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]