Difference between revisions of "Mathematics"
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==Origin== | ==Origin== | ||
Plural of obsolete ''mathematic''‘mathematics,’ from Old French ''mathematique'', from [[Latin]] ''(ars) mathematica'' ‘mathematical (art),’ from [[Greek]] ''mathēmatikē'' (''tekhnē''), from the base of ''manthanein'' ‘[[learn]].’ | Plural of obsolete ''mathematic''‘mathematics,’ from Old French ''mathematique'', from [[Latin]] ''(ars) mathematica'' ‘mathematical (art),’ from [[Greek]] ''mathēmatikē'' (''tekhnē''), from the base of ''manthanein'' ‘[[learn]].’ | ||
| − | *[ | + | *[https://en.wikipedia.org/wiki/16th_century late 16th Century] |
==Definitions== | ==Definitions== | ||
*1:the [[abstract]] [[science]] of [[number]], [[quantity]], and [[space]]. Mathematics may be studied in its own right (pure mathematics), or as it is applied to other [[disciplines]] such as [[physics]] and engineering (applied mathematics). | *1:the [[abstract]] [[science]] of [[number]], [[quantity]], and [[space]]. Mathematics may be studied in its own right (pure mathematics), or as it is applied to other [[disciplines]] such as [[physics]] and engineering (applied mathematics). | ||
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Mathematicians seek out [[patterns]] 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]]. | Mathematicians seek out [[patterns]] 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 [ | + | Rigorous [[arguments]] first appeared in [https://en.wikipedia.org/wiki/Greek_mathematics Greek mathematics], most notably in [https://en.wikipedia.org/wiki/Euclid Euclid]'s ''[https://en.wikipedia.org/wiki/Euclid%27s_Elements Elements]''. Since the pioneering work of [https://en.wikipedia.org/wiki/Giuseppe_Peano Giuseppe Peano] (1858–1932), [https://en.wikipedia.org/wiki/David_Hilbert David Hilbert] (1862–1943), and others on [https://en.wikipedia.org/wiki/Foundations_of_mathematics 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. |
| − | [ | + | [https://en.wikipedia.org/wiki/Galileo_Galilei 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]]."[https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss Carl Friedrich Gauss] (1777–1855) referred to mathematics as "the Queen of the Sciences". [https://en.wikipedia.org/wiki/Benjamin_Peirce Benjamin Peirce] (1809–1880) called mathematics "the [[science]] that draws necessary [[conclusions]]". 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." 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." French mathematician [https://en.wikipedia.org/wiki/Claire_Voisin Claire Voisin] states "There is [[creative]] drive in mathematics, it's all about movement trying to [[express]] itself." |
| − | Mathematics is used throughout the world as an essential [[tool]] in many fields, including [[natural science]], engineering, [[medicine]], [[finance]] and the [[social sciences]]. [ | + | Mathematics is used throughout the world as an essential [[tool]] in many fields, including [[natural science]], engineering, [[medicine]], [[finance]] and the [[social sciences]]. [https://en.wikipedia.org/wiki/Applied_mathematics 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 [https://en.wikipedia.org/wiki/Game_theory game theory]. Mathematicians also engage in [https://en.wikipedia.org/wiki/Pure_mathematics 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.[https://en.wikipedia.org/wiki/Mathematics] |
[[Category: Mathematics]] | [[Category: Mathematics]] | ||
Latest revision as of 01:24, 13 December 2020
Origin
Plural of obsolete mathematic‘mathematics,’ from Old French mathematique, from Latin (ars) mathematica ‘mathematical (art),’ from Greek mathēmatikē (tekhnē), from the base of manthanein ‘learn.’
Definitions
- 1:the abstract science of number, quantity, and space. Mathematics may be studied in its own right (pure mathematics), or as it is applied to other disciplines such as physics and engineering (applied mathematics).
•2: [ often treated as pl. ] the mathematical aspects of something: the mathematics of general relativity
Description
Mathematics is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.
Mathematicians seek out patterns 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 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.
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."Carl Friedrich Gauss (1777–1855) referred to mathematics as "the Queen of the Sciences". Benjamin Peirce (1809–1880) called mathematics "the science that draws necessary conclusions". 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." 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." French mathematician Claire Voisin states "There is creative drive in mathematics, it's all about movement trying to express itself."
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.[1]
