open-problems

Open problems, research agendas, and papers in Math for AI Safety — public from draft stage onward

Integer multiplication below n log n: a conditional witness kappa = 6685733/10^10 (> 2^-11) for T(n) = O(n (log n)^(1-kappa)) in the multitape model, building on OpenAI's problem and Colkitt's integer-mult-bounds: certificates, independent replays, Lean 4 checks

Open problems in math, science and engineering. One number to beat, one program that checks every answer.

Open problems in AI safety, stated self-contained for statisticians. A companion to Lionel Levine MAIS.

A toolkit for AI agents to explore and attempt Erdős's 1,179 unsolved mathematical problems

A single index to every SAIR Foundation challenge entered: the open problem each one states, the repository holding the method and the code, and what that method actually reached. Open science competitions in mathematics and computation, run by the Foundation for Science and AI Research.

The live, agent-readable frontier of AI mathematics: open problems, AI attempts, solution claims, verification, replay candidates, Skill and MCP.

An AI agent for open mathematical problems — honest by design.

A source-linked index of open math problems solved, refuted, or settled with AI — tracking the July 2026 wave. Verification-status badges, Lean/DRAT certificates, priority caveats.

The minimal elements of the prime numbers which are > b written in the positional numeral system with radix b, as digit strings under the subsequence ordering, for 2 ≤ b ≤ 36

C.Algebra System derived fron own Author works.

The agent chooses the problem. CI chooses whether mathematics happened.

Deterministic 3SUM in O(n^1.995782) and APSP / (min,+) / all-edges Exact Triangle in O(n^2.995943), improving Alman–Vassilevska Williams: proofs, certificates, Lean 4 checks, and a list of closed ideas to avoid duplicate work

GF(2) Möbius / zeta transform in o(N log N) XOR gates, the first asymptotic improvement over Yates (1937) for circuits with cancellation: proofs, certificates, Lean 4 checks, and closed ideas. Asymptotic only, AI-checked, not yet human-refereed.

Auditable difficulty profiles for all 8,785 UnsolvedMath problems, with AI-relative estimates, rationales, methodology, and machine-readable data.

Open & hard research problems across 35 fields of AI and machine learning, organized by topic — each with a problem statement, formal setting, SOTA, what is known, what is not known, why it is hard, current (2026) research, a concrete next experiment, references, and a worked example.

AI agents attack open problems in mathematics; every result is a Lean 4 proof the computer checks: no sorry, no extra axioms.

Catalog of 112 open physics problems tagged by publication culture, refutability and agent tractability, with a sprint protocol and a live board.

A curated, open catalogue of 100 famous unsolved math problems — and a space to propose ideas and approaches. Contributions welcome.

An open, Lean-checked effort on the three Rule 30 Prize problems: proofs with natural-language arguments, reproducible findings, and documented negative results.