Ancient Greek mathematician Euclid (holding calipers), 3rd century BC, as imagined by Raphael in this detail from the School of Athens (1509–1511)

Mathematics is the study of numbers, shapes, and patterns. The word comes from the Greek μάθημα (máthema), meaning "science, knowledge, or learning", and is sometimes shortened to maths (in British Commonwealth countries) or math (in North America).

It is the study of:

• Numbers: including how things can be counted.
• Structure: including how things are organized, but also how they can be or could have been. This subfield is usually called algebra.
• Place: where things are, and spatial arrangement, including arrangements of spaces themselves. This subfield is usually called geometry.
• Change: how things become different. This subfield is usually called analysis.

Applied math is useful for solving problems in the real world. People working in business, science, engineering, and construction use mathematics.