AI × SCIENCE · OPEN PROBLEMS

Unknown, Q.E.D.

Quod erat demonstrandum.

Tracking every scientific problem solved by AI. Each record states how complete the result is, how it was verified and where it came from, and anyone can annotate or challenge it.

Grades

SolvedAI found, or led the way to, a complete and new solution.
PartialAn improved bound, a new construction or a special case; the problem stays open.
Prior artThe “new” solution AI produced was already in the literature.
UnverifiedClaimed publicly but not yet independently checked.

Problems

Newest first · 119 of 262 records
FieldAllMathComputer scienceBiologyPhysicsChemistry
GradeAllSolvedPartialPrior artUnverified
  1. 2026Math · Diophantine geometry
    A 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.GPT-6 Astra (OpenAI)✓ Passed Epoch AI's verifier0 notes
    Partial
  2. 2025-12-30Math · Number theory
    Erdős Problem #1095Partial progress by Aristotle (30 Dec 2025): new proof of (slightly weaker) partial result (Lean). 2 AI contributions are recorded in all.Aristotle✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  3. 2025-12-18Math · Irrationality
    Erdős Problem #264Partial progress by Aristotle (18 Dec 2025): new proof of partial result (Lean).Aristotle✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  4. 2025-12-16Math · Analysis
    Erdős 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.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✓ Listed in Tao's wiki0 notes
    Partial
  5. 2025-12-04Math · Number theory
    Erdős Problem #43Partial progress by Aristotle (4 Dec 2025): new proof of partial result (Lean).Aristotle✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  6. 2025-11-29Math · Number theory
    Erdős Problem #124Partial progress by Aristotle (29 Nov 2025): partial result (Lean).Aristotle✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  7. 2025-11-27Math · Number theory
    Erdős Problem #488Partial progress by Aristotle (27 Nov 2025): new solution to variant problem (Lean). 2 AI contributions are recorded in all.Aristotle✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  8. 2025-11-23Math · Number theory
    Erdős Problem #942Partial progress by Gemini (23 Nov 2025): new proof found. 2 AI contributions are recorded in all.Gemini✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  9. 2025-11-20Math · Number theory
    Erdős Problem #367Partial progress by Boris Alexeev, Wouter van Doorn and Terence Tao with Aristotle and Gemini Deep Think (20 Nov 2025): partial result.Boris Alexeev, Wouter van Doorn and Terence Tao with Aristotle and Gemini Deep Think✓ Listed in Tao's wiki0 notes
    Partial
  10. 2025-11-03Math · Mathematical discovery
    Kakeya and Nikodym sets in finite fieldsAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.AlphaEvolve (Google DeepMind)✓ Construction can be checked directly · Preprint (arXiv, 2025)0 notes
    Partial
  11. 2025-11-03Math · Mathematical discovery
    3D Kakeya problemAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.AlphaEvolve (Google DeepMind)✓ Construction can be checked directly · Preprint (arXiv, 2025)0 notes
    Partial
  12. 2025-11-03Math · Mathematical discovery
    An autocorrelation problem related to Sidon setsAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.AlphaEvolve (Google DeepMind)✓ Construction can be checked directly · Preprint (arXiv, 2025)0 notes
    Partial
  13. 2025-11-03Math · Mathematical discovery
    How 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.AlphaEvolve (Google DeepMind)✓ Construction can be checked directly · Preprint (arXiv, 2025)0 notes
    Partial
  14. 2025-11-03Math · Mathematical discovery
    The Arithmetic Kakeya ConjectureAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.AlphaEvolve (Google DeepMind)✓ Construction can be checked directly · Preprint (arXiv, 2025)0 notes
    Partial
  15. 2025-11-03Math · Mathematical discovery
    Spherical DesignsAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.AlphaEvolve (Google DeepMind)✓ Construction can be checked directly · Preprint (arXiv, 2025)0 notes
    Partial
  16. 2025-11-03Math · Mathematical discovery
    Packing in a dilateAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.AlphaEvolve (Google DeepMind)✓ Construction can be checked directly · Preprint (arXiv, 2025)0 notes
    Partial
  17. 2025-11-03Math · Mathematical discovery
    Circle packing in a square / rectangleAlphaEvolve improved the best known bound; the record has since been surpassed. The problem remains open.AlphaEvolve (Google DeepMind)✓ Construction can be checked directly · Preprint (arXiv, 2025)0 notes
    Partial
  18. 2025-11-03Math · Mathematical discovery
    Factoring N! into N numbersAlphaEvolve improved the best known bound; the record has since been surpassed. The problem remains open.AlphaEvolve (Google DeepMind)✓ Construction can be checked directly · Preprint (arXiv, 2025)0 notes
    Partial
  19. 2025-11-03Math · Mathematical discovery
    An 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.AlphaEvolve (Google DeepMind)✓ Construction can be checked directly · Preprint (arXiv, 2025)0 notes
    Partial
  20. 2025-11-03Math · Mathematical discovery
    Sum-difference problem IAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.AlphaEvolve (Google DeepMind)✓ Construction can be checked directly · Preprint (arXiv, 2025)0 notes
    Partial
  21. 2025-11-03Math · Mathematical discovery
    Sum-difference problem IIIAlphaEvolve improved the best known bound; the record has since been surpassed. The problem remains open.AlphaEvolve (Google DeepMind)✓ Construction can be checked directly · Preprint (arXiv, 2025)0 notes
    Partial
  22. 2025-11-03Math · Mathematical discovery
    Heilbronn problem in a fixed bounding boxAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.AlphaEvolve (Google DeepMind)✓ Construction can be checked directly · Preprint (arXiv, 2025)0 notes
    Partial
  23. 2025-11-03Math · Mathematical discovery
    Heilbronn 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.AlphaEvolve (Google DeepMind)✓ Construction can be checked directly · Preprint (arXiv, 2025)0 notes
    Partial
  24. 2025-11-03Math · Mathematical discovery
    Erdős minimum overlap problemAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.AlphaEvolve (Google DeepMind)✓ Construction can be checked directly · Preprint (arXiv, 2025)0 notes
    Partial
  25. 2025-11-03Math · Mathematical discovery
    Max to min ratiosAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.AlphaEvolve (Google DeepMind)✓ Construction can be checked directly · Preprint (arXiv, 2025)0 notes
    Partial
  26. 2025-11-03Math · Mathematical discovery
    Subsets 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.AlphaEvolve (Google DeepMind)✓ Construction can be checked directly · Preprint (arXiv, 2025)0 notes
    Partial
  27. 2025-11-03Math · Mathematical discovery
    The no 5 on a sphere problemAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.AlphaEvolve (Google DeepMind)✓ Construction can be checked directly · Preprint (arXiv, 2025)0 notes
    Partial
  28. 2025-11-03Math · Mathematical discovery
    The Ring Loading ProblemAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.AlphaEvolve (Google DeepMind)✓ Construction can be checked directly · Preprint (arXiv, 2025)0 notes
    Partial
  29. 2025-11-03Math · Mathematical discovery
    The 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.AlphaEvolve (Google DeepMind)✓ Construction can be checked directly · Preprint (arXiv, 2025)0 notes
    Partial
  30. 2025-11-03Math · Mathematical discovery
    Difference BasesAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.AlphaEvolve (Google DeepMind)✓ Construction can be checked directly · Preprint (arXiv, 2025)0 notes
    Partial
  31. 2025-11-03Math · Mathematical discovery
    Kissing numbersAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.AlphaEvolve (Google DeepMind)✓ Construction can be checked directly · Preprint (arXiv, 2025)0 notes
    Partial
  32. 2025-11-03Math · Mathematical discovery
    Kakeya needle problemAlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.AlphaEvolve (Google DeepMind)✓ Construction can be checked directly · Preprint (arXiv, 2025)0 notes
    Partial
  33. 2025-11-03Math · Number theory
    Erdős Problem #1097Partial progress by AlphaEvolve (3 Nov 2025): slight improvement to past construction.AlphaEvolve✓ Listed in Tao's wiki0 notes
    Partial
  34. 2025-11-03Math · Number theory
    Erdős Problem #36Partial progress by AlphaEvolve (3 Nov 2025): slight improvement to past construction. 2 AI contributions are recorded in all.AlphaEvolve✓ Listed in Tao's wiki0 notes
    Partial
  35. 2025-11-03Math · Geometry
    Erdős Problem #507Partial progress by AlphaEvolve (3 Nov 2025): surpassed some past constructions.AlphaEvolve✓ Listed in Tao's wiki0 notes
    Partial
  36. 2025-08-09Math · Number theory
    Erdős 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.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✓ Listed in Tao's wiki0 notes
    Partial
  37. 2025-05Computer science · Algorithms
    4×4 complex matrix multiplication: AlphaEvolve finds a 48-multiplication algorithmAlphaEvolve found an algorithm that multiplies 4×4 complex matrices with 48 scalar multiplications, one fewer than the 49 needed by applying Strassen's method recursively.AlphaEvolve (Google DeepMind)✓ Can be checked directly0 notes
    Partial
  38. 2025Math · Number theory
    Erdős Problem #493Partial progress by Aristotle, GPT and Seed Prover (2025): new or existing proof found (Lean).Aristotle, GPT and Seed Prover✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  39. 2023-12Math · Combinatorics
    The cap set problem: FunSearch finds a larger cap set in dimension 8A program search system driven by a large language model produced the largest known cap set in dimension 8 and improved the asymptotic lower bound. The problem itself remains open.FunSearch (Google DeepMind)✓ Peer reviewed (Nature, 2023) · Construction can be checked directly0 notes
    Partial