The theory of numbers is one of the oldest branches of mathematics, going back more than two thousand years in China, Greece, and India. It is concerned with the study of whole numbers, prime numbers, and polynomial equations involving them. The third of these goes by the name Diophantine equations after the Alexandrian/Greek mathematician Diophantus. Gauss, who laid many of the foundations of modern number theory, called it the “Queen of Mathematics”. At the time, and for many years after, it was considered as very much on the theoretical and pure side of mathematics. However, in our modern digital/discrete world the deeper truths and techniques that have been developed to study whole numbers play an increasingly significant role in applications.
Many of the central problems in the theory of numbers are elementary and easy to state; but the experience of generations of mathematicians shows that they can be extraordinarily difficult to resolve. Success, when it is achieved, often relies on sophisticated tools from many fields of mathematics. This is no coincidence, since aspects of these fields were introduced and developed in efforts to resolve classical problems in number theory.