On March 24, Jiping Zhang, a member of the Chinese Academy of Sciences, Boya Chair Professor and Director of the Sino-Russian Mathematics Center at Peking University, was invited to deliver a Chern Lecture titled "Recent Advances in Group Representation Theory" at the Chern Institute of Mathematics (CIM). The lecture was also part of the celebrations commemorating CIM's 40th anniversary. Prior to the event, Chengming Bai, Vice President of Nankai University, met with Professor Jiping Zhang at the Shiing-Shen Building. The meeting was attended by Yiming Long and Weiping Zhang, both members of the Chinese Academy of Sciences and professors at CIM, along with several other faculty members from the institute.
Professor Zhang began his lecture by congratulating CIM on its remarkable achievements and contributions to the advancement of Chinese mathematics over the past four decades. He then introduced two groundbreaking developments in group representation theory—the proofs of Brauer's Height Zero Conjecture and the McKay Conjecture—and highlighted their profound impact on mathematics and related disciplines.
The Height Zero Conjecture, proposed by Brauer in 1955, had long been a central problem in the representation theory of group modules. It was finally solved in 2024 by Malle and Tiep, making a major breakthrough that significantly advanced group representation theory. The recent proof of the McKay Conjecture by Späth and Cabanes also has had an enormous impact both within and beyond mathematics. Quanta Magazine hailed it as "an absolutely spectacular achievement" and underscored the pivotal role of group theory in mathematics. Professor Zhang recalled a conversation between him and a renowned mathematician in Europe who remarked that group theory is "remodeling mathematics".
Starting with counting, Professor Zhang reviewed the developmental history of algebra, and further, that of mathematics as a whole. He emphasized that mathematics ought to be an integrated and unified entity, noting that all its branches should be more closely connected amid their advancement, rather than becoming increasingly isolated.
He recalled the four major revolutions in physics, fully affirmed the key roles that analysis, geometry and algebra had played in the first three revolutions, and then predicted that category theory would play a major part in the fourth one.
Regarding artificial intelligence, Professor Zhang also shared his views on this emerging technology and noted that the advancement of AI will bring both new support and challenges to mathematics. He foresees that mathematical research in the near future will rely not only on mathematicians themselves, but also the collaboration between humans and computers. He also believes that while AI may outperform some individuals in certain mathematical fields, it will never surpass the collective wisdom of humanity. AI's primary function is not to create, but to integrate information — for creativity remains a unique strength of human beings.
At the end of his lecture, Professor Zhang re-emphasized the importance of integration. He argued that only by integrating algebra into different research fields can mathematics, as a whole, achieve better development.
In the discussion session, Professor Zhang patiently answered questions from the audience, discussed the connections between group theory and physics with NKU faculty members and students, and provided further explanation regarding the McKay Conjecture. He encouraged the students to develop their own creativity and independence, as well as their abilities in learning, living and organizing.
