From Mathematics to Generic Programming

5. The Emergence of Modern Number Theory

Mathematicians have tried in vain to this dayto discover some order in the sequence of prime numbers,and we have reason to believe that it is a mysteryinto which the human mind will never penetrate.Leonhard Euler

In the previous chapter, we saw how the fledging field of number theory, which had fascinated the ancient Greeks, was revived in medieval Europe after a long period of dormancy. But number theory in its modern sense really emerged a few hundred years later, in 17th-century France. For this chapter, we are going to put programming aside for a bit and learn some of the results discovered by 17th-century French mathematicians, which we’ll use for some important computer applications later on.