LLM Mathematical Reasoning

The field investigates whether language models can carry out arithmetic, multi-step problem solving, and proof construction reliably—not just produce correct-looking answers. Common approaches include chain-of-thought prompting, supervised and reinforcement learning, test-time search and voting, tool use with code or computer algebra, and formal verification with proof assistants such as Lean. Evaluation spans word-problem and contest benchmarks such as GSM8K, MATH, and AIME, as well as formal proof tasks like miniF2F; newer tests probe robustness to equivalent transformations, multilingual inputs, and research-level problems. Models can perform strongly on familiar contest tasks, but generalization, faithful reasoning, proof quality, and reliable verification remain unresolved tensions, especially on open-ended research mathematics.