The modern use and development of numbers and counting began with the rise of cities as a result of the need to organize people and allocate goods and resources.
Addition, subtraction, multiplication and division of numbers are important to trade and have been employed by civilizations for thousands of years.
Algebra deals with solving problems that involve mathematical symbols. The simplest of such problems were studied as long ago as 1900 BCE.
The Pythagorean theorem relates the side lengths of a right triangle and was known to the ancient scholars and builders of Babylonia, Egypt, Greece, China and India.
Geometry focuses on the properties of space and the size and shape of objects. Its investigation dates back to the earliest recorded civilizations.
Primes are numbers having exactly one divisor other than 1. They are the building blocks of all counting numbers and were studied as early as 250 BCE.
The computation of π, the ratio of a circle's circumference to its diameter, has been of practical and mathematical interest in both the ancient and modern world.
Polyhedra are solids consisting of polygons joined at their edges. They were known to the ancients from nature and used in art, architecture and games of chance.