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. 2026-04-04Math · Graph theory
    Erdős Problem #629Partial progress by Gemini 3.1 Pro and GPT-5.4 Thinking (4 Apr 2026): partial result.Gemini 3.1 Pro and GPT-5.4 Thinking✓ Listed in Tao's wiki0 notes
    Partial
  2. 2026-04-04Math · Additive combinatorics
    Erdős Problem #749Partial progress by Aron Bhalla with GPT-5.4 Thinking (4 Apr 2026): partial result; 🟡 Solution to variant problem.Aron Bhalla with GPT-5.4 Thinking✓ Listed in Tao's wiki0 notes
    Partial
  3. 2026-03-31Math · Number theory
    Erdős Problem #374Partial progress by Terence Tao with GPT-5.4 Pro (31 Mar 2026): partial result.Terence Tao with GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Partial
  4. 2026-03-24Math · Analysis
    Erdős Problem #1132Partial progress by Terence Tao with AlphaEvolve, Claude, Gemini Pro and GPT-5.4 Pro (24 Mar 2026): partial result.Terence Tao with AlphaEvolve, Claude, Gemini Pro and GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Partial
  5. 2026-03-23Math · Number theory
    Erdős Problem #342Partial progress by Przemek Chojecki with GPT-5.2 Pro and GPT-5.4 Pro (23 Mar 2026): partial result.Przemek Chojecki with GPT-5.2 Pro and GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Partial
  6. 2026-03-19Math · Number theory
    Erdős Problem #25Partial progress by Przemek Chojecki with GPT-5.4 Pro (19 Mar 2026): partial result.Przemek Chojecki with GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Partial
  7. 2026-03-18Math · Combinatorics
    Erdős Problem #1183Partial progress by Przemek Chojecki and Quanyu Tang with GPT-5.4 Pro (18 Mar 2026): partial result.Przemek Chojecki and Quanyu Tang with GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Partial
  8. 2026-03-18Math · Number theory
    Erdős Problem #943Partial progress by Przemek Chojecki with GPT-5.4 Pro (18 Mar 2026): partial result.Przemek Chojecki with GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Partial
  9. 2026-03-15Math · Number theory
    Erdős Problem #396Partial progress by Malek Zribi with Claude, Codex and GPT (15 Mar 2026): partial result. 2 AI contributions are recorded in all.Malek Zribi with Claude, Codex and GPT✓ Listed in Tao's wiki0 notes
    Partial
  10. 2026-03-14Math · Combinatorics
    Erdős Problem #120Partial progress by DeepMind prover agent (14 Mar 2026): solution to variant problem (Lean).DeepMind prover agent✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  11. 2026-03-11Math · Number theory
    Erdős Problem #423Partial progress by Quanyu Tang and Nat Sothanaphan with GPT-5.2 Thinking and GPT-5.4 Thinking (11 Mar 2026): partial result.Quanyu Tang and Nat Sothanaphan with GPT-5.2 Thinking and GPT-5.4 Thinking✓ Listed in Tao's wiki0 notes
    Partial
  12. 2026-03-09Math · Number theory
    Erdős Problem #349Partial progress by GPT-5.2 Thinking (9 Mar 2026): improved partial result.GPT-5.2 Thinking✓ Listed in Tao's wiki0 notes
    Partial
  13. 2026-03-06Math · Analysis
    Erdős Problem #1039Partial progress by Houi with Aristotle and Claude Opus 4.6 (6 Mar 2026): partial result (Lean). 2 AI contributions are recorded in all.Houi with Aristotle and Claude Opus 4.6✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  14. 2026-03-01Math · Analysis
    Erdős Problem #513Partial progress by GPT-5.2 Thinking (1 Mar 2026): slight improvement to past construction.GPT-5.2 Thinking✓ Listed in Tao's wiki0 notes
    Partial
  15. 2026-02-27Math · Geometry
    Erdős Problem #1090Partial progress by Aristotle and Gemini 3 Flash (27 Feb 2026): proof found (Lean).Aristotle and Gemini 3 Flash✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  16. 2026-02-21Math · Geometry
    Erdős Problem #846Partial progress by DeepMind prover agent; OpenAI internal model (independently) (21 Feb 2026): full solution (Lean); 🟢 Full solution.DeepMind prover agent; OpenAI internal model (independently)✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  17. 2026-02-16Math · Number theory
    Erdős Problem #872Partial progress by GPT-5.2 Pro (16 Feb 2026): partial result. 3 AI contributions are recorded in all.GPT-5.2 Pro✓ Listed in Tao's wiki0 notes
    Partial
  18. 2026-02-14Math · Geometry
    Erdős Problem #1082Partial progress by DeepMind prover agent (14 Feb 2026): counterexample to one part (Lean).DeepMind prover agent✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  19. 2026-02-11Math · Combinatorics
    Erdős Problem #776Partial progress by Yixin He and Quanyu Tang with GPT-5.2 Thinking (11 Feb 2026): partial result.Yixin He and Quanyu Tang with GPT-5.2 Thinking✓ Listed in Tao's wiki0 notes
    Partial
  20. 2026-02-05Math · Number theory
    Erdős Problem #851Partial progress by GPT-5.2 Pro (5 Feb 2026): full solution (building upon 🟡 Romanoff (1934)).GPT-5.2 Pro✓ Listed in Tao's wiki0 notes
    Partial
  21. 2026-02-01Math · Analysis
    Erdős Problem #1040Partial progress by Aletheia (1 Feb 2026): solution to one part of problem; 🔴 incorrect solution to other part.Aletheia✓ Listed in Tao's wiki0 notes
    Partial
  22. 2026-02-01Math · Geometry
    Erdős Problem #1089Partial progress by Aletheia (1 Feb 2026): full solution found.Aletheia✓ Listed in Tao's wiki0 notes
    Partial
  23. 2026-02-01Math · Geometry
    Erdős Problem #654Partial progress by Aletheia (1 Feb 2026): partial result.Aletheia✓ Listed in Tao's wiki0 notes
    Partial
  24. 2026-02-01Math · Graph theory
    Erdős Problem #75Partial progress by Aletheia (1 Feb 2026): solution to variant problem (implicit in literature). 2 AI contributions are recorded in all.Aletheia✓ Listed in Tao's wiki0 notes
    Partial
  25. 2026-02-01Math · Number theory
    Erdős Problem #935Partial progress by Aletheia (1 Feb 2026): solution to one part of problem.Aletheia✓ Listed in Tao's wiki0 notes
    Partial
  26. 2026-01-30Math · Analysis
    Erdős Problem #524Partial progress by Gemini, GPT-5.2 and Grok (30 Jan 2026): improved partial result. 2 AI contributions are recorded in all.Gemini, GPT-5.2 and Grok✓ Listed in Tao's wiki0 notes
    Partial
  27. 2026-01-30Math · Number theory
    Erdős Problem #635Partial progress by Aristotle and GPT-5.2 Pro (30 Jan 2026): solution to one part of problem (Lean).Aristotle and GPT-5.2 Pro✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  28. 2026-01-28Math · Analysis
    Erdős Problem #1048Partial progress by Aristotle (28 Jan 2026): proof found (Lean), which is a specific case of Pommerenke.Aristotle✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  29. 2026-01-28Math · Number theory
    Erdős Problem #218Partial progress by GPT (28 Jan 2026): conditional solution.GPT✓ Listed in Tao's wiki0 notes
    Partial
  30. 2026-01-27Math · Number theory
    Erdős Problem #951Partial progress by GPT-5.2 Pro (27 Jan 2026): solution to variant problem. 3 AI contributions are recorded in all.GPT-5.2 Pro✓ Listed in Tao's wiki0 notes
    Partial
  31. 2026-01-23Math · Number theory
    Erdős Problem #783Partial progress by GPT-5.2 (23 Jan 2026): partial result.GPT-5.2✓ Listed in Tao's wiki0 notes
    Partial
  32. 2026-01-20Math · Additive combinatorics
    Erdős Problem #788Partial progress by GPT-5.2 Pro (20 Jan 2026): new partial result.GPT-5.2 Pro✓ Listed in Tao's wiki0 notes
    Partial
  33. 2026-01-19Math · Number theory
    Erdős Problem #684Partial progress by Quanyu Tang with GPT-5.2 Thinking (19 Jan 2026): partial result. 3 AI contributions are recorded in all.Quanyu Tang with GPT-5.2 Thinking✓ Listed in Tao's wiki0 notes
    Partial
  34. 2026-01-13Math · Number theory
    Erdős Problem #460Partial progress by Przemek Chojecki with GPT-5.2 (13 Jan 2026): reduction to a simpler problem.Przemek Chojecki with GPT-5.2✓ Listed in Tao's wiki0 notes
    Partial
  35. 2026-01-13Math · Number theory
    Erdős Problem #868Partial progress by GPT-5.2 multi-agent system (13 Jan 2026): new partial result.GPT-5.2 multi-agent system✓ Listed in Tao's wiki0 notes
    Partial
  36. 2026-01-12Math · Number theory
    Erdős Problem #679Partial progress by Aristotle (12 Jan 2026): improved proof by reducing dependence on prime number theorem.Aristotle✓ Listed in Tao's wiki0 notes
    Partial
  37. 2026-01-10Math · Number theory
    Erdős Problem #401Partial progress by Boris Alexeev, Kevin Barreto, Liam Price and Nat Sothanaphan with Aristotle and GPT-5.2 Pro (10 Jan 2026): full solution (Lean); solution to variant problem.Boris Alexeev, Kevin Barreto, Liam Price and Nat Sothanaphan with Aristotle and GPT-5.2 Pro✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  38. 2026-01-07Math · Number theory
    Erdős Problem #477Partial progress by AlphaProof (7 Jan 2026): solution to variant problem (Lean).AlphaProof✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  39. 2026-01-07Math · Ramsey theory
    Erdős Problem #949Partial progress by AlphaProof (7 Jan 2026): solution to variant problem (Lean).AlphaProof✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  40. 2026-01-05Math · Number theory
    Erdős Problem #871Partial progress by Claude Opus 4.5 and Gemini 3 Pro (5 Jan 2026): existing partial result upgraded to full solution (Lean).Claude Opus 4.5 and Gemini 3 Pro✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial