Riemann-Bench: A Benchmark for Moonshot Mathematics

📅 2026-04-08
📈 Citations: 0
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🤖 AI Summary
This study addresses the lack of reliable evaluation of artificial intelligence systems on genuine mathematical research, despite their strong performance on Olympiad-style problems. To bridge this gap, the authors introduce a novel private benchmark comprising 25 expert-level problems, meticulously designed by leading mathematicians and validated through double-blind review, emphasizing deep theoretical understanding over procedural problem-solving tricks. Evaluation employs a programmatic verifier to check unique closed-form solutions and an unbiased statistical estimator based on 100 independent runs per problem, permitting models to leverage coding, search, and open-ended reasoning. Results reveal that all state-of-the-art models achieve success rates below 10%, underscoring a substantial disparity between current AI capabilities and human expertise in research-grade mathematical reasoning.

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📝 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.
Problem

Research questions and friction points this paper is trying to address.

mathematical reasoning
AI benchmark
research-level mathematics
Riemann-Bench
frontier models
Innovation

Methods, ideas, or system contributions that make the work stand out.

Riemann-Bench
research-level mathematics
double-blind verification
programmatic verification
unconstrained research agent
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