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. 2025-11-03Math · Geometry
    Erdős Problem #507Partial progress by AlphaEvolve (3 Nov 2025): surpassed some past constructions.AlphaEvolve✓ Listed in Tao's wiki0 notes
    Partial
  2. 2025-11-02Math · Geometry
    Erdős Problem #94GPT-5 found that the problem had already been solved in the literature (2 Nov 2025).GPT-5✓ Listed in Tao's wiki0 notes
    Prior art
  3. 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
  4. 2025-10-25Math · Number theory
    Erdős Problem #347Full solution by Enrique Barschkis, Wouter van Doorn, jbbaehr22, Bartosz Naskrecki and Terence Tao with Aristotle, Claude Opus, Codex and GPT, formalized in Lean (25 Oct 2025).Enrique Barschkis, Wouter van Doorn, jbbaehr22, Bartosz Naskrecki and Terence Tao with Aristotle, Claude Opus, Codex and GPT✓ Lean formalization · Listed in Tao's wiki0 notes
    Solved
  5. 2025-10-20Math · Number theory
    Erdős Problem #645GPT-5 found that the problem had already been solved in the literature (20 Oct 2025).GPT-5✓ Listed in Tao's wiki0 notes
    Prior art
  6. 2025-10-19Math · Number theory
    Erdős Problem #1099ChatGPT Deep research, Gemini and Gemini Deep Research found that the problem had already been solved in the literature (19 Oct 2025).ChatGPT Deep research, Gemini and Gemini Deep Research✓ Listed in Tao's wiki0 notes
    Prior art
  7. 2025-10-15Math · Analysis
    Erdős Problem #515GPT-5 found that the problem had already been solved in the literature (15 Oct 2025).GPT-5✓ Listed in Tao's wiki0 notes
    Prior art
  8. 2025-10-14Math · Combinatorics
    Erdős Problem #903GPT-5 found that the problem had already been solved in the literature (14 Oct 2025).GPT-5✓ Listed in Tao's wiki0 notes
    Prior art
  9. 2025-10-13Math · Graph theory
    Erdős Problem #1079GPT-5 found that the problem had already been solved in the literature (13 Oct 2025).GPT-5✓ Listed in Tao's wiki0 notes
    Prior art
  10. 2025-10-13Math · Geometry
    Erdős Problem #223GPT-5 found that the problem had already been solved in the literature (13 Oct 2025).GPT-5✓ Listed in Tao's wiki0 notes
    Prior art
  11. 2025-10-13Math · Analysis
    Erdős Problem #494GPT-5 found that the problem had already been solved in the literature (13 Oct 2025).GPT-5✓ Listed in Tao's wiki0 notes
    Prior art
  12. 2025-10-13Math · Graph theory
    Erdős Problem #621GPT-5 found that the problem had already been solved in the literature (13 Oct 2025).GPT-5✓ Listed in Tao's wiki0 notes
    Prior art
  13. 2025-10-13Math · Number theory
    Erdős Problem #822GPT-5 found that the problem had already been solved in the literature (13 Oct 2025).GPT-5✓ Listed in Tao's wiki0 notes
    Prior art
  14. 2025-10-12Math · Analysis
    Erdős Problem #1043GPT-5 found that the problem had already been solved in the literature (12 Oct 2025). 3 AI contributions are recorded in all.GPT-5✓ Lean formalization · Listed in Tao's wiki0 notes
    Prior art
  15. 2025-10-11Math · Number theory
    Erdős Problem #339GPT-5 found that the problem had already been solved in the literature (11 Oct 2025).GPT-5✓ Listed in Tao's wiki0 notes
    Prior art
  16. 2025-09-30Math · Graph theory
    Erdős Problem #737GPT-5 found that the problem had already been solved in the literature (30 Sep 2025).GPT-5✓ Listed in Tao's wiki0 notes
    Prior art
  17. 2025-09-29Math · Graph theory
    Erdős Problem #1008GPT-5 found that the problem had already been solved in the literature (29 Sep 2025).GPT-5✓ Listed in Tao's wiki0 notes
    Prior art
  18. 2025-08-09Math · Number theory
    Erdős Problem #686Partial progress by Adenwalla, Stijn Cambie, Wouter van Doorn, Vjekoslav Kovač, Miklos, Nat Sothanaphan, Quanyu Tang, Terence Tao, vilc and Malek Zribi with AlphaProof, Claude, Gemini Deep Think, GPT-5.2 Thinking, GPT-5.4 Thinking and Seed 2.0 Pro (9 Aug 2025): various partial results.Adenwalla, Stijn Cambie, Wouter van Doorn, Vjekoslav Kovač, Miklos, Nat Sothanaphan, Quanyu Tang, Terence Tao, vilc and Malek Zribi with AlphaProof, Claude, Gemini Deep Think, GPT-5.2 Thinking, GPT-5.4 Thinking and Seed 2.0 Pro✓ Listed in Tao's wiki0 notes
    Partial
  19. 2025-05Computer science · Algorithms
    4×4 complex matrix multiplication: AlphaEvolve finds a 48-multiplication algorithmAlphaEvolve found an algorithm that multiplies 4×4 complex matrices with 48 scalar multiplications, one fewer than the 49 needed by applying Strassen's method recursively.AlphaEvolve (Google DeepMind)✓ Can be checked directly0 notes
    Partial
  20. 2025Math · Additive combinatorics
    Erdős Problem #198AlphaProof found a new proof of a problem that was already solved (2025).AlphaProof✓ Listed in Tao's wiki0 notes
    Prior art
  21. 2025Math · Number theory
    Erdős Problem #493Partial progress by Aristotle, GPT and Seed Prover (2025): new or existing proof found (Lean).Aristotle, GPT and Seed Prover✓ Lean formalization · Listed in Tao's wiki0 notes
    Partial
  22. 2023-12Math · Combinatorics
    The cap set problem: FunSearch finds a larger cap set in dimension 8A program search system driven by a large language model produced the largest known cap set in dimension 8 and improved the asymptotic lower bound. The problem itself remains open.FunSearch (Google DeepMind)✓ Peer reviewed (Nature, 2023) · Construction can be checked directly0 notes
    Partial