King University

This review systematically surveys the progress, challenges, and prospects of AI for Mathematics (AI4Math), organizing the field into problem-specific modeling (guiding intuition, constructing counterexamples, formal reasoning in closed systems) and general-purpose modeling (natural language reasoning, formal reasoning, mathematical information retrieval), and reports the authors' own PKU undergraduate and PhD qualifying exam evaluations: GPT-4 averages below 60 while reasoning-enhanced models such as o1, DeepSeek-R1, o3-mini, and Gemini 2.5 Pro mostly exceed 90, with o3-mini averaging 84.4 on 58 PhD qualifying exam problems, while research-level mathematics remains an open challenge.

This review systematically surveys the progress, challenges, and prospects of AI for Mathematics (AI4Math), organizing the field into problem-specific modeling (guiding intuition, constructing counterexamples, formal reasoning in closed systems) and general-purpose modeling (natural language reasoning, formal reasoning, mathematical information retrieval), and reports the authors' own PKU undergraduate and PhD qualifying exam evaluations: GPT-4 averages below 60 while reasoning-enhanced models such as o1, DeepSeek-R1, o3-mini, and Gemini 2.5 Pro mostly exceed 90, with o3-mini averaging 84.4 on 58 PhD qualifying exam problems, while research-level mathematics remains an open challenge.