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 · 262 records
FieldAllMathComputer scienceBiologyPhysicsChemistry
GradeAllSolvedPartialPrior artUnverified
  1. 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
  2. 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
  3. 2026-02-01Math · Discrepancy
    Erdős Problem #992Aletheia found that the problem had already been solved in the literature (1 Feb 2026).Aletheia✓ Listed in Tao's wiki0 notes
    Prior art
  4. 2026-01-31Math · Algebra
    Erdős Problem #1123Gemini Deep Research found that the problem had already been solved in the literature (31 Jan 2026).Gemini Deep Research✓ Listed in Tao's wiki0 notes
    Prior art
  5. 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
  6. 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
  7. 2026-01-29Math · Irrationality
    Erdős Problem #1051Full solution by Aletheia, formalized in Lean (29 Jan 2026).Aletheia✓ Lean formalization · Listed in Tao's wiki0 notes
    Solved
  8. 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
  9. 2026-01-28Math · Number theory
    Erdős Problem #218Partial progress by GPT (28 Jan 2026): conditional solution.GPT✓ Listed in Tao's wiki0 notes
    Partial
  10. 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
  11. 2026-01-26Math · Irrational
    Erdős Problem #1147GPT-5.2 Thinking found that the problem had already been solved in the literature (26 Jan 2026).GPT-5.2 Thinking✓ Listed in Tao's wiki0 notes
    Prior art
  12. 2026-01-26Math · Graph theory
    Erdős Problem #533GPT found that the problem had already been solved in the literature (26 Jan 2026).GPT✓ Listed in Tao's wiki0 notes
    Prior art
  13. 2026-01-26Math · Graph theory
    Erdős Problem #705GPT found that the problem had already been solved in the literature (26 Jan 2026). 2 AI contributions are recorded in all.GPT✓ Listed in Tao's wiki0 notes
    Prior art
  14. 2026-01-24Math · Group theory
    Erdős Problem #1161GPT-5.2 Thinking found that the problem had already been solved in the literature (24 Jan 2026).GPT-5.2 Thinking✓ Listed in Tao's wiki0 notes
    Prior art
  15. 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
  16. 2026-01-21Math · Analysis
    Erdős Problem #1047Aristotle found a new proof of a problem that was already solved (21 Jan 2026).Aristotle✓ Lean formalization · Listed in Tao's wiki0 notes
    Prior art
  17. 2026-01-21Math · Number theory
    Erdős Problem #543Full solution by GPT-5.2 Pro (21 Jan 2026).GPT-5.2 Pro✓ Listed in Tao's wiki0 notes
    Solved
  18. 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
  19. 2026-01-19Math · Graph theory
    Erdős Problem #1007Aristotle found a new proof of a problem that was already solved (19 Jan 2026).Aristotle✓ Lean formalization · Listed in Tao's wiki0 notes
    Prior art
  20. 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
  21. 2026-01-19Math · Additive combinatorics
    Erdős Problem #847GPT-5.2 Pro found that the problem had already been solved in the literature (19 Jan 2026).GPT-5.2 Pro✓ Listed in Tao's wiki0 notes
    Prior art
  22. 2026-01-17Math · Analysis
    Erdős Problem #1129GPT-5.2 Pro found that the problem had already been solved in the literature (17 Jan 2026).GPT-5.2 Pro✓ Listed in Tao's wiki0 notes
    Prior art
  23. 2026-01-17Math · Analysis
    Erdős Problem #1130GPT-5.2 Pro found that the problem had already been solved in the literature (17 Jan 2026).GPT-5.2 Pro✓ Listed in Tao's wiki0 notes
    Prior art
  24. 2026-01-17Math · Number theory
    Erdős Problem #281GPT-5.2 Pro produced a solution (17 Jan 2026); the problem turned out to have been solved already, by a different argument: Davenport and Erdős (1936) + Rogers (in Halberstam-Roth (1966)).GPT-5.2 Pro✓ Listed in Tao's wiki0 notes
    Prior art
  25. 2026-01-17Math · Set theory
    Erdős Problem #591ChatGPT Deep research found that the problem had already been solved in the literature (17 Jan 2026). 2 AI contributions are recorded in all.ChatGPT Deep research✓ Listed in Tao's wiki0 notes
    Prior art
  26. 2026-01-14Math · Geometry
    Erdős Problem #224Codex and GPT-5.2 Thinking found a new proof of a problem that was already solved (14 Jan 2026).Codex and GPT-5.2 Thinking✓ Lean formalization · Listed in Tao's wiki0 notes
    Prior art
  27. 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
  28. 2026-01-13Math · Geometry
    Erdős Problem #659Full solution by Benjamin Grayzel with Gemini 3 (13 Jan 2026). 2 AI contributions are recorded in all.Benjamin Grayzel with Gemini 3✓ Listed in Tao's wiki0 notes
    Solved
  29. 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
  30. 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
  31. 2026-01-10Math · Number theory
    Erdős Problem #205Full solution by Aristotle and GPT-5.2 Thinking, formalized in Lean (10 Jan 2026).Aristotle and GPT-5.2 Thinking✓ Lean formalization · Listed in Tao's wiki0 notes
    Solved
  32. 2026-01-10Math · Number theory
    Erdős Problem #397Aristotle and GPT-5.2 Pro produced a solution (10 Jan 2026), but a comparable result was already in the literature: China TST competition (2012). 3 AI contributions are recorded in all.Aristotle and GPT-5.2 Pro✓ Lean formalization · Listed in Tao's wiki0 notes
    Prior art
  33. 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
  34. 2026-01-08Math · Number theory
    Erdős Problem #729Full solution by Aristotle and GPT-5.2 Pro, formalized in Lean (8 Jan 2026).Aristotle and GPT-5.2 Pro✓ Lean formalization · Listed in Tao's wiki0 notes
    Solved
  35. 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
  36. 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
  37. 2026-01-06Math · Number theory
    Erdős Problem #728Full solution by Aristotle and GPT-5.2 Pro, formalized in Lean (6 Jan 2026).Aristotle and GPT-5.2 Pro✓ Lean formalization · Listed in Tao's wiki0 notes
    Solved
  38. 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
  39. 2026-01-02Math · Ramsey theory
    Erdős Problem #965GPT found that the problem had already been solved in the literature (2 Jan 2026).GPT✓ Listed in Tao's wiki0 notes
    Prior art
  40. 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