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.
