Theory of numbers | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-02-18

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Number_theory


00:02:11 1 History
00:02:21 1.1 Origins
00:02:29 1.1.1 Dawn of arithmetic
00:08:58 1.1.2 Classical Greece and the early Hellenistic period
00:13:22 1.1.3 Diophantus
00:18:52 1.1.4 Āryabhaṭa, Brahmagupta, Bhāskara
00:21:33 1.1.5 Arithmetic in the Islamic golden age
00:22:33 1.1.6 Western Europe in the Middle Ages
00:23:17 1.2 Early modern number theory
00:23:27 1.2.1 Fermat
00:29:35 1.2.2 Euler
00:33:49 1.2.3 Lagrange, Legendre, and Gauss
00:37:31 1.3 Maturity and division into subfields
00:40:00 2 Main subdivisions
00:40:10 2.1 Elementary tools
00:41:33 2.2 Analytic number theory
00:44:05 2.3 Algebraic number theory
00:51:08 2.4 Diophantine geometry
00:59:13 3 Recent approaches and subfields
00:59:57 3.1 Probabilistic number theory
01:02:05 3.2 Arithmetic combinatorics
01:05:26 3.3 Computations in number theory
01:09:35 4 Applications
01:10:48 5 Prizes
01:11:12 6 See also



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SUMMARY
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Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theorists study prime numbers as well as the properties of objects made out of integers (for example, rational numbers) or defined as generalizations of the integers (for example, algebraic integers).
Integers can be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory are often best understood through the study of analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes or other number-theoretic objects in some fashion (analytic number theory). One may also study real numbers in relation to rational numbers, for example, as approximated by the latter (Diophantine approximation).
The older term for number theory is arithmetic. By the early twentieth century, it had been superseded by "number theory". (The word "arithmetic" is used by the general public to mean "elementary calculations"; it has also acquired other meanings in mathematical logic, as in Peano arithmetic, and computer science, as in floating point arithmetic.) The use of the term arithmetic for number theory regained some ground in the second half of the 20th century, arguably in part due to French influence. In particular, arithmetical is preferred as an adjective to number-theoretic.