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A Survey on Large Language Models for Mathematical Reasoning

Paper · 2025 · Peng-Yuan Wang, Tian-Shuo Liu, Chenyang Wang et al.

Summary

This survey, by Peng-Yuan Wang et al. (mainly Nanjing University), maps how large language models became capable of solving mathematical problems. It contrasts this with older rule-based and semantic-parsing systems that relied heavily on hand engineering. The authors split the capability into two parts:

  • Comprehension: learned during pre-training on mathematical corpora such as textbooks, papers and problem sets, increasingly supplemented with filtered and synthetic data.
  • Answer generation: has moved from predicting an answer directly to producing step-by-step Chain-of-Thought (CoT) solutions.

The review then groups enhancement techniques into prompting (In-Context Learning, CoT), supervised fine-tuning with distillation, reinforcement learning, search at inference time, self-improvement, and use of external tools or retrieval. Long CoT and "test-time scaling" receive particular attention. The paper offers no new data or benchmark. Its contribution is a unified taxonomy plus a diagnosis of open problems: exploration efficiency, wasteful reasoning paths, and weak transfer beyond mathematics. This makes it a useful entry point for anyone adapting reasoning methods to other fields.

Key points

  • Figure 1 tracks rapid gains in mathematical ability from 2024/3 to 2025/3. It covers open models (DeepSeek-Math 7B, Qwen2.5-Math 7B, QwQ-32B-preview, DeepSeek R1 671B, Qwen3) and closed ones (O1, O3, Claude 3.7 Sonnet, Gemini 2.0 Flash Thinking).
  • Grok 3 Beta is cited at 83.9% on AIME 2024. Against MAA human data, that score would rank among the top 2.5% of contestants.
  • The authors name three central challenges:
    • exploring efficiently under limited sampling budgets during RL;
    • producing lengthy or sub-optimal reasoning chains, since outcome-only rewards ignore step quality;
    • generalizing poorly from math to open-ended domains.
  • Proposed remedies include:
    • verification-aware optimization, using formal proof systems such as Lean to check intermediate steps;
    • tool and retrieval integration, organized through the learnware paradigm;
    • scaling up reward models;
    • generative reward models trained via long CoT RL.
  • The survey positions itself against earlier reviews that cover traditional methods, datasets and fine-tuning, multi-modal math, System 2 thinking, and RL for reasoning.

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

 Institutions

 Fields, topics and concepts

Cite

Cite as Peng-Yuan Wang, Tian-Shuo Liu, Chenyang Wang, Yi-Di Wang, Shu Yan, Cheng-Xing Jia, Xu-Hui Liu, Xin-Wei Chen, Jia-Cheng Xu, Ziniu Li and Yang Yu. 2025. A Survey on Large Language Models for Mathematical Reasoning. arXiv:2506.08446.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.48550/arxiv.2506.08446 · arXiv 2506.08446

@misc{wang2025survey,
  title = {{A Survey on Large Language Models for Mathematical Reasoning}},
  author = {Peng-Yuan Wang, Tian-Shuo Liu, Chenyang Wang, Yi-Di Wang, Shu Yan, Cheng-Xing Jia, Xu-Hui Liu, Xin-Wei Chen, Jia-Cheng Xu, Ziniu Li and Yang Yu},
  year = {2025},
  doi = {10.48550/arxiv.2506.08446},
  eprint = {2506.08446},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2506.08446}
}

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