Riemann-Bench: A Benchmark for Moonshot Mathematics
AI 摘要
论文提出了一个名为Riemann-Bench的数学推理benchmark,用于评估AI在研究级数学问题上的能力。
主要贡献
- 提出了新的研究级数学benchmark
- 评估了前沿模型在复杂数学问题上的表现
- 揭示了模型在研究级数学推理上的不足
方法论
专家设计高难度数学问题,双盲验证确保正确性,使用无偏估计器评估模型在多次运行中的表现。
原文摘要
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.