数学推理是评估人类智能基础认知能力的基石。近年来，用于自动求解数学问题的大语言模型（Large Language Models，LLMs）开发热度显著攀升。然而，数学问题类型纷繁多样，面向LLM的技术在不同数据集和设置下接受评估，这种多样性导致人们难以厘清这一新兴领域的真实进展与障碍。本综述聚焦四个核心维度展开研究：其一，全面梳理已被探究的各类数学问题及其对应的数据集；其二，考察为求解数学问题而提出的各类面向LLM的技术；其三，概述影响LLMs求解数学问题的因素与相关关切；其四，阐明该领域仍存的挑战。据我们所知，本综述是首批针对数学领域LLMs发展格局的广泛研究之一，为这一快速演进领域的当前现状、已有成果及未来挑战提供了整体性视角。
英文摘要：
Mathematical reasoning serves as a cornerstone for assessing the fundamental cognitive capabilities of human intelligence. In recent times, there has been a notable surge in the development of Large Language Models (LLMs) geared towards the automated resolution of mathematical problems. However, the landscape of mathematical problem types is vast and varied, with LLM-oriented techniques undergoing evaluation across diverse datasets and settings. This diversity makes it challenging to discern the true advancements and obstacles within this burgeoning field. This survey endeavors to address four pivotal dimensions: i) a comprehensive exploration of the various mathematical problems and their corresponding datasets that have been investigated; ii) an examination of the spectrum of LLM-oriented techniques that have been proposed for mathematical problem-solving; iii) an overview of factors and concerns affecting LLMs in solving math; and iv) an elucidation of the persisting challenges within this domain. To the best of our knowledge, this survey stands as one of the first extensive examinations of the landscape of LLMs in the realm of mathematics, providing a holistic perspective on the current state, accomplishments, and future challenges in this rapidly evolving field.
Towards Spoken Mathematical Reasoning: Benchmarking Speech-based Models over Multi-faceted Math Problems
Institute for Infocomm Research (I 2 R), A*STAR, Singapore（信息与通信研究 institute（I2R），A*STAR，新加坡）；Centre for Frontier AI Research (CFAR), A*STAR, Singapore（前沿人工智能研究 centre（CFAR），A*STAR，新加坡）
Riazi-8B: An Urdu Large Language Model for Mathematical Reasoning
School of Electrical Engineering and Computer Science (SEECS)（电气工程与计算机科学学院）；National University of Sciences and Technology (NUST)（国家科学与技术大学）；Department of Communication, Quality Management and Information Systems（通信、质量管理与信息系统系）；Mid Sweden University（中瑞典大学）
MathMist: A Parallel Multilingual Benchmark Dataset for Mathematical Problem Solving and Reasoning
BRAC University（布拉克大学）；United International University（国际联合大学）；Qatar Computing Research Institute（卡塔尔计算研究所）；Center for Computational & Data Sciences, Independent University, Bangladesh（计算与数据科学中心，独立大学，孟加拉国）；Amazon GenAI（亚马逊生成人工智能）；University of Virginia（弗吉尼亚大学）
A Survey of Mathematical Reasoning in the Era of Multimodal Large Language Model: Benchmark, Method & Challenges
The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；The Hong Kong University of Science and Technology（香港科技大学）；Nanyang Technological University（南洋理工大学）；Squirrel Ai Learning（松鼠Ai学习）
Is Your Model Really A Good Math Reasoner? Evaluating Mathematical Reasoning with Checklist
Xi’an Jiaotong-Liverpool University（西交利物浦大学）；University of Liverpool（利物浦大学）；University of Macau（澳门大学）；HKUST（香港科技大学）；Microsoft Research Asia（微软亚洲研究院）；Duke Kunshan University（昆山杜克大学）
Math-LLaVA: Bootstrapping Mathematical Reasoning for Multimodal Large Language Models
University of Electronic Science and Technology of China（电子科技大学）；Tongji University（同济大学）；National University of Singapore（新加坡国立大学）；Singapore University of Technology and Design（新加坡科技设计大学）
Atomic Thinking of LLMs: Decoupling and Exploring Mathematical Reasoning Abilities
Sun Yat-sen University（中山大学）；Tsinghua University（清华大学）；ByteDance Inc（字节跳动公司）；Arizona State University（亚利桑那州立大学）；Tencent Youtu Lab（腾讯优图实验室）；Fudan University（复旦大学）；Harbin Institute of Technology (Shenzhen)（哈尔滨工业大学（深圳））；Guangdong Provincial Key Laboratory of Fire Science and Intelligent Emergency Technology（广东省消防科学与智能应急技术重点实验室）；University of Illinois Chicago（伊利诺伊大学香槟分校）
Mathematical Reasoning in Large Language Models: Benchmarks, Architectures, Evaluation, and Open Challenges
organization= School of Electrical Engineering；Computer Science, National University of Science；organization= School of Computing, Data；Mathematical Sciences, Western Sydney University, Indonesia；organization= Department of Communication, Quality Management；Information Systems, Mid Sweden University, Östersund Campus, Sweden
The Hong Kong Polytechnic University（香港理工大学）；Southern University of Science and Technology（南方科技大学）；Tsinghua University（清华大学）；Reallm Labs（Reallm实验室）；Wuhan University（武汉大学）；The University of Hong Kong（香港大学）
A Survey on Large Language Models for Mathematical Reasoning
National Key Laboratory for Novel Software Technology（国家新型软件技术重点实验室）；School of Artificial Intelligence（人工智能学院）；Nanyang Technological University（南洋理工大学）；Skywork AI Singapore（Skywork AI新加坡）；The Chinese University of Hong Kong Shenzhen（香港中文大学（深圳））
Key-Point-Driven Mathematical Reasoning Distillation of Large Language Model
Institute of Information Engineering, Chinese Academy of Sciences（中国科学院信息工程研究所）；School of Cyber Security, University of Chinese Academy of Sciences（中国科学院大学网络空间安全学院）；School of Artificial Intelligence, Beijing Normal University（北京师范大学人工智能学院）
Forward-Backward Reasoning in Large Language Models for Mathematical Verification
Southern University of Science and Technology（南方科技大学）；Hong Kong University of Science and Technology（香港科技大学）；Huawei Noah’s Ark Lab（华为诺亚方舟实验室）；Peking University（北京大学）
