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 · 42 of 262 records
FieldAllMathComputer scienceBiologyPhysicsChemistry
GradeAllSolvedPartialPrior artUnverified
  1. 2026-07-30Math · Arithmetic geometry
    A 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.GPT-5.6 Sol (OpenAI)✓ Passed Epoch AI's verifier0 notes
    Prior art
  2. 2026-04-06Math · Number theory
    Erdős Problem #26DeepMind prover agent produced a solution (6 Apr 2026), but a comparable result was already in the literature: Ruzsa.DeepMind prover agent✓ Listed in Tao's wiki0 notes
    Prior art
  3. 2026-03-28Math · Graph theory
    Erdős Problem #574GPT-5.4 Pro found that the problem had already been solved in the literature (28 Mar 2026).GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Prior art
  4. 2026-03-06Math · Number theory
    Erdős Problem #650ChatGPT Deep research found that the problem had already been solved in the literature (6 Mar 2026). 2 AI contributions are recorded in all.ChatGPT Deep research✓ Listed in Tao's wiki0 notes
    Prior art
  5. 2026-02-25Math · Number theory
    Erdős Problem #966Aristotle produced a solution (25 Feb 2026), but a comparable result was already in the literature: Spencer (unpublished).Aristotle✓ Lean formalization · Listed in Tao's wiki0 notes
    Prior art
  6. 2026-02-01Math · Graph theory
    Erdős Problem #1105Aletheia found that the problem had already been solved in the literature (1 Feb 2026).Aletheia✓ Listed in Tao's wiki0 notes
    Prior art
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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
  12. 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
  13. 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
  14. 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
  15. 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
  16. 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
  17. 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
  18. 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
  19. 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
  20. 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
  21. 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
  22. 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
  23. 2025-12-27Math · Distances
    Erdős Problem #958Aristotle found a new proof of a problem that was already solved (27 Dec 2025).Aristotle✓ Lean formalization · Listed in Tao's wiki0 notes
    Prior art
  24. 2025-12-26Math · Number theory
    Erdős Problem #897Archivara and Aristotle produced a solution (26 Dec 2025), but a comparable result was already in the literature: Wirsing (1981).Archivara and Aristotle✓ Lean formalization · Listed in Tao's wiki0 notes
    Prior art
  25. 2025-12-25Math · Number theory
    Erdős Problem #333Claude Opus 4.5 and GPT-5.2 Pro produced a solution (25 Dec 2025), but a comparable result was already in the literature: Erdős and Newman (1977). 2 AI contributions are recorded in all.Claude Opus 4.5 and GPT-5.2 Pro✓ Lean formalization · Listed in Tao's wiki0 notes
    Prior art
  26. 2025-12-21Math · Number theory
    Erdős Problem #379Seed Prover 1.5 found a new proof of a problem that was already solved (21 Dec 2025).Seed Prover 1.5✓ Listed in Tao's wiki0 notes
    Prior art
  27. 2025-12-03Math · Number theory
    Erdős Problem #481GPT found that the problem had already been solved in the literature (3 Dec 2025).GPT✓ Listed in Tao's wiki0 notes
    Prior art
  28. 2025-11-02Math · Geometry
    Erdős Problem #94GPT-5 found that the problem had already been solved in the literature (2 Nov 2025).GPT-5✓ Listed in Tao's wiki0 notes
    Prior art
  29. 2025-10-20Math · Number theory
    Erdős Problem #645GPT-5 found that the problem had already been solved in the literature (20 Oct 2025).GPT-5✓ Listed in Tao's wiki0 notes
    Prior art
  30. 2025-10-19Math · Number theory
    Erdős Problem #1099ChatGPT Deep research, Gemini and Gemini Deep Research found that the problem had already been solved in the literature (19 Oct 2025).ChatGPT Deep research, Gemini and Gemini Deep Research✓ Listed in Tao's wiki0 notes
    Prior art
  31. 2025-10-15Math · Analysis
    Erdős Problem #515GPT-5 found that the problem had already been solved in the literature (15 Oct 2025).GPT-5✓ Listed in Tao's wiki0 notes
    Prior art
  32. 2025-10-14Math · Combinatorics
    Erdős Problem #903GPT-5 found that the problem had already been solved in the literature (14 Oct 2025).GPT-5✓ Listed in Tao's wiki0 notes
    Prior art
  33. 2025-10-13Math · Graph theory
    Erdős Problem #1079GPT-5 found that the problem had already been solved in the literature (13 Oct 2025).GPT-5✓ Listed in Tao's wiki0 notes
    Prior art
  34. 2025-10-13Math · Geometry
    Erdős Problem #223GPT-5 found that the problem had already been solved in the literature (13 Oct 2025).GPT-5✓ Listed in Tao's wiki0 notes
    Prior art
  35. 2025-10-13Math · Analysis
    Erdős Problem #494GPT-5 found that the problem had already been solved in the literature (13 Oct 2025).GPT-5✓ Listed in Tao's wiki0 notes
    Prior art
  36. 2025-10-13Math · Graph theory
    Erdős Problem #621GPT-5 found that the problem had already been solved in the literature (13 Oct 2025).GPT-5✓ Listed in Tao's wiki0 notes
    Prior art
  37. 2025-10-13Math · Number theory
    Erdős Problem #822GPT-5 found that the problem had already been solved in the literature (13 Oct 2025).GPT-5✓ Listed in Tao's wiki0 notes
    Prior art
  38. 2025-10-12Math · Analysis
    Erdős Problem #1043GPT-5 found that the problem had already been solved in the literature (12 Oct 2025). 3 AI contributions are recorded in all.GPT-5✓ Lean formalization · Listed in Tao's wiki0 notes
    Prior art
  39. 2025-10-11Math · Number theory
    Erdős Problem #339GPT-5 found that the problem had already been solved in the literature (11 Oct 2025).GPT-5✓ Listed in Tao's wiki0 notes
    Prior art
  40. 2025-09-30Math · Graph theory
    Erdős Problem #737GPT-5 found that the problem had already been solved in the literature (30 Sep 2025).GPT-5✓ Listed in Tao's wiki0 notes
    Prior art