Mathematical Sciences: Mathematical Science: Modular forms, Elliptic curves and galois reprentations"

这个奖支持怀尔斯教授在数论方面的研究。本课题的目的是试图证明在有理数域上的某些椭圆曲线族是模的，这是Shimura-Taniyama-Weil的著名猜想。一般来说，方法是证明合适的伽罗瓦表示，其值在2 × 2矩阵中，项在字段中有三个元素，总是由模形式产生的。这是数论领域的研究。数论从整数和诸如整数能被整数整除之类的问题开始。它是数学中最古老的领域之一，最初纯粹出于审美原因而追求它。然而，在过去的半个世纪里，它已经成为开发计算机科学新算法和电子学新纠错码的重要工具。

This award supports the research of Professor Wiles to work in number theory. The aim of this project is to try to prove that certain families of elliptic curves over the field of rationals is modular, the famous conjecture of Shimura-Taniyama-Weil. The approach will be to prove in general that suitable Galois representations with values in the two by two matrices , with entries in the field with three elements, always arise from modular forms. This is research in the field of number theory. Number theory starts with the whole numbers and questions such as the divisibility of one whole number by another. It is among the oldest fields of mathematics and it was originally pursued for purely aesthetic reasons. However, within the last half century, it has become an essential tool in developing new algorithms for computer science and new error correcting codes for electronics.