Will an AI lab announce another Millennium Prize solution by December 31, 2026?

- [2026-09-08] OpenAI announced that an internal model had resolved the Navier-Stokes Millennium problem. The paper's author line is "OPENAI", and OpenAI said it won't claim the prize. This is the "first" claim. Navier-Stokes is excluded from this market's qualifying list, so it does not count toward resolution. https://scenarica.substack.com/p/the-referee-will-see-you-eventually (also https://www.quantamagazine.org/ai-has-solved-one-of-maths-1-million-millennium-prize-problems-20260908/) - [2026-09-11] The Clay Institute referred to the Navier-Stokes problem as "apparently been settled" (quoted in Scenarica). It has not given formal recognition. https://scenarica.substack.com/p/the-referee-will-see-you-eventually - [2026-09-11] 28 Fields Medalists published an open letter warning against AI firms treating unsolved problems as benchmarks. https://en.wikipedia.org/wiki/2026_in_artificial_intelligence - [2026-08-10] Anthropic (primary page) said an unreleased Claude model raised the proved lower bound for the share of zeta zeros on the critical line from 41.6% to 67.2%. Anthropic stated Claude did not prove the Riemann Hypothesis and that the technique is not expected to lead to a proof. This is partial progress and would not qualify. https://www.anthropic.com/research/riemann-zeta - [2026-10-06] OpenAI posted 722 manuscripts from an unreleased internal model, covering about 4,000 posed problems in 372 families of results. These include a Riemann-adjacent result: a zero-free half-plane Re(s)>7/8 for Dirichlet L-functions, the "quasi-Riemann hypothesis". Social-media and crypto-news summaries also mention Hodge-related material (a Milnes/Weil-class paper). These are partial results, not claimed solutions of the Millennium problems. https://x.com/i/trending/2107582154993451288 ; https://www.kucoin.com/news/flash/openai-solves-722-math-problems-quasi-riemann-hypothesis-proven - [2026-10-07] OpenAI withdrew 3 of the manuscripts after finding a sign error in a paper on Weil classes, leaving 719. About 300 of them have Lean formalisations. https://scenarica.substack.com/p/the-referee-will-see-you-eventually - [2026-10-06] Thomas Bloom's Erdős-problems site stopped counting solved problems and paused new proof claims, citing the pace of AI results. https://scenarica.substack.com/p/the-referee-will-see-you-eventually - [2026-10-09] A Polymarket contract on which Millennium problem an AI lab will announce next, with an end-2027 horizon, had "no solution" at 29.5%. This is a sibling market, not this contract. Source: Scenarica, which itself estimates a second claim by 2027-06-30 at about 46%. https://scenarica.substack.com/p/the-referee-will-see-you-eventually - [2026-10-12] A Manifold market on "AI solves a Millennium problem by EOY 2027" was reported at 83%. It is play money, and it probably counts the Navier-Stokes claim, so it is not comparable to this market. https://tech-insider.org/ai-millennium-problem-manifold-odds-eoy-2027/ - [2026-10-13] WBUR (13 Oct) said the OpenAI Navier-Stokes solution is "still being evaluated". Mathematicians dispute whether the forced version OpenAI solved is the problem everyone had in mind. https://wbur.org/onpoint/2026/10/13/ai-steamrolling-math-solve - [2026-10-15] As of today I found no announcement by any eligible lab claiming a solution to the Riemann Hypothesis, P vs NP, Yang-Mills, Hodge or BSD. Searches turned up only partial results and a fringe human arXiv RH claim (not an eligible lab). OpenAI's pace is high and its unreleased model is described as stronger than GPT-6 Astra. https://www.hpcwire.com/aiwire/2026/09/16/unsolved-for-90-years-openai-says-ai-cracked-millennium-prize-problem-in-88-hours/ - [2026-09-08] OpenAI said its Navier-Stokes work began on Sept 1 after it heard a rumour that another Millennium problem had been resolved. That rumour is unidentified. https://www.cnn.com/2026/09/09/business/openai-millennium-problems-navier-stokes-hnk BOTTOM LINE: Only Navier-Stokes (excluded) has been claimed so far. Labs, chiefly OpenAI and Anthropic, are releasing large volumes of partial results on RH, Hodge and related problems, but they have so far framed these explicitly as progress rather than solutions. A qualifying claim would need a new full-solution announcement within about 11 weeks. NOT FOUND: any scheduled event before 2027-01-01 where a lab is due to announce a Millennium result; any lab or credible report of a rumoured imminent RH, P vs NP, Yang-Mills, Hodge or BSD claim; a Clay Institute formal ruling on Navier-Stokes. A full read of the OpenAI math GitHub repository was also not obtained.

- [2026-09-08] OpenAI announced an internal-model "solution" to Navier–Stokes (finite-time blow-up with smooth forcing, Lean-formalised). The agents reached the result on Sep 5, about 88 hours after launch. The effort started Sep 1 after a rumour. OpenAI said it was testing the model on all open Millennium problems, and it shifted agents away from the others once the Euler result appeared. It does not intend to claim the prize. This is the only AI-lab Millennium claim to date. Navier–Stokes is excluded from this market. https://openai.com/index/navier-stokes-solution/ - [2026-09-11] Clay said the problem had "apparently been settled", but had not declared it solved or awarded the prize as of Oct 12. Reported by a secondary source. https://tech-insider.org/ai-millennium-problem-manifold-odds-eoy-2027 - [2026-09-18] Reports say OpenAI told the NYT it had made "substantial progress on another Millennium Prize problem" and is pacing disclosure. A later update names Hodge. Explainx rates the Hodge naming as "more confirmed", but it is still unverified. OpenAI's own statement does not name the problem. The same source says no lab had announced a Hodge result as of Sep 11. https://www.explainx.ai/blog/millennium-prize-problems-ai-solved-fact-check-2026 - [2026-10-06/07] OpenAI published "Sharing AI progress in mathematics", with hundreds of results, including partial results on Hodge variants and Riemann-type cases. Polymarket's description calls these partial and not a claimed solution. Partial results do not qualify under the rules. https://openai.com/index/sharing-ai-progress-in-mathematics/ (listed on the fetched OpenAI page; content not read) - [Human-era base rate] Only one Millennium problem (Poincaré) has been officially solved in 26 years, and Perelman declined the prize. The human base rate is near zero for a 2.5-month window. https://en.wikipedia.org/wiki/Millennium_Prize_Problems - [Machine-era pace] The Scenarica analysis (Oct 2026) cites silver at the IMO in July 2024, gold in July 2025, and a Millennium-class claim in September 2026. It puts the chance of a second claim by 30 Jun 2027 at "a little under one in two" (46%). It says only one of the five remaining problems has "a visible crowbar" (a counterexample could settle it). Opinion, not a track record. https://scenarica.substack.com/p/the-referee-will-see-you-eventually - [2026-10-12] Manifold "AI solves a Millennium problem by EOY 2027" was at 83%. This is a looser question that likely counts Navier–Stokes. Reported by a secondary source. https://tech-insider.org/ai-millennium-problem-manifold-odds-eoy-2027 - [2026-10-09] Polymarket sibling: "Which Millennium problem will AI solve next?" had "no solution" by end-2027 at 29.5%. A later snapshot (about Oct 10) had it at 34–35%. Next-problem shares: Hodge about 31%, BSD about 20–22%, Yang–Mills 7.4%, Riemann about 2.7%, P vs NP about 2.2%. https://polymarket.com/event/which-millennium-prize-problem-will-ai-solve-next - [2026-10 snapshot] Polymarket sibling strikes of this event: the Dec 31, 2027 strike was priced at about 75%. The Sep 30, 2026 strike was at 15% on Sep 16, and it has since expired with no qualifying announcement found. The implied hazard is that a share of the 2027 probability falls in 2026. The Dec 31, 2026 strike is this contract, so its price is omitted. https://polymarket.com/event/ai-lab-announces-another-millennium-prize-solution-by - [2026-09-11] Polymarket posted the Dec 2026 strike at 71–72% right after the Navier–Stokes news. The price later fell, which shows the early market over-reacted. Also, a commenter noted the market resolves on announcement, not on validity. https://x.com/Polymarket/status/2098511775574499638 - [2026-09-11] 28 Fields Medalists published an open letter criticising AI firms for treating unsolved problems as benchmarks. This is a possible soft brake on hype claims. It is not a block. https://en.wikipedia.org/wiki/2026_in_artificial_intelligence - [2026-09-18] Resolution-relevant behaviour: OpenAI's own announcement said "resolves" and gave a Lean proof, so a similar announcement would clearly qualify. Labs are also rumoured to be racing (Anthropic-linked researchers did the forced Euler work). Anthropic-employee-plus-NYU work is jointly attributed, which would count if framed as a lab result. https://www.cnn.com/2026/09/09/business/openai-millennium-problems-navier-stokes-hnk BOTTOM LINE: The reference class is thin. The human base rate is about zero, but there is exactly one precedent of an AI lab announcing a Millennium solution, in September 2026, with a credible report that a second (reportedly Hodge) was close and being held back. Expert and market estimates for a claim over about 15 months run at roughly 46–70%. The 2.5-month window to end-2026 is much shorter, and the earlier 71% price drifted down. NOT FOUND: Any lab announcement of a solution to Hodge, BSD, Yang–Mills, Riemann or P vs NP as of Oct 15, 2026. The full text of OpenAI's Oct 6 post. The Kalshi contract prices. The Scenarica page, which could not be fetched in full.

YES means: an eligible AI lab (or its official representative) announces, by 11:59 PM ET on Dec 31, 2026, that it has solved RH, P vs NP, Yang-Mills, Hodge or BSD. Navier-Stokes does not count. Partial results do not count. - [2026-10-07] OpenAI's own Oct 6 release shows how close its framing sits to a full claim. Altman highlighted four results from the 722 manuscripts. One is the Hodge conjecture for all CM abelian varieties, which is a restricted case and has no Lean proof yet. OpenAI's catalog says that, combined with Milne's earlier theorems, the result yields the Tate conjecture over finite fields. It is a special case, so it does not qualify, but it shows OpenAI is producing full-strength results on Hodge-adjacent classes. https://officechai.com/ai/openai-releases-ai-generated-proofs-of-quasi-riemann-hypothesis-unique-games-conjecture-hodge-conjecture-for-cm-abelian-varieties/ - [2026-10-07] The same piece says Altman flagged the claims as not yet confirmed by outside mathematicians. It also says the Riemann result (zero-free for Re>7/8) "doesn't earn a Millennium Prize". OpenAI is currently labelling these as partial, which is the main obstacle to YES. https://officechai.com/ai/openai-releases-ai-generated-proofs-of-quasi-riemann-hypothesis-unique-games-conjecture-hodge-conjecture-for-cm-abelian-varieties/ - [2026-09-22] The number behind the pace: OpenAI's new internal model began training on Aug 28 and, within about a month, had solved over 100 long-standing problems. OpenAI's own mathematicians were "surprised" by the speed. The Decoder reports that a second Millennium problem, Hodge, is "reportedly" among the solved ones, which is a report and not an OpenAI statement. https://the-decoder.com/openai-says-its-internal-model-solved-over-100-long-standing-math-problems-after-just-a-month-of-training/ - [2026-09-22] Mechanism for continued acceleration: OpenAI's advisory group at the IAS may advise on how results are shared, but it is explicitly excluded from advising on the pace of OpenAI's internal mathematics progress. Disclosure norms can change, but the research is not slowed. https://the-decoder.com/openai-says-its-internal-model-solved-over-100-long-standing-math-problems-after-just-a-month-of-training/ - [2026-09-17 to 2026-09-18] The Information (anonymous source) reported that OpenAI staff expect a Hodge solve "relatively soon". The same report says OpenAI may take longer to announce it because it wants to avoid another PR dispute with mathematicians. This cuts both ways. The result may exist already, and the delay is about presentation. https://www.aol.ca/articles/openai-reportedly-trying-solve-hodge-001047000.html ; https://superpowerdaily.com/posts/openai-may-delay-a-reported-hodge-conjecture-result-after-math-backlash - [2026-09-17] OpenAI's NYT statement named no problem. The Information is the only source that names Hodge, and its source is anonymous. https://fourweekmba.com/ai-openai-hodge-conjecture-clay-scoreboard/ - [2026-09-24] A tracker (VibeMathed) lists an unreleased OpenAI model proving the BSD formula in Selmer corank at most one. It marks this as a "Partial result" and unreviewed. This is a second partial route, on BSD, in addition to Hodge. It is a third-party tracker, so treat it as a lead. https://vibemathed.com/problem/bsd-formula-selmer-corank-one - [2026-09-14] Rumours that Anthropic and OpenAI are both racing on BSD circulated on social media and crypto-news sites. Kalshi's "BSD next before 2045" contract jumped to 38% on Sep 14. These are unverified rumours, and I found no lab confirmation. https://tech-insider.org/birch-swinnerton-dyer-solved-before-2045-kalshi-odds/ ; https://www.kucoin.com/news/flash/openai-claims-breakthroughs-on-multiple-millennium-math-problems - [2026-10-07] Precedent for a fast announcement: the Navier-Stokes work ran from a Sept 1 start to an announcement on Sept 8. The Euclidean-plane five-colour result is dated Sept 23. So a claim can appear within days of the model finding it. An unreleased model that "chews" through about 4,000 problems in a month could plausibly hit a Millennium problem with little warning. https://www.adamspencer.com.au/post/the-maths-alanche - [2026-10-05] IEEE Spectrum reports that OpenAI, Anthropic and Google are all "steamrollering" mathematics. More than one eligible lab is pushing, and any one of them announcing would resolve YES. The eligible list also includes Harmonic, Axiom, Math Inc and DeepMind. https://spectrum.ieee.org/millennium-prize-ai - [2026-10-06] OpenAI's blog says it will keep releasing results and is working to release the model responsibly. Further drops are likely before year-end. https://openai.com/index/sharing-ai-progress-in-mathematics/ - [2026-10-07] The resolution is literal: it needs an announcement that a problem is "solved", with no outside confirmation required. A lab post saying that it "resolves" Hodge, in the style of the Navier-Stokes post, would count even if it is later disputed. https://officechai.com/ai/openai-releases-ai-generated-proofs-of-quasi-riemann-hypothesis-unique-germs-conjecture-hodge-conjecture-for-cm-abelian-varieties/ Single most likely path to YES: OpenAI posts a full Hodge claim (or less likely BSD), with a paper and probably Lean or expert co-signers, as a follow-on drop before Dec 31. Its prerequisites are: - the internal model actually produced a full argument, which the Sept 17 Information reporting suggests but does not confirm; - OpenAI finishes the IAS-advised release process; - OpenAI chooses to use "solved" wording rather than "progress". BOTTOM LINE: The strongest YES case is OpenAI's one-month pace, an anonymously sourced Hodge claim "expected relatively soon", and a literal resolution rule that needs no external verification. Against that, OpenAI's Oct 6 release deliberately stopped at special cases (CM abelian varieties) and labelled them unconfirmed. NOT FOUND: any lab statement naming a full Hodge, BSD, RH, P vs NP or Yang-Mills solution. Any announced date for a next OpenAI math release. Any Google, Anthropic or other eligible lab claim. I did not read the GitHub repo or the full OpenAI Oct 6 post, only its summary.

YES means: an eligible AI lab (OpenAI, Anthropic, Google and so on) announces by 11:59 PM ET on 2026-12-31 that it has solved the Riemann Hypothesis, P vs NP, Yang-Mills, Hodge or BSD. A claim about Navier-Stokes, partial results or credit given only to outside researchers do not count. - [2026-10-07] Sam Altman picked four of OpenAI's 722 manuscripts as the biggest. One was Hodge, but only for CM abelian varieties, a narrow special class. The same OpenAI release had Riemann as the zero-free region Re(s)>7/8 only. The Hodge manuscript has no Lean proof. OfficeChai says plainly that the Riemann result "doesn't earn a Millennium Prize" and that the Hodge conjecture "is wide open in general". Altman himself called these claims not yet confirmed by outside mathematicians. OpenAI's own Oct 6-7 framing was therefore explicitly partial. A later full-solution announcement would be a break from that framing. https://officechai.com/ai/openai-releases-ai-generated-proofs-of-quasi-riemann-hypothesis-unique-games-conjecture-hodge-conjecture-for-cm-abelian-varieties/ - [2026-10-07] A catalog reader says OpenAI's Hodge family 032 (dated Sep 30) has no Lean link, and that 137 families lack formalisation. The reader concludes neither Riemann nor Hodge, as Clay states them, is solved. Because the Hodge-leaning work was already published as a partial result on Sep 30–Oct 4, the "held-back Hodge solution" has arguably already been disclosed in partial form. That shrinks the pool of undisclosed full solutions. https://pasqualepillitteri.it/en/news/21359/openai-millennium-problems-riemann-hodge (search snippet; page not fetchable) - [2026-09-17] The "close to Hodge" story rests on one anonymous source in The Information. It says staff expect a solve "relatively soon", and that any announcement could be delayed. OpenAI wants to get messaging right after the Navier-Stokes PR crisis. OpenAI's own statement named no problem and gave no timeline. A cautious, delayed-disclosure posture lowers the chance of a full claim landing in a 11-week window. https://the-decoder.com/openai-reportedly-closes-in-on-solving-the-hodge-conjecture-its-second-millennium-prize-problem/ (snippet only; fetch blocked) - [2026-09-18] Kingy.ai lists "Hodge already solved", "BSD near completion" and the "Aeon" model as unconfirmed. It says there is no public paper, named theorem or second Lean formalisation for the second problem. Rumour quality is poor. An earlier rumour (Curran, Sep 5) was a self-described prediction with no inside source, and it was wrong about the actor. https://kingy.ai/news/openai-next-millennium-prize-problem-hodge/ - [2026-10-05] IEEE Spectrum, written after the Sept 8 claim, says the Anthropic August Riemann work made progress on a related problem "but not on its main mission". It says OpenAI is "reportedly" focusing on Hodge. No Google, Anthropic or other lab has been reported with a full-solution claim. Only OpenAI has shown any pattern of announcing. The bulk of probability sits on a single actor with a public caution stance. https://spectrum.ieee.org/millennium-prize-ai - [2026-10-11] The Navier-Stokes claim has drawn a priority dispute, doubts over the forced version, and Clay's non-recognition. Wikipedia notes Clay only considers solutions two years after publication. OpenAI says it won't claim the prize. The backlash has a cost: Fields Medalists' letter, Tao's criticism, credit disputes. These raise the reputational price of a second overreach, and OpenAI said it consulted an IAS advisory group on release. That favours slower, vetted releases than the Sep 8 one. https://en.wikipedia.org/wiki/Millennium_Prize_Problems - [2026-10-07] Resolution technicality: the Navier-Stokes claim was a counterexample-style forced case. A similar "narrow-variant" claim on Hodge (CM abelian varieties) is a partial result under the rules. Labs now have a clear template of presenting variants as progress, and the rules require that the announcement "express that the problem has been solved". The next likely OpenAI disclosures (more of the 722-manuscript style) would again be partial, so the status-quo path resolves NO. https://officechai.com/ai/openai-releases-ai-generated-proofs-of-quasi-riemann-hypothesis-unique-games-conjecture-hodge-conjecture-for-cm-abelian-varieties/ - [2026-10-12] Manifold's 83% price (Oct 12) is for a different, looser question (end of 2027, any Millennium problem, probably counting Navier-Stokes), and is play money. The 35% of volume in one day is a spike driven by the Oct 6–7 news, not an informative hazard rate for this strike. https://tech-insider.org/ai-millennium-problem-manifold-odds-eoy-2027/ - [2026-09-05] Rumour-track record: a viral claim that Anthropic had "solved some millennium problems" (Sep 4–5) proved to be a prediction without a source. Trueo priced the specific claim at 1%. The only real event that followed was OpenAI's Navier-Stokes claim, and Anthropic's confirmed output was an Aug 10 bound improvement it said would not lead to a proof. https://x.com/AGTPinsights/status/2096081768629551208 - [Time arithmetic, 2026-10-15] From Sep 8 to Oct 15 (37 days) OpenAI made one excluded claim and published many partial results, and no qualifying full claim, despite a 10,000-agent run costing an estimated $15–20 million. That is zero qualifying events in the five weeks after the push began, with 77 days left. Only 1 of the 5 qualifying problems (per Scenarica's Oct estimate) has a plausible short-path "counterexample" route. https://wbur.org/onpoint/2026/10/13/ai-steamrolling-math-solve BOTTOM LINE: A qualifying YES needs a full-solution claim on one of five much harder problems within 77 days. Every disclosure so far has been explicitly partial, the only specific lead (Hodge) was already published as a narrow partial result, and backlash plus IAS-vetted release practice favours caution. The status quo of partial results points to NO. NOT FOUND: Any lab statement, paper or credible report of a full solution to Riemann, P vs NP, Yang-Mills, Hodge or BSD. Any scheduled lab announcement date before 2027-01-01. A Google/DeepMind claim. Fetches of the Decoder and Pillitteri pages were blocked, so those points rest on snippets.