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families produced by an unreleased model; about 42% are formalized in Lean, none is peer reviewed, and three were withdrawn a day later over a sign error.未検証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
- 2026-08-20数学 · Arithmetic geometryElliptic curves over ℚ of rank at least 30 and 31Claude, working with Levent Alpöge and Ava Howell, found elliptic curves over ℚ with at least 30 and then 31 independent rational points, beating the record of 29 set in 2024.部分的結果
- 2026-08-12数学 · CombinatoricsA Hadamard matrix of order 668Anthropic researcher Levent Alpöge posted Hadamard matrices for every order up to 2000 where none was known, including 668, found by three people working with Claude; an independent check confirmed the matrix, but the method is unpublished.完全解
- 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
- 2026-07-30数学 · Arithmetic geometryA genus-2 curve with a rational torsion point of prime order at least 31GPT-5.6 Sol passed Epoch AI's verifier with such a curve, but the curve came from an existing public database; Epoch itself says the solution was latent in the literature.既知文献
- 2026-07-26数学 · CombinatoricsShorter superpermutations on 8, 9 and 10 symbolsNew superpermutations shorter than Egan's 2018 bound were posted for 8, 9 and 10 symbols; those for 9 and 10 were developed interactively with GPT-5.6 Sol, which then retrieved them to pass Epoch AI's verifier.部分的結果
- 2026-06-29数学 · GeometryErdős Problem #1070Partial progress by Ákos Dúcz and Dániel Varga with Codex and GPT-5.5 (29 Jun 2026): partial result.部分的結果
- 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 · CombinatoricsErdős Problem #21Partial progress by Varun Sivashankar with Aristotle and GPT-5.5 Pro (23 Jun 2026): partial result (Lean).部分的結果
- 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 #1054Partial progress by Claude Opus 4.8, GPT-5.5 Pro and Principia Math (22 Jun 2026): partial result (Lean).部分的結果
- 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 · Number theoryErdős Problem #536Partial progress by Codex and GPT-5.5 Pro (22 Jun 2026): partial result (Lean).部分的結果
- 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
- 2026-06-21数学 · AnalysisErdős Problem #1197Full solution by Aristotle, Claude Opus 4.7 and GPT-5.4 Pro, formalized in Lean (21 Jun 2026).完全解
- 2026-06-21数学 · Additive combinatoricsErdős Problem #176Partial progress by Codex and GPT-5.5 Pro (21 Jun 2026): partial result (Lean). 2 AI contributions are recorded in all.部分的結果
- 2026-06-21数学 · Number theoryErdős Problem #346Full solution by Kenta Kitamura with Codex and GPT, formalized in Lean (21 Jun 2026). 2 AI contributions are recorded in all.完全解
- 2026-06-21数学 · Number theoryErdős Problem #865Full solution by Ricky Cipollini with GPT-5.5 Pro (21 Jun 2026).完全解
- 2026-06-21数学 · Number theoryErdős Problem #948Full solution by Aristotle and GPT-5.5 Pro, formalized in Lean (21 Jun 2026).完全解
- 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
- 2026-06-19数学 · Number theoryErdős Problem #451Partial progress by Wouter van Doorn and Quanyu Tang with Aristotle and GPT-5.5 Pro (19 Jun 2026): partial result (Lean).部分的結果
- 2026-06-19数学 · Graph theoryErdős Problem #81Partial progress by Wouter van Doorn with Aristotle and GPT-5.5 Pro (19 Jun 2026): partial result (Lean).部分的結果
- 2026-06-17数学 · Number theoryErdős Problem #306Partial progress by Shisheng Li with Claude and Claude Code (17 Jun 2026): partial result (Lean). 2 AI contributions are recorded in all.部分的結果
- 2026-06-16数学 · Graph theoryErdős Problem #986Full solution by Domagoj Bradač with Claude and OpenAI internal model (16 Jun 2026).完全解
- 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
- 2026-06-14数学 · Number theoryErdős Problem #326Full solution by Aron Bhalla with Aristotle, Codex and GPT-5.5, formalized in Lean (14 Jun 2026).完全解
- 2026-06-10数学 · Number theoryErdős Problem #539Partial progress by Codex, GPT-5.5 and ProofCouncil (10 Jun 2026): partial result (Lean).部分的結果
- 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