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". Other practitioners of mathematics 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.
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.
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.