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 · 61 of 262 records
FieldAllMathComputer scienceBiologyPhysicsChemistry
GradeAllSolvedPartialPrior artUnverified
  1. 2026-08-12Math · Combinatorics
    A Hadamard matrix of order 668Anthropic researcher Levent Alpöge posted Hadamard matrices for every order up to 2000 where none was known, including 668, found by three people working with Claude; an independent check confirmed the matrix, but the method is unpublished.Claude (Anthropic) with three human researchers✓ Matrix checked independently (Nechita, 2026-08-13) · Marked solved by Epoch AI (provisional)0 notes
    Solved
  2. 2026-06-21Math · Analysis
    Erdős Problem #1197Full solution by Aristotle, Claude Opus 4.7 and GPT-5.4 Pro, formalized in Lean (21 Jun 2026).Aristotle, Claude Opus 4.7 and GPT-5.4 Pro✓ Lean formalization · Listed in Tao's wiki0 notes
    Solved
  3. 2026-06-21Math · Number theory
    Erdős Problem #346Full solution by Kenta Kitamura with Codex and GPT, formalized in Lean (21 Jun 2026). 2 AI contributions are recorded in all.Kenta Kitamura with Codex and GPT✓ Lean formalization · Listed in Tao's wiki0 notes
    Solved
  4. 2026-06-21Math · Number theory
    Erdős Problem #865Full solution by Ricky Cipollini with GPT-5.5 Pro (21 Jun 2026).Ricky Cipollini with GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Solved
  5. 2026-06-21Math · Number theory
    Erdős Problem #948Full solution by Aristotle and GPT-5.5 Pro, formalized in Lean (21 Jun 2026).Aristotle and GPT-5.5 Pro✓ Lean formalization · Listed in Tao's wiki0 notes
    Solved
  6. 2026-06-16Math · Graph theory
    Erdős Problem #986Full solution by Domagoj Bradač with Claude and OpenAI internal model (16 Jun 2026).Domagoj Bradač with Claude and OpenAI internal model✓ Listed in Tao's wiki0 notes
    Solved
  7. 2026-06-14Math · Number theory
    Erdős Problem #326Full solution by Aron Bhalla with Aristotle, Codex and GPT-5.5, formalized in Lean (14 Jun 2026).Aron Bhalla with Aristotle, Codex and GPT-5.5✓ Lean formalization · Listed in Tao's wiki0 notes
    Solved
  8. 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
  9. 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
  10. 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
  11. 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
  12. 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
  13. 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
  14. 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
  15. 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
  16. 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
  17. 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
  18. 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
  19. 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
  20. 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
  21. 2026-04-26Math · Number theory
    Erdős Problem #896Full solution by Przemek Chojecki with GPT-5.5 Pro (26 Apr 2026).Przemek Chojecki with GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Solved
  22. 2026-04-25Math · Number theory
    Erdős Problem #1138Full solution by Kireet Cheri, Sourish Kumrawat and Hrishi Sunder with GPT-5.5 Pro and GPT-5.5 Thinking (25 Apr 2026).Kireet Cheri, Sourish Kumrawat and Hrishi Sunder with GPT-5.5 Pro and GPT-5.5 Thinking✓ Listed in Tao's wiki0 notes
    Solved
  23. 2026-04-25Math · Number theory
    Erdős Problem #38Full solution by GPT-5.5 Pro (25 Apr 2026).GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Solved
  24. 2026-04-25Math · Number theory
    Erdős Problem #888Full solution by Przemek Chojecki with Aristotle and GPT-5.5 Pro (25 Apr 2026).Przemek Chojecki with Aristotle and GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Solved
  25. 2026-04-24Math · Number theory
    Erdős Problem #330Full solution by David Turturean with GPT-5.5 Pro (24 Apr 2026).David Turturean with GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Solved
  26. 2026-04-23Math · Graph theory
    Erdős Problem #1014Full solution by OpenAI internal model (23 Apr 2026).OpenAI internal model✓ Listed in Tao's wiki0 notes
    Solved
  27. 2026-04-23Math · Number theory
    Erdős Problem #1190Full solution by Boon Suan Ho with GPT-5.4 Pro (23 Apr 2026). 2 AI contributions are recorded in all.Boon Suan Ho with GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Solved
  28. 2026-04-23Math · Covering systems
    Erdős Problem #202Full solution by Boon Suan Ho with GPT-5.4 Pro (23 Apr 2026). 2 AI contributions are recorded in all.Boon Suan Ho with GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Solved
  29. 2026-04-22Math · Number theory
    Erdős Problem #863Full solution by Boon Suan Ho with GPT-5.4 Pro (22 Apr 2026).Boon Suan Ho with GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Solved
  30. 2026-04-21Math · Combinatorics
    Erdős Problem #603Full solution by Przemek Chojecki with GPT-5.4 Pro (21 Apr 2026).Przemek Chojecki with GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Solved
  31. 2026-04-21Math · Analysis
    Erdős Problem #996Full solution by Boon Suan Ho with GPT-5.4 Pro (21 Apr 2026).Boon Suan Ho with GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Solved
  32. 2026-04-19Math · Number theory
    Erdős Problem #1195Full solution by Boon Suan Ho with GPT-5.4 Pro (19 Apr 2026).Boon Suan Ho with GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Solved
  33. 2026-04-16Math · Number theory
    Erdős Problem #1217Full solution by GPT-5.4 Pro (16 Apr 2026).GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Solved
  34. 2026-04-16Math · Additive combinatorics
    Erdős Problem #741Full solution by DeepMind prover agent, formalized in Lean (16 Apr 2026). 3 AI contributions are recorded in all.DeepMind prover agent✓ Lean formalization · Listed in Tao's wiki0 notes
    Solved
  35. 2026-04-15Math · Number theory
    Erdős Problem #858Full solution by Przemek Chojecki with GPT-5.4 Pro (15 Apr 2026).Przemek Chojecki with GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Solved
  36. 2026-04-14Math · Irrationality
    Erdős Problem #258Full solution by GPT-5.4 Pro (14 Apr 2026).GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Solved
  37. 2026-04-13Math · Number theory
    Erdős Problem #1196Full solution by GPT-5.4 Pro (13 Apr 2026). 2 AI contributions are recorded in all.GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Solved
  38. 2026-04-09Math · Chromatic number
    Erdős Problem #1091Full solution by OpenAI internal model (9 Apr 2026).OpenAI internal model✓ Listed in Tao's wiki0 notes
    Solved
  39. 2026-04-09Math · Number theory
    Erdős Problem #1141Full solution by OpenAI internal model (9 Apr 2026). 2 AI contributions are recorded in all.OpenAI internal model✓ Listed in Tao's wiki0 notes
    Solved
  40. 2026-04-09Math · Geometry
    Erdős Problem #960Full solution by OpenAI internal model (9 Apr 2026).OpenAI internal model✓ Listed in Tao's wiki0 notes
    Solved