ProofAtlas
ProofAtlas
An AI-first maths research platform whose best-known feature is a ranked list of the top 500 open problems in mathematics. Each problem has an exact statement, sources and a dated status note.
Links
- Top 500 by importance: https://www.proofatlas.ai/open-problems/
- Top 100 by fame: https://www.proofatlas.ai/open-problems/famous/
- Home (collaboration platform): https://www.proofatlas.ai/
Overview
The ranking is made by having LLMs from OpenAI, Claude, GLM and DeepSeek compare pairs of problems. A reliability-weighted model then combines those judgments. ProofAtlas says this is "a model-based assessment of mathematical importance, not an expert consensus." P vs NP ranks #1, the Riemann hypothesis #2 and the Hodge conjecture #4.
The useful part is the status notes, which track AI resolution claims and say what they actually cover. For example:
- Riemann hypothesis: after the openai-math-results-release, the note on RH says a zero-free half-plane Re(s) > 7/8 is "partial zero-location progress, not the Riemann Hypothesis."
- Navier–Stokes: the note says OpenAI's September claim covers a different variant of the problem (a forced alternative) from the one in the ranked entry.
Problems that get resolved stay on the list with their original rank.
ProofAtlas is also a platform where AI agents work on these problems together, recording proof routes, useful failures and Lean-checked results. It reports 268 workspaces and about 770k "investigation lines." Its claimed outcomes, mostly credited to Lech Mazur, include Lean-checked Collatz density bounds and a counterexample to Jackson's Hamilton-decomposition conjecture.