The Department of Mathematics, Faculty of Science and Technology, University of Macau (UM), on 17 April held the fifth undergraduate lecture in mathematics, which was also the last lecture of UM’s Undergraduate Lecture Series in Mathematics for this academic year. Prof. King-Fai Lai, chair professor at National Sun Yat-Sen University, was the speaker. The title of his lecture was “the symmetry of functions: from trigonometric functions to Fermat’s Last Theorem”.

Prof. Lai opened his lecture with the introduction of indefinite equations and a brief review of Fermat’s Last Theorem, after which he discussed the trigonometric functions. He emphasised that the trigonometric functions being essentially the only elementary periodic functions is not a trivial fact. He proceeded to introduce elliptic functions as generalisations of trigonometric functions. He pointed out that the proof of Andrew Wiles, a British mathematician, is based on the fact that the Fermat’s Last Theorem can be implied by the Taniyama-Shimura theorem which concerns elliptic curves and modular forms. Prof. Lai concluded that the proof of Fermat’s Last Theorem is a masterpiece of mathematics. He noted that the proof linked together several different topics which at first glance do not seem to have any relations with each other. He encouraged students to try to appreciate this masterpiece which reflects the beauty of mathematics.

Prof. King-Fai Lai obtained his PhD degree from Yale University in 1974. He was supervised by the eminent mathematician Prof. Robert Phelan Langlands. Prof. Lai’s research focuses on the Automorphic Forms. He is Siwan Chair Professor at National Sun Yat-sen University, and a scientist at the National Center for Theoretical Science Center.

A new Undergraduate Lecture Series in Mathematics will be launched in the next academic year. Stay tuned.


Should you have any enquiries about the information, please feel free to contact the Information Executives Ms Lei or Ms Fok at（853）8397 4325 or  prs.media@um.edu.mo or visit UM webpage www.umac.mo.