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RadonBench is a new benchmark comparing classical and learning-guided search methods (exhaustive extension, greedy local search, PatternBoost, AlphaZero, AlphaEvolve) for constructing maximum-cardinality Radon-free lattice configurations. None of the audited runs reached the open targets of 11 points in Z^3 or 21 points in Z^4, but the study establishes reproducible near-miss baselines for AI-assisted mathematical discovery.
This paper presents a Geometry-Aware Monte Carlo Tree Search framework for solving extremal combinatorial geometry problems on n×n grids, achieving new best-known results on five out of six tested problems, including improvements for the No-Three-in-Line problem.
The OpenAI reasoning model successfully constructed a counterexample, disproving the 80-year-old Erdős unit distance conjecture, demonstrating the capability of general-purpose models to solve open math problems.