A Survey on Mathematical Reasoning and Optimization with Large Language Models

• URL: http://arxiv.org/abs/2503.17726v1
• Date: Sat, 22 Mar 2025 10:49:32 GMT
• Title: A Survey on Mathematical Reasoning and Optimization with Large Language Models
• Authors: Ali Forootani,
• Abstract summary: Recent advancements in Large Language Models (LLMs) have significantly improved AI-driven mathematical reasoning, theorem proving, and optimization techniques.<n>This survey explores the evolution of mathematical problem-solving in AI, from early statistical learning approaches to modern deep learning and transformer-based methodologies.
• Score: 0.5439020425819
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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