This award supports the research in number theory of Professor Hendrik Lenstra of the University of California at Berkeley. Dr. Lenstra has proposed to continue his research in several directions. In primality testing and factorization of large integers, he will study the newest factoring algorithm, known as the Number Field Sieve, and work on the practical implementation of a primality test. In algebraic number theory, he will investigate the existence of governing fields and study the class group structure of abelian fields. Except for counting, number theory, which is the study of the properties of the whole numbers, is the oldest branch of mathematics. In modern days, problems in number theory have furnished the driving force to creation of new mathematics in the fields of pure algebra, analysis, and geometry; some of the most recent and most astonishing applications of number theory have appeared in theoretical computer science and coding theory.
