A Survey on Large Language Models for Mathematical Reasoning

Fuente: arXiv
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Hauptverfasser: Wang, Peng-Yuan, Liu, Tian-Shuo, Wang, Chenyang, Wang, Yi-Di, Yan, Shu, Jia, Cheng-Xing, Liu, Xu-Hui, Chen, Xin-Wei, Xu, Jia-Cheng, Li, Ziniu, Yu, Yang
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Veröffentlicht: 2025
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author Wang, Peng-Yuan
Liu, Tian-Shuo
Wang, Chenyang
Wang, Yi-Di
Yan, Shu
Jia, Cheng-Xing
Liu, Xu-Hui
Chen, Xin-Wei
Xu, Jia-Cheng
Li, Ziniu
Yu, Yang
author_facet Wang, Peng-Yuan
Liu, Tian-Shuo
Wang, Chenyang
Wang, Yi-Di
Yan, Shu
Jia, Cheng-Xing
Liu, Xu-Hui
Chen, Xin-Wei
Xu, Jia-Cheng
Li, Ziniu
Yu, Yang
contents Mathematical reasoning has long represented one of the most fundamental and challenging frontiers in artificial intelligence research. In recent years, large language models (LLMs) have achieved significant advances in this area. This survey examines the development of mathematical reasoning abilities in LLMs through two high-level cognitive phases: comprehension, where models gain mathematical understanding via diverse pretraining strategies, and answer generation, which has progressed from direct prediction to step-by-step Chain-of-Thought (CoT) reasoning. We review methods for enhancing mathematical reasoning, ranging from training-free prompting to fine-tuning approaches such as supervised fine-tuning and reinforcement learning, and discuss recent work on extended CoT and "test-time scaling". Despite notable progress, fundamental challenges remain in terms of capacity, efficiency, and generalization. To address these issues, we highlight promising research directions, including advanced pretraining and knowledge augmentation techniques, formal reasoning frameworks, and meta-generalization through principled learning paradigms. This survey tries to provide some insights for researchers interested in enhancing reasoning capabilities of LLMs and for those seeking to apply these techniques to other domains.
format Preprint
id arxiv_https___arxiv_org_abs_2506_08446
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A Survey on Large Language Models for Mathematical Reasoning
Wang, Peng-Yuan
Liu, Tian-Shuo
Wang, Chenyang
Wang, Yi-Di
Yan, Shu
Jia, Cheng-Xing
Liu, Xu-Hui
Chen, Xin-Wei
Xu, Jia-Cheng
Li, Ziniu
Yu, Yang
Artificial Intelligence
Computation and Language
Mathematical reasoning has long represented one of the most fundamental and challenging frontiers in artificial intelligence research. In recent years, large language models (LLMs) have achieved significant advances in this area. This survey examines the development of mathematical reasoning abilities in LLMs through two high-level cognitive phases: comprehension, where models gain mathematical understanding via diverse pretraining strategies, and answer generation, which has progressed from direct prediction to step-by-step Chain-of-Thought (CoT) reasoning. We review methods for enhancing mathematical reasoning, ranging from training-free prompting to fine-tuning approaches such as supervised fine-tuning and reinforcement learning, and discuss recent work on extended CoT and "test-time scaling". Despite notable progress, fundamental challenges remain in terms of capacity, efficiency, and generalization. To address these issues, we highlight promising research directions, including advanced pretraining and knowledge augmentation techniques, formal reasoning frameworks, and meta-generalization through principled learning paradigms. This survey tries to provide some insights for researchers interested in enhancing reasoning capabilities of LLMs and for those seeking to apply these techniques to other domains.
title A Survey on Large Language Models for Mathematical Reasoning
topic Artificial Intelligence
Computation and Language
url https://arxiv.org/abs/2506.08446