# Lean Workbook: A large-scale Lean problem set formalized from natural language math problems

arXiv: https://arxiv.org/abs/2406.03847 · HTML: https://mlsanity.com/paper/2406.03847/

## Key facts

- Cited by 122 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 34 references that are in the map.
- First posted on arXiv 6 Jun 2024.

## Builds on (most cited first, 24 of 24)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [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)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Galactica: A Large Language Model for Science](https://mlsanity.com/paper/2211.09085/) (2022)
- [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)
- [Draft, Sketch, and Prove: Guiding Formal Theorem Provers with Informal Proofs](https://mlsanity.com/paper/2210.12283/) (2022)
- [Autoformalization with Large Language Models](https://mlsanity.com/paper/2205.12615/) (2022)
- [Thinking Fast and Slow with Deep Learning and Tree Search](https://mlsanity.com/paper/1705.08439/) (2017)
- [DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Data](https://mlsanity.com/paper/2405.14333/) (2024)
- [HyperTree Proof Search for Neural Theorem Proving](https://mlsanity.com/paper/2205.11491/) (2022)
- [ProofNet: Autoformalizing and Formally Proving Undergraduate-Level Mathematics](https://mlsanity.com/paper/2302.12433/) (2023)
- [Formal Mathematics Statement Curriculum Learning](https://mlsanity.com/paper/2202.01344/) (2022)
- [The Lean mathematical library](https://mlsanity.com/paper/1910.09336/) (2019)
- [Proof Artifact Co-training for Theorem Proving with Language Models](https://mlsanity.com/paper/2102.06203/) (2021)
- [Learning to Prove Theorems via Interacting with Proof Assistants](https://mlsanity.com/paper/1905.09381/) (2019)
- [Thor: Wielding Hammers to Integrate Language Models and Automated Theorem Provers](https://mlsanity.com/paper/2205.10893/) (2022)
- [FIMO: A Challenge Formal Dataset for Automated Theorem Proving](https://mlsanity.com/paper/2309.04295/) (2023)
- [MUSTARD: Mastering Uniform Synthesis of Theorem and Proof Data](https://mlsanity.com/paper/2402.08957/) (2024)
- [Multilingual Mathematical Autoformalization](https://mlsanity.com/paper/2311.03755/) (2023)
- [LLMSTEP: LLM proofstep suggestions in Lean](https://mlsanity.com/paper/2310.18457/) (2023)
- [Autoformalizing Euclidean Geometry](https://mlsanity.com/paper/2405.17216/) (2024)

## Built on by (most cited first, 30 of 122)

- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [The Landscape of Agentic Reinforcement Learning for LLMs: A Survey](https://mlsanity.com/paper/2509.02547/) (2025)
- [DeepSeek-Prover-V1.5: Harnessing Proof Assistant Feedback for Reinforcement Learning and Monte-Carlo Tree Search](https://mlsanity.com/paper/2408.08152/) (2024)
- [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)
- [CWM: An Open-Weights LLM for Research on Code Generation with World Models](https://mlsanity.com/paper/2510.02387/) (2025)
- [BFS-Prover: Scalable Best-First Tree Search for LLM-based Automatic Theorem Proving](https://mlsanity.com/paper/2502.03438/) (2025)
- [Formal Mathematical Reasoning: A New Frontier in AI](https://mlsanity.com/paper/2412.16075/) (2024)
- [Rewarding the Unlikely: Lifting GRPO Beyond Distribution Sharpening](https://mlsanity.com/paper/2506.02355/) (2025)
- [STP: Self-play LLM Theorem Provers with Iterative Conjecturing and Proving](https://mlsanity.com/paper/2502.00212/) (2025)
- [TheoremLlama: Transforming General-Purpose LLMs into Lean4 Experts](https://mlsanity.com/paper/2407.03203/) (2024)
- [Herald: A Natural Language Annotated Lean 4 Dataset](https://mlsanity.com/paper/2410.10878/) (2024)
- [A Survey on Large Language Models for Mathematical Reasoning](https://mlsanity.com/paper/2506.08446/) (2025)
- [Solver-Informed RL: Grounding Large Language Models for Authentic Optimization Modeling](https://mlsanity.com/paper/2505.11792/) (2025)
- [Seed-Prover 1.5: Mastering Undergraduate-Level Theorem Proving via Learning from Experience](https://mlsanity.com/paper/2512.17260/) (2025)
- [InternLM2.5-StepProver: Advancing Automated Theorem Proving via Critic-Guided Search](https://mlsanity.com/paper/2410.15700/) (2024)
- [HunyuanProver: A Scalable Data Synthesis Framework and Guided Tree Search for Automated Theorem Proving](https://mlsanity.com/paper/2412.20735/) (2024)
- [Reliable Evaluation and Benchmarks for Statement Autoformalization](https://mlsanity.com/paper/2406.07222/) (2024)
- [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)
- [Chain-of-Reasoning: Towards Unified Mathematical Reasoning in Large Language Models via a Multi-Paradigm Perspective](https://mlsanity.com/paper/2501.11110/) (2025)
- [Scaling up Multi-Turn Off-Policy RL and Multi-Agent Tree Search for LLM Step-Provers](https://mlsanity.com/paper/2509.06493/) (2025)
- [Leanabell-Prover: Posttraining Scaling in Formal Reasoning](https://mlsanity.com/paper/2504.06122/) (2025)
- [MA-LoT: Model-Collaboration Lean-based Long Chain-of-Thought Reasoning enhances Formal Theorem Proving](https://mlsanity.com/paper/2503.03205/) (2025)
- [ATLAS: Autoformalizing Theorems through Lifting, Augmentation, and Synthesis of Data](https://mlsanity.com/paper/2502.05567/) (2025)
- [RL Grokking Recipe: How Does RL Unlock and Transfer New Algorithms in LLMs?](https://mlsanity.com/paper/2509.21016/) (2025)
- [Solving Inequality Proofs with Large Language Models](https://mlsanity.com/paper/2506.07927/) (2025)
- [Aria: An Agent For Retrieval and Iterative Auto-Formalization via Dependency Graph](https://mlsanity.com/paper/2510.04520/) (2025)
- [ReForm: Reflective Autoformalization with Prospective Bounded Sequence Optimization](https://mlsanity.com/paper/2510.24592/) (2025)
- [REAL-Prover: Retrieval Augmented Lean Prover for Mathematical Reasoning](https://mlsanity.com/paper/2505.20613/) (2025)

## Abstract (arXiv)

Large language models have demonstrated impressive capabilities across various natural language processing tasks, especially in solving mathematical problems. However, large language models are not good at math theorem proving using formal languages like Lean. A significant challenge in this area is the scarcity of training data available in these formal languages. To address this issue, we propose a novel pipeline that iteratively generates and filters synthetic data to translate natural language mathematical problems into Lean 4 statements, and vice versa. Our results indicate that the synthetic data pipeline can provide useful training data and improve the performance of LLMs in translating and understanding complex mathematical problems and proofs. Our final dataset contains about 57K formal-informal question pairs along with searched proof from the math contest forum and 21 new IMO questions. We open-source our code at https://github.com/InternLM/InternLM-Math and our data at https://huggingface.co/datasets/InternLM/Lean-Workbook.