{"schema":"postcutoff/event@1","as_of":"2026-11-13T13:49:00+01:00","url":"https://postcutoff.com/e/2026-09-21-openai-100-open-problems-claim/","md":"https://postcutoff.com/e/2026-09-21-openai-100-open-problems-claim/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":"2026-09-21-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":"On 21 Sep 2026 OpenAI said an unnamed internal model had resolved more than 100 long-standing open problems during about 24 days of training (28 Aug – 21 Sep).","category":"science","category_label":"Science & math","importance":3,"confidence":"low","status":{"key":"pending","labels":["Awaiting review"]},"sources":[{"n":1,"title":"GitHub: openai/math (the released list, 6 Oct 2026)","url":"https://github.com/openai/math","type":"code","group":"primary","domain":"github.com"},{"n":2,"title":"OpenAI: Sharing AI progress in mathematics (6 Oct 2026)","url":"https://openai.com/index/sharing-ai-progress-in-mathematics/","type":"official","group":"primary","domain":"openai.com"},{"n":3,"title":"FrontierMath Erdős benchmark (arXiv 2609.25050)","url":"https://arxiv.org/abs/2609.25050","type":"paper","group":"primary","domain":"arxiv.org"},{"n":4,"title":"OEIS Open benchmark (arXiv 2608.11941)","url":"https://arxiv.org/abs/2608.11941","type":"paper","group":"primary","domain":"arxiv.org"},{"n":5,"title":"OpenAI: Advisory Group on Mathematics and Artificial Intelligence","url":"https://openai.com/index/advisory-group-on-mathematics-and-ai/","type":"official","group":"primary","domain":"openai.com"},{"n":6,"title":"TechCrunch: OpenAI forms math advisory group as its AI resolves more than 100 open problems","url":"https://techcrunch.com/2026/09/21/openai-forms-math-advisory-group-as-its-ai-resolves-more-than-100-open-problems/","type":"press","group":"press","domain":"techcrunch.com"},{"n":7,"title":"The Decoder: OpenAI says internal model solved over 100 long-standing math problems","url":"https://the-decoder.com/openai-says-its-internal-model-solved-over-100-long-standing-math-problems-after-just-a-month-of-training/","type":"press","group":"press","domain":"the-decoder.com"},{"n":8,"title":"The Verge (23 Sep): OpenAI wants to consult elite mathematicians about how to not fumble again","url":"https://www.theverge.com/ai-artificial-intelligence/999167/openai-elite-mathematicians-panel","type":"press","group":"press","domain":"theverge.com"},{"n":9,"title":"The Verge (28 Sep): OpenAI keeps bulldozing mathematicians (Hairer interview)","url":"https://www.theverge.com/ai-artificial-intelligence/1001477/openai-math-advisory-group","type":"press","group":"press","domain":"theverge.com"},{"n":10,"title":"Terence Tao blog: Announcing the Advisory Group on Mathematics and Artificial Intelligence","url":"https://terrytao.wordpress.com/2026/09/21/advisory-group-on-mathematics-and-artificial-intelligence/","type":"discussion","group":"reactions","domain":"terrytao.wordpress.com"},{"n":11,"title":"Thomas Bloom on X: FrontierMath Erdős thread","url":"https://x.com/thomasfbloom/status/2095630765035864260","type":"discussion","group":"reactions","domain":"x.com"}],"official":5,"filed":"2026-09-29","updated":"2026-10-10","orgs":["OpenAI"],"title":"OpenAI says an internal model resolved 100+ long-standing open problems in 24 days of training (list released 6 Oct: 722 manuscripts)","summary":"On 21 Sep 2026 OpenAI said an unnamed internal model had resolved more than 100 long-standing open problems during about 24 days of training (28 Aug – 21 Sep). It released no list and no proofs, and did not define 'resolved'. It also formed a 9-member Advisory Group on Mathematics and AI at IAS Princeton, including Timothy Gowers, Edward Witten and Martin Hairer. On 6 Oct 2026 OpenAI released the list: 722 manuscripts in 372 result families on GitHub, partly Lean-formalized (see 2026-10-06-openai-math-release-722-manuscripts).","key_facts":["Claim: 100+ open problems resolved in ~24 days of training; no evidence released as of 29 Sep 2026","Released 6 Oct 2026: github.com/openai/math, 722 manuscripts in 372 families from ~4,000 posed problems (~3 h ChatGPT Pro compute per result), with Lean formalizations for 162 manuscripts (review 'unchecked'); claims include the quasi-Riemann hypothesis, Unique Games, Hodge for CM abelian varieties and free group factor isomorphism","Advisory Group on Mathematics and AI (9 members) at the Institute for Advanced Study; per its own announcement (Tao blog) it formed after OpenAI approached members, but it is independent of any AI company and unpaid","Sober counterpoint: Epoch's 'FrontierMath Erdős' benchmark (68 open Erdős problems, Lean, $300/problem): GPT-6 Astra 3%, all others 0% (arXiv 2609.25050)","OEIS Open benchmark: models resolved 147 of 492 formalised open OEIS conjectures (30%) at $50/attempt (arXiv 2608.11941)","Side effect: on 22 Sep Francesco Deangelis posted an unchecked ChatGPT Astra proof of the Mumford–Shah conjecture to document priority, explicitly because of this announcement (arXiv 2609.26732)","The Verge (28 Sep): AGMAI member Martin Hairer said 'We don't work for OpenAI, are not paid by them, and it's totally independent', and that the group had begun talks with other frontier labs. Asked about plans: 'we, well, you know, started two days ago'. Hairer also described OpenAI altering manuscripts 'sneakily' after criticism","Critics quoted by The Verge: Álvaro Lozano-Robledo (UConn) on OpenAI's 'almost solved another Millennium problem' line, 'That sentence makes no sense in mathematics'; Colva Roney-Dougal (St Andrews) said it is 'somewhat agonizing' to know a large number of results may soon be announced"],"key_numbers":[],"tags":["math","claims","unverified","openai"],"science":{"field":"mathematics","subfield":"multiple","problem":"Unspecified 'long-standing open problems'","result":"Claimed resolution of 100+ open problems; unverified.","open_since":"","ai_system":["OpenAI internal model (unnamed)"],"human_role":"Unknown","verification":{"key":"preprint","label":"Preprint only","text":"List and manuscripts released 6 Oct 2026; partly Lean-formalized, mostly not yet independently verified"},"status":"pending","shock":""},"body_md":"## What happened\n\nOpenAI made a sweeping claim about a model still in training while announcing an advisory body of leading mathematicians.\n\n### Update, 6 Oct 2026: the list is out\nOpenAI published the promised results as a GitHub repository with 722 manuscripts in 372 families, far more than \"100+\".\nMany come with Lean proofs, and it released reasoning summaries and compute estimates, as AGMAI had recommended. See\n2026-10-06-openai-math-release-722-manuscripts and the separate entries for the most famous claims.\n\n## Why it matters\n\nIf substantiated, it would mean open problems are being resolved at industrial scale. Until a list and proofs appear it is an unverified claim, and it contrasts with independent benchmarks where most open Erdős problems still resist all models.","disputed":[{"label":"Verification","text":"List and manuscripts released 6 Oct 2026; partly Lean-formalized, mostly not yet independently verified","sources":[]}],"related":[{"id":"2026-10-08-alphaproof-nexus-science-paper","url":"https://postcutoff.com/e/2026-10-08-alphaproof-nexus-science-paper/","date":"2026-10-08","date_precision":"day","short_title":"Google DeepMind's AlphaProof Nexus paper published in Science","deck":"LLM + Lean agent resolved 9 of 353 open Erdős problems and 44 of 492 OEIS conjectures","takeaway":"This is a peer-reviewed, fully formal account of LLM agents solving open research problems at scale and at low cost.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":16,"official":4,"filed":"2026-10-10","updated":"2026-10-10","orgs":["Google DeepMind"]},{"id":"2026-10-06-openai-math-release-722-manuscripts","url":"https://postcutoff.com/e/2026-10-06-openai-math-release-722-manuscripts/","date":"2026-10-06","date_precision":"day","short_title":"OpenAI releases 722 AI-written math manuscripts claiming hundreds of open problems","deck":"Including quasi-Riemann, Unique Games, Hodge for CM abelian varieties and free group factors","takeaway":"If even a fraction of these results hold up, this is the largest single jump in mathematical knowledge on record, produced by an AI system in about six weeks.","category":"science","category_label":"Science & math","importance":5,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":79,"official":13,"filed":"2026-10-07","updated":"2026-10-29","orgs":["OpenAI"]},{"id":"2026-09-30-ai-assisted-conjecture-wave-summer-2026","url":"https://postcutoff.com/e/2026-09-30-ai-assisted-conjecture-wave-summer-2026/","date":"2026-09-30","date_precision":"day","short_title":"Summer 2026 flood: dozens of named conjectures settled on arXiv with disclosed AI help","deck":null,"takeaway":"This entry catalogues about 50 of them, with the AI role as the authors state it.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":11,"official":5,"filed":"2026-09-30","updated":"2026-10-19","orgs":["OpenAI","Anthropic","Google DeepMind","various mathematicians"]},{"id":"2026-09-22-mumford-shah-conjecture-astra-claim","url":"https://postcutoff.com/e/2026-09-22-mumford-shah-conjecture-astra-claim/","date":"2026-09-22","date_precision":"day","short_title":"Mathematician posts an unchecked ChatGPT Astra proof of the planar Mumford–Shah conjecture (1989), citing OpenAI's '100 open problems' claim","deck":null,"takeaway":"If correct, it would settle one of the best-known open problems in the calculus of variations.","category":"science","category_label":"Science & math","importance":4,"confidence":"low","status":{"key":"pending","labels":["Awaiting review"]},"sources":1,"official":1,"filed":"2026-09-30","updated":"2026-10-19","orgs":["Francesco Deangelis","University of Münster","OpenAI"]},{"id":"2026-09-08-openai-navier-stokes-blowup","url":"https://postcutoff.com/e/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":"It is the first credible AI claim on a Clay Millennium Prize problem, even if only a technically permitted variant.","category":"science","category_label":"Science & math","importance":5,"confidence":"medium","status":{"key":"disputed","labels":["Disputed"]},"sources":42,"official":4,"filed":"2026-09-29","updated":"2026-10-29","orgs":["OpenAI"]},{"id":"2026-09-03-frontiermath-erdos-astra-disproves-erdos-problem-1","url":"https://postcutoff.com/e/2026-09-03-frontiermath-erdos-astra-disproves-erdos-problem-1/","date":"2026-09-03","date_precision":"day","short_title":"Pre-release GPT-6 Astra disproves Erdős's 'first serious problem' (1931, $500) and proves the rational-exponents conjecture, all Lean-verified, in Epoch's FrontierMath Erdős runs","deck":null,"takeaway":"Problem #1 is probably the longest-standing open Erdős problem.","category":"science","category_label":"Science & math","importance":5,"confidence":"high","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":10,"official":7,"filed":"2026-09-30","updated":"2026-10-16","orgs":["OpenAI","Epoch AI"]},{"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"]}],"people":[{"id":"terence-tao","name":"Terence Tao","url":"https://postcutoff.com/person/terence-tao/"},{"id":"timothy-gowers","name":"Timothy Gowers","url":"https://postcutoff.com/person/timothy-gowers/"},{"id":"thomas-bloom","name":"Thomas Bloom","url":"https://postcutoff.com/person/thomas-bloom/"}],"posts":[{"id":"2026-09-08-openai-navier-stokes-tweet","title":"OpenAI: 'We're sharing a solution to the Navier-Stokes Millennium Prize Problem'","url":"https://postcutoff.com/p/2026-09-08-openai-navier-stokes-tweet/"},{"id":"2026-09-21-openai-math-advisory-group","title":"Advisory Group on Mathematics and Artificial Intelligence","url":"https://postcutoff.com/p/2026-09-21-openai-math-advisory-group/"},{"id":"2026-09-21-tao-announcing-agmai","title":"Announcing the Advisory Group on Mathematics and Artificial Intelligence","url":"https://postcutoff.com/p/2026-09-21-tao-announcing-agmai/"},{"id":"2026-09-17-gowers-why-i-didnt-sign-fields-letter","title":"Why I didn't sign the Fields medallists' letter","url":"https://postcutoff.com/p/2026-09-17-gowers-why-i-didnt-sign-fields-letter/"},{"id":"2026-09-08-brown-lee-sedol-moment","title":"Noam Brown: OpenAI mathematicians had their 'Lee Sedol moment'","url":"https://postcutoff.com/p/2026-09-08-brown-lee-sedol-moment/"},{"id":"2026-09-03-thomasfbloom-frontiermath-erdos","title":"Thomas Bloom: A big day for AI and mathematics — FrontierMath Erdős","url":"https://postcutoff.com/p/2026-09-03-thomasfbloom-frontiermath-erdos/"}],"videos":[],"models":[],"changes":[{"date":"2026-10-10","type":"edit","text":"Linked [Google DeepMind's AlphaProof Nexus paper published in Science](https://postcutoff.com/e/2026-10-08-alphaproof-nexus-science-paper/) (AlphaProof Nexus, published in Science 8 Oct 2026)"},{"date":"2026-10-07","type":"edit","text":"List released on 6 Oct (openai/math); retitled, linked the release entry, updated verification status"},{"date":"2026-10-05","type":"edit","text":"Added The Verge's Sept 23 and Sept 28 AGMAI pieces (Hairer interview, critics' quotes)"},{"date":"2026-09-30","type":"edit","text":"Linked the Mumford–Shah priority posting and the FrontierMath Erdős resolutions"},{"date":"2026-09-29","type":"edit","text":"Added post link(s)"},{"date":"2026-09-29","type":"edit","text":"Added post link(s) (2) from Google/DeepMind + math posts pass"},{"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":"2026-10-10","human_review":null,"version":{"date":"2026-10-10"}},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":144,"in_training_data":false},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":83,"in_training_data":false},{"model_id":"gemini-4-hydrogen","name":"Gemini 4 Hydrogen","cutoff":"2026-03","days_after":174,"in_training_data":false},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":113,"in_training_data":false}],"short_url":null}