**Mathematics** (

colloquially,

**maths**, or

**math**), is the body of knowledge centered on concepts such as

quantity,

structure,

space, and

change, and also the academic discipline that studies them.

Benjamin Peirce called it "the science that draws necessary conclusions".

[2] Other practitioners of mathematics

[3][4] maintain that mathematics is the science of pattern, that

mathematicians seek out patterns whether found in numbers, space, science, computers, imaginary abstractions, or elsewhere. Mathematicians explore such concepts, aiming to formulate new

conjectures and establish their truth by

rigorous deduction from appropriately chosen

axioms and

definitions.

[5]Through the use of

abstraction and

logical reasoning, mathematics evolved from

counting,

calculation,

measurement, and the systematic study of the

shapes and

motions of physical objects. Knowledge and use of basic mathematics have always been an inherent and integral part of individual and group life. Refinements of the basic ideas are visible in mathematical texts originating in

ancient Egypt,

Mesopotamia,

ancient India,

ancient China, and

ancient Greece. Rigorous arguments first appear in

Euclid's

*Elements*. The development continued in fitful bursts until the

Renaissance period of the

16th century, when mathematical innovations interacted with new

scientific discoveries, leading to an acceleration in research that continues to the present day.

[6]Today, mathematics is used throughout the world in many fields, including

natural science,

engineering,

medicine, and the

social sciences such as

economics.

Applied mathematics, the application of mathematics to such fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new disciplines. Mathematicians also engage in

pure mathematics, or mathematics for its own sake, without having any application in mind, although applications for what began as pure mathematics are often discovered later.

[7]