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

Trusted AI mathematics workbench: ProblemContract to Attempt to verified proof/counterexample bundles with SymPy and Lean evidence gates.

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

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 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 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

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 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

C.Algebra System derived fron own Author works.

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.

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.

v1.0 — Publication-grade map of 112 open physics problems: open-math culture, agentic sprints, epistemology. Live board on GitHub Pages.

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

CLI and workspace for Paul Erdos problems.

Deterministic Subset Sum faster than meet-in-the-middle: 2^{0.4986298 n}, derandomising Ye–Li and OpenAI's 2^{0.49n} construction. Proofs, interval certificates, Lean 4 checks, and closed ideas. Preprint, not peer reviewed.

The hypothesis: the dimensionless constants of physics are counts, arithmetic and topological invariants of a compact geometry, with no continuously adjustable parameter. This repository is the program's charter and its list of open problems.