The Research Center for Mathematics of Artificial Intelligence addresses major national strategic needs in the field of artificial intelligence by advancing innovations in mathematical theories and algorithmic research. It dedicates to improving intelligent models in terms of accuracy, computational efficiency, and security, while enhancing optimization algorithms with superior agility, adaptability, trustworthiness, and interpretability. Cutting-edge research at the center spans agile and adaptive intelligent optimization methods, along with trustworthiness and interpretability studies of intelligent models. Significant technological breakthroughs have been achieved in several key areas, including but not limited to: logical reasoning and proof systems for large language models, trustworthy intelligent optimization methodologies, and rapid-generation algorithms for high-dimensional, highly dynamic multi-agent games. These pioneering contributions have yielded a series of internationally influential innovations.