Paper 2511.22570
DeepSeekMath-V2: Towards Self-Verifiable Mathematical Reasoning
- Published
- Nov 2025
- Research lab
- DeepSeek
- Citations
- 60
- GitHub
- 1.6K stars
01 In brief
Summary
DeepSeekMath-V2 is a large language model for natural-language theorem proving, built on DeepSeek-V3.2-Exp-Base, that achieves self-verifiable mathematical reasoning.
The authors argue that final-answer rewards are insufficient because correct answers do not guarantee correct reasoning and are inapplicable to theorem proving.
They train a verifier using reinforcement learning with expert-annotated proof scores and introduce meta-verification to reduce hallucinated issues.
A proof generator is then trained using the verifier as a reward model, incentivizing it to identify and resolve issues in its own proofs.
The verifier and generator are iteratively improved in a synergistic cycle, with scaled verification compute enabling automated labeling of new proofs.
DeepSeekMath-V2 outperforms GPT-5-Thinking-High and Gemini 2.5-Pro on CNML-level problems, and with scaled test-time compute achieves gold-level scores on IMO 2025 and CMO 2024, and 118/120 on Putnam 2024, surpassing the highest human score of 90.
On IMO-ProofBench, it outperforms DeepMind's DeepThink (IMO Gold) on the basic set and remains competitive on the advanced set.
02 From the paper
Abstract
Large language models have made significant progress in mathematical reasoning, which serves as an important testbed for AI and could impact scientific research if further advanced. By scaling reasoning with reinforcement learning that rewards correct final answers, LLMs have improved from poor performance to saturating quantitative reasoning competitions like AIME and HMMT in one year. However, this approach faces fundamental limitations. Pursuing higher final answer accuracy doesn't address a key issue: correct answers don't guarantee correct reasoning. Moreover, many mathematical tasks like theorem proving require rigorous step-by-step derivation rather than numerical answers, making final answer rewards inapplicable. To push the limits of deep reasoning, we believe it is necessary to verify the comprehensiveness and rigor of mathematical reasoning. Self-verification is particularly important for scaling test-time compute, especially for open problems without known solutions. Towards self-verifiable mathematical reasoning, we investigate how to train an accurate and faithful LLM-based verifier for theorem proving. We then train a proof generator using the verifier as the reward model, and incentivize the generator to identify and resolve as many issues as possible in their own proofs before finalizing them. To maintain the generation-verification gap as the generator becomes stronger, we propose to scale verification compute to automatically label new hard-to-verify proofs, creating training data to further improve the verifier. Our resulting model, DeepSeekMath-V2, demonstrates strong theorem-proving capabilities, achieving gold-level scores on IMO 2025 and CMO 2024 and a near-perfect 118/120 on Putnam 2024 with scaled test-time compute.