Core Viewpoint - The article discusses the current state and future potential of AI in assisting mathematical research, highlighting both advancements and limitations in AI's capabilities to solve complex mathematical problems. Group 1: AI Advancements in Mathematics - The U.S. Defense Advanced Research Projects Agency (DARPA) launched the "Exponential Mathematics" program to develop AI systems that can significantly enhance mathematical research efficiency [1] - New generation large language models (LLMs) like OpenAI's o3 and Anthropic's Claude 4 Thinking have shown improvements, performing at levels close to excellent high school students in competitions [2] - Google's AlphaProof system combines LLMs with chess AI, achieving results comparable to silver medalists in the International Mathematical Olympiad [2] - The AlphaEvolve model from Google has found solutions to long-standing mathematical and computational problems that outperform existing human methods [2] Group 2: Limitations of AI in Mathematics - Despite impressive performances, experts believe that current AI models lack the capability to assist in genuine mathematical research, as competition problems are more like intellectual games with certain patterns [2] - A test by Epoch AI revealed that LLMs struggled with high-difficulty problems designed to avoid previously seen training data, indicating significant limitations in their problem-solving abilities [3] - AI faces challenges with "super long reasoning chains," where complex problems may require millions of steps to solve, making it difficult for AI to find the correct solutions [5] Group 3: Innovative Approaches and Future Directions - Researchers are developing methods to package multiple steps into "super steps" to tackle complex problems, which has led to breakthroughs in classic unsolved problems [5][6] - The exploration of new mathematical ideas is crucial, and AI tools like AlphaEvolve can generate and refine solutions, allowing for human intervention to provide inspiration [7] - AI is seen as a potential tool for discovering new mathematical objects, but it currently lacks true creativity, with significant innovations still attributed to human mathematicians [8]