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数学 · Diophantine geometryA genus-2 curve with 648 rational pointsGPT-6 Astra found a genus-2 curve with 648 rational points, beating the record of 642 set by Elkies and Stoll in 2008; the deeper uniformity question remains open.部分的結果
- 2025-12-30数学 · Number theoryErdős Problem #1095Partial progress by Aristotle (30 Dec 2025): new proof of (slightly weaker) partial result (Lean). 2 AI contributions are recorded in all.部分的結果
- 2025-12-18数学 · IrrationalityErdős Problem #264Partial progress by Aristotle (18 Dec 2025): new proof of partial result (Lean).部分的結果
- 2025-12-16数学 · AnalysisErdős Problem #1038Partial progress by catsflowers5544, jspier, Junnosuke Koizumi, Kenneth Mendoza, Nat Sothanaphan, Terence Tao and Hua Xu with AlphaEvolve, Claude Fable 5, Codex, GPT-5.2 Thinking, GPT-5.4 Thinking and GPT-5.5 (16 Dec 2025): partial result.部分的結果
- 2025-12-04数学 · Number theoryErdős Problem #43Partial progress by Aristotle (4 Dec 2025): new proof of partial result (Lean).部分的結果
- 2025-11-29数学 · Number theoryErdős Problem #124Partial progress by Aristotle (29 Nov 2025): partial result (Lean).部分的結果
- 2025-11-27数学 · Number theoryErdős Problem #488Partial progress by Aristotle (27 Nov 2025): new solution to variant problem (Lean). 2 AI contributions are recorded in all.部分的結果
- 2025-11-23数学 · Number theoryErdős Problem #942Partial progress by Gemini (23 Nov 2025): new proof found. 2 AI contributions are recorded in all.部分的結果
- 2025-11-20数学 · Number theoryErdős Problem #367Partial progress by Boris Alexeev, Wouter van Doorn and Terence Tao with Aristotle and Gemini Deep Think (20 Nov 2025): partial result.部分的結果
- 2025-11-03数学 · Mathematical discoveryKakeya and Nikodym sets in finite fieldsAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.部分的結果
- 2025-11-03数学 · Mathematical discovery3D Kakeya problemAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.部分的結果
- 2025-11-03数学 · Mathematical discoveryAn autocorrelation problem related to Sidon setsAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.部分的結果
- 2025-11-03数学 · Mathematical discoveryHow much can an autocorrelation of a non-negative function resemble an indicator function?AlphaEvolve improved the best known bound; the record has since been surpassed. The problem remains open.部分的結果
- 2025-11-03数学 · Mathematical discoveryThe Arithmetic Kakeya ConjectureAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.部分的結果
- 2025-11-03数学 · Mathematical discoverySpherical DesignsAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.部分的結果
- 2025-11-03数学 · Mathematical discoveryPacking in a dilateAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.部分的結果
- 2025-11-03数学 · Mathematical discoveryCircle packing in a square / rectangleAlphaEvolve improved the best known bound; the record has since been surpassed. The problem remains open.部分的結果
- 2025-11-03数学 · Mathematical discoveryFactoring N! into N numbersAlphaEvolve improved the best known bound; the record has since been surpassed. The problem remains open.部分的結果
- 2025-11-03数学 · Mathematical discoveryAn autocorrelation problem with functions that can take negative valuesAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.部分的結果
- 2025-11-03数学 · Mathematical discoverySum-difference problem IAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.部分的結果
- 2025-11-03数学 · Mathematical discoverySum-difference problem IIIAlphaEvolve improved the best known bound; the record has since been surpassed. The problem remains open.部分的結果
- 2025-11-03数学 · Mathematical discoveryHeilbronn problem in a fixed bounding boxAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.部分的結果
- 2025-11-03数学 · Mathematical discoveryHeilbronn problem in an arbitrary convex bounding boxAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.部分的結果
- 2025-11-03数学 · Mathematical discoveryErdős minimum overlap problemAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.部分的結果
- 2025-11-03数学 · Mathematical discoveryMax to min ratiosAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.部分的結果
- 2025-11-03数学 · Mathematical discoverySubsets of the grid with no isosceles trianglesAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.部分的結果
- 2025-11-03数学 · Mathematical discoveryThe no 5 on a sphere problemAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.部分的結果
- 2025-11-03数学 · Mathematical discoveryThe Ring Loading ProblemAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.部分的結果
- 2025-11-03数学 · Mathematical discoveryThe three-dimensional moving sofa problem with two perpendicular turnsAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.部分的結果
- 2025-11-03数学 · Mathematical discoveryDifference BasesAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.部分的結果
- 2025-11-03数学 · Mathematical discoveryKissing numbersAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.部分的結果
- 2025-11-03数学 · Mathematical discoveryKakeya needle problemAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.部分的結果
- 2025-11-03数学 · Number theoryErdős Problem #1097Partial progress by AlphaEvolve (3 Nov 2025): slight improvement to past construction.部分的結果
- 2025-11-03数学 · Number theoryErdős Problem #36Partial progress by AlphaEvolve (3 Nov 2025): slight improvement to past construction. 2 AI contributions are recorded in all.部分的結果
- 2025-11-03数学 · GeometryErdős Problem #507Partial progress by AlphaEvolve (3 Nov 2025): surpassed some past constructions.部分的結果
- 2025-08-09数学 · Number theoryErdős Problem #686Partial progress by Adenwalla, Stijn Cambie, Wouter van Doorn, Vjekoslav Kovač, Miklos, Nat Sothanaphan, Quanyu Tang, Terence Tao, vilc and Malek Zribi with AlphaProof, Claude, Gemini Deep Think, GPT-5.2 Thinking, GPT-5.4 Thinking and Seed 2.0 Pro (9 Aug 2025): various partial results.部分的結果
- 2025-05計算機科学 · アルゴリズム4×4 複素行列の積：AlphaEvolve が乗算 48 回のアルゴリズムを発見AlphaEvolve は 4×4 の複素行列の積を 48 回のスカラー乗算で計算するアルゴリズムを見つけ、Strassen の方法を再帰的に用いた場合の 49 回を改良した。部分的結果
- 2025数学 · Number theoryErdős Problem #493Partial progress by Aristotle, GPT and Seed Prover (2025): new or existing proof found (Lean).部分的結果
- 2023-12数学 · 組合せ論キャップ集合問題：FunSearch が 8 次元でより大きなキャップ集合を発見大規模言語モデルが駆動するプログラム探索システムが、8 次元で既知最大のキャップ集合を与え、漸近的な下界を改良した。元の問題は未解決のまま。部分的結果