The Ultimate Top 500 Open Problems in Mathematics
proofatlas.ai/open-problems/
Weeks of work by 4 LLM families (GPT 6, Fable 5.1, GLM-5.3, DeepSeek V4 Pro). 34,890 pairwise judgments across 1,227 candidate problems. They ran repeated discovery rounds, source checks, deduplication, and clarification of exact problem statements. Models compared problems using source-backed descriptions without seeing the existing rankings or other models' judgments.
The comparisons considered the significance of a resolution, centrality to the field, connections across disciplines, scholarly and public recognition, and potential scientific or practical impact. Results were statistically combined and checked for ranking uncertainty and sensitivity to individual model families. Includes theoretical computer science, and mathematical physics.
The list includes plain-language explanations, sources, notes on what remains open, and links to related research where available.
Where the targets of recent AI results would rank if they were still open:
#21 — Smooth-forced Navier–Stokes breakdown (Fefferman C).
#32 — Unforced three-dimensional Euler blowup.
#92 — The Jacobian conjecture in general dimension.
#167 — Whether every group is sofic.
#211 — The planar unit-distance conjecture.
Note that the recently announced Navier–Stokes result concerns flow driven by a smooth external force. #4 entry is unforced three-dimensional Navier–Stokes global regularity (Fefferman's statement A), which remains open. Showing that a forced flow can develop a singularity does not settle whether singularities can arise without external forcing.