Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the abstract study of topics encompassing quantity,[2] structure,[3] space,[2] change,[4][5] and other properties;[6] it has no generally accepted definition.[7][8]
Mathematicians seek out patterns[9][10] and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof.
The research required to solve mathematical problems can take years or
even centuries of sustained inquiry. Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions.
When those mathematical structures are good models of real phenomena,
then mathematical reasoning can provide insight or predictions about
nature.
Through the use of abstraction and logical reasoning, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.[11]
Galileo Galilei
(1564–1642) said, "The universe cannot be read until we have learned
the language and become familiar with the characters in which it is
written. It is written in mathematical language, and the letters are
triangles, circles and other geometrical figures, without which means it
is humanly impossible to comprehend a single word. Without these, one
is wandering about in a dark labyrinth."[12] Carl Friedrich Gauss (1777–1855) referred to mathematics as "the Queen of the Sciences."[13] Benjamin Peirce (1809–1880) called mathematics "the science that draws necessary conclusions."[14]
David Hilbert said of mathematics: "We are not speaking here of
arbitrariness in any sense. Mathematics is not like a game whose tasks
are determined by arbitrarily stipulated rules. Rather, it is a
conceptual system possessing internal necessity that can only be so and
by no means otherwise."[15] Albert Einstein
(1879–1955) stated that "as far as the laws of mathematics refer to
reality, they are not certain; and as far as they are certain, they do
not refer to reality."[16]
Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics,
the branch of mathematics concerned with application of mathematical
knowledge to other fields, inspires and makes use of new mathematical
discoveries, which has led to the development of entirely new
mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics,
or mathematics for its own sake, without having any application in
mind. There is no clear line separating pure and applied mathematics,
and practical applications for what began as pure mathematics are often
discovered.[17]
Tidak ada komentar:
Posting Komentar