Mathematical reasoning serves as a fundamental pillar for problem-solving in education, science, and industry, acting as a critical benchmark for evaluating AI systems. As Large Language Models (LLMs) evolve, understanding their performance in mathematical contexts has become a primary research focus. This comprehensive survey synthesizes recent advancements by analyzing approximately 120 peer-reviewed studies and preprints, providing a unified analytical framework to assess current progress and limitations.
The study introduces a systematic taxonomy of mathematical datasets, distinguishing between pretraining corpora, supervised fine-tuning (SFT) resources, and evaluation benchmarks categorized by varying levels of reasoning complexity. It further examines reasoning architectures and training strategies, including tool integration, verifier-guided reasoning, and parameter-efficient adaptation. These methodologies are evaluated based on their impact on the robustness and generalization of reasoning processes.
Moreover, the paper provides a comparative evaluation of existing metrics, highlighting the critical gap between final-answer accuracy and process-level reasoning verification. It identifies recurring failure modes, such as issues with reasoning faithfulness, benchmark biases, and generalization constraints. The analysis outlines key research directions focused on improving symbolic grounding and evaluation reliability to develop more robust and trustworthy LLM-based reasoning systems.
