MathDuels: Evaluating LLMs as Problem Posers and Solvers

• URL: http://arxiv.org/abs/2604.21916v2
• Date: Mon, 27 Apr 2026 04:18:43 GMT
• Title: MathDuels: Evaluating LLMs as Problem Posers and Solvers
• Abstract summary: MathDuels is a self-play benchmark in which models occupy dual roles.<n>Each author math problems under adversarial prompting and solves problems authored by every other participant.<n>A Rasch model jointly estimates solver abilities and problem difficulties.
• Score: 9.727695321331483
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: As frontier language models attain near-ceiling performance on static mathematical benchmarks, existing evaluations are increasingly unable to differentiate model capabilities, largely because they cast models solely as solvers of fixed problem sets. We introduce MathDuels, a self-play benchmark in which models occupy dual roles: each authors math problems under adversarial prompting and solves problems authored by every other participant. Problems are produced through a three-stage generation pipeline (meta-prompting, problem generation, and difficulty amplification), and validated by an independent verifier that excludes ill-posed questions. A Rasch model (Rasch, 1993) jointly estimates solver abilities and problem difficulties; author quality is derived from the difficulties of each model's authored problems. Experiments across 19 frontier models reveal that authoring and solving capabilities are partially decoupled, and that dual-role evaluation reveals capability separations invisible in single-role benchmarks. As newer models enter the arena, they produce problems that defeat previously dominant solvers, so the benchmark's difficulty co-evolves with participant strength rather than saturating at a fixed ceiling. We host a public leaderboard that updates as new models are released.

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