{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-survey-on-mathematical-reasoning-and","title":"A Survey on Mathematical Reasoning and Optimization with Large Language Models","arxiv_id":"2503.17726","date":"2025-03-22","proceeding":null,"authors":["Ali Forootani"],"abstract":"Mathematical reasoning and optimization are fundamental to artificial intelligence and computational problem-solving. Recent advancements in Large Language Models (LLMs) have significantly improved AI-driven mathematical reasoning, theorem proving, and optimization techniques. This survey explores the evolution of mathematical problem-solving in AI, from early statistical learning approaches to modern deep learning and transformer-based methodologies. We review the capabilities of pretrained language models and LLMs in performing arithmetic operations, complex reasoning, theorem proving, and structured symbolic computation. A key focus is on how LLMs integrate with optimization and control frameworks, including mixed-integer programming, linear quadratic control, and multi-agent optimization strategies. We examine how LLMs assist in problem formulation, constraint generation, and heuristic search, bridging theoretical reasoning with practical applications. We also discuss enhancement techniques such as Chain-of-Thought reasoning, instruction tuning, and tool-augmented methods that improve LLM's problem-solving performance. Despite their progress, LLMs face challenges in numerical precision, logical consistency, and proof verification. Emerging trends such as hybrid neural-symbolic reasoning, structured prompt engineering, and multi-step self-correction aim to overcome these limitations. Future research should focus on interpretability, integration with domain-specific solvers, and improving the robustness of AI-driven decision-making. This survey offers a comprehensive review of the current landscape and future directions of mathematical reasoning and optimization with LLMs, with applications across engineering, finance, and scientific research.","url_abs":"https://arxiv.org/abs/2503.17726v1","url_pdf":"https://arxiv.org/pdf/2503.17726v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"a-survey-on-mathematical-reasoning-and","repo_url":"https://github.com/ali-forootani/a-survey-on-mathematical-reasoning-and-optimization-with-large-language-models","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"automated-theorem-proving","task_name":"Automated Theorem Proving"},{"task_slug":"heuristic-search","task_name":"Heuristic Search"},{"task_slug":"mathematical-problem-solving","task_name":"Mathematical Problem-Solving"},{"task_slug":"mathematical-reasoning","task_name":"Mathematical Reasoning"},{"task_slug":"prompt-engineering","task_name":"Prompt Engineering"},{"task_slug":"survey","task_name":"Survey"}],"methods":[{"method_slug":"focus","method_name":"Focus"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2503.17726","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}