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What (who) is number theory - definition
Number theory
![his proof]] of [[Fermat's Last Theorem]].](https://commons.wikimedia.org/wiki/Special:FilePath/Andrew wiles1-3.jpg?width=200 "his proof]] of [[Fermat's Last Theorem]].")
![[[Al-Haytham]] as seen by the West: on the frontispiece of ''[[Selenographia]]'' Alhasen {{sic}} represents knowledge through reason and Galileo knowledge through the senses.](https://commons.wikimedia.org/wiki/Special:FilePath/Hevelius Selenographia frontispiece.png?width=200 "[[Al-Haytham]] as seen by the West: on the frontispiece of ''[[Selenographia]]'' Alhasen {{sic}} represents knowledge through reason and Galileo knowledge through the senses.")
![The action of the [[modular group]] on the [[upper half plane]]. The region in grey is the standard [[fundamental domain]].](https://commons.wikimedia.org/wiki/Special:FilePath/ModularGroup-FundamentalDomain.svg?width=200 "The action of the [[modular group]] on the [[upper half plane]]. The region in grey is the standard [[fundamental domain]].")
![Number theorists [[Paul Erdős]] and [[Terence Tao]] in 1985, when Erdős was 72 and Tao was 10.](https://commons.wikimedia.org/wiki/Special:FilePath/Paul Erdos with Terence Tao.jpg?width=200 "Number theorists [[Paul Erdős]] and [[Terence Tao]] in 1985, when Erdős was 72 and Tao was 10.")
BRANCH OF PURE MATHEMATICS DEVOTED PRIMARILY TO THE STUDY OF THE INTEGERS
Theory of numbers; Elementary number theory; Number Theory; Number theorist; Number theorists; Num theory; Higher arithemetic; Higher arithmetic; Combinatorial number theory; History of number theory; Applications of number theory; Number theoretic
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics.
Computational number theory
STUDY OF ALGORITHMS FOR PERFORMING NUMBER THEORETIC COMPUTATIONS
Algorithmic number theory; Computational Number Theory
In mathematics and computer science, computational number theory, also known as algorithmic number theory, is the study of
Typographical Number Theory
AXIOMATIC SYSTEM
Typographical number theory
Typographical Number Theory (TNT) is a formal axiomatic system describing the natural numbers that appears in Douglas Hofstadter's book Gödel, Escher, Bach. It is an implementation of Peano arithmetic that Hofstadter uses to help explain Gödel's incompleteness theorems.
Examples of use of number theory
1. Students at Pyongyang Middle School No. 1 smoothly solved mathematic problems in various fields including number theory, algebra, geometry and combination set forth by the Olympiad.