Number theory

Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers. It contains many results and open problems that are easily understood, even by non-mathematicians. More generally, the field has come to be concerned with wider classes of problems that have arisen naturally from the study of integers. Number theory may be subdivided into several fields, according to the methods used and the type of questions investigated. See for example the list of number theory topics. Mathematicians working in the field of number theory are called number theorists.

Related Topics:
Pure mathematics - Integer - List of number theory topics - Mathematicians

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

The term "arithmetic" is also used to refer to number theory. This is a somewhat older term, which is no longer as popular as it once was. Number theory used to be called the higher arithmetic, but this is dropping out of use. Nevertheless, it still shows up in the names of mathematical fields (arithmetic functions, arithmetic of elliptic curves, fundamental theorem of arithmetic). This sense of the term arithmetic should not be confused either with elementary arithmetic, or with the branch of logic which studies Peano arithmetic as a formal system.

Related Topics:
Arithmetic - Arithmetic functions - Arithmetic of elliptic curves - Fundamental theorem of arithmetic - Elementary arithmetic - Logic - Peano arithmetic - Formal system

~ ~ ~ ~ ~ ~ ~ ~ ~ ~