Advances in Number Theory Between 1900 and 1949
Overview
The latter part of the nineteenth century and the first half of the twentieth saw major advances in many branches of mathematics, including the theory of numbers. Work on classic problems in the field led to important advances in our understanding of numbers and their relationships to each other. New work by both renowned and emerging mathematicians pointed the way to solutions of other classic problems, and also promised future advances. Much of this work focused on prime numbers, numbers that are only divisible by 1 and themselves. Although prime numbers have enchanted mathematicians for centuries, only in the last century or so did many of their properties begin to be better understood, including how to generate them and how to factor very large numbers into their prime components. Recent improvements in computer technology has made prime numbers central to many methods of encrypting information for personal, business, or governmental security.
Background
A number is an abstraction. It is difficult to explain to someone what, for example, the number 5 is without directly or indirectly referring to the number 5 itself. However, there are few arguments in daily life about the properties of the number 5.
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