澳門大學本科生數學講座系列之五 函數的對稱性質：從三角函數到費馬大定理

Prof. King-Fai Lai gives a lecture on “the symmetry of functions: from trigonometric functions to Fermat’s Last Theorem”

黎景輝教授從三角函數談費馬大定理

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.

澳門大學科技學院數學系本學年本科生數學講座系列日前圓滿結束。壓軸演講嘉賓請來台灣中山大學應用數學系講座教授黎景輝於何賢中心HG02演講廳開講“函數的對稱性質：從三角函數到費馬大定理”。

黎景輝教授先介紹“不定方程”的數學概念，並簡要回顧費馬大定理。隨後，黎教授介紹了三角函數和由三角函數匯出的橢圓方程，並指出作為唯一的一類基本週期函數，三角函數的存在並不簡單，他又指出英國數學家Adnrew Wiles關於費馬大定理的證明，是基於谷山志村定理；而谷山志村定理建立了橢圓曲線和模形式之間的重要聯繫。黎教授總結指，費馬大定理串聯起數個看似完全無關的數學主題，該定理的證明是數學界的大師級精品，並鼓勵學生們欣賞該證明的內在數學美。

黎景輝教授於美國耶魯大學跟從數學大師 Robert Phelan Langlands學習多年，1974年於該校取得數學博士學位，並長期致力於自守型式理論研究。目前，黎教授是台灣中山大學的西灣講座教授與國家科學理論中心(南區)中心科學家。是次講座為本學年系列講座最後一場，新的系列講座將於下學年推出，敬請留意相關資訊。