Pure mathematics, also known as theoretical mathematics, is a part of mathematics that studies abstract concepts, concepts that don't necessarily have real-world applications. Pure mathematics can be divided into five branches, namely analysis, algebra, geometry, logic, and number theory.

Pure mathematics can be contrasted with applied mathematics, which comprises mathematics applied to real-world applications such as physics, engineering, computer science, economics, and the like. Although pure mathematics is concerned with increasing abstract knowledge without considering potential practical uses, there is no sharp dividing line between pure and applied mathematics; advances in pure mathematics have been valuable in furthering many achievements in science and engineering.