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
- 2026-09-10Computer science · Social choiceThe core in approval-based committee elections is never emptyBecker, Greger and Peters proved that every approval-based committee election has a committee in the core, computable in polynomial time; their arXiv paper says the proof was obtained with GPT-6 Astra.Unverified
- 2026-02-28Computer science · CombinatoricsClaude'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.Solved
- 2025-05Computer science · Algorithms4×4 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.Partial