Will AI solve 0 more Millennium Prize Problems in 2026?

The question asks whether AI solves zero qualifying problems in 2026. That is the same as asking whether no eligible lab announces a solution to Birch–Swinnerton-Dyer, Hodge, P vs NP, Riemann or Yang–Mills by 2026-12-31. As of 2026-10-17 I found no such announcement. The only lab claim of a full Millennium solution so far is Navier–Stokes, which the rules exclude. - [2026-09-08] OpenAI announced an internal model had resolved Navier–Stokes. The claim is a finite-time blow-up with a smooth external force, using about 10,000 agents over 88 hours, plus a Lean formalization. OpenAI says it won't claim the prize. This is excluded from the market. https://www.quantamagazine.org/ai-has-solved-one-of-maths-1-million-millennium-prize-problems-20260908/ - [2026-09-11] A tracker that cites Clay's overview lists Birch–Swinnerton-Dyer, Hodge, P vs NP, Riemann and Yang–Mills as unsolved, with no authoritative completed AI solution. It lists Navier–Stokes as "Active" at Clay. I could not load claymath.org directly. https://kingy.ai/millennium-prize-problems-ai/ - [2026-08-10] Anthropic published a preprint and blog post on an unreleased Claude's attempt at the Riemann hypothesis. It failed to prove it, but raised the proportion of zeros known to lie on the critical line from 41.6% to about 67%. Anthropic itself says this is not a solution. https://www.livescience.com/technology/artificial-intelligence/this-is-what-happened-with-claude-and-me-ais-failed-attempt-to-crack-the-riemann-hypothesis-led-mathematician-to-a-breakthrough - [2026-10-06] OpenAI released a GitHub repo, openai/math. It holds 719 manuscripts in 372 families, produced by an unreleased internal model, with about 42% of top-line results formalized in Lean. Its README says some unformalized results could have issues. https://github.com/openai/math - [2026-10-06] Two items in the repo touch the market's problems. The README names a zero-free region for the Riemann zeta function as an exception to the standard procedure. It also names a "proof of the Hodge Conjecture for CM abelian varieties", which is a special case. Neither is a claim of the full conjectures. https://github.com/openai/math - [2026-10-07] Secondary coverage says the repo's Riemann result is a partial "quasi-Riemann" result, a zero-free region for Re(s) greater than 7/8 or 11/12. These sources say it is not the full hypothesis. They also say the model reportedly established a Birch–Swinnerton-Dyer formula for a broad class of cases, which is partial. https://www.mindstudio.ai/blog/openai-722-math-proofs-release - [2026-10-07] A KuCoin news item claimed OpenAI "proved the Riemann Hypothesis". This contradicts the repo README and the other coverage, so treat it as unreliable. https://www.kucoin.com/news/flash/openai-solves-722-math-problems-quasi-riemann-hypothesis-proven - [2026-10-13] A WBUR On Point broadcast says the Navier–Stokes solution is still being evaluated. It also says OpenAI recently released more than 700 papers. https://wbur.org/onpoint/2026/10/13/ai-steamrolling-math-solve - [2026-10-16] OpenAI gave $5M to the Simons Foundation to help mathematicians vet AI results. This points to a verification backlog, not a new claim. https://cryptobriefing.com/openai-simons-foundation-ai-math-initiative - [2026-09-11] 28 Fields Medalists published an open letter warning about AI companies treating unsolved problems as benchmarks. https://en.wikipedia.org/wiki/2026_in_artificial_intelligence - [2026-09-05] A Manifold play-money market on whether an AI solves any Millennium problem in 2026 stood at 38%. This was before the Navier–Stokes announcement and counts Navier–Stokes, so it is not comparable to this contract. https://tech-insider.org/ai-solves-millennium-prize-problem-2026-manifold-odds/ - [2026-10-04] A fact-check noted that a rumor of an Anthropic Millennium claim traced to one user's labeled prediction. It found no Anthropic source, paper or Clay submission. https://www.explainx.ai/blog/millennium-prize-problems-ai-solved-fact-check-2026 BOTTOM LINE: No qualifying announcement exists as of 2026-10-17. OpenAI's Navier–Stokes claim is excluded, and the Riemann, Hodge and Birch–Swinnerton-Dyer outputs so far are partial or special-case results. The pace of lab output is rapid (about 10 results in August, 100+ in September, 719 manuscripts in October), so a surprise full claim before year-end is possible, but nothing currently shows one. NOT FOUND: A direct fetch of claymath.org and the openai.com announcement pages. Any scheduled event before 2026-12-31 that would produce a qualifying announcement. Any Google, DeepMind or Anthropic claim of a qualifying problem. Any live Polymarket sibling contracts.

- [2026-10-17] The sibling count market "How many more Millennium Prize Problems will AI solve in 2026?" showed "0" at about 77%, "1" at 18%, "2" at 5% and "3" at 2.5%. Volume was about $352k. The page also says October releases of hundreds of other machine-generated proofs did not reach any further Millennium problem. This is a snapshot taken at fetch time, so it may be stale. https://polymarket.com/event/how-many-more-millennium-prize-problems-will-ai-solve-in-2026 - [2026-09-16] The sibling "AI lab announces another Millennium Prize solution by...?" market had these prices: - by 30 Sep 2026: 15% - by 31 Dec 2026: 47% - by 31 Dec 2027: 76% Trading volume was $234k. The prices were taken shortly after launch and look inconsistent with the count market above. They imply a much higher chance of a December-2026 announcement than the count market does. https://polymarket.com/event/ai-lab-announces-another-millennium-prize-solution-by - [2026-09-30] The "OpenAI announces another Millennium Prize solution by...?" market had these prices: - by 30 Sep 2026: 13% - by 31 Dec 2026: 44% - by 31 Dec 2027: 71% The market has since moved. A Polymarket science listing later showed the OpenAI-by-Dec-2026 strike at 25%. The 13% for 30 September did not resolve Yes, since no qualifying announcement is reported. https://polymarket.com/event/openai-announces-another-millennium-prize-solution-by - [2026-10-10] The "Which problem will AI solve next?" market gave these prices: - no solution by Dec 2027: about 34% - Hodge: about 31% - Birch and Swinnerton-Dyer: about 20% - Yang-Mills: about 7% - Riemann Hypothesis: about 3% The page cites October "partial results on Hodge variants" and "quasi-Riemann cases". I did not verify either claim. https://polymarket.com/event/which-millennium-prize-problem-will-ai-solve-next - [2026-09-08] OpenAI announced a Lean-formalized, AI-generated proof that Navier-Stokes develops a finite-time singularity. This was the first lab announcement of a Millennium problem. OpenAI said it does not intend to claim the prize. Navier-Stokes is excluded from this market. https://openai.com/index/navier-stokes-solution/ - [2026-09-08] Quanta reported that the work came about 88 hours after the agents started, using about 10,000 agents. It was also triggered by a rumor (not borne out) that Alpöge (Anthropic) and Buckmaster had solved a Millennium problem. CNN carried the same account. The result is contested, with a priority dispute and doubts about whether it covers the prize's natural case. This shows that a lab race can produce fast, sudden announcements. https://www.quantamagazine.org/ai-has-solved-one-of-maths-1-million-millennium-prize-problems-20260908/ - [2026-09-11] OpenAI told the NYT it had made "substantial progress on another Millennium Prize problem" and was working out how to share it. The problem was not named, and rumors about Hodge and Birch and Swinnerton-Dyer were unconfirmed. "Progress" would not count under this market's rules. The statement is reported second-hand via explainx.ai, and explainx.ai's own scorecard said P vs NP and Yang-Mills had no AI progress. https://www.explainx.ai/blog/millennium-prize-problems-ai-solved-fact-check-2026 - [2026-10-17] Historical base rate: only one Millennium problem, Poincaré, has ever been officially declared solved (Perelman, 2002–03, prize awarded in 2010). The Clay Institute reportedly only considers proposed solutions at least two years after publication. For all five qualifying problems, no lab announcement existed before September 2026. Note that this market resolves on a lab's announcement, with no Clay confirmation needed. https://en.wikipedia.org/wiki/Millennium_Prize_Problems - [2026-10-12] A Manifold market on an AI solving a Millennium problem by the end of 2027 traded at about 83%. A tech-news write-up pointed out that "solved" is ambiguous, and that this probably reflects Navier-Stokes. https://tech-insider.org/ai-millennium-problem-manifold-odds-eoy-2027/ - [2026-09-20] A related Manifold market, "At least 5 Millennium Prize problems solved by end of 2026?", quoted the Polymarket count book at 7.5% for that outcome. Another Manifold market, "Will a Millennium Prize Problem be solved in 2026?", was at about 97–98%. It likely counts Navier-Stokes, so it does not bear on this contract. https://manifold.markets/Plant/5-millennium-prize-problems-solved - [2026-09-25] The "Will CMI declare a Millennium Prize Problem solved by Dec 31, 2026?" market had $403k traded. Resolution there needs a CMI declaration, which the two-year rule makes very unlikely in 2026. The price shown on the page I fetched belongs to a different related market, so I did not record one. https://polymarket.com/event/will-cmi-declare-a-millennium-prize-problem-solved-by-20260723160122979 - [2026-10-17] Reference-class point: the one precedent is a single announcement in September 2026 that took about a week of compute. It was triggered by a competitor rumor, and the problem chosen (Navier-Stokes) was the one most open to an explicit counterexample and Lean checking. The remaining five problems are mostly existence or proof problems with no obvious blow-up construction. Hodge, BSD and Yang-Mills are the likeliest next candidates in the "next problem" market. BOTTOM LINE: The historical base rate for a Millennium problem being claimed is essentially zero until September 2026, and the one precedent was an unusual Navier-Stokes case that this market excludes. OpenAI's unnamed "second problem" progress and the lab race raise the tail risk of a claim before year-end, and the market's prices for a December-2026 announcement are inconsistent (about 77% for zero versus 44–47% for an announcement by 31 December). NOT FOUND: A named second problem from OpenAI or any other lab, and any lab announcement of a qualifying problem since 2026-09-08. I also found no expert estimates or polls with track records. The Polymarket sibling pages were only readable as snapshots, and I could not confirm the date of each price.

YES means: no eligible AI lab announces a full solution to Birch–Swinnerton-Dyer, Hodge, P vs NP, Riemann or Yang–Mills between now and 2026-12-31. Navier–Stokes is excluded. - [2026-10-07] OpenAI's own changelog withdrew three Hodge-related manuscripts after a sign error. They were "Algebraicity of Weil classes on split abelian eightfolds", the Kuga–Satake paper, and "The rational Hodge conjecture for products of K3 surfaces". The changelog also lists 14 repaired manuscripts, including the BSD paper "Exact Birch–Swinnerton-Dyer Formula from Low Selmer Corank", and says 300 of 719 top-line results (about 42%) are formalized in Lean. The most plausible candidate (Hodge) lost its strongest sub-results one day after release. The BSD result is still a conditional low-corank formula. The self-correction suggests the lab is cautious about overclaiming. https://github.com/openai/math/blob/main/history.md - [2026-10-08] Named mathematicians urged caution about the release. MIT's Andrew Sutherland said claims should be treated as unverified until the model is released and results can be replicated. Daniel Litt questioned the secrecy. OpenAI has not released the model, so any "solved" claim would face immediate public skepticism. https://aiweekly.co/alerts/openai-pulls-three-ai-generated-math-papers-over-sign-error - [2026-10-09] The Hodge material that remains covers the rational Hodge conjecture for CM abelian varieties. That is a special case, and it "requires its own scrutiny". The full conjecture covers all smooth projective complex varieties. https://kingy.ai/blog/openai-math-722-manuscripts-results-proofs-compute-costs/ - [2026-10-06] OpenAI's official October 6 post reportedly names neither Riemann nor Hodge. The Riemann item is a "quasi-Riemann" zero-free region, with a human-edited writeup for Re(s) > 11/12. Even when OpenAI released ~700 papers, it did not frame any as a full Millennium solution. That is a revealed preference against claiming a full solution. https://pasqualepillitteri.it/en/news/21359/openai-millennium-problems-riemann-hodge - [2026-09-11] Clay's Navier–Stokes statement called its process "deliberately unhurried". The rules require refereed publication, then two years, then general acceptance. Per Hacker News discussion, OpenAI's self-hosted posting does not count as publication. This lowers the incentive for labs to rush a premature "solved" claim on the remaining problems before year-end. https://news.ycombinator.com/item?id=49668706 - [2026-09-11] 28 Fields Medalists signed "A Severe Misalignment of AI in Mathematics". OpenAI's Navier–Stokes claim also drew a priority dispute, with the Buckmaster–Alpöge dispute as the main case. Reputational costs of an overclaim are now high. https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_priority_controversy - [2026-08] Anthropic's Riemann work had two Anthropic mathematicians validate it. It said it does not expect Claude's techniques to lead to a proof. The other leading lab is therefore pessimistic about Riemann in its own words. A Claude-solves-Navier–Stokes rumor traced to one user's labeled prediction. https://www.explainx.ai/blog/millennium-prize-problems-ai-solved-fact-check-2026 - [2026-09-11] The explainx.ai scorecard shows nothing from labs on Yang–Mills ("silence"), and the same page shows no progress on P vs NP. OpenAI's "second problem" statement to the NYT named no problem and said "progress", not "solved". It did not appear to be a claim of completion. https://www.explainx.ai/blog/millennium-prize-problems-ai-solved-fact-check-2026 - [2026-09-14] A Kalshi contract on BSD being the next problem solved before 2045 reportedly traded at 38%, but the page says no BSD breakthrough had been confirmed. It reflects rumor-driven trading, not evidence. https://tech-insider.org/birch-swinnerton-dyer-solved-before-2045-kalshi-odds/ - [2026-10-17] Single most likely path to YES (no announcement): OpenAI's second-problem work stays at the "partial result" level (Hodge for special classes, BSD formula, zero-free region). The error-prone, unformalized backlog gets audited, and no lab publicly says "solved" in the remaining 10 weeks. Prerequisites are that no lab announces a full Hodge or BSD result and that DeepMind and Anthropic stay silent on these problems. Everything found so far fits that path, and nothing scheduled forces an announcement. BOTTOM LINE: The evidence consistently shows partial results, retractions and cautious lab language, with no scheduled event that forces a full-solution claim. The risk to YES is a surprise Hodge or BSD claim from OpenAI or Anthropic, which the "OpenAI second problem" statement and the Hodge/BSD rumors keep alive. NOT FOUND: Any named lab claim of a full Hodge, BSD, P vs NP, Riemann or Yang–Mills solution. Any Google DeepMind statement on these problems. Any dated plan for a lab announcement before 2026-12-31. A direct fetch of the openai.com announcement pages and claymath.org.

YES means: no eligible AI lab announces a solution to BSD, Hodge, P vs NP, Riemann or Yang–Mills by 2026-12-31 11:59 PM ET. In other words, zero qualifying announcements. - [2026-10-06] OpenAI's 722-manuscript release (372 result families) contains only scoped results on the market's problems. Its two procedural exceptions are a Riemann zero-free region and the rational Hodge conjecture for CM abelian varieties. Emergent Mind's mapping lists 235 results with Lean formalizations. Commentators on that page describe the BSD result as holding for a density-one set of curves, not for all. The page does not show any lab claim of a full conjecture. https://www.emergentmind.com/openai-math-explorer - [2026-10-07] The largest lab output so far did not include a full claim on any qualifying problem. OpenAI had said (per the Sept 11 NYT item) it had "substantial progress" on a second problem, and the Oct 6 dump is the plausible vehicle for that progress. A lab that was close to a full Hodge or BSD result had every incentive to say so there, and it did not. Hodge and BSD were presented as special cases or density results. https://www.emergentmind.com/openai-math-explorer - [2026-10-13] The Navier–Stokes claim, OpenAI's only Millennium announcement, is still contested six weeks after it was made. Scientific American reports experts saying the proof differs from the approach OpenAI described. The Clay Institute has been reviewing it since release. The Decoder (summarising SciAm) says Clay is reviewing it and that mathematicians were angered by the loose GitHub dump. A lab that has just been publicly challenged on rigor has reason to be more careful before announcing "solved" on a second problem. https://the-decoder.com/mathematicians-say-openai-doesnt-understand-its-own-navier-stokes-proof/ - [2026-10-06] An arXiv paper by Bastounis, Circelli and Hansen ("Navier-Stokes lost in translation") argues OpenAI's Lean code does not match its natural-language proof. It does not say the proof is wrong. Reported 2026-10-16, it shows that even Lean-backed claims draw credibility attacks. This raises the reputational cost of an overreaching claim. https://startupfortune.com/a-new-paper-says-openais-navier-stokes-proof-and-its-lean-code-dont-match/ - [2026-09-21] The one precedent was a special case. The problem statement allowed an external force, and the AI found an explicit construction exploiting that "loophole". A rebuttal paper (arXiv 2609.20803) shows the method cannot extend to the force-free problem. Mathematicians say LLMs are good at constructing explicit objects and weaker at building new theory. The remaining five problems are existence or proof statements with no comparable explicit-construction route, and the Millennium problems Hodge, BSD, RH and Yang–Mills each need new theory. https://www.scientificamerican.com/article/did-openai-solve-the-wrong-navier-stokes-problem/ - [2026-08-10] Anthropic said the techniques behind its Riemann zero-density result are not expected to lead to a proof of RH (Aug 10–13 post). Per explainx, the Sept 26 Anthropic nine-loop N=4 SYM amplitude work was not a mass-gap attempt. Those are the only reported Anthropic results near the qualifying problems, and neither is a claim. https://www.explainx.ai/blog/millennium-prize-problems-ai-solved-fact-check-2026 - [2026-09-11] The rumor trail for Hodge and BSD rests on an anonymous X post ("I am told…") and a Information-sourced "expect relatively soon" report. Kingy.ai notes there is no public paper, named theorem or second Lean formalization. The Oct 6 release is the closest thing to a Hodge output, and it is only the CM case, which builds on Milne's earlier theorems. https://kingy.ai/news/openai-next-millennium-prize-problem-hodge/ - [2026-10-16] The resolution wording is strict. It requires an announcement that the problem "has been solved", presented as the lab's own work. OpenAI has already shown a pattern of wording around this: it said it would not claim the Navier–Stokes prize and used "substantial progress" for the second problem. Labs can publish special-case or "partial" results without triggering YES. Partial results, progress, and congratulating outside mathematicians are all expressly excluded. Rumor posts, KuCoin-type headlines and individual employees' tweets do not qualify. https://openai.com/index/navier-stokes-solution/ - [2026-09-14] Prediction-market overreaction is the main risk to the NO side. Kalshi's BSD "next Millennium" contract jumped 38 points on Sept 14 on the back of rumors alone, with no BSD breakthrough confirmed. Price spikes on rumor are not evidence of an announcement. https://tech-insider.org/birch-swinnerton-dyer-solved-before-2045-kalshi-odds/ - [2026-10-17] Deadline arithmetic: about 10 weeks remain (Oct 17 to Dec 31), and the holiday period reduces the odds of launches. The only claim to date followed roughly a year of human–AI work and a one-week compute burst. Nothing in the evidence shows a second lab-grade full proof is pending verification. Clay reviewing Navier–Stokes since September also sets the benchmark: claims are slow to validate. This market needs no Clay confirmation, but labs' own caution is the practical filter. https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_priority_controversy BOTTOM LINE: Status quo favours NO. Neither the biggest dump of AI math (Oct 6) nor the second-problem "progress" statement produced a full claim on any qualifying problem. Scrutiny of the Navier–Stokes claim, and the fact that the remaining five problems lack an easy construction route, argue against a full claim in 10 weeks. The residual risk is a sudden OpenAI, Anthropic or Google announcement of Hodge or BSD (the lab-race tail). NOT FOUND: Any lab statement claiming a full solution of BSD, Hodge, P vs NP, Riemann or Yang–Mills. Any Google/DeepMind claim. Any scheduled announcement event before 2026-12-31. A direct read of the openai/math README (I relied on secondary mappings). I also did not search for or report this contract's own price.