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Mathematics (disambiguation)

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Mathematics
From Wikipedia, the free encyclopedia
This article is about the study of topics, such as quantity and structure. For other uses, see
Mathematics (disambiguation).
"Math" redirects here. For other uses, see Math (disambiguation).
Euclid, Greek mathematician, 3rd century BC, as imagined by Raphael in this detail from The
School of Athens.
[1]
Mathematics is the study of topics such as quantity (numbers),
[2]
structure,
[3]
space,
[2]
and
change.
[4][5][6]
There is a range of views among mathematicians and philosophers as to the exact
scope and definition of mathematics.
[7][8]
Mathematicians seek out patterns
[9][10]
and use them to formulate new conjectures.
Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When
mathematical structures are good models of real phenomena, then mathematical reasoning can
provide insight or predictions about nature. Through the use of abstraction and logic,
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. The research required to solve mathematical problems can take
years or even centuries of sustained inquiry.
Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements.
Since the pioneering work of Giuseppe Peano (18581932), David Hilbert (18621943), 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. 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 (15641642) 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

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is wandering about in a dark labyrinth."
[12]
Carl Friedrich Gauss (17771855) referred to
mathematics as "the Queen of the Sciences".
[13]
Benjamin Peirce (18091880) 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
(18791955) 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]
French mathematician Claire Voisin
states "There is creative drive in mathematics, it's all about movement trying to express itself."
[17]
Mathematics is used throughout the world as an essential tool in many fields, including natural
science, engineering, medicine, finance 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.
[18]
Contents
1 History
o 1.1 Evolution
o 1.2 Etymology
2 Definitions of mathematics
3 Inspiration, pure and applied mathematics, and aesthetics
4 Notation, language, and rigor
5 Fields of mathematics
o 5.1 Foundations and philosophy
o 5.2 Pure mathematics
o 5.3 Applied mathematics
6 Mathematical awards
7 Mathematics as science
8 See also
9 Notes
10 References
11 Further reading
12 External links
History
Evolution
Main article: History of mathematics

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Mathematics From Wikipedia, the free encyclopedia This article is about the study of topics, such as quantity and structure. For other uses, see Mathematics (disambiguation). "Math" redirects here. For other uses, see Math (disambiguation). Euclid, Greek mathematician, 3rd century BC, as imagined by Raphael in this detail from The School of Athens.[1] Mathematics is the study of topics such as quantity (numbers),[2] structure,[3] space,[2] and change.[4][5][6] There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.[7][8] Mathematicians seek out patterns[9][10] and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, 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. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19 ...
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