AI4Math: Looking for problems in pure mathematics that could be solved by AI, and advancing our understanding along the way.

Introduction

Given the drastic improvement of analytical reasoning ability of AIs, more and more open problems in pure mathematics have been cracked. Notable examples from 2026 include: unit-distance conjecture, Jacobian conjecture for n >= 3 (for which Terence Tao wrote a great exposition), the existence of non-sofic groups(heuristically, a group that cannot be approximated by any finite structure, no matter how large), Hadamard conjecture with matrix of order 668, and Erdos problem 183.

Many of these are part of a paper “Ten advances in mathematics and theoretical computer science” published by OpenAI in mid 2026.

A great example of a “non-solution” is related to the Riemann Hypothesis. Anthropic’s Claude was recently told to attack the Riemann hypothesis. It failed to prove RH, but during the search it improved the known lower bound for the fraction of zeta zeros satisfying RH from 41.6% to 67.2%.

The website VibeMathed documents recent progress on AI contributions to math proofs. A large fraction of these problems have been fully solved with the help of AI, and a smaller but still significant portion of them are Lean-verified.

Ethics and Meaning in Math Research

List of Problems

  • Converse of Wolstenholme’s Theorem.

  • Exact small Ramsey numbers.

    • As of 2026, R(5,5) has been bounded between 43 and 46, making it potentially feasible for AI-assisted computation.

  • Kissing number in dimension 5.

    • Exact kissing numbers are known in dimensions 1, 2, 3, 4, 8, 24 only.
    • AI-assisted research has proved fruitful in the highly-related sphere-packing problems.

  • 2D Jacobian conjecture.

    • Obvious given the progress on the same conjecture for higher dimensions.

Interesting Results

None for now.