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. 2026-06-09Math · Graph theory
    Erdős Problem #619Full solution by Claude Fable 5, Codex and GPT-5.5, formalized in Lean (9 Jun 2026).Claude Fable 5, Codex and GPT-5.5✓ Lean formalization · Listed in Tao's wiki0 notes
    Solved
  2. 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
  3. 2026-06-05Math · Number theory
    Erdős Problem #696Full solution by Jake Mallen and David Turturean with Aristotle, Claude Code, Claude Opus 4.7 and GPT-5.5 Pro, formalized in Lean (5 Jun 2026).Jake Mallen and David Turturean with Aristotle, Claude Code, Claude Opus 4.7 and GPT-5.5 Pro✓ Lean formalization · Listed in Tao's wiki0 notes
    Solved
  4. 2026-06-04Math · Set theory
    Erdős Problem #623A claim by Sungchul Lee with GPT-5.5 Pro (4 Jun 2026) that has not yet been verified: candidate full solution.Sungchul Lee with GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Unverified
  5. 2026-06-01Math · Combinatorics
    Erdős Problem #501A claim by Sungchul Lee with GPT-5.5 Pro (1 Jun 2026) that has not yet been verified: candidate conditional partial result (conditional solution to first part).Sungchul Lee with GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Unverified
  6. 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
  7. 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
  8. 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
  9. 2026-05-21Math · Formal proof search
    AlphaProof Nexus: Lean-checked proofs of open Erdős problems and OEIS conjecturesGoogle DeepMind's AlphaProof Nexus autonomously proved 9 of 353 open Erdős problems (several as variants or parts) and 44 of 492 OEIS conjectures, all checked in Lean; the work was published in Science in October 2026.AlphaProof Nexus (Google DeepMind)✓ Lean 4 proofs, build instructions public · Published in Science (2026-10-08)0 notes
    Solved
  10. 2026-05-20Math · Geometry
    Erdős Problem #90Full solution by OpenAI internal model (20 May 2026). 3 AI contributions are recorded in all.OpenAI internal model✓ Listed in Tao's wiki0 notes
    Solved
  11. 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
  12. 2026-05-15Math · Additive combinatorics
    Erdős Problem #819A claim by Yu Leon Liu with GPT-5.5 and Rethlas (15 May 2026) that has not yet been verified: candidate partial result.Yu Leon Liu with GPT-5.5 and Rethlas✓ Listed in Tao's wiki0 notes
    Unverified
  13. 2026-05-13Math · Number theory
    Erdős Problem #327A claim by Yu Leon Liu with GPT-5.5 and Rethlas (13 May 2026) that has not yet been verified: candidate partial result.Yu Leon Liu with GPT-5.5 and Rethlas✓ Listed in Tao's wiki0 notes
    Unverified
  14. 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
  15. 2026-05-08Math · Number theory
    Erdős Problem #690Full solution by Davide Crapis and Shouqiao Wang with Multiscalar Fields System (8 May 2026).Davide Crapis and Shouqiao Wang with Multiscalar Fields System✓ Listed in Tao's wiki0 notes
    Solved
  16. 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
  17. 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
  18. 2026-05-04Math · Number theory
    Erdős Problem #456A claim by David Turturean with GPT-5.5 Pro (4 May 2026) that has not yet been verified: candidate partial result (solutions to first part and second part; conditional solution to third part).David Turturean with GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Unverified
  19. 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
  20. 2026-05-03Math · Number theory
    Erdős Problem #283Full solution by Kevin Barreto and Liam Price with GPT-5.5 Pro (3 May 2026).Kevin Barreto and Liam Price with GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Solved
  21. 2026-05-03Math · Number theory
    Erdős Problem #288A claim by Ritvik Nayak with GPT-5.5 Thinking (3 May 2026) that has not yet been verified: candidate partial result.Ritvik Nayak with GPT-5.5 Thinking✓ Listed in Tao's wiki0 notes
    Unverified
  22. 2026-05-03Math · Number theory
    Erdős Problem #351Full solution by Kevin Barreto and Liam Price with GPT-5.5 Pro (3 May 2026).Kevin Barreto and Liam Price with GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Solved
  23. 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
  24. 2026-05-03Math · Graph theory
    Erdős Problem #750Full solution by Przemek Chojecki with GPT-5.5 Pro (3 May 2026).Przemek Chojecki with GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Solved
  25. 2026-05-02Math · Number theory
    Erdős Problem #390A claim by Samuel Mausberg with GPT-5.5 Pro (2 May 2026) that has not yet been verified: candidate partial result.Samuel Mausberg with GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Unverified
  26. 2026-05-02Math · Number theory
    Erdős Problem #870A claim by David Turturean with GPT-5.4 Pro and GPT-5.5 Pro (2 May 2026) that has not yet been verified: candidate full solution.David Turturean with GPT-5.4 Pro and GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Unverified
  27. 2026-05-01Math · Number theory
    Erdős Problem #694Full solution by GPT-5.5 Pro (1 May 2026).GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Solved
  28. 2026-04-30Math · Analysis
    Erdős Problem #1151Full solution by Przemek Chojecki with GPT-5.5 Pro (30 Apr 2026).Przemek Chojecki with GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Solved
  29. 2026-04-30Math · Number theory
    Erdős Problem #1201A claim by Przemek Chojecki with GPT-5.5 Pro (30 Apr 2026) that has not yet been verified: candidate full solution.Przemek Chojecki with GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Unverified
  30. 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
  31. 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
  32. 2026-04-29Math · Analysis
    Erdős Problem #1133A claim by Przemek Chojecki with GPT-5.5 Pro (29 Apr 2026) that has not yet been verified: candidate full solution.Przemek Chojecki with GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Unverified
  33. 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
  34. 2026-04-29Math · Number theory
    Erdős Problem #873A claim by Ritvik Nayak with GPT-5.4 Thinking (29 Apr 2026) that has not yet been verified: candidate partial result. 2 AI contributions are recorded in all.Ritvik Nayak with GPT-5.4 Thinking✓ Listed in Tao's wiki0 notes
    Unverified
  35. 2026-04-28Math · Chromatic number
    Erdős Problem #1092Full solution by Przemek Chojecki with GPT-5.5 Pro (28 Apr 2026).Przemek Chojecki with GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Solved
  36. 2026-04-27Math · Number theory
    Erdős Problem #1101A claim by GPT-5.5 Pro (27 Apr 2026) that has not yet been verified: candidate partial result (solution to second part).GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Unverified
  37. 2026-04-27Math · Number theory
    Erdős Problem #42Full solution by Harjas Sandhu with GPT-5.5 Pro (27 Apr 2026). 2 AI contributions are recorded in all.Harjas Sandhu with GPT-5.5 Pro✓ Lean formalization · Listed in Tao's wiki0 notes
    Solved
  38. 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
  39. 2026-04-27Math · Graph theory
    Erdős Problem #836A claim by GPT-5.5 Pro (27 Apr 2026) that has not yet been verified: candidate partial result (solution to second part).GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Unverified
  40. 2026-04-27Math · Geometry
    Erdős Problem #953Full solution by Przemek Chojecki with GPT-5.5 Pro (27 Apr 2026).Przemek Chojecki with GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Solved