# DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition

arXiv: https://arxiv.org/abs/2504.21801 · HTML: https://mlsanity.com/paper/2504.21801/

## Key facts

- Cited by 287 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 20 of its 38 references that are in the map.
- First posted on arXiv 30 Apr 2025.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 20 of 20)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [Generative Language Modeling for Automated Theorem Proving](https://mlsanity.com/paper/2009.03393/) (2020)
- [DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Data](https://mlsanity.com/paper/2405.14333/) (2024)
- [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)
- [Kimina-Prover Preview: Towards Large Formal Reasoning Models with Reinforcement Learning](https://mlsanity.com/paper/2504.11354/) (2025)
- [Goedel-Prover: A Frontier Model for Open-Source Automated Theorem Proving](https://mlsanity.com/paper/2502.07640/) (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)
- [STP: Self-play LLM Theorem Provers with Iterative Conjecturing and Proving](https://mlsanity.com/paper/2502.00212/) (2025)
- [Decomposing the Enigma: Subgoal-based Demonstration Learning for Formal Theorem Proving](https://mlsanity.com/paper/2305.16366/) (2023)
- [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)
- [Leanabell-Prover: Posttraining Scaling in Formal Reasoning](https://mlsanity.com/paper/2504.06122/) (2025)
- [Formal Theorem Proving by Rewarding LLMs to Decompose Proofs Hierarchically](https://mlsanity.com/paper/2411.01829/) (2024)
- [SubgoalXL: Subgoal-based Expert Learning for Theorem Proving](https://mlsanity.com/paper/2408.11172/) (2024)

## Built on by (most cited first, 30 of 287)

- [Absolute Zero: Reinforced Self-play Reasoning with Zero Data](https://mlsanity.com/paper/2505.03335/) (2025)
- [The Landscape of Agentic Reinforcement Learning for LLMs: A Survey](https://mlsanity.com/paper/2509.02547/) (2025)
- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [Goedel-Prover-V2: Scaling Formal Theorem Proving with Scaffolded Data Synthesis and Self-Correction](https://mlsanity.com/paper/2508.03613/) (2025)
- [WebShaper: Agentically Data Synthesizing via Information-Seeking Formalization](https://mlsanity.com/paper/2507.15061/) (2025)
- [Seed-Prover: Deep and Broad Reasoning for Automated Theorem Proving](https://mlsanity.com/paper/2507.23726/) (2025)
- [DeepSeekMath-V2: Towards Self-Verifiable Mathematical Reasoning](https://mlsanity.com/paper/2511.22570/) (2025)
- [Rewarding the Unlikely: Lifting GRPO Beyond Distribution Sharpening](https://mlsanity.com/paper/2506.02355/) (2025)
- [Breaking the Exploration Bottleneck: Rubric-Scaffolded Reinforcement Learning for General LLM Reasoning](https://mlsanity.com/paper/2508.16949/) (2025)
- [Hilbert: Recursively Building Formal Proofs with Informal Reasoning](https://mlsanity.com/paper/2509.22819/) (2025)
- [Aristotle: IMO-level Automated Theorem Proving](https://mlsanity.com/paper/2510.01346/) (2025)
- [LEXam: Benchmarking Legal Reasoning on 340 Law Exams](https://mlsanity.com/paper/2505.12864/) (2025)
- [DeepAnalyze: Agentic Large Language Models for Autonomous Data Science](https://mlsanity.com/paper/2510.16872/) (2025)
- [Numina-Lean-Agent: An Open and General Agentic Reasoning System for Formal Mathematics](https://mlsanity.com/paper/2601.14027/) (2026)
- [FormalMATH: Benchmarking Formal Mathematical Reasoning of Large Language Models](https://mlsanity.com/paper/2505.02735/) (2025)
- [Code as Agent Harness](https://mlsanity.com/paper/2605.18747/) (2026)
- [Solver-Informed RL: Grounding Large Language Models for Authentic Optimization Modeling](https://mlsanity.com/paper/2505.11792/) (2025)
- [Solving Formal Math Problems by Decomposition and Iterative Reflection](https://mlsanity.com/paper/2507.15225/) (2025)
- [VERINA: Benchmarking Verifiable Code Generation](https://mlsanity.com/paper/2505.23135/) (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)
- [Trust Region On-Policy Distillation](https://mlsanity.com/paper/2606.01249/) (2026)
- [Scaling Reasoning, Losing Control: Evaluating Instruction Following in Large Reasoning Models](https://mlsanity.com/paper/2505.14810/) (2025)
- [Scaling up Multi-Turn Off-Policy RL and Multi-Agent Tree Search for LLM Step-Provers](https://mlsanity.com/paper/2509.06493/) (2025)
- [Dynamic Mixture of Curriculum LoRA Experts for Continual Multimodal Instruction Tuning](https://mlsanity.com/paper/2506.11672/) (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)
- [DeepTheorem: Advancing LLM Reasoning for Theorem Proving Through Natural Language and Reinforcement Learning](https://mlsanity.com/paper/2505.23754/) (2025)
- [Get Experience from Practice: LLM Agents with Record & Replay](https://mlsanity.com/paper/2505.17716/) (2025)

## Abstract (arXiv)

We introduce DeepSeek-Prover-V2, an open-source large language model designed for formal theorem proving in Lean 4, with initialization data collected through a recursive theorem proving pipeline powered by DeepSeek-V3. The cold-start training procedure begins by prompting DeepSeek-V3 to decompose complex problems into a series of subgoals. The proofs of resolved subgoals are synthesized into a chain-of-thought process, combined with DeepSeek-V3's step-by-step reasoning, to create an initial cold start for reinforcement learning. This process enables us to integrate both informal and formal mathematical reasoning into a unified model. The resulting model, DeepSeek-Prover-V2-671B, achieves state-of-the-art performance in neural theorem proving, reaching 88.9% pass ratio on the MiniF2F-test and solving 49 out of 658 problems from PutnamBench. In addition to standard benchmarks, we introduce ProverBench, a collection of 325 formalized problems, to enrich our evaluation, including 15 selected problems from the recent AIME competitions (years 24-25). Further evaluation on these 15 AIME problems shows that the model successfully solves 6 of them. In comparison, DeepSeek-V3 solves 8 of these problems using majority voting, highlighting that the gap between formal and informal mathematical reasoning in large language models is substantially narrowing.