數學科學獎
2015

2015年度邵逸夫數學科學獎頒予格爾德・法爾廷斯 (Gerd Faltings)及亨里克・伊萬尼克(Henryk Iwaniec)，以表彰他們對數論基本工具的推行及發展，讓他們及其他人能夠解決存在已久的經典問題。格爾德•法爾廷斯是德國馬克斯普朗克數學研究所所長。亨里克・伊萬尼克是美國羅格斯大學數學系New Jersey講座教授。

數論的研究對象是整數、素數以及與它們相關的多項方程式。其核心問題通常易於陳述，但非常難以解答。成功解答的例子亦有賴很多不同數學領域的工具。這種情況並非巧合，因為其中一些數學領域正是為了要解決經典數論問題而開發的。格爾德・法爾廷斯及亨里克・伊萬尼克在代數、分析學、代數及算術幾何學、自守式及ζ 函数理論等領域中發展了很多最具效力的現代數學工具。他們及其他人利用這些工具，解答了許多存在已久的經典問題。

The theory of numbers is one of the oldest branches of mathematics, going back more than two thousand years in China, Greece, and India. It is concerned with the study of whole numbers, prime numbers, and polynomial equations involving them. The third of these goes by the name Diophantine equations after the Alexandrian/Greek mathematician Diophantus. Gauss, who laid many of the foundations of modern number theory, called it the “Queen of Mathematics”. At the time, and for many years after, it was considered as very much on the theoretical and pure side of mathematics. However, in our modern digital/discrete world the deeper truths and techniques that have been developed to study whole numbers play an increasingly significant role in applications.

Many of the central problems in the theory of numbers are elementary and easy to state; but the experience of generations of mathematicians shows that they can be extraordinarily difficult to resolve. Success, when it is achieved, often relies on sophisticated tools from many fields of mathematics. This is no coincidence, since aspects of these fields were introduced and developed in efforts to resolve classical problems in number theory.