---
title: "DeepSeekMath — Shao 2024"
description: "Open language models have trailed closed systems like GPT-4 and Gemini-Ultra on competition-level mathematics."
authors: ["Zhihong Shao", "Peiyi Wang", "Qihao Zhu", "Runxin Xu", "Junxiao Song", "Xiao Bi", "Haowei Zhang", "Mingchuan Zhang", "Y. K. Li", "Y. Wu", "Daya Guo"]
year: 2024
venue: "arXiv:2402.03300"
source: "https://arxiv.org/abs/2402.03300"
doi: "10.48550/arxiv.2402.03300"
arxiv: "2402.03300"
licence: "arXiv — non-exclusive licence to distribute"
licence_url: "https://arxiv.org/licenses/nonexclusive-distrib/1.0/license.html"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/shao-2024-deepseekmath-pushing-limits-mathematical-reasoning/"
---
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# DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models

**Authors:** [Zhihong Shao](https://md.research.elamur.ai/free/en/authors/zhihong-shao/), [Peiyi Wang](https://md.research.elamur.ai/free/en/authors/peiyi-wang/), [Qihao Zhu](https://md.research.elamur.ai/free/en/authors/qihao-zhu/), [Runxin Xu](https://md.research.elamur.ai/free/en/authors/runxin-xu/), [Junxiao Song](https://md.research.elamur.ai/free/en/authors/junxiao-song/), [Xiao Bi](https://md.research.elamur.ai/free/en/authors/xiao-bi/), [Haowei Zhang](https://md.research.elamur.ai/free/en/authors/haowei-zhang/), Mingchuan Zhang, Y. K. Li, [Y. Wu](https://md.research.elamur.ai/free/en/authors/y-wu/), [Daya Guo](https://md.research.elamur.ai/free/en/authors/daya-guo/) · **Year:** 2024 · **Venue:** arXiv:2402.03300 · **Licence:** [arXiv — non-exclusive licence to distribute](https://arxiv.org/licenses/nonexclusive-distrib/1.0/license.html)

**Links:** [Publisher's page](https://arxiv.org/abs/2402.03300) · [PDF](https://arxiv.org/pdf/2402.03300v3) · [DOI 10.48550/arxiv.2402.03300](https://doi.org/10.48550/arxiv.2402.03300) · [arXiv 2402.03300](https://arxiv.org/abs/2402.03300) · [OpenAlex](https://openalex.org/W4391631327)

**Citations:** 99 citations (openalex-snapshot · 2026-10-14) · [1914](#cited-by) in our library, of the 140673 papers whose bibliographies we read

## Summary
Open language models have trailed closed systems like GPT-4 and Gemini-Ultra on competition-level mathematics. To narrow this gap, the authors continue pre-training DeepSeek-Coder-Base-v1.5 7B on 500B tokens. The core of this data is the DeepSeekMath Corpus, 120B math tokens taken from Common Crawl. The corpus was built in rounds. A fastText classifier, first trained on OpenWebMath, scores web pages. Human annotators then mark math-heavy domains and URL paths, and the larger seed set is used to retrain the classifier. Next, the base model is instruction-tuned on chain-of-thought, program-of-thought and tool-integrated solutions. It is then trained with GRPO, a PPO variant that drops the critic network. GRPO instead takes its baseline from the rewards of several answers sampled for the same question, which cuts memory use. The resulting DeepSeekMath-RL 7B scores 51.7% on MATH with no tools and no voting. It is the first open model to pass 50% there, close to GPT-4. The work shows that well-filtered web data and cheaper RL can make a small open model competitive with much larger ones.

## Key points
- The DeepSeekMath Corpus (120B tokens) is about 7× larger than the math web data used for Minerva and about 9× larger than OpenWebMath. It includes non-English pages, which improves results on Chinese benchmarks such as CMATH and Gaokao.
- DeepSeekMath-Base 7B reaches 64.2% on GSM8K and 36.2% on MATH, beating Minerva 540B. Math training also raises MMLU and BBH scores. Starting from a code model helps, while adding arXiv papers brought no measurable gain.
- GRPO uses only part of the English instruction data and still raises GSM8K from 82.9% to 88.2%, MATH from 46.8% to 51.7% and CMATH from 84.6% to 88.8%. With self-consistency over 64 samples, MATH reaches 60.9%.
- The paper treats RFT, DPO, PPO and GRPO as cases of one RL framework. RL improves Maj@K but not Pass@K, which suggests it makes the model's outputs more reliable rather than giving it new abilities.
- Limitations: the model is weaker on geometry and formal proofs than closed models, and few-shot prompting does not help it the way it helps GPT-4. Code and models are at github.com/deepseek-ai/DeepSeek-Math.

*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: [Mathematics & statistics](https://md.research.elamur.ai/free/en/shelves/mathematics/)

## Cited by

Cited by

1914 papers of our library cite it (of the 140673 whose bibliographies we read); 48 of them have a page here, 1866 not yet.

- [L1: Controlling How Long A Reasoning Model Thinks With Reinforcement Learning](https://md.research.elamur.ai/free/en/papers/aggarwal-2025-l1-controlling-long-reasoning-model/)
- [SmolLM2: When Smol Goes Big -- Data-Centric Training of a Small Language Model](https://md.research.elamur.ai/free/en/papers/allal-2025-smollm2-smol-goes-big-data/)
- [AlphaMath Almost Zero: Process Supervision without Process](https://md.research.elamur.ai/free/en/papers/chen-2024-alphamath-almost-zero-process-supervision/)
- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://md.research.elamur.ai/free/en/papers/chen-2025-towards-reasoning-era-survey-long/)
- [Process Reinforcement through Implicit Rewards](https://md.research.elamur.ai/free/en/papers/cui-2025-process-reinforcement-through-implicit-rewards/)
- [DeepSeek-Coder-V2: Breaking the Barrier of Closed-Source Models in Code Intelligence](https://md.research.elamur.ai/free/en/papers/deepseek-2024-ai-deepseek-coder-v2-breaking-barrier/)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://md.research.elamur.ai/free/en/papers/deepseek-2025-ai-deepseek-r1-incentivizing-reasoning-capability/)
- [DeepSeek-V3.2: Pushing the Frontier of Open Large Language Models](https://md.research.elamur.ai/free/en/papers/deepseek-2025-ai-deepseek-v3-2-pushing/)
- [Cognitive Behaviors that Enable Self-Improving Reasoners, or, Four Habits of Highly Effective STaRs](https://md.research.elamur.ai/free/en/papers/gandhi-2025-cognitive-behaviors-that-enable-self/)
- [Omni-MATH: A Universal Olympiad Level Mathematic Benchmark For Large Language Models](https://md.research.elamur.ai/free/en/papers/gao-2024-omni-math-universal-olympiad-level/)
- [GLM-4.5: Agentic, Reasoning, and Coding (ARC) Foundation Models](https://md.research.elamur.ai/free/en/papers/glm-2025-4-glm-4-5-agentic/)
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- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://md.research.elamur.ai/free/en/papers/jin-2025-search-r1-training-llms-reason/)
- [Training Language Models to Self-Correct via Reinforcement Learning](https://md.research.elamur.ai/free/en/papers/kumar-2024-training-language-models-self-correct/)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://md.research.elamur.ai/free/en/papers/lambert-2024-tulu-3-pushing-frontiers-open/)
- [Dicta-LM 3.0: Advancing The Frontier of Hebrew Sovereign LLMs](https://md.research.elamur.ai/free/en/papers/langstream-2026-shmidman-dicta-lm-3-0-advancing/)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://md.research.elamur.ai/free/en/papers/liu-2025-understanding-r1-zero-like-training/)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://md.research.elamur.ai/free/en/papers/luo-2023-wizardmath-empowering-mathematical-reasoning-large/)
- [Adaptive Emotion Management in Human-robot Dialogue using Online Group Relative Policy Optimization](https://md.research.elamur.ai/free/en/papers/manaseryan-2026-adaptive-emotion-management-human-robot/)
- [DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition](https://md.research.elamur.ai/free/en/papers/ren-2025-deepseek-prover-v2-advancing-formal/)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://md.research.elamur.ai/free/en/papers/sheng-2024-hybridflow-flexible-efficient-rlhf-framework/)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://md.research.elamur.ai/free/en/papers/snell-2024-scaling-llm-test-time-compute/)
- [R1-Searcher: Incentivizing the Search Capability in LLMs via Reinforcement Learning](https://md.research.elamur.ai/free/en/papers/song-2025-r1-searcher-incentivizing-search/)
- [Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models](https://md.research.elamur.ai/free/en/papers/sui-2025-stop-overthinking-survey-efficient-reasoning/)
- [AuthorMix: Modular Authorship Style Transfer via Layer-wise Adapter Mixing](https://md.research.elamur.ai/free/en/papers/thillainathan-2026-authormix-modular-authorship-style-transfer/)
- [Interpretable Preferences via Multi-Objective Reward Modeling and Mixture-of-Experts](https://md.research.elamur.ai/free/en/papers/wang-2024-interpretable-preferences-multi-objective-reward/)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://md.research.elamur.ai/free/en/papers/wang-2025-80-20-rule-high-entropy/)
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- [Logic-RL: Unleashing LLM Reasoning with Rule-Based Reinforcement Learning](https://md.research.elamur.ai/free/en/papers/xie-2025-logic-rl-unleashing-llm/)
- [DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Data](https://md.research.elamur.ai/free/en/papers/xin-2024-deepseek-prover-advancing-theorem-proving/)
- [DeepSeek-Prover-V1.5: Harnessing Proof Assistant Feedback for Reinforcement Learning and Monte-Carlo Tree Search](https://md.research.elamur.ai/free/en/papers/xin-2024-deepseek-prover-v1-5-harnessing/)
- [A Practical Evaluation Method for Long-Form Simultaneous Speech-to-Speech Translation](https://md.research.elamur.ai/free/en/papers/xue-2026-practical-evaluation-method-long-form/)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://md.research.elamur.ai/free/en/papers/yang-2024-qwen2-5-math-technical-report/)
- [Qwen3 Technical Report](https://md.research.elamur.ai/free/en/papers/yang-2025-qwen3-technical-report/)
- [LIMO: Less is More for Reasoning](https://md.research.elamur.ai/free/en/papers/ye-2025-limo-less-more-reasoning/)
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- [Instruction Tuning for Large Language Models: A Survey](https://md.research.elamur.ai/free/en/papers/zhang-2023-instruction-tuning-large-language-models/)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://md.research.elamur.ai/free/en/papers/zhang-2025-lessons-developing-process-reward-models/)
- [A Survey of Large Language Models](https://md.research.elamur.ai/free/en/papers/zhao-2023-survey-large-language-models/)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://md.research.elamur.ai/free/en/papers/zheng-2024-llamafactory-unified-efficient-fine-tuning/)
- [Group Sequence Policy Optimization](https://md.research.elamur.ai/free/en/papers/zheng-2025-group-sequence-policy-optimization/)
- [Simplify-Pro: A Two-level and Progressive LLM-based Framework for Auto Long Text Simplification](https://md.research.elamur.ai/free/en/papers/zhou-2026-simplify-pro-two-level-progressive/)
- [Large Language Models for Information Retrieval: A Survey](https://md.research.elamur.ai/free/en/papers/zhu-2023-large-language-models-information-retrieval/)
- [BigCodeBench: Benchmarking Code Generation with Diverse Function Calls and Complex Instructions](https://md.research.elamur.ai/free/en/papers/zhuo-2024-bigcodebench-benchmarking-code-generation-diverse/)

## Cite

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@misc{shao2024deepseekmath,
  title = {{DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models}},
  author = {Shao, Zhihong and Wang, Peiyi and Zhu, Qihao and Xu, Runxin and Song, Junxiao and Bi, Xiao and Zhang, Haowei and Zhang, Mingchuan and Li, Y. K. and Wu, Y. and Guo, Daya},
  year = {2024},
  doi = {10.48550/arxiv.2402.03300},
  eprint = {2402.03300},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2402.03300}
}
```

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