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DeepSeekMath-V2: Towards Self-Verifiable Mathematical Reasoning

Paper · 2025 · Zhihong Shao, Yuxiang Luo, Chengda Lu et al.

Summary

Reinforcement learning that only checks final answers has let LLMs master answer-based contests like AIME and HMMT. However, it cannot tell sound reasoning from lucky guesses and gives no training signal for theorem proving. DeepSeekMath-V2, built on DeepSeek-V3.2-Exp-Base, addresses this by teaching a model to check proofs written in natural language. The authors first train a verifier with RL on expert-graded proofs for olympiad problems collected from AoPS. They then add a meta-verifier that penalizes invented flaws in the verifier's critiques. The verifier acts as a reward model for a proof generator, which must also grade its own output honestly. This pushes the generator to find and repair errors before answering. As the generator improves, extra verification compute auto-labels difficult new proofs, so the verifier can be retrained without more human annotation. With scaled test-time search, the single resulting model reaches gold-medal level on IMO 2025 and CMO 2024 and scores 118/120 on Putnam 2024. The work suggests that self-checking LLMs are a viable path toward reliable mathematical AI, including on problems with no reference solutions.

Key points

  • Training data: 17,503 proof-oriented problems were crawled from Art of Problem Solving (AoPS) contest collections. Experts scored candidate proofs on a three-level scale (0, 0.5, 1).
  • Meta-verification: This step raised the average quality of the verifier's analyses from 0.85 to 0.96 on a validation split, while the accuracy of predicted proof scores stayed the same.
  • Generator reward: The reward weights proof quality at α = 0.76 and the accuracy of the generator's self-assessment at β = 0.24.
  • Competition results:
    • IMO 2025: 5 of 6 problems solved.
    • CMO 2024: 4 problems solved plus partial credit on another.
    • Putnam 2024: 118/120, above the best human score of 90.
    • Test-time search ran up to 16 refinement rounds with 64 verification passes per candidate proof.
  • IMO-ProofBench: On the basic set, the model outperforms DeepMind's DeepThink (IMO Gold); on the advanced set, it remains competitive. Model and method are released on GitHub (deepseek-ai/DeepSeek-Math-V2).

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

 Fields, topics and concepts

📚 Shelves 5The field of science this work belongs to (OpenAlex fields).Computer Science · 18,614 worksArtificial Intelligence · 17,965 worksArts and Humanities · 17,450 worksLanguage and Linguistics · 17,296 worksComputational Theory and Mathematics · 321 works

🧭 Topics 1Research subjects and languages the work is about.Reasoning · 1,685 works

Cite

Cite as Zhihong Shao, Yuxiang Luo, Chengda Lu, Z.Z. Ren, Jiewen Hu, Tian Ye, Zhibin Gou, Shirong Ma and Xiaokang Zhang. 2025. DeepSeekMath-V2: Towards Self-Verifiable Mathematical Reasoning. arXiv:2511.22570.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.48550/arxiv.2511.22570 · arXiv 2511.22570

@misc{shao2025deepseekmath,
  title = {{DeepSeekMath-V2: Towards Self-Verifiable Mathematical Reasoning}},
  author = {Zhihong Shao, Yuxiang Luo, Chengda Lu, Z.Z. Ren, Jiewen Hu, Tian Ye, Zhibin Gou, Shirong Ma and Xiaokang Zhang},
  year = {2025},
  doi = {10.48550/arxiv.2511.22570},
  eprint = {2511.22570},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2511.22570}
}

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