Recently, at the Guangzhou satellite venue of the International Joint Conference on Artificial Intelligence (IJCAI) 2025, one of the world’s leading conferences in the field of AI, Professor Shing-Tung Yau, internationally renowned mathematician, Fields Medalist, Dean of Qiuzhen College at Tsinghua University, Director of the Yau Mathematical Sciences Center at Tsinghua University (YMSC), and President of the Beijing Institute of Mathematical Sciences and Applications (BIMSA), was invited by the Program Chair, Professor James T. Kwok of the Hong Kong University of Science and Technology, IEEE Fellow, to deliver a keynote lecture titled Advancing Artificial Intelligence through Modern Mathematical Theories.

As one of the longest-standing and most influential international academic conferences in AI, IJCAI has brought together leading researchers at the forefront of AI worldwide since its founding in 1969. It is widely recognized as one of the top-tier conferences in the global computer science community, ranking among the top 1% of conferences in the field. Owing to this academic standing, IJCAI attracts approximately 3,000 to 5,000 leading scholars from around the world each year, and its past invited speakers have included Turing Award and Nobel Prize laureates.

The main conference was held in Montréal, Canada, from August 16 to 22, 2025, with a satellite event in Guangzhou from August 29 to 31, attracting researchers and students from across the globe. The invited speaker lineup for this year’s conference was equally distinguished. In addition to Professor Yau, Professor Yoshua Bengio of the University of Montreal, a Turing Award laureate and a pioneering figure in deep learning, was also invited to speak, drawing widespread international attention. The conference further featured a number of prominent scholars from around the world, including Toby Walsh, Fellow of the Australian Academy of Science; Harry Shum, Member of the U.S. National Academy of Engineering; and Yew-Soon Ong, Fellow of IEEE and The Academy of Engineering, Singapore. Their participation not only highlighted the international influence of the conference, but also reaffirmed IJCAI’s academic stature and authority as a premier event in AI.

At the beginning of his lecture, Professor Yau reviewed the historical development of both mathematics and AI. He noted that mathematics has, since ancient times, provided humanity with the fundamental language and methods for understanding the world. From geometry and topology to analysis and partial differential equations, mathematics has gradually built a solid framework for interpreting the laws of nature. AI, meanwhile, has made rapid progress in recent decades, particularly driven by deep learning, demonstrating remarkable empirical success. However, he emphasized that the mathematical foundations of AI have yet to be systematically established, and that this remains a key challenge for future breakthroughs.

After outlining the development of the two fields, Professor Yau stressed that the integration of mathematics and AI is a natural and inevitable trend. Mathematics can provide AI with a unified theoretical framework, while the continued development of AI raises new questions that, in turn, drive advances in mathematics. He further illustrated, through concrete examples, how modern mathematical tools can contribute to AI research. For instance, conformal geometry and manifold learning offer new perspectives for neural network architectures and may help improve model design; topological theory (GLMY homology theory) and statistical methods (IdopNetworks) help uncover the intrinsic structures of biological networks and complex data; nonlinear partial differential equations (PDEs) provide theoretical support for data-efficient learning and decision-making under uncertainty; and the Yau–Yau nonlinear filter proposed by his team has demonstrated unique potential in modeling complex dynamic systems.

Looking ahead, Professor Yau shared his views on future directions. He noted that geometric and analytic methods will play an important role in enhancing the interpretability of AI, while topological and algebraic theories will provide new tools for scientific discovery and interdisciplinary research. The deep integration of mathematics and AI, he argued, will lay the foundation for building more robust, transparent, and generalizable intelligent systems.

Professor Yau also introduced to the audience the work of Qiuzhen College at Tsinghua University, the Beijing Institute of Mathematical Sciences and Applications (BIMSA), and the Yau Mathematical Sciences Center at Tsinghua University (YMSC) in talent cultivation, fundamental research, and interdisciplinary exploration. These institutions not only bring together world-class mathematicians and young scholars, but also actively engage in international academic collaboration, with a shared commitment to advancing the interdisciplinary integration of mathematics and AI.

The lecture venue was filled to capacity, with scholars and students from diverse academic backgrounds listening attentively and engaging actively in discussion. During the Q&A session, the audience raised a range of frontier questions, including how mathematical theories can be used to explain the behavior of generative AI models and what directions may lead to breakthroughs in neural network interpretability. After the lecture, many participants continued to exchange research ideas with Professor Yau and took commemorative photos with him.

Professor Shing-Tung Yau’s lecture not only demonstrated the unique value that mathematics can bring to the development of AI, but also offered important insights into the future direction of interdisciplinary research.