# From solving equations to Galois theory

On December 25, 2020, Professor Qin Hourong of Nanjing University was invited to conducted an academic exchange in room 526, Xingjian Building at Nanjing Normal University. Professor Chen Yonggao presided over the lecture, Professor Xia Jianguo, Professor Ji Chungang, Professor Dai Lixia, Professor Zhou Haiyan, Associate professor Zhang Haicheng and some graduate students and senior undergraduates attended the lecture.

Professor Qin made a report entitled "From solving equations to Galois theory". Algebraic equations are the most basic research objects in mathematics, and solving equations is the central task of mathematics. Beginning with a review of the history of the solution of quadratic, cubic and quadrantal algebraic equations, Professor Qin elaborated some concepts in modern algebra, the Abel-Ruffini theorem, and the great Galois theory in a simple and profound way. Finally, he explained how Galois's theory solves some classical geometric problems gracefully.

In the report, the teachers and students had an in-depth exchange and discussion on the content of the report. Professor Qin answered the questions raised by everyone in detail, and encouraged the students to think hard, find problems and try to solve new problems in research. The report successful completed.