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 · 118 of 262 records
FieldAllMathComputer scienceBiologyPhysicsChemistry
GradeAllSolvedPartialPrior artUnverified
  1. 2026-08-20Math · Arithmetic geometry
    Elliptic curves over ℚ of rank at least 30 and 31Claude, working with Levent Alpöge and Ava Howell, found elliptic curves over ℚ with at least 30 and then 31 independent rational points, beating the record of 29 set in 2024.Claude (Anthropic) with Levent Alpöge and Ava Howell✓ Rank ≥ 31 curve verified by ICARM (2026-09-25) · Marked solved (human + AI) by Epoch AI0 notes
    Partial
  2. 2026-07-26Math · Combinatorics
    Shorter superpermutations on 8, 9 and 10 symbolsNew superpermutations shorter than Egan's 2018 bound were posted for 8, 9 and 10 symbols; those for 9 and 10 were developed interactively with GPT-5.6 Sol, which then retrieved them to pass Epoch AI's verifier.William Echols with GPT-5.6 Sol (n = 9, 10); Uku Raudvere (n = 8)✓ Passed Epoch AI's verifier0 notes
    Partial
  3. 2026-06-29Math · Geometry
    Erdős Problem #1070Partial progress by Ákos Dúcz and Dániel Varga with Codex and GPT-5.5 (29 Jun 2026): partial result.Ákos Dúcz and Dániel Varga with Codex and GPT-5.5✓ Listed in Tao's wiki0 notes
    Partial
  4. 2026-06-23Math · Combinatorics
    Erdős Problem #21Partial progress by Varun Sivashankar with Aristotle and GPT-5.5 Pro (23 Jun 2026): partial result (Lean).Varun Sivashankar with Aristotle and GPT-5.5 Pro✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  5. 2026-06-22Math · Number theory
    Erdős Problem #1054Partial progress by Claude Opus 4.8, GPT-5.5 Pro and Principia Math (22 Jun 2026): partial result (Lean).Claude Opus 4.8, GPT-5.5 Pro and Principia Math✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  6. 2026-06-22Math · Number theory
    Erdős Problem #536Partial progress by Codex and GPT-5.5 Pro (22 Jun 2026): partial result (Lean).Codex and GPT-5.5 Pro✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  7. 2026-06-21Math · Additive combinatorics
    Erdős Problem #176Partial progress by Codex and GPT-5.5 Pro (21 Jun 2026): partial result (Lean). 2 AI contributions are recorded in all.Codex and GPT-5.5 Pro✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  8. 2026-06-19Math · Number theory
    Erdős Problem #451Partial progress by Wouter van Doorn and Quanyu Tang with Aristotle and GPT-5.5 Pro (19 Jun 2026): partial result (Lean).Wouter van Doorn and Quanyu Tang with Aristotle and GPT-5.5 Pro✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  9. 2026-06-19Math · Graph theory
    Erdős Problem #81Partial progress by Wouter van Doorn with Aristotle and GPT-5.5 Pro (19 Jun 2026): partial result (Lean).Wouter van Doorn with Aristotle and GPT-5.5 Pro✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  10. 2026-06-17Math · Number theory
    Erdős Problem #306Partial progress by Shisheng Li with Claude and Claude Code (17 Jun 2026): partial result (Lean). 2 AI contributions are recorded in all.Shisheng Li with Claude and Claude Code✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  11. 2026-06-10Math · Number theory
    Erdős Problem #539Partial progress by Codex, GPT-5.5 and ProofCouncil (10 Jun 2026): partial result (Lean).Codex, GPT-5.5 and ProofCouncil✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  12. 2026-06-08Math · Number theory
    Erdős Problem #931Partial progress by Adenwalla and Malek Zribi with Claude and GPT-5.4 (8 Jun 2026): partial result.Adenwalla and Malek Zribi with Claude and GPT-5.4✓ Listed in Tao's wiki0 notes
    Partial
  13. 2026-05-29Math · Geometry
    Erdős Problem #352Partial progress by Aleksandar Bulj and Vjekoslav Kovač with GPT-5.4 Pro and GPT-5.5 Pro (29 May 2026): partial result of variant problem.Aleksandar Bulj and Vjekoslav Kovač with GPT-5.4 Pro and GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Partial
  14. 2026-05-28Math · Number theory
    Erdős Problem #52Partial progress by Thomas Bloom, Will Sawin, Carl Schildkraut and Dmitrii Zhelezov with GPT-5.5 Pro (28 May 2026): solution to variant problem. 4 AI contributions are recorded in all.Thomas Bloom, Will Sawin, Carl Schildkraut and Dmitrii Zhelezov with GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Partial
  15. 2026-05-27Math · Geometry
    Erdős Problem #503Partial progress by Przemek Chojecki, Junnosuke Koizumi and RealBelgian with GPT-5.5 Pro (27 May 2026): partial result.Przemek Chojecki, Junnosuke Koizumi and RealBelgian with GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Partial
  16. 2026-05-16Math · Number theory
    Erdős Problem #345Partial progress by Wouter van Doorn with Aristotle and GPT (16 May 2026): partial result (Lean).Wouter van Doorn with Aristotle and GPT✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  17. 2026-05-09Math · Irrationality
    Erdős Problem #263Partial progress by Aristotle, Claude Opus 4.7 and GPT-5.5 Pro (9 May 2026): partial result (Lean) (solution to second part).Aristotle, Claude Opus 4.7 and GPT-5.5 Pro✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  18. 2026-05-07Math · Graph theory
    Erdős Problem #1032Partial progress by Codex and GPT-5.5 Pro (7 May 2026): improved partial result (Lean).Codex and GPT-5.5 Pro✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  19. 2026-05-07Math · Additive combinatorics
    Erdős Problem #875Partial progress by Lech Mazur with Codex and GPT-5.5 Pro (7 May 2026): partial result (Lean).Lech Mazur with Codex and GPT-5.5 Pro✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  20. 2026-05-04Math · Number theory
    Erdős Problem #866Partial progress by Wouter van Doorn with Aristotle and GPT-5.3 Instant (4 May 2026): partial result (Lean).Wouter van Doorn with Aristotle and GPT-5.3 Instant✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  21. 2026-05-03Math · Number theory
    Erdős Problem #393Partial progress by David Turturean with GPT-5.5 Pro (3 May 2026): conditional partial result.David Turturean with GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Partial
  22. 2026-04-30Math · Number theory
    Erdős Problem #983Partial progress by GPT-5.5 Pro (30 Apr 2026): partial result (solution to first part).GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Partial
  23. 2026-04-29Math · Number theory
    Erdős Problem #1004Partial progress by GPT-5.5 Pro (29 Apr 2026): partial result (implicit in literature).GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Partial
  24. 2026-04-29Math · Number theory
    Erdős Problem #1143Partial progress by Przemek Chojecki with GPT-5.5 Pro (29 Apr 2026): partial result (implicit in literature).Przemek Chojecki with GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Partial
  25. 2026-04-27Math · Number theory
    Erdős Problem #535Partial progress by Kireet Cheri, Sourish Kumrawat and Hrishi Sunder with GPT-5.5 Thinking (27 Apr 2026): partial result (implicit in literature).Kireet Cheri, Sourish Kumrawat and Hrishi Sunder with GPT-5.5 Thinking✓ Listed in Tao's wiki0 notes
    Partial
  26. 2026-04-25Math · Analysis
    Erdős Problem #521Partial progress by Vjekoslav Kovač with GPT-5.5 Pro (25 Apr 2026): solution to variant problem. 2 AI contributions are recorded in all.Vjekoslav Kovač with GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Partial
  27. 2026-04-23Math · Additive combinatorics
    Erdős Problem #1194Partial progress by GPT-5.4 Pro (23 Apr 2026): partial result. 2 AI contributions are recorded in all.GPT-5.4 Pro✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  28. 2026-04-21Math · Graph theory
    Erdős Problem #610Partial progress by Przemek Chojecki with Aristotle and GPT-5.4 Pro (21 Apr 2026): full solution (Lean) (implicit in literature).Przemek Chojecki with Aristotle and GPT-5.4 Pro✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  29. 2026-04-21Math · Analysis
    Erdős Problem #995Partial progress by Boon Suan Ho with GPT-5.4 Pro (21 Apr 2026): partial result.Boon Suan Ho with GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Partial
  30. 2026-04-20Math · Analysis
    Erdős Problem #514Partial progress by Przemek Chojecki with GPT-5.4 Pro (20 Apr 2026): partial result (solutions to first part and second part). 2 AI contributions are recorded in all.Przemek Chojecki with GPT-5.4 Pro✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  31. 2026-04-19Math · Number theory
    Erdős Problem #1062Partial progress by Damek Davis with GPT-5.4 Pro (19 Apr 2026): partial result.Damek Davis with GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Partial
  32. 2026-04-19Math · Number theory
    Erdős Problem #415Partial progress by Przemek Chojecki with GPT-5.4 Pro (19 Apr 2026): partial result.Przemek Chojecki with GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Partial
  33. 2026-04-18Math · Number theory
    Erdős Problem #675Partial progress by Boon Suan Ho with GPT-5.4 Pro (18 Apr 2026): partial result.Boon Suan Ho with GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Partial
  34. 2026-04-16Math · Number theory
    Erdős Problem #976Partial progress by Aron Bhalla with GPT-5.4 (16 Apr 2026): conditional partial result.Aron Bhalla with GPT-5.4✓ Listed in Tao's wiki0 notes
    Partial
  35. 2026-04-15Math · Number theory
    Erdős Problem #1209Partial progress by Enrique Barschkis with GPT-5.4 Pro (15 Apr 2026): partial result (Lean).Enrique Barschkis with GPT-5.4 Pro✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  36. 2026-04-15Math · Number theory
    Erdős Problem #251Partial progress by GPT-5.4 Pro (15 Apr 2026): solution to variant problem.GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Partial
  37. 2026-04-15Math · Number theory
    Erdős Problem #852Partial progress by Aron Bhalla with GPT-5.4 (15 Apr 2026): partial result. 2 AI contributions are recorded in all.Aron Bhalla with GPT-5.4✓ Listed in Tao's wiki0 notes
    Partial
  38. 2026-04-14Math · Number theory
    Erdős Problem #366Partial progress by Automated research pipeline (14 Apr 2026): conditional partial result.Automated research pipeline✓ Listed in Tao's wiki0 notes
    Partial
  39. 2026-04-10Math · Additive combinatorics
    Erdős Problem #138Partial progress by DeepMind prover agent (10 Apr 2026): partial result (Lean). 2 AI contributions are recorded in all.DeepMind prover agent✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  40. 2026-04-07Math · Number theory
    Erdős Problem #12Partial progress by DeepMind prover agent (7 Apr 2026): partial result (Lean) (solutions to first part and second part). 2 AI contributions are recorded in all.DeepMind prover agent✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial