AI × SCIENCE · 未解決問題トラッカー
未知、証明終わり。
Where AI turns unknowns into Q.E.D.
AI が解いた科学の問題をひとつ残らず追跡します。各記録には結果の格付け、検証の方法、元の出典を明記し、誰でも注釈や異議を書き込めます。
格付け基準
完全解AI が単独で、または主導して、完全かつ新しい解を与えた。
部分的結果評価の改良、新しい構成、特殊な場合の解決。元の問題は未解決のまま。
既知文献AI が示した「新しい解」は既存の文献にすでにあった。
未検証公に主張されているが、まだ独立に検証されていない。
問題一覧
- 2026-10-06数学 · AnalysisLittlewood polynomials with large normalized Mahler measureAn internal OpenAI model produced a preprint proving that real ultraflat Littlewood polynomials exist, which settles an Epoch AI open problem; the proof has not yet been independently checked.未検証
- 2026-10-06数学 · Mathematics and theoretical CSOpenAI's release of 372 result families in mathematicsOpenAI released 719 manuscripts in 372 result families produced by an unreleased model; about 42% are formalized in Lean, none is peer reviewed, and three were withdrawn a day later over a sign error.未検証
- 2026-09-17数学 · Number theoryApéry-style irrationality proofs: ζ(5) and Catalan's constantA preprint proving that ζ(5) is irrational, now formalized in Lean by a third party, led Epoch AI to mark this open problem solved by human and AI; no primary source we found describes the AI's role.未検証
- 2026-09-10計算機科学 · Social choiceThe core in approval-based committee elections is never emptyBecker, Greger and Peters proved that every approval-based committee election has a committee in the core, computable in polynomial time; their arXiv paper says the proof was obtained with GPT-6 Astra.未検証
- 2026-09-08数学 · Partial differential equationsNavier–Stokes: OpenAI's claim of finite-time blowup with smooth forcingOpenAI claims an internal model proved that a 3D incompressible fluid starting at rest can develop a singularity in finite time under a smooth external force, one of the four forms of the Millennium Prize problem; the 166-page proof is unverified and its priority is disputed.未検証
- 2026-08-09数学 · Number theoryThe inverse Galois problem for the Mathieu group M23Huang, Jackson, Lee, Poonen, Pries and Zhang gave an explicit degree-23 polynomial over ℚ with Galois group M23, the last sporadic simple group not yet realized; Epoch AI credits AI as instrumental, but the paper has not been peer reviewed.未検証
- 2026-08-01数学 · Mathematics and theoretical CSOpenAI's “ten advances” in mathematics and theoretical computer scienceOpenAI announced ten results produced with GPT-6 Astra, from sphere-packing bounds to Ramsey numbers, with Lean certificates; none has been peer reviewed, and two face credit disputes from mathematicians.未検証
- 2026-06-27数学 · Graph theoryErdős Problem #1033A claim by GPT-5.5 Pro (27 Jun 2026) that has not yet been verified: candidate partial result.未検証
- 2026-06-27数学 · Number theoryErdős Problem #731A claim by Eric Li with GPT (27 Jun 2026) that has not yet been verified: candidate full solution.未検証
- 2026-06-24数学 · Number theoryErdős Problem #1061A claim by Eric Li with GPT (24 Jun 2026) that has not yet been verified: candidate full solution.未検証
- 2026-06-24数学 · Number theoryErdős Problem #730A claim by GPT-5.5 Pro (24 Jun 2026) that has not yet been verified: candidate full solution.未検証
- 2026-06-23数学 · Set theoryErdős Problem #1177A claim by Eric Li with GPT (23 Jun 2026) that has not yet been verified: candidate full solution.未検証
- 2026-06-23数学 · Number theoryErdős Problem #432A claim by Sungchul Lee with GPT-5.5 Pro (23 Jun 2026) that has not yet been verified: candidate partial result.未検証
- 2026-06-23数学 · Set theoryErdős Problem #593A claim by Eric Li with GPT (23 Jun 2026) that has not yet been verified: candidate full solution.未検証
- 2026-06-22数学 · Number theoryErdős Problem #400A claim by Eric Li with GPT (22 Jun 2026) that has not yet been verified: candidate partial result.未検証
- 2026-06-22数学 · Graph theoryErdős Problem #550A claim by GPT (22 Jun 2026) that has not yet been verified: candidate full solution.未検証
- 2026-06-22数学 · AnalysisErdős Problem #671A claim by Codex and GPT-5.5 Pro (22 Jun 2026) that has not yet been verified: candidate full solution (Lean).未検証
- 2026-06-22数学 · Number theoryErdős Problem #768A claim by Eric Li with GPT (22 Jun 2026) that has not yet been verified: candidate full solution.未検証
- 2026-06-19数学 · Number theoryErdős Problem #1139A claim by Przemek Chojecki, gavinsherry, Liam Price and Terence Tao with GPT-5.2 Pro and GPT-5.5 Pro (19 Jun 2026) that has not yet been verified: candidate full solution.未検証
- 2026-06-14数学 · GeometryErdős Problem #1208A claim by Sungchul Lee with GPT-5.5 Pro (14 Jun 2026) that has not yet been verified: candidate partial result.未検証
- 2026-06-09数学 · Number theoryAn explicit presentation of the absolute Galois group of ℚ₂AI models produced a candidate explicit presentation of the absolute Galois group of the 2-adic numbers, the one case left open; Lean formalizations exist but rely on cited results, and the write-up is not peer reviewed.未検証
- 2026-06-04数学 · Set theoryErdős Problem #623A claim by Sungchul Lee with GPT-5.5 Pro (4 Jun 2026) that has not yet been verified: candidate full solution.未検証
- 2026-06-01数学 · CombinatoricsErdős Problem #501A claim by Sungchul Lee with GPT-5.5 Pro (1 Jun 2026) that has not yet been verified: candidate conditional partial result (conditional solution to first part).未検証
- 2026-05-15数学 · Additive combinatoricsErdős Problem #819A claim by Yu Leon Liu with GPT-5.5 and Rethlas (15 May 2026) that has not yet been verified: candidate partial result.未検証
- 2026-05-13数学 · Number theoryErdős Problem #327A claim by Yu Leon Liu with GPT-5.5 and Rethlas (13 May 2026) that has not yet been verified: candidate partial result.未検証
- 2026-05-04数学 · Number theoryErdős Problem #456A claim by David Turturean with GPT-5.5 Pro (4 May 2026) that has not yet been verified: candidate partial result (solutions to first part and second part; conditional solution to third part).未検証
- 2026-05-03数学 · Number theoryErdős Problem #288A claim by Ritvik Nayak with GPT-5.5 Thinking (3 May 2026) that has not yet been verified: candidate partial result.未検証
- 2026-05-02数学 · Number theoryErdős Problem #390A claim by Samuel Mausberg with GPT-5.5 Pro (2 May 2026) that has not yet been verified: candidate partial result.未検証
- 2026-05-02数学 · Number theoryErdős Problem #870A claim by David Turturean with GPT-5.4 Pro and GPT-5.5 Pro (2 May 2026) that has not yet been verified: candidate full solution.未検証
- 2026-04-30数学 · Number theoryErdős Problem #1201A claim by Przemek Chojecki with GPT-5.5 Pro (30 Apr 2026) that has not yet been verified: candidate full solution.未検証
- 2026-04-29数学 · AnalysisErdős Problem #1133A claim by Przemek Chojecki with GPT-5.5 Pro (29 Apr 2026) that has not yet been verified: candidate full solution.未検証
- 2026-04-29数学 · Number theoryErdős Problem #873A claim by Ritvik Nayak with GPT-5.4 Thinking (29 Apr 2026) that has not yet been verified: candidate partial result. 2 AI contributions are recorded in all.未検証
- 2026-04-27数学 · Number theoryErdős Problem #1101A claim by GPT-5.5 Pro (27 Apr 2026) that has not yet been verified: candidate partial result (solution to second part).未検証
- 2026-04-27数学 · Graph theoryErdős Problem #836A claim by GPT-5.5 Pro (27 Apr 2026) that has not yet been verified: candidate partial result (solution to second part).未検証
- 2026-04-27数学 · GeometryErdős Problem #956A claim by Przemek Chojecki with Aristotle and GPT-5.5 Pro (27 Apr 2026) that has not yet been verified: candidate full solution.未検証
- 2026-04-26数学 · AnalysisErdős Problem #1131A claim by GPT-5.5 Pro (26 Apr 2026) that has not yet been verified: candidate partial result.未検証
- 2026-04-25数学 · AnalysisErdős Problem #906A claim by Adriano Almeida with Unspecified (25 Apr 2026) that has not yet been verified: candidate full solution. 2 AI contributions are recorded in all.未検証
- 2026-04-22数学 · Set theoryErdős Problem #598A claim by Przemek Chojecki with Aristotle and GPT-5.4 Pro (22 Apr 2026) that has not yet been verified: candidate partial result.未検証
- 2026-04-15数学 · Number theoryErdős Problem #856A claim by Przemek Chojecki with GPT-5.4 Pro (15 Apr 2026) that has not yet been verified: candidate full solution.未検証
- 2025-10-29数学 · Number theoryErdős Problem #689A claim by Boris Alexeev, Przemek Chojecki, Dogmachine, jleng01, Mehtaab Sawhney, Terence Tao and Malek Zribi with Codex, GPT-5.2 and GPT-5.5 Pro (29 Oct 2025) that has not yet been verified: candidate full solution.未検証