# Goedel-Prover-V2: Scaling Formal Theorem Proving with Scaffolded Data Synthesis and Self-Correction

arXiv: https://arxiv.org/abs/2508.03613 · HTML: https://mlsanity.com/paper/2508.03613/

## Key facts

- Cited by 154 papers in the map (data through 14 Oct 2026).
- Placed in Self-play RL for reasoning, one of 13 directions in Synthetic data and self-improvement for LLMs.
- Builds on 43 of its 86 references that are in the map.
- First posted on arXiv 5 Aug 2025.

## Placed in

- Synthetic data and self-improvement for LLMs / [Self-play RL for reasoning](https://mlsanity.com/synth/self-play-rl-for-reasoning/)

## Builds on (most cited first, 30 of 43)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Teaching Large Language Models to Self-Debug](https://mlsanity.com/paper/2304.05128/) (2023)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Robust fine-tuning of zero-shot models](https://mlsanity.com/paper/2109.01903/) (2021)
- [YaRN: Efficient Context Window Extension of Large Language Models](https://mlsanity.com/paper/2309.00071/) (2023)
- [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)
- [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)
- [DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Data](https://mlsanity.com/paper/2405.14333/) (2024)
- [RepairAgent: An Autonomous, LLM-Based Agent for Program Repair](https://mlsanity.com/paper/2403.17134/) (2024)
- [Is Self-Repair a Silver Bullet for Code Generation?](https://mlsanity.com/paper/2306.09896/) (2023)
- [DeepSeek-Prover-V1.5: Harnessing Proof Assistant Feedback for Reinforcement Learning and Monte-Carlo Tree Search](https://mlsanity.com/paper/2408.08152/) (2024)
- [ProofNet: Autoformalizing and Formally Proving Undergraduate-Level Mathematics](https://mlsanity.com/paper/2302.12433/) (2023)
- [Mitigating the Alignment Tax of RLHF](https://mlsanity.com/paper/2309.06256/) (2023)
- [Kimina-Prover Preview: Towards Large Formal Reasoning Models with Reinforcement Learning](https://mlsanity.com/paper/2504.11354/) (2025)
- [AIMO-2 Winning Solution: Building State-of-the-Art Mathematical Reasoning Models with OpenMathReasoning dataset](https://mlsanity.com/paper/2504.16891/) (2025)
- [PutnamBench: Evaluating Neural Theorem-Provers on the Putnam Mathematical Competition](https://mlsanity.com/paper/2407.11214/) (2024)
- [Goedel-Prover: A Frontier Model for Open-Source Automated Theorem Proving](https://mlsanity.com/paper/2502.07640/) (2025)
- [Baldur: Whole-Proof Generation and Repair with Large Language Models](https://mlsanity.com/paper/2303.04910/) (2023)

## Built on by (most cited first, 30 of 154)

- [WoW: Towards a World omniscient World model Through Embodied Interaction](https://mlsanity.com/paper/2509.22642/) (2025)
- [Hilbert: Recursively Building Formal Proofs with Informal Reasoning](https://mlsanity.com/paper/2509.22819/) (2025)
- [AdvancedIF: Rubric-Based Benchmarking and Reinforcement Learning for Advancing LLM Instruction Following](https://mlsanity.com/paper/2511.10507/) (2025)
- [Code as Agent Harness](https://mlsanity.com/paper/2605.18747/) (2026)
- [Seed-Prover 1.5: Mastering Undergraduate-Level Theorem Proving via Learning from Experience](https://mlsanity.com/paper/2512.17260/) (2025)
- [Ax-Prover: A Deep Reasoning Agentic Framework for Theorem Proving in Mathematics and Quantum Physics](https://mlsanity.com/paper/2510.12787/) (2025)
- [Scaling up Multi-Turn Off-Policy RL and Multi-Agent Tree Search for LLM Step-Provers](https://mlsanity.com/paper/2509.06493/) (2025)
- [FATE: A Formal Benchmark Series for Frontier Algebra of Multiple Difficulty Levels](https://mlsanity.com/paper/2511.02872/) (2025)
- [Advancing Mathematics Research with AI-Driven Formal Proof Search](https://mlsanity.com/paper/2605.22763/) (2026)
- [Adaptation of Agentic AI: A Survey of Post-Training, Memory, and Skills](https://mlsanity.com/paper/2512.16301/) (2025)
- [Aria: An Agent For Retrieval and Iterative Auto-Formalization via Dependency Graph](https://mlsanity.com/paper/2510.04520/) (2025)
- [ProofFlow: A Dependency Graph Approach to Faithful Proof Autoformalization](https://mlsanity.com/paper/2510.15981/) (2025)
- [ReForm: Reflective Autoformalization with Prospective Bounded Sequence Optimization](https://mlsanity.com/paper/2510.24592/) (2025)
- [A Minimal Agent for Automated Theorem Proving](https://mlsanity.com/paper/2602.24273/) (2026)
- [AI co-mathematician: Accelerating mathematicians with agentic AI](https://mlsanity.com/paper/2605.06651/) (2026)
- [MLS-Bench: A Holistic and Rigorous Assessment of AI Systems on Building Better AI](https://mlsanity.com/paper/2605.08678/) (2026)
- [StepFun-Formalizer: Unlocking the Autoformalization Potential of LLMs through Knowledge-Reasoning Fusion](https://mlsanity.com/paper/2508.04440/) (2025)
- [DRPO: Efficient Reasoning via Decoupled Reward Policy Optimization](https://mlsanity.com/paper/2510.04474/) (2025)
- [IMProofBench: Benchmarking AI on Research-Level Mathematical Proof Generation](https://mlsanity.com/paper/2509.26076/) (2025)
- [R3L: Reflect-then-Retry Reinforcement Learning with Language-Guided Exploration, Pivotal Credit, and Positive Amplification](https://mlsanity.com/paper/2601.03715/) (2026)
- [AlgoVeri: An Aligned Benchmark for Verified Code Generation on Classical Algorithms](https://mlsanity.com/paper/2602.09464/) (2026)
- [LEAP: Supercharging LLMs for Formal Mathematics with Agentic Frameworks](https://mlsanity.com/paper/2606.03303/) (2026)
- [LeanMarathon: Toward Reliable AI Co-Mathematicians through Long-Horizon Lean Autoformalization](https://mlsanity.com/paper/2606.05400/) (2026)
- [HERMES: Towards Efficient and Verifiable Mathematical Reasoning in LLMs](https://mlsanity.com/paper/2511.18760/) (2025)
- [Goedel-Code-Prover: Hierarchical Proof Search for Open State-of-the-Art Code Verification](https://mlsanity.com/paper/2603.19329/) (2026)
- [ASSESS: A Semantic and Structural Evaluation Framework for Statement Similarity](https://mlsanity.com/paper/2509.22246/) (2025)
- [MerLean: An Agentic Framework for Autoformalization in Quantum Computation](https://mlsanity.com/paper/2602.16554/) (2026)
- [Scaling Self-Play with Self-Guidance](https://mlsanity.com/paper/2604.20209/) (2026)
- [Formal Conjectures: An Open and Evolving Benchmark for Verified Discovery in Mathematics](https://mlsanity.com/paper/2605.13171/) (2026)
- [Beyond Compilation: Evaluating Faithful Natural-Language-to-Lean Statement Formalization](https://mlsanity.com/paper/2606.31002/) (2026)

## Abstract (arXiv)

We introduce Goedel-Prover-V2, a series of open-source language models that set a new state-of-the-art in automated theorem proving. Built on the standard expert iteration and reinforcement learning pipeline, our approach incorporates three key innovations: (1) Scaffolded data synthesis: We generate synthetic tasks of increasing difficulty to train the model to master increasingly complex theorems; (2) Verifier-guided self-correction: We enable the model to iteratively revise its proofs by leveraging feedback from the Lean compiler; (3) Model averaging: We merge model checkpoints to mitigate the decrease in model output diversity in later stages of training. Our small model, Goedel-Prover-V2-8B, reaches 84.6% pass@32 on MiniF2F and outperforms DeepSeek-Prover-V2-671B under the same metric, despite being 80X smaller. Our flagship model, Goedel-Prover-V2-32B, achieves 88.1% on MiniF2F at pass@32 in standard mode and 90.4% in self-correction mode, outperforming prior SOTA by a large margin. Additionally, our flagship model solves 86 problems on PutnamBench at pass@184, securing the first place among open-source models on the leaderboard, surpassing DeepSeek-Prover-V2-671B's record of solving 47 problems by pass@1024 with a significantly smaller model size and compute budget. At the time of its release (July-August 2025), Goedel-Prover-V2 achieves the strongest overall performance among all open-source theorem provers. It also ranks among the top-performing models--including closed-source systems with publicly reported performance--under a constrained test-time compute budget. Our models, code, and data are released at https://github.com/Goedel-LM/Goedel-Prover-V2.