Number Theory

Number theory is the study of numbers and their properties. In many other branches of mathematics, numbers are used strictly to convey information (e.g. 75%, 3 apples, 2x² - 1). Number theory, on the other hand, studies numbers (usually the integers or some subset thereof, like the natural numbers) for their own sake. The properties of numbers are indeed fascinating.

The first number theorist was probably Pythagoras, who believed that "all is number". The later Greeks, who were no doubt influenced by him, valued number theory (which they called arithmetic) above arithmetic (which they called logistic). The Greeks' mathematical discoveries were a cause (or perhaps a symptom) of their contempt for practical mathematics.

Number theory is a fairly wide branch of mathematics. For a few starting points, you may want to look at my congruences page, or my Fundamental Theorem of Arithmetic page.