Number Theory

Number theory or, in older usage, arithmetic is a branch of pure mathematics devoted primarily to the study of the integers. It is sometimes called "The Queen of Mathematics" because of its foundational place in the discipline. Number theorists study prime numbers as well as the properties of objects made out of integers (e.g., rational numbers) or defined as generalizations of the integers (e.g., 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 anal
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An Introduction to the Theory of Numbers
Elementary Number Theory
A Classical Introduction to Modern Number Theory (Graduate Texts in Mathematics, 84)
Fermat's Enigma
An Introduction to the Theory of Numbers
Introduction to Analytic Number Theory
Rational Points on Elliptic Curves (Undergraduate Texts in Mathematics)
The Higher Arithmetic: An Introduction to the Theory of Numbers
Number Theory (Dover Books on Mathematics)
A Concise Introduction to the Theory of Numbers (Volume 0)
Prime Numbers and the Riemann Hypothesis
Elements of Number Theory (Undergraduate Texts in Mathematics)
On Numbers and Games
The Music of the Primes
104 Number Theory Problems: From the Training of the USA IMO Team
Machine Learning by Samuel HackReal and Complex Analysis by Walter RudinVisual Complex Analysis by Tristan NeedhamThe Math of Neural Networks by Michael TaylorOn Numbers and Games by John H. Conway
Not Pop-Science - Mathematics
111 books — 10 voters

An Introduction To The Theory Of Numbers by G.H. HardyA classical introduction to modern number theory by Kenneth F. IrelandRational Points on Elliptic Curves by Joseph H. SilvermanA Course in Arithmetic by Jean-Pierre SerreThe Higher Arithmetic by Harold Davenport
Number Theory (MMath)
50 books — 8 voters

Information Theory by Robert B. AshA First Course in Geometry by Edward T. WalshReal Analysis by Gabriel KlambauerHistory of the Theory of Numbers, Volume II by Leonard Eugene DicksonPerplexing Mazes by Lee Daniel Quinn
Mathematics
20 books — 1 voter


No part of mathematics is ever, in the long run, "useless." Most of number theory has very few "practical" applications. That does not reduce its importance, and if anything it enhances its fascination. No one can predict when what seems to be a most obscure theorem may suddenly be called upon to play some vital and hitherto unsuspected role. ...more
C. Stanley Ogilvy, Excursions in Number Theory

Some numbers, even large ones, have no factors - except themselves, of course, and 1. These are called prime numbers, because everything they are starts with themselves. They are original, gnarled, unpredictable, the freaks of the number world.
Richard Friedberg

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