---
title: "A Survey on Large Language Models for Mathematical Reasoning"
description: "The paper offers no new data or benchmark. 170 references, cited by 17 papers here. Among them: 9."
authors: ["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", "Yang Yu"]
year: 2025
venue: "arXiv:2506.08446"
source: "https://arxiv.org/abs/2506.08446"
doi: "10.48550/arxiv.2506.08446"
arxiv: "2506.08446"
licence: "CC BY 4.0 (arXiv)"
licence_url: "http://creativecommons.org/licenses/by/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/wang-2025-survey-large-language-models-mathematical/"
---
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# A Survey on Large Language Models for Mathematical Reasoning

**Authors:** Peng-Yuan Wang, Tian-Shuo Liu, [Chenyang Wang](https://md.research.elamur.ai/free/en/authors/chenyang-wang/), Yi-Di Wang, Shu Yan, Cheng-Xing Jia, Xu-Hui Liu, Xin-Wei Chen, Jia-Cheng Xu, [Ziniu Li](https://md.research.elamur.ai/free/en/authors/ziniu-li/) and [Yang Yu](https://md.research.elamur.ai/free/en/authors/yang-yu/) · **Year:** 2025 · **Venue:** [arXiv:2506.08446](https://md.research.elamur.ai/free/en/venues/acm-computing-surveys/) ([ACM Computing Surveys 2025](https://md.research.elamur.ai/free/en/venues/acm-computing-surveys/2025/)) · **Publisher:** [Association for Computing Machinery](https://md.research.elamur.ai/free/en/publishers/association-for-computing-machinery/) · **Licence:** [CC BY 4.0 (arXiv)](http://creativecommons.org/licenses/by/4.0/)

**Links:** [Publisher's page](https://arxiv.org/abs/2506.08446) · [PDF](https://arxiv.org/pdf/2506.08446) · [DOI 10.48550/arxiv.2506.08446](https://doi.org/10.48550/arxiv.2506.08446) · [arXiv 2506.08446](https://arxiv.org/abs/2506.08446) · [OpenAlex](https://openalex.org/W7117259628)

**Citations:** 9 citations (OpenAlex, 2026-10-14) · [17](https://md.research.elamur.ai/free/en/papers/wang-2025-survey-large-language-models-mathematical/cited-by/) in our library, of the 149,439 papers whose bibliographies we read

## 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

- [Nanyang Technological University](https://md.research.elamur.ai/free/en/universities/nanyang-technological-university/) — University, Singapore, Singapore · 193 works · 27,739 citations
- [Nanjing University](https://md.research.elamur.ai/free/en/universities/nanjing-university/) — University, Nanjing, China · 102 works · 8,589 citations
- [Chinese University of Hong Kong, Shenzhen](https://md.research.elamur.ai/free/en/universities/chinese-university-of-hong-kong-shenzhen/) — University, Shenzhen, China · 57 works · 3,238 citations

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🧭 Topics (2): [🧠 Language models & pretraining](https://md.research.elamur.ai/free/en/topics/language-models/) · 4,145 works · [🧮 Reasoning](https://md.research.elamur.ai/free/en/topics/reasoning/) · 1,948 works

## 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.

```bibtex
@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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