# PutnamBench: Evaluating Neural Theorem-Provers on the Putnam Mathematical Competition

arXiv: https://arxiv.org/abs/2407.11214 · HTML: https://mlsanity.com/paper/2407.11214/

## Key facts

- Cited by 165 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 57 references that are in the map.
- First posted on arXiv 15 Jul 2024.

## Builds on (most cited first, 15 of 15)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [LeanDojo: Theorem Proving with Retrieval-Augmented Language Models](https://mlsanity.com/paper/2306.15626/) (2023)
- [MiniF2F: a cross-system benchmark for formal Olympiad-level mathematics](https://mlsanity.com/paper/2109.00110/) (2021)
- [Generative Language Modeling for Automated Theorem Proving](https://mlsanity.com/paper/2009.03393/) (2020)
- [Draft, Sketch, and Prove: Guiding Formal Theorem Provers with Informal Proofs](https://mlsanity.com/paper/2210.12283/) (2022)
- [HyperTree Proof Search for Neural Theorem Proving](https://mlsanity.com/paper/2205.11491/) (2022)
- [The Lean mathematical library](https://mlsanity.com/paper/1910.09336/) (2019)
- [Baldur: Whole-Proof Generation and Repair with Large Language Models](https://mlsanity.com/paper/2303.04910/) (2023)
- [Learning to Prove Theorems via Interacting with Proof Assistants](https://mlsanity.com/paper/1905.09381/) (2019)
- [An In-Context Learning Agent for Formal Theorem-Proving](https://mlsanity.com/paper/2310.04353/) (2023)
- [Generating Correctness Proofs with Neural Networks](https://mlsanity.com/paper/1907.07794/) (2019)
- [Decomposing the Enigma: Subgoal-based Demonstration Learning for Formal Theorem Proving](https://mlsanity.com/paper/2305.16366/) (2023)
- [Graph2Tac: Online Representation Learning of Formal Math Concepts](https://mlsanity.com/paper/2401.02949/) (2024)
- [Online Machine Learning Techniques for Coq: A Comparison](https://mlsanity.com/paper/2104.05207/) (2021)

## Built on by (most cited first, 30 of 165)

- [DeepSeek-V4: Towards Highly Efficient Million-Token Context Intelligence](https://mlsanity.com/paper/2606.19348/) (2026)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI](https://mlsanity.com/paper/2411.04872/) (2024)
- [Kimina-Prover Preview: Towards Large Formal Reasoning Models with Reinforcement Learning](https://mlsanity.com/paper/2504.11354/) (2025)
- [Chain-of-Thought Reasoning In The Wild Is Not Always Faithful](https://mlsanity.com/paper/2503.08679/) (2025)
- [Goedel-Prover-V2: Scaling Formal Theorem Proving with Scaffolded Data Synthesis and Self-Correction](https://mlsanity.com/paper/2508.03613/) (2025)
- [Goedel-Prover: A Frontier Model for Open-Source Automated Theorem Proving](https://mlsanity.com/paper/2502.07640/) (2025)
- [Seed-Prover: Deep and Broad Reasoning for Automated Theorem Proving](https://mlsanity.com/paper/2507.23726/) (2025)
- [Formal Mathematical Reasoning: A New Frontier in AI](https://mlsanity.com/paper/2412.16075/) (2024)
- [STP: Self-play LLM Theorem Provers with Iterative Conjecturing and Proving](https://mlsanity.com/paper/2502.00212/) (2025)
- [Proof or Bluff? Evaluating LLMs on 2025 USA Math Olympiad](https://mlsanity.com/paper/2503.21934/) (2025)
- [Challenging the Boundaries of Reasoning: An Olympiad-Level Math Benchmark for Large Language Models](https://mlsanity.com/paper/2503.21380/) (2025)
- [MegaScience: Pushing the Frontiers of Post-Training Datasets for Science Reasoning](https://mlsanity.com/paper/2507.16812/) (2025)
- [Aristotle: IMO-level Automated Theorem Proving](https://mlsanity.com/paper/2510.01346/) (2025)
- [FormalMATH: Benchmarking Formal Mathematical Reasoning of Large Language Models](https://mlsanity.com/paper/2505.02735/) (2025)
- [Seed-Prover 1.5: Mastering Undergraduate-Level Theorem Proving via Learning from Experience](https://mlsanity.com/paper/2512.17260/) (2025)
- [ErrorRadar: Benchmarking Complex Mathematical Reasoning of Multimodal Large Language Models Via Error Detection](https://mlsanity.com/paper/2410.04509/) (2024)
- [LeanAgent: Lifelong Learning for Formal Theorem Proving](https://mlsanity.com/paper/2410.06209/) (2024)
- [Theoretical Physics Benchmark (TPBench) -- a Dataset and Study of AI Reasoning Capabilities in Theoretical Physics](https://mlsanity.com/paper/2502.15815/) (2025)
- [CombiBench: Benchmarking LLM Capability for Combinatorial Mathematics](https://mlsanity.com/paper/2505.03171/) (2025)
- [Prover Agent: An Agent-Based Framework for Formal Mathematical Proofs](https://mlsanity.com/paper/2506.19923/) (2025)
- [Ax-Prover: A Deep Reasoning Agentic Framework for Theorem Proving in Mathematics and Quantum Physics](https://mlsanity.com/paper/2510.12787/) (2025)
- [The Open Proof Corpus: A Large-Scale Study of LLM-Generated Mathematical Proofs](https://mlsanity.com/paper/2506.21621/) (2025)
- [Leanabell-Prover-V2: Verifier-integrated Reasoning for Formal Theorem Proving via Reinforcement Learning](https://mlsanity.com/paper/2507.08649/) (2025)
- [FATE: A Formal Benchmark Series for Frontier Algebra of Multiple Difficulty Levels](https://mlsanity.com/paper/2511.02872/) (2025)
- [ATLAS: Autoformalizing Theorems through Lifting, Augmentation, and Synthesis of Data](https://mlsanity.com/paper/2502.05567/) (2025)
- [Formal Theorem Proving by Rewarding LLMs to Decompose Proofs Hierarchically](https://mlsanity.com/paper/2411.01829/) (2024)
- [Solving Inequality Proofs with Large Language Models](https://mlsanity.com/paper/2506.07927/) (2025)
- [A benchmark for vericoding: formally verified program synthesis](https://mlsanity.com/paper/2509.22908/) (2025)
- [ReForm: Reflective Autoformalization with Prospective Bounded Sequence Optimization](https://mlsanity.com/paper/2510.24592/) (2025)

## Abstract (arXiv)

We present PutnamBench, a new multi-language benchmark for evaluating the ability of neural theorem-provers to solve competition mathematics problems. PutnamBench consists of 1692 hand-constructed formalizations of 640 theorems sourced from the William Lowell Putnam Mathematical Competition, the premier undergraduate-level mathematics competition in North America. All the problems have formalizations in Lean 4 and Isabelle; a substantial subset also has Coq formalizations. PutnamBench requires significant problem-solving ability and proficiency in a broad range of topics taught in undergraduate mathematics courses. We use PutnamBench to evaluate several established neural and symbolic theorem-provers. These approaches can only solve a handful of the PutnamBench problems, establishing the benchmark as a difficult open challenge for research on neural theorem-proving. PutnamBench is available at https://github.com/trishullab/PutnamBench.