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MATHEMATICS 
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 Piano (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 (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 Violin 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.

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Mathematics

  • 1. MATHEMATICS 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 Piano (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 (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
  • 2. 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 Violin 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.