Riemann-Bench: A Benchmark for Moonshot Mathematics

• URL: http://arxiv.org/abs/2604.06802v1
• Date: Wed, 08 Apr 2026 08:16:37 GMT
• Title: Riemann-Bench: A Benchmark for Moonshot Mathematics
• Abstract summary: Recent AI systems have achieved gold-medal-level performance on the International Mathematical Olympiad.<n>We introduce bench, a private benchmark of 25 expert-curated problems designed to evaluate AI systems on research-level mathematics.
• Score: 0.12430801435092285
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Recent AI systems have achieved gold-medal-level performance on the International Mathematical Olympiad, demonstrating remarkable proficiency at competition-style problem solving. However, competition mathematics represents only a narrow slice of mathematical reasoning: problems are drawn from limited domains, require minimal advanced machinery, and can often reward insightful tricks over deep theoretical knowledge. We introduce \bench{}, a private benchmark of 25 expert-curated problems designed to evaluate AI systems on research-level mathematics that goes far beyond the olympiad frontier. Problems are authored by Ivy League mathematics professors, graduate students, and PhD-holding IMO medalists, and routinely took their authors weeks to solve independently. Each problem undergoes double-blind verification by two independent domain experts who must solve the problem from scratch, and yields a unique, closed-form solution assessed by programmatic verifiers. We evaluate frontier models as unconstrained research agents, with full access to coding tools, search, and open-ended reasoning, using an unbiased statistical estimator computed over 100 independent runs per problem. Our results reveal that all frontier models currently score below 10\%, exposing a substantial gap between olympiad-level problem solving and genuine research-level mathematical reasoning. By keeping the benchmark fully private, we ensure that measured performance reflects authentic mathematical capability rather than memorization of training data.

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