The Bernoulli numbers : a brief primer

In this primer, we explore the diverse properties of a rational sequence known as the Bernoulli numbers. Since the discovery of the numbers in the early eighteenth century, mathematicians have uncovered a vast web of connections between them and core branches of mathematics. We begin with an overview of the historical developments leading to the derivation of the Bernoulli numbers, then use a process similar to that of Jakob Bernoulli to derive the sequence, and finally consider a variety of applications. We hope, above all, to demonstrate how useful and unexpected mathematics can be.