Riemann-Bench: A Benchmark for Moonshot Mathematics

TL;DR

Riemann-Bench is a private, expert-curated benchmark of 25 research-level math problems designed to evaluate AI systems' deep mathematical reasoning beyond olympiad-level skills.

Contribution

The paper introduces Riemann-Bench, a novel private benchmark with expert-verified research-level problems to assess AI mathematical reasoning capabilities.

Findings

Frontier models score below 10% on the benchmark.

Current models show a large gap compared to human research-level reasoning.

The benchmark is private to prevent memorization and ensure genuine evaluation.

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.