On October 13th, despite the cold weather and a chilly autumn drizzle, Tianjin University’s eighth conference room on the Weijin Road campus was packed with zealous teachers and students. “I am very glad today to come to Tianjin University, a university with a longer history than Peking University.” Professor Tian Gang, an academician of the Chinese Academy of Sciences and the vice-president of Peking University said, which raised a round of laughter and instantly endeared him to the audience.

Professor Tian Gang started his lecture with a simple question “What is a regular polyhedron?” There are only five kinds of regular polyhedrons. This is the famous result of the ancient Greek mathematician Euclid's "Geometry Original" around 300 B.C. Then he introduced the outstanding mathematician Euler, who while blind completed many papers by mental arithmetic and became the most prolific mathematician in history. The Euler formula is known as one of the most beautiful formulas and many constants, formulas and theorems named after Euler can be found in many branches of mathematics.

Professor Tian Gang introduced the process of using the Euler formula to prove that there are only five regular polyhedrons, and the contributions made by mathematicians such as Descartes, Leibniz, Euler and Cauchy in the proof. The Euler formula of convex polyhedrons can be extended to arbitrary topological space. Afterwards, Tian Gang explained the definition and principle of the Euler number in more general topological space and the famous Hopf theorem. He used football and other common things in life as examples to help the audience understand how to define the Euler numbers in more general space.

The counting geometry problem is a mathematical problem that originated more than two thousand years ago. The study of the number of solutions of multivariable algebraic equations is an important branch of algebraic geometry. Professor Tian said that since the 1990s, inspired by the study of field theory, the research of counting geometry is more systematic and closely related to other branches of mathematics such as representation theory and differential equations. Professor Tian introduced his collaboration work with Professor Ruan Yongbin in giving a strict definition of n(d) in 1993 and obtaining the recursive formula of n(d), contributing to the development of Gromov-Witten theory (GW theory), which promotes the development of counting geometry and provides a mathematical basis for important problems.

During the Q & A session, Professor Tian answered individual questions, discussing with students how to conduct more effective and in-depth study and research, and how to achieve true self-improvement. He untangled the history of the Euler formula, illustrated a large number of examples from daily life, displayed frontier problems in mathematics, helped the audience learn more about the history of mathematics and have a more intuitive understanding of highly abstract concepts and theories in modern mathematics. He said mathematical research was endless, and expressed the hope that more mathematical talents will make more contributions in the future.

By the School of Mathematics

Editors: Eva Yin & Doris Harrington