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 · 39 of 262 records
FieldAllMathComputer scienceBiologyPhysicsChemistry
GradeAllSolvedPartialPrior artUnverified
  1. 2026-10-06Math · Analysis
    Littlewood polynomials with large normalized Mahler measureAn internal OpenAI model produced a preprint proving that real ultraflat Littlewood polynomials exist, which settles an Epoch AI open problem; the proof has not yet been independently checked.OpenAI internal model✓ Lean formalization supplied by OpenAI · Marked solved by Epoch AI0 notes
    Unverified
  2. 2026-10-06Math · Mathematics and theoretical CS
    OpenAI's release of 372 result families in mathematicsOpenAI released 719 manuscripts in 372 result families produced by an unreleased model; about 42% are formalized in Lean, none is peer reviewed, and three were withdrawn a day later over a sign error.OpenAI internal model✓ Lean formalizations for about 42% of top-line results0 notes
    Unverified
  3. 2026-09-17Math · Number theory
    Apéry-style irrationality proofs: ζ(5) and Catalan's constantA preprint proving that ζ(5) is irrational, now formalized in Lean by a third party, led Epoch AI to mark this open problem solved by human and AI; no primary source we found describes the AI's role.Aabir Fauzan (ζ(5)); OpenAI internal model (Catalan's constant)✓ Lean formalization of the ζ(5) proof (third party) · Marked solved (human + AI) by Epoch AI0 notes
    Unverified
  4. 2026-09-08Math · Partial differential equations
    Navier–Stokes: OpenAI's claim of finite-time blowup with smooth forcingOpenAI claims an internal model proved that a 3D incompressible fluid starting at rest can develop a singularity in finite time under a smooth external force, one of the four forms of the Millennium Prize problem; the 166-page proof is unverified and its priority is disputed.OpenAI internal model, with GPT-6 Astra for the Lean formalization✓ Lean formalization by OpenAI (its fidelity is disputed)0 notes
    Unverified
  5. 2026-08-09Math · Number theory
    The inverse Galois problem for the Mathieu group M23Huang, Jackson, Lee, Poonen, Pries and Zhang gave an explicit degree-23 polynomial over ℚ with Galois group M23, the last sporadic simple group not yet realized; Epoch AI credits AI as instrumental, but the paper has not been peer reviewed.Huang, Jackson, Lee, Poonen, Pries and Zhang, with Claude and ChatGPT models✓ Marked solved (human + AI) by Epoch AI0 notes
    Unverified
  6. 2026-08-01Math · Mathematics and theoretical CS
    OpenAI's “ten advances” in mathematics and theoretical computer scienceOpenAI announced ten results produced with GPT-6 Astra, from sphere-packing bounds to Ramsey numbers, with Lean certificates; none has been peer reviewed, and two face credit disputes from mathematicians.GPT-6 Astra (OpenAI)✓ Lean certificates published · Partial independent audit (arXiv:2608.14673)0 notes
    Unverified
  7. 2026-06-27Math · Graph theory
    Erdős Problem #1033A claim by GPT-5.5 Pro (27 Jun 2026) that has not yet been verified: candidate partial result.GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Unverified
  8. 2026-06-27Math · Number theory
    Erdős Problem #731A claim by Eric Li with GPT (27 Jun 2026) that has not yet been verified: candidate full solution.Eric Li with GPT✓ Listed in Tao's wiki0 notes
    Unverified
  9. 2026-06-24Math · Number theory
    Erdős Problem #1061A claim by Eric Li with GPT (24 Jun 2026) that has not yet been verified: candidate full solution.Eric Li with GPT✓ Listed in Tao's wiki0 notes
    Unverified
  10. 2026-06-24Math · Number theory
    Erdős Problem #730A claim by GPT-5.5 Pro (24 Jun 2026) that has not yet been verified: candidate full solution.GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Unverified
  11. 2026-06-23Math · Set theory
    Erdős Problem #1177A claim by Eric Li with GPT (23 Jun 2026) that has not yet been verified: candidate full solution.Eric Li with GPT✓ Listed in Tao's wiki0 notes
    Unverified
  12. 2026-06-23Math · Number theory
    Erdős Problem #432A claim by Sungchul Lee with GPT-5.5 Pro (23 Jun 2026) that has not yet been verified: candidate partial result.Sungchul Lee with GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Unverified
  13. 2026-06-23Math · Set theory
    Erdős Problem #593A claim by Eric Li with GPT (23 Jun 2026) that has not yet been verified: candidate full solution.Eric Li with GPT✓ Listed in Tao's wiki0 notes
    Unverified
  14. 2026-06-22Math · Number theory
    Erdős Problem #400A claim by Eric Li with GPT (22 Jun 2026) that has not yet been verified: candidate partial result.Eric Li with GPT✓ Listed in Tao's wiki0 notes
    Unverified
  15. 2026-06-22Math · Graph theory
    Erdős Problem #550A claim by GPT (22 Jun 2026) that has not yet been verified: candidate full solution.GPT✓ Listed in Tao's wiki0 notes
    Unverified
  16. 2026-06-22Math · Analysis
    Erdős Problem #671A claim by Codex and GPT-5.5 Pro (22 Jun 2026) that has not yet been verified: candidate full solution (Lean).Codex and GPT-5.5 Pro✓ Lean formalization · Listed in Tao's wiki0 notes
    Unverified
  17. 2026-06-22Math · Number theory
    Erdős Problem #768A claim by Eric Li with GPT (22 Jun 2026) that has not yet been verified: candidate full solution.Eric Li with GPT✓ Listed in Tao's wiki0 notes
    Unverified
  18. 2026-06-19Math · Number theory
    Erdős Problem #1139A claim by Przemek Chojecki, gavinsherry, Liam Price and Terence Tao with GPT-5.2 Pro and GPT-5.5 Pro (19 Jun 2026) that has not yet been verified: candidate full solution.Przemek Chojecki, gavinsherry, Liam Price and Terence Tao with GPT-5.2 Pro and GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Unverified
  19. 2026-06-14Math · Geometry
    Erdős Problem #1208A claim by Sungchul Lee with GPT-5.5 Pro (14 Jun 2026) that has not yet been verified: candidate partial result.Sungchul Lee with GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Unverified
  20. 2026-06-09Math · Number theory
    An explicit presentation of the absolute Galois group of ℚ₂AI models produced a candidate explicit presentation of the absolute Galois group of the 2-adic numbers, the one case left open; Lean formalizations exist but rely on cited results, and the write-up is not peer reviewed.Claude Fable 5 (per Epoch AI) and GPT-5.5 Pro, with David Roe and David Turturean✓ Two Lean formalizations relying on cited results · Marked solved by Epoch AI0 notes
    Unverified
  21. 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
  22. 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
  23. 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
  24. 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
  25. 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
  26. 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
  27. 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
  28. 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
  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. 2026-04-29Math · 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
  31. 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
  32. 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
  33. 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
  34. 2026-04-27Math · Geometry
    Erdős Problem #956A claim by Przemek Chojecki with Aristotle and GPT-5.5 Pro (27 Apr 2026) that has not yet been verified: candidate full solution.Przemek Chojecki with Aristotle and GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Unverified
  35. 2026-04-26Math · Analysis
    Erdős Problem #1131A claim by GPT-5.5 Pro (26 Apr 2026) that has not yet been verified: candidate partial result.GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Unverified
  36. 2026-04-25Math · Analysis
    Erdős Problem #906A claim by Adriano Almeida with Unspecified (25 Apr 2026) that has not yet been verified: candidate full solution. 2 AI contributions are recorded in all.Adriano Almeida with Unspecified✓ Listed in Tao's wiki0 notes
    Unverified
  37. 2026-04-22Math · Set theory
    Erdős Problem #598A claim by Przemek Chojecki with Aristotle and GPT-5.4 Pro (22 Apr 2026) that has not yet been verified: candidate partial result.Przemek Chojecki with Aristotle and GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Unverified
  38. 2026-04-15Math · Number theory
    Erdős Problem #856A claim by Przemek Chojecki with GPT-5.4 Pro (15 Apr 2026) that has not yet been verified: candidate full solution.Przemek Chojecki with GPT-5.4 Pro✓ Listed in Tao's wiki0 notes
    Unverified
  39. 2025-10-29Math · Number theory
    Erdős Problem #689A claim by Boris Alexeev, Przemek Chojecki, Dogmachine, jleng01, Mehtaab Sawhney, Terence Tao and Malek Zribi with Codex, GPT-5.2 and GPT-5.5 Pro (29 Oct 2025) that has not yet been verified: candidate full solution.Boris Alexeev, Przemek Chojecki, Dogmachine, jleng01, Mehtaab Sawhney, Terence Tao and Malek Zribi with Codex, GPT-5.2 and GPT-5.5 Pro✓ Listed in Tao's wiki0 notes
    Unverified