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. 2026-04-09Math · Analysis
    Erdős Problem #990Full solution by OpenAI internal model (9 Apr 2026).OpenAI internal model✓ Listed in Tao's wiki0 notes
    Solved
  2. 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
  3. 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
  4. 2026-04-04Math · Graph theory
    Erdős Problem #629Partial progress by Gemini 3.1 Pro and GPT-5.4 Thinking (4 Apr 2026): partial result.Gemini 3.1 Pro and GPT-5.4 Thinking✓ Listed in Tao's wiki0 notes
    Partial
  5. 2026-04-04Math · Additive combinatorics
    Erdős Problem #749Partial progress by Aron Bhalla with GPT-5.4 Thinking (4 Apr 2026): partial result; 🟡 Solution to variant problem.Aron Bhalla with GPT-5.4 Thinking✓ Listed in Tao's wiki0 notes
    Partial
  6. 2026-04-03Math · Sidon sets
    Erdős Problem #152Full solution by DeepMind prover agent, formalized in Lean (3 Apr 2026).DeepMind prover agent✓ Lean formalization · Listed in Tao's wiki0 notes
    Solved
  7. 2026-04-01Math · Number theory
    Erdős Problem #1202Full solution by GPT-5.4 Pro (1 Apr 2026).GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Solved
  8. 2026-03-31Math · Number theory
    Erdős Problem #374Partial progress by Terence Tao with GPT-5.4 Pro (31 Mar 2026): partial result.Terence Tao with GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Partial
  9. 2026-03-31Math · Number theory
    Erdős Problem #380Full solution by Terence Tao with GPT-5.4 Pro (31 Mar 2026).Terence Tao with GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Solved
  10. 2026-03-31Math · Analysis
    Erdős Problem #997Full solution by OpenAI internal model (31 Mar 2026).OpenAI internal model✓ Listed in Tao's wiki0 notes
    Solved
  11. 2026-03-30Math · Number theory
    Erdős Problem #125Full solution by DeepMind prover agent, formalized in Lean (30 Mar 2026). 2 AI contributions are recorded in all.DeepMind prover agent✓ Lean formalization · Listed in Tao's wiki0 notes
    Solved
  12. 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
  13. 2026-03-26Math · Number theory
    Erdős Problem #369Full solution by Sky Yang with GPT (26 Mar 2026).Sky Yang with GPT✓ Listed in Tao's wiki0 notes
    Solved
  14. 2026-03-24Math · Analysis
    Erdős Problem #1132Partial progress by Terence Tao with AlphaEvolve, Claude, Gemini Pro and GPT-5.4 Pro (24 Mar 2026): partial result.Terence Tao with AlphaEvolve, Claude, Gemini Pro and GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Partial
  15. 2026-03-24Math · Analysis
    Erdős Problem #1153Full solution by Aron Bhalla, Nat Sothanaphan and Terence Tao with AlphaEvolve, Claude, Gemini Pro, GPT-5.2 Thinking and GPT-5.4 Pro (24 Mar 2026).Aron Bhalla, Nat Sothanaphan and Terence Tao with AlphaEvolve, Claude, Gemini Pro, GPT-5.2 Thinking and GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Solved
  16. 2026-03-23Math · Number theory
    Erdős Problem #342Partial progress by Przemek Chojecki with GPT-5.2 Pro and GPT-5.4 Pro (23 Mar 2026): partial result.Przemek Chojecki with GPT-5.2 Pro and GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Partial
  17. 2026-03-19Math · Number theory
    Erdős Problem #25Partial progress by Przemek Chojecki with GPT-5.4 Pro (19 Mar 2026): partial result.Przemek Chojecki with GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Partial
  18. 2026-03-18Math · Combinatorics
    Erdős Problem #1183Partial progress by Przemek Chojecki and Quanyu Tang with GPT-5.4 Pro (18 Mar 2026): partial result.Przemek Chojecki and Quanyu Tang with GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Partial
  19. 2026-03-18Math · Number theory
    Erdős Problem #943Partial progress by Przemek Chojecki with GPT-5.4 Pro (18 Mar 2026): partial result.Przemek Chojecki with GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Partial
  20. 2026-03-16Math · Number theory
    Erdős Problem #1148Full solution by Ingo Althöfer, Przemek Chojecki and Wouter van Doorn with Gemini 3 Pro, Gemini 3.1 Pro, GPT-5.2 Pro, GPT-5.2 Thinking and GPT-5.4 Pro (16 Mar 2026). 2 AI contributions are recorded in all.Ingo Althöfer, Przemek Chojecki and Wouter van Doorn with Gemini 3 Pro, Gemini 3.1 Pro, GPT-5.2 Pro, GPT-5.2 Thinking and GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Solved
  21. 2026-03-15Math · Number theory
    Erdős Problem #396Partial progress by Malek Zribi with Claude, Codex and GPT (15 Mar 2026): partial result. 2 AI contributions are recorded in all.Malek Zribi with Claude, Codex and GPT✓ Listed in Tao's wiki0 notes
    Partial
  22. 2026-03-14Math · Combinatorics
    Erdős Problem #120Partial progress by DeepMind prover agent (14 Mar 2026): solution to variant problem (Lean).DeepMind prover agent✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  23. 2026-03-11Math · Number theory
    Erdős Problem #423Partial progress by Quanyu Tang and Nat Sothanaphan with GPT-5.2 Thinking and GPT-5.4 Thinking (11 Mar 2026): partial result.Quanyu Tang and Nat Sothanaphan with GPT-5.2 Thinking and GPT-5.4 Thinking✓ Listed in Tao's wiki0 notes
    Partial
  24. 2026-03-09Math · Number theory
    Erdős Problem #349Partial progress by GPT-5.2 Thinking (9 Mar 2026): improved partial result.GPT-5.2 Thinking✓ Listed in Tao's wiki0 notes
    Partial
  25. 2026-03-06Math · Analysis
    Erdős Problem #1039Partial progress by Houi with Aristotle and Claude Opus 4.6 (6 Mar 2026): partial result (Lean). 2 AI contributions are recorded in all.Houi with Aristotle and Claude Opus 4.6✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  26. 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
  27. 2026-03-02Math · Number theory
    Erdős Problem #457Full solution by Aristotle and GPT-5.2 Pro, formalized in Lean (2 Mar 2026).Aristotle and GPT-5.2 Pro✓ Lean formalization · Listed in Tao's wiki0 notes
    Solved
  28. 2026-03-01Math · Analysis
    Erdős Problem #513Partial progress by GPT-5.2 Thinking (1 Mar 2026): slight improvement to past construction.GPT-5.2 Thinking✓ Listed in Tao's wiki0 notes
    Partial
  29. 2026-02-28Computer science · Combinatorics
    Claude's cycles: decomposing a 3D torus digraph into Hamiltonian cyclesClaude Opus 4.6 found a construction that splits a digraph from Knuth's forthcoming TAOCP section into three Hamiltonian cycles for every odd m; Knuth proved it and it was formalized in Lean. The even case has a separate, unverified AI proof.Claude Opus 4.6 (Anthropic), coached by Filip Stappers; proof by Donald Knuth✓ Proof written by Knuth · Lean formalization (Kim Morrison)0 notes
    Solved
  30. 2026-02-27Math · Geometry
    Erdős Problem #1090Partial progress by Aristotle and Gemini 3 Flash (27 Feb 2026): proof found (Lean).Aristotle and Gemini 3 Flash✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  31. 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
  32. 2026-02-21Math · Geometry
    Erdős Problem #846Partial progress by DeepMind prover agent; OpenAI internal model (independently) (21 Feb 2026): full solution (Lean); 🟢 Full solution.DeepMind prover agent; OpenAI internal model (independently)✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  33. 2026-02-16Math · Number theory
    Erdős Problem #872Partial progress by GPT-5.2 Pro (16 Feb 2026): partial result. 3 AI contributions are recorded in all.GPT-5.2 Pro✓ Listed in Tao's wiki0 notes
    Partial
  34. 2026-02-14Math · Geometry
    Erdős Problem #1082Partial progress by DeepMind prover agent (14 Feb 2026): counterexample to one part (Lean).DeepMind prover agent✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  35. 2026-02-11Math · Combinatorics
    Erdős Problem #776Partial progress by Yixin He and Quanyu Tang with GPT-5.2 Thinking (11 Feb 2026): partial result.Yixin He and Quanyu Tang with GPT-5.2 Thinking✓ Listed in Tao's wiki0 notes
    Partial
  36. 2026-02-05Math · Number theory
    Erdős Problem #851Partial progress by GPT-5.2 Pro (5 Feb 2026): full solution (building upon 🟡 Romanoff (1934)).GPT-5.2 Pro✓ Listed in Tao's wiki0 notes
    Partial
  37. 2026-02-01Math · Analysis
    Erdős Problem #1040Partial progress by Aletheia (1 Feb 2026): solution to one part of problem; 🔴 incorrect solution to other part.Aletheia✓ Listed in Tao's wiki0 notes
    Partial
  38. 2026-02-01Math · Geometry
    Erdős Problem #1089Partial progress by Aletheia (1 Feb 2026): full solution found.Aletheia✓ Listed in Tao's wiki0 notes
    Partial
  39. 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
  40. 2026-02-01Math · Geometry
    Erdős Problem #654Partial progress by Aletheia (1 Feb 2026): partial result.Aletheia✓ Listed in Tao's wiki0 notes
    Partial