Overview

Number theory has often been thought of as one of the bastions of "pure" mathematics, unsullied by application to real-world problems and in which mathematics is pursued for the sheer beauty of the concepts involved. Starting in the latter part of the nineteenth century, however, some actual applications of number theory began to emerge. In the first half of the twentieth century, this trend continued. In addition, mathematicians began to prove some important points about specific numbers, such as π, e (the base for natural logarithms), the square root of two, and others. This work led to some very interesting and important advances in the way these numbers are viewed. In addition, since many of these irrational and transcendental numbers are widely used in physics, engineering, and other practical disciplines...