# Riemann-Bench: A Benchmark for Moonshot Mathematics

arXiv: https://arxiv.org/abs/2604.06802 · HTML: https://mlsanity.com/paper/2604.06802/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 42 references that are in the map.
- First posted on arXiv 8 Apr 2026.

## Builds on (most cited first, 30 of 32)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [Humanity's Last Exam](https://mlsanity.com/paper/2501.14249/) (2025)
- [MiniF2F: a cross-system benchmark for formal Olympiad-level mathematics](https://mlsanity.com/paper/2109.00110/) (2021)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition](https://mlsanity.com/paper/2504.21801/) (2025)
- [Omni-MATH: A Universal Olympiad Level Mathematic Benchmark For Large Language Models](https://mlsanity.com/paper/2410.07985/) (2024)
- [Mathematical Capabilities of ChatGPT](https://mlsanity.com/paper/2301.13867/) (2023)
- [SciBench: Evaluating College-Level Scientific Problem-Solving Abilities of Large Language Models](https://mlsanity.com/paper/2307.10635/) (2023)
- [FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI](https://mlsanity.com/paper/2411.04872/) (2024)
- [Proving Test Set Contamination in Black Box Language Models](https://mlsanity.com/paper/2310.17623/) (2023)
- [Don't Make Your LLM an Evaluation Benchmark Cheater](https://mlsanity.com/paper/2311.01964/) (2023)
- [ProofNet: Autoformalizing and Formally Proving Undergraduate-Level Mathematics](https://mlsanity.com/paper/2302.12433/) (2023)
- [TheoremQA: A Theorem-driven Question Answering dataset](https://mlsanity.com/paper/2305.12524/) (2023)
- [PutnamBench: Evaluating Neural Theorem-Provers on the Putnam Mathematical Competition](https://mlsanity.com/paper/2407.11214/) (2024)
- [Benchmark Data Contamination of Large Language Models: A Survey](https://mlsanity.com/paper/2406.04244/) (2024)
- [MathBench: Evaluating the Theory and Application Proficiency of LLMs with a Hierarchical Mathematics Benchmark](https://mlsanity.com/paper/2405.12209/) (2024)
- [Gold-medalist Performance in Solving Olympiad Geometry with AlphaGeometry2](https://mlsanity.com/paper/2502.03544/) (2025)
- [DeepSeekMath-V2: Towards Self-Verifiable Mathematical Reasoning](https://mlsanity.com/paper/2511.22570/) (2025)
- [Functional Benchmarks for Robust Evaluation of Reasoning Performance, and the Reasoning Gap](https://mlsanity.com/paper/2402.19450/) (2024)
- [Have LLMs Advanced Enough? A Challenging Problem Solving Benchmark For Large Language Models](https://mlsanity.com/paper/2305.15074/) (2023)
- [Challenging the Boundaries of Reasoning: An Olympiad-Level Math Benchmark for Large Language Models](https://mlsanity.com/paper/2503.21380/) (2025)
- [ARB: Advanced Reasoning Benchmark for Large Language Models](https://mlsanity.com/paper/2307.13692/) (2023)
- [Lean Copilot: Large Language Models as Copilots for Theorem Proving in Lean](https://mlsanity.com/paper/2404.12534/) (2024)

## Built on by (most cited first, 8 of 8)

- [Soohak: A Mathematician-Curated Benchmark for Evaluating Research-level Math Capabilities of LLMs](https://mlsanity.com/paper/2605.09063/) (2026)
- [ResearchMath-14K: Scaling Research-Level Mathematics via Agents](https://mlsanity.com/paper/2605.28003/) (2026)
- [Beyond Accuracy: Evaluating Strategy Diversity in LLM Mathematical Reasoning](https://mlsanity.com/paper/2605.09292/) (2026)
- [Benchmarks in Leipzig](https://mlsanity.com/paper/2606.05818/) (2026)
- [The Ramanujan Challenge For AI](https://mlsanity.com/paper/2607.09721/) (2026)
- [Ask-E: An Environment for Calibrated Question Generation](https://mlsanity.com/paper/2608.06933/) (2026)
- [Chartography: A Benchmark for Professional Chart Understanding](https://mlsanity.com/paper/2608.10677/) (2026)
- [Investigating Human--AI Discrepancies via Multiple-Solution Problems](https://mlsanity.com/paper/2609.34258/) (2026)

## Abstract (arXiv)

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 Riemann-Bench, a private benchmark of 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.