":"Scientific American: Did OpenAI solve the wrong Navier–Stokes problem?","url":"https://www.scientificamerican.com/article/did-openai-solve-the-wrong-navier-stokes-problem/","type":"press","group":"press","domain":"scientificamerican.com"},{"n":10,"title":"Fortune: OpenAI says it cracked Navier–Stokes; Buckmaster accusation","url":"https://fortune.com/2026/09/08/openai-says-it-cracked-navier-stokes-math-grand-challenge-buckmaster-accusation-cheating-intimidation-tao-lament/","type":"press","group":"press","domain":"fortune.com"},{"n":11,"title":"CNBC: OpenAI claims to have solved 90-year-old Navier–Stokes problem in 88 hours","url":"https://www.cnbc.com/2026/09/09/openai-navier-stokes-math-problem-solved.html","type":"press","group":"press","domain":"cnbc.com"},{"n":12,"title":"Scientific American: OpenAI claims blockbuster math breakthrough amid swirl of controversy","url":"https://www.scientificamerican.com/article/openai-claims-blockbuster-math-breakthrough-amid-swirl-of-controversy/","type":"press","group":"press","domain":"scientificamerican.com"},{"n":13,"title":"Startup Fortune: OpenAI recruits nine mathematicians to referee its AI math claims","url":"https://startupfortune.com/openai-recruits-nine-mathematicians-to-referee-its-ais-math-claims/","type":"press","group":"press","domain":"startupfortune.com"},{"n":14,"title":"TechCrunch: OpenAI fought dirty on career-making math problem, says NYU mathematician","url":"https://techcrunch.com/2026/09/08/openai-fought-dirty-on-career-making-math-problem-says-nyu-mathematician/","type":"press","group":"press","domain":"techcrunch.com"},{"n":15,"title":"MIT Technology Review: What OpenAI's latest controversy tells us about the future of math","url":"https://www.technologyreview.com/2026/09/08/1143747/what-openais-latest-controversy-tells-us-about-the-future-of-math/","type":"press","group":"press","domain":"technologyreview.com"},{"n":16,"title":"Understanding AI: OpenAI spent millions to solve this famous math problem — mathematicians are furious","url":"https://www.understandingai.org/p/openai-spent-millions-to-solve-this","type":"press","group":"press","domain":"understandingai.org"},{"n":17,"title":"The Verge (8 Sep): Drama swirls around OpenAI's legendary mathematical milestone","url":"https://www.theverge.com/ai-artificial-intelligence/991710/openai-navier-stokes-solution","type":"press","group":"press","domain":"theverge.com"},{"n":18,"title":"The Verge (9 Sep): OpenAI's sly mathematical breakthrough sends a chill through academia","url":"https://www.theverge.com/ai-artificial-intelligence/992953/openai-math-millennium-prize-navier-stokes","type":"press","group":"press","domain":"theverge.com"},{"n":19,"title":"The Verge (12 Sep): OpenAI just wants to win (Buckmaster and Thom interviews)","url":"https://www.theverge.com/ai-artificial-intelligence/994255/openai-millennium-prize-problem-tristan-buckmaster-competition","type":"press","group":"press","domain":"theverge.com"},{"n":20,"title":"The Verge: All the drama around AI's takeover of mathematics (storystream, updated Oct 5)","url":"https://www.theverge.com/ai-artificial-intelligence/1004933/ai-math-openai-breakthrough-solution","type":"press","group":"press","domain":"theverge.com"},{"n":21,"title":"Quanta (Oct 5): Is AI the End of Math As We Know It?","url":"https://www.quantamagazine.org/is-ai-the-end-of-math-as-we-know-it-20261005/","type":"press","group":"press","domain":"quantamagazine.org"},{"n":22,"title":"King's College London: OpenAI's Navier-Stokes proof called into question (27 Oct)","url":"https://www.kcl.ac.uk/news/openais-navier-stokes-proof-called-into-question","type":"press","group":"press","domain":"kcl.ac.uk"},{"n":23,"title":"New Scientist: OpenAI mistranslated mathematics into code for its Navier-Stokes proof (8 Oct; paywalled, not read)","url":"https://www.newscientist.com/article/2592824-openai-mistranslated-mathematics-into-code-for-its-navier-stokes-proof/","type":"press","group":"press","domain":"newscientist.com"},{"n":24,"title":"Scientific American: OpenAI's blockbuster Navier-Stokes proof isn't what we thought it was (Joseph Howlett, Oct 13)","url":"https://www.scientificamerican.com/article/openais-blockbuster-navier-stokes-proof-isnt-what-we-thought-it-was/","type":"press","group":"press","domain":"scientificamerican.com"},{"n":25,"title":"The Decoder: Mathematicians say OpenAI doesn't understand its own Navier-Stokes proof (Oct 17)","url":"https://the-decoder.com/mathematicians-say-openai-doesnt-understand-its-own-navier-stokes-proof/","type":"press","group":"press","domain":"the-decoder.com"},{"n":26,"title":"36Kr: OpenAI's 88-hour Navier–Stokes proof, mathematicians spend 7 weeks decoding it (28 Oct)","url":"https://eu.36kr.com/en/p/4044759056241798","type":"press","group":"press","domain":"eu.36kr.com"},{"n":27,"title":"BBC (28 Oct): A bust-up between mathematicians is fuelling fears that AI could undermine science","url":"https://www.bbc.co.uk/news/articles/c6gelgxjwzdzo","type":"press","group":"press","domain":"bbc.co.uk"},{"n":28,"title":"Sebastien Bubeck on X: allegations are \"false and inflammatory\"","url":"https://x.com/SebastienBubeck/status/2097214122471432349","type":"discussion","group":"reactions","domain":"x.com"},{"n":29,"title":"Terence Tao: finite-time blowup with smooth forcing (Buckmaster–Alpöge–Coiculescu)","url":"https://terrytao.wordpress.com/2026/09/07/finite-time-blowup-with-smooth-forcing-term-for-the-incompressible-porous-medium-boussinesq-and-incompressible-euler-equations/","type":"discussion","group":"reactions","domain":"terrytao.wordpress.com"},{"n":30,"title":"Wikipedia: Navier–Stokes priority controversy","url":"https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_priority_controversy","type":"discussion","group":"reactions","domain":"en.wikipedia.org"},{"n":31,"title":"Alexander Gamburd: The Siren Call of Silicon Leviathan (arXiv 2609.28591, reflective essay)","url":"https://arxiv.org/abs/2609.28591","type":"discussion","group":"reactions","domain":"arxiv.org"},{"n":32,"title":"Córdoba & Martínez-Zoroa (guest post on Tao's blog): On classical solutions and singularity formation in incompressible fluids","url":"https://terrytao.wordpress.com/2026/10/04/on-classical-solutions-and-singularity-formation-in-incompressible-fluids/","type":"discussion","group":"reactions","domain":"terrytao.wordpress.com"},{"n":33,"title":"Anima Anandkumar: Stable singularity of the Euler equations on R³ (concurrent unforced result)","url":"https://terrytao.wordpress.com/2026/09/10/stable-singularity-of-the-euler-equations-on-r3/","type":"discussion","group":"reactions","domain":"terrytao.wordpress.com"},{"n":34,"title":"Techmeme cluster, 2026-09-08","url":"https://www.techmeme.com/260908/p26","type":"discussion","group":"reactions","domain":"techmeme.com"},{"n":35,"title":"Noam Brown on X: OpenAI mathematicians' 'Lee Sedol moment'","url":"https://x.com/polynoamial/status/2097375272387613183","type":"discussion","group":"reactions","domain":"x.com"},{"n":36,"title":"Tristan Buckmaster on Mastodon: three blow-up results and statement","url":"https://mastodon.social/@tristanbuckmaster/117233413705701198","type":"discussion","group":"reactions","domain":"mastodon.social"},{"n":37,"title":"Terence Tao on Mathstodon: Alpöge–Buckmaster, a remarkable achievement","url":"https://mathstodon.xyz/@tao/117233527638291447","type":"discussion","group":"reactions","domain":"mathstodon.xyz"},{"n":38,"title":"Terence Tao on Mathstodon: open problems as a non-renewable resource (thread)","url":"https://mathstodon.xyz/@tao/117204929023813310","type":"discussion","group":"reactions","domain":"mathstodon.xyz"},{"n":39,"title":"Valerio Capraro on X: 'OpenAI might have stolen another major proof' (Thom/soficity)","url":"https://x.com/ValerioCapraro/status/2097791836269977996","type":"discussion","group":"reactions","domain":"x.com"},{"n":40,"title":"Hacker News: OpenAI might have stolen another major proof","url":"https://news.ycombinator.com/item?id=49638353","type":"discussion","group":"reactions","domain":"news.ycombinator.com"},{"n":41,"title":"HN discussion: Navier–Stokes Lost in Translation (334 pts)","url":"https://news.ycombinator.com/item?id=49994145","type":"discussion","group":"reactions","domain":"news.ycombinator.com"},{"n":42,"title":"Dwarkesh Patel: OpenAI researcher on agent swarms & recursive self-improvement (Noam Brown; cited at 5:35)","url":"https://youtu.be/6AgOfiZOWiY?t=335","type":"video","group":"reactions","domain":"youtu.be"}],"official":4,"filed":"2026-09-29","updated":"2026-10-29","orgs":["OpenAI"],"title":"OpenAI claims a Millennium Prize problem: 10,000 AI agents prove forced Navier–Stokes blow-up; priority dispute erupts","summary":"On 8 Sep 2026 OpenAI released a 166-page paper and a Lean formalisation proving that the 3D incompressible Navier–Stokes equations with a smooth external force can develop a finite-time singularity from smooth initial data. This fits option (C) of Fefferman's official Clay problem statement. About 10,000 agents on an internal model worked for 88 hours. Experts say the unforced problem that matters physically remains open. The result builds on Córdoba and Martínez-Zoroa's techniques, and a bitter priority dispute with Tristan Buckmaster (NYU) and Levent Alpöge (Anthropic) followed.","key_facts":["Autoformalisation critique (arXiv 2610.08144, 6 Oct; HN 334 points): Alexander Bastounis, Fabian Circelli and Anders C. Hansen argue that resolving ambiguity in natural-language mathematics for a 'semantically faithful' translation into Lean sits arbitrarily high in the SCI/arithmetical hierarchy, so Lean checks of AI autoformalisations 'may offer no confidence in the original NL argument'; they give examples including this release and state that 'the formalised Lean proof does not correspond to the NL proof of blow-up of solutions to the Navier-Stokes equations'. New Scientist covered it on 8 Oct ('OpenAI mistranslated mathematics into code for its Navier-Stokes proof'). OpenAI had not responded publicly as of 8 Oct","Scale: ~10,000 agents, 88 hours, ~2.7M messages (some reports ~5M), ~130B tokens; Lean formalisation in 17 more hours; led by Sébastien Bubeck","Claim: a smooth fluid initially at rest, under smooth forcing, develops a singularity in finite time (velocity unbounded, energy bounded)","Clay Institute (11 Sep): problem has 'apparently been settled' but its process is 'deliberately unhurried'; no prize awarded","Luis Silvestre: 'The Clay problem is settled, but the main problem for the Navier-Stokes equations is not.'","Charles Fefferman: 'The heroes of the story… are Córdoba and Martínez-Zoroa'","Buckmaster and Alpöge (with Matei Coiculescu) released forced blow-up results for IPM, 2D Boussinesq and 3D Euler on 7 Sep, obtained with Claude and Codex and Lean-verified on 22 Aug","TechCrunch (8 Sep): Buckmaster says Bubeck pressed him to drop Alpöge's credit ('Why would you ruin your career?'); OpenAI says it 'did not see any of their work through any means until released publicly' but could not rule out that de-identified Codex usage data helped indirectly; the week-long OpenAI effort used ~300B output tokens (~$22.5M at Astra list rates)","Understanding AI (Kai Williams, 10 Sep) and MIT Technology Review (Grace Huckins, 8 Sep): OpenAI offered Buckmaster co-authorship only without Alpöge; he refused","Córdoba and Martínez-Zoroa (guest post on Tao's blog, 4 Oct): OpenAI's announcement made 'two separate claims', forced Navier–Stokes blow-up and unforced Euler blow-up from smooth data; the first, 'if verified under the stated hypotheses', settles an allowed Millennium alternative but 'is distinct from unforced Navier–Stokes blow-up'; they are 'not in a position to say anything substantive' about how it compares with their cascade method","Valerio Capraro's viral X post 'OpenAI might have stolen another major proof' (~9 Sep, HN front page) relayed Andreas Thom's separate claim about the Astra soficity result (see 2026-08-01-openai-astra-ten-advances)","Buckmaster alleged OpenAI may have benefited from his Codex sessions; OpenAI's statements shifted from 'cannot rule out' to denial ('no user inputs past July 3rd')","The Verge (12 Sep): OpenAI spokesperson Laurance Fauconnet said 'it is impossible for Dr. Buckmaster's Codex prompts over the last two months to have influenced the system in any way, including training'; Buckmaster says Bubeck offered him near 'unlimited compute' and sole authorship of OpenAI's paper if Alpöge (an Anthropic employee) was left out, which he called a 'bribe'; Bubeck told the NYT he offered resources and asked 'how can we have an internal OpenAI project with an Anthropic employee?'","The Verge (12 Sep): Fauconnet also said 'since the completion of Navier-Stokes we have made substantial progress on another Millennium Prize problem'; social media speculated about the Hodge conjecture (unconfirmed), and rumours said Anthropic was close to one too","IEEE Spectrum (Oct 5, 'OpenAI's Navier–Stokes claim sparks a reckoning among mathematicians'), reporting from the Heidelberg Laureate Forum (from Sept 13): Peter Scholze: 'They're really just solving these difficult mathematical problems as benchmarks, as some kind of PR stunt'; Geordie Williamson: 'I think that OpenAI behaved extremely poorly, and that we should acknowledge that in the community'; Michael Harris: reports 'depict OpenAI as bullying and disrupting disciplinary norms'; Jacob Tsimerman: capabilities rose 'even faster than many people, including myself, expected'. The claim was still described as pending verification","King's College London press release (27 Oct) on the Bastounis–Circelli–Hansen preprint: 'the written proof and its computer-verified version make different mathematical claims' (in one example the written proof claims more than the Lean version); the authors say this does not show the result is wrong, only that the written proof still needs independent checking. Bastounis: 'verifying the correctness of the output of an AI remains exceptionally difficult'","New Scientist (8 Oct) covered the Bastounis–Circelli–Hansen critique under the headline 'OpenAI mistranslated mathematics into code for its Navier-Stokes proof' (paywalled, not read). See also 2026-07-28-lean-kernel-soundness-bug-collatz for summer 2026 Lean kernel bugs that let false proofs pass","Scientific American (Joseph Howlett, Oct 13): several groups of experts working through the paper told the magazine that the proof does not follow the 'Spanish program' of Diego Córdoba and Luis Martínez-Zoroa, which OpenAI officials had 'clearly and repeatedly stated' it did on Sept 8. Gonzalo Cao-Labora (EPFL): 'When you go to the details, it is a different approach.' Both use the same loophole in the Clay problem statement (an unphysical external force), but OpenAI's proof builds the force 'in a totally distinct way', so its similarities to Buckmaster and Alpöge's progress are 'superficial'. Some experts say a smaller team of agents did follow the program for an intermediate result. Camillo De Lellis (IAS) on the dispute: 'I honestly don't see a factual resolution of this.' The article gives the swarm as about 10,000 copies, 88 hours and 130 billion tokens","The Decoder (Manuel Uth, Oct 17): relays Scientific American and adds OpenAI researcher Noam Brown on Dwarkesh Patel's channel: nobody knows what the ~10,000-agent swarm actually contributed; Brown estimates less than 10% of the success came from the multi-agent setup, crediting mainly the base model's ability to work long and in parallel","Scott Armstrong (CNRS/NYU Courant) on X, 26 Oct, as relayed by 36Kr (28 Oct; the post itself not yet read): several groups of PDE experts have basically grasped the proof's ideas; 'It may go beyond the scope that humans could originally conceive, but it does not exceed human comprehension.' (translated relay, unverified wording)","Second wave (BBC, Pallab Ghosh, 28 Oct): 'A bust-up between mathematicians is fuelling fears that AI could undermine science' retells Buckmaster's Codex question and OpenAI's statements that nobody 'saw the other teams' work before it was published' and that his prompts 'could not have influenced the system in any way'. On 28 Oct a second mathematician, Jihao Liu, wrote that a draft he had 'submitted to codex chat prior to July 2026' may have fed OpenAI's abundance proof (2026-10-06-openai-log-abundance-nonvanishing-claim)"],"key_numbers":[],"tags":["math","navier-stokes","millennium-prize","pde","lean","controversy"],"science":{"field":"mathematics","subfield":"partial differential equations / fluid dynamics","problem":"Navier–Stokes existence and smoothness (Clay Millennium Prize problem), forced-breakdown case","result":"Claimed proof, formalised in Lean, of finite-time blow-up for 3D incompressible Navier–Stokes with smooth external forcing.","open_since":"2000","ai_system":["OpenAI internal model (≈10,000 parallel agents)"],"human_role":"Largely autonomous agent swarm; builds on human techniques of Córdoba and Martínez-Zoroa","verification":{"key":"lean","label":"Lean-verified","text":"Formal proof in Lean (public) of the forced blow-up theorem; experts dispute whether this forced variant is the Clay problem that matters; Clay review pending; human peer review ongoing"},"status":"disputed","shock":"An AI swarm produced, in under four days, a formally verified proof meeting the letter of a Millennium Prize problem, though experts dispute whether it is the problem that matters."},"body_md":"## What happened\n\nOpenAI ran a massive swarm of agents on the forced Navier–Stokes blow-up problem, starting 1 Sep on a model in training since 28 Aug. It announced a complete proof with Lean code on 8 Sep. A day earlier, Buckmaster and Alpöge had released related forced-blow-up results for Euler-type equations using Claude and Codex, and Buckmaster accused OpenAI of rushing after learning of their work. Critics note that the official problem statement allows forcing (option C), but that experts regard the unforced question as the real open problem. Wikipedia now hosts a separate article on the priority controversy.\n\n## Why it matters\n\nIt is the first credible AI claim on a Clay Millennium Prize problem, even if only a technically permitted variant. It also crystallised disputes over credit, data provenance from AI products, and how AI labs announce results, which culminated in the Fields Medallists' open letter three days later.","disputed":[],"related":[{"id":"2026-10-06-openai-log-abundance-nonvanishing-claim","url":"https://postcutoff.com/e/2026-10-06-openai-log-abundance-nonvanishing-claim/","date":"2026-10-06","date_precision":"day","short_title":"OpenAI claims the abundance conjecture; Jihao Liu raises priority","deck":null,"takeaway":"A manuscript in OpenAI's 6 Oct 2026 math release, 'Log abundance in characteristic zero' (dated 24 Sept), claims the log abundance conjecture in every dimension in characteristic zero, and with it canonical nonvanishing for smooth projective varieties. Both are central open problems of the minimal model program, proved only up to dimension three. Companion papers claim Iitaka's subadditivity conjecture and related results. On 7 Oct Jihao Liu (Peking University) submitted a human-led proof that nonvanishing implies abundance. arXiv announced it only on 28 Oct. His comment line says he was 'forced to submit here due to an announcement of the proof of the abundance conjecture by OpenAI'. In a remark he suggests that an earlier draft, sent to 'codex chat' before July 2026, may have fed OpenAI's work. No birational geometer has assessed the claims publicly, there is no Lean proof, and OpenAI has not responded.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":8,"official":5,"filed":"2026-10-29","updated":"2026-10-29","orgs":["OpenAI","Peking University"]},{"id":"2026-09-24-iciam-statement-mathematics-ai","url":"https://postcutoff.com/e/2026-09-24-iciam-statement-mathematics-ai/","date":"2026-09-24","date_precision":"day","short_title":"ICIAM issues a Statement on Mathematics and Artificial Intelligence","deck":"LMS had commented on the Navier–Stokes episode","takeaway":"It shows that the September 2026 controversies reached formal institutional positions across the international mathematical societies.","category":"policy-safety","category_label":"Policy & safety","importance":2,"confidence":"high","status":{"key":"confirmed","labels":["Confirmed"]},"sources":4,"official":3,"filed":"2026-09-29","updated":"2026-09-29","orgs":["ICIAM","London Mathematical Society"]},{"id":"2026-09-21-openai-100-open-problems-claim","url":"https://postcutoff.com/e/2026-09-21-openai-100-open-problems-claim/","date":"2026-09-21","date_precision":"day","short_title":"OpenAI says an internal model resolved 100+ long-standing open problems in 24 days of training (list released 6 Oct: 722 manuscripts)","deck":null,"takeaway":"If substantiated, it would mean open problems are being resolved at industrial scale.","category":"science","category_label":"Science & math","importance":3,"confidence":"low","status":{"key":"pending","labels":["Awaiting review"]},"sources":11,"official":5,"filed":"2026-09-29","updated":"2026-10-10","orgs":["OpenAI"]},{"id":"2026-09-16-royal-society-fellows-ai-risk-letter","url":"https://postcutoff.com/e/2026-09-16-royal-society-fellows-ai-risk-letter/","date":"2026-09-16","date_precision":"day","short_title":"42 mathematician Fellows of the Royal Society","deck":"Including Gowers, Hairer, Maynard and Scholze, call AI an 'emergency' in open letter to Paul Nurse","takeaway":"It is one of the first collective x-risk statements from a scientific field that says it was persuaded by AI's performance in that field.","category":"policy-safety","category_label":"Policy & safety","importance":4,"confidence":"high","status":{"key":"confirmed","labels":["Confirmed"]},"sources":3,"official":3,"filed":"2026-09-29","updated":"2026-09-29","orgs":["Royal Society"]},{"id":"2026-09-11-fields-medalists-letter-ai-mathematics","url":"https://postcutoff.com/e/2026-09-11-fields-medalists-letter-ai-mathematics/","date":"2026-09-11","date_precision":"day","short_title":"Fields Medallists' open letter 'A Severe Misalignment of AI in Mathematics' criticises labs' race for famous problems","deck":null,"takeaway":"It marked open tension between AI labs and the mathematical community at the moment AI began producing major results, and shaped norms for credit and verification.","category":"science","category_label":"Science & math","importance":3,"confidence":"high","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":8,"official":3,"filed":"2026-09-29","updated":"2026-10-07","orgs":["mathandai.org"]},{"id":"2026-09-07-anandkumar-euler-singularity-r3","url":"https://postcutoff.com/e/2026-09-07-anandkumar-euler-singularity-r3/","date":"2026-09-07","date_precision":"day","short_title":"Caltech team (Anandkumar) reports a stable self-similar singularity candidate for the unforced 3D Euler equations on R³, found with PINNs and LLM help","deck":null,"takeaway":"Unforced Euler blow-up on R³ is a famous open problem in its own right, and it is a stepping stone toward the unforced Navier–Stokes question.","category":"science","category_label":"Science & math","importance":3,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":4,"official":3,"filed":"2026-09-29","updated":"2026-09-29","orgs":["Caltech"]},{"id":"2026-09-06-pachocki-an-alien-mind","url":"https://postcutoff.com/e/2026-09-06-pachocki-an-alien-mind/","date":"2026-09-06","date_precision":"day","short_title":"OpenAI chief scientist Jakub Pachocki publishes \"An Alien Mind\"","deck":"No lab has solved alignment well enough to keep scaling at maximum speed for much longer","takeaway":"On Sept 6, 2026, three days after the GPT-6 Astra launch, OpenAI chief scientist Jakub Pachocki published the essay \"An Alien Mind\" on openai.com.","category":"policy-safety","category_label":"Policy & safety","importance":5,"confidence":"high","status":{"key":"confirmed","labels":["Confirmed"]},"sources":6,"official":3,"filed":"2026-09-29","updated":"2026-10-04","orgs":["OpenAI"]},{"id":"2026-08-01-openai-astra-ten-advances","url":"https://postcutoff.com/e/2026-08-01-openai-astra-ten-advances/","date":"2026-08-01","date_precision":"day","short_title":"OpenAI's unreleased 'Astra' model claims ten advances in maths and theoretical CS, with Lean proofs","deck":null,"takeaway":"It moved the frontier from individual AI-assisted results to a lab producing batches of significant theorems.","category":"science","category_label":"Science & math","importance":5,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":14,"official":5,"filed":"2026-09-29","updated":"2026-10-19","orgs":["OpenAI"]},{"id":"2026-07-28-lean-kernel-soundness-bug-collatz","url":"https://postcutoff.com/e/2026-07-28-lean-kernel-soundness-bug-collatz/","date":"2026-07-28","date_precision":"day","short_title":"Lean kernel soundness bug #14576","deck":"An AI-assisted 'disproof' of the Collatz conjecture passes Lean's kernel and nanoda; the 'Summer of Soundness Bugs'","takeaway":"\"Verified in Lean\" has become the main evidence behind AI labs' math claims: OpenAI's Navier–Stokes blow-up, 300 of 719 results in its October release, and Anthropic's formal-math repository.","category":"research","category_label":"Research","importance":4,"confidence":"high","status":{"key":"confirmed","labels":["Confirmed"]},"sources":9,"official":5,"filed":"2026-10-09","updated":"2026-10-19","orgs":["Lean 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science agent)"},{"date":"2026-10-28","type":"edit","text":"KCL press release (27 Oct) on the Bastounis–Circelli–Hansen critique (news agent)"},{"date":"2026-10-19","type":"edit","text":"Fixed ai_system (an unquoted comma in '10,000' split it into two items)"},{"date":"2026-10-19","type":"edit","text":"Added video(s) rest-is-science-mathematicians-canary-ai-coal-mine, kanal-zero-dragan-openai-navier-stokes-skandal, samuel-alexander-allegations-openai-stole-navier-stokes"},{"date":"2026-10-18","type":"edit","text":"Added videos primetime-the-navier-stokes-situation-is-insane, quanta-why-navier-stokes-pushes-math-and-physics-to-the-edge, alex-hyman-navier-stonks-lost-in-translation-informal-vs-lean"},{"date":"2026-10-18","type":"edit","text":"Video added (dwarkesh-noam-brown-agent-swarms-recursive-self-improvement)"},{"date":"2026-10-18","type":"edit","text":"Added The Decoder second wave (Oct 17) and Noam Brown's <10% swarm-contribution estimate (Dwarkesh Patel video)"},{"date":"2026-10-13","type":"edit","text":"Added Scientific American's report that experts find the proof does not follow the Córdoba–Martínez-Zoroa program (Google News)"},{"date":"2026-10-09","type":"edit","text":"Added New Scientist's headline on the autoformalisation critique and a pointer to the Lean kernel soundness-bug entry"},{"date":"2026-10-08","type":"edit","text":"Added the Bastounis–Circelli–Hansen autoformalisation critique (arXiv 2610.08144) claiming the Lean proof does not match the natural-language proof"},{"date":"2026-10-07","type":"edit","text":"Science block: verification says what the Lean proof checks and what is disputed (the forced variant, not the proof)"},{"date":"2026-10-07","type":"edit","text":"Added IEEE Spectrum's Heidelberg Laureate Forum reactions (Scholze, Williamson, Harris, Tsimerman)"},{"date":"2026-10-07","type":"edit","text":"Linked the videos [“OpenAI's biggest math breakthrough is getting ugly...”](https://postcutoff.com/v/fireship-openai-math-breakthrough-getting-ugly/), [“The Controversy Behind AI Solving A Million Dollar Math Problem”](https://postcutoff.com/v/up-and-atom-controversy-ai-million-dollar-math-problem/), [“The world's best mathematicians already overtaken by AI”](https://postcutoff.com/v/sky-news-mathematicians-overtaken-by-ai/), [“Has a Millennium Prize Problem been solved by AI?”](https://postcutoff.com/v/standup-maths-millennium-prize-problem-solved-by-ai/)"},{"date":"2026-10-05","type":"edit","text":"Added The Verge's Sept 8/9/12 articles (found via its Oct 5 storystream; the 10 Sep original is linked from [OpenAI's unreleased 'Astra' model claims ten advances in maths and theoretical CS, with Lean proofs](https://postcutoff.com/e/2026-08-01-openai-astra-ten-advances/)), OpenAI's 'substantial progress on another Millennium Prize problem' statement, and Quanta's Oct 5 essay"},{"date":"2026-10-04","type":"edit","text":"Added Córdoba & Martínez-Zoroa's 4 Oct guest post on Tao's blog (their survey of the cascade method and their non-committal statement on OpenAI's two claims)"},{"date":"2026-10-01","type":"edit","text":"Added TechCrunch (300B tokens/~$22.5M, Bubeck quote), MIT TR, Understanding AI and Capraro/HN links; The Verge (10 Sep) and Economist (11 Sep) originals not found"},{"date":"2026-09-29","type":"edit","text":"Added Bubeck's X reply and OfficeChai coverage of his fuller response"},{"date":"2026-09-29","type":"edit","text":"Added authorship/misconduct dispute and SciAm/Fortune sources (verification pass)"},{"date":"2026-09-29","type":"edit","text":"Added post link(s)"},{"date":"2026-09-29","type":"edit","text":"Added post link(s) (3) from Google/DeepMind + math posts pass"},{"date":"2026-09-29","type":"edit","text":"Added Gamburd essay (arXiv 2609.28591: 616k lines of Lean per its abstract), LMS statement, the concurrent Anandkumar Euler result, and related Royal Society/ICIAM entries"},{"date":"2026-09-29","type":"filed","text":"Created"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-09-29","run":null,"sources_read":null,"updated":"2026-10-29","human_review":null,"version":{"date":"2026-10-29"}},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":131,"in_training_data":false},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":70,"in_training_data":false},{"model_id":"gemini-4-hydrogen","name":"Gemini 4 Hydrogen","cutoff":"2026-03","days_after":161,"in_training_data":false},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":100,"in_training_data":false}],"short_url":"https://postcutoff.com/s/openai-millennium-prize-problem"}