# Number Theory

Number theory (or arithmetic) is a branch of pure mathematics devoted primarily to the study of the integers. 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 analytical objects (e.g., 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, e.g., 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 By the early twentieth century, it had been superseded by "number theory".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.

### Other articles related to "number theory, theory, number, numbers":

Ludwig Stickelberger - Mathematical Contributions - Number Theory
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Number Theory - Literature
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... mathematician Subbayya Sivasankaranarayana Pillai (1901–1950), known for his work in number theory Kollagunta Gopalaiyer Ramanathan (1920–1992), known for his ... Ramanujam (1938–1974), worked on number theory and algebraic geometry T ... Vijayaraghavan (1902–1955), worked on Pisot-Vijayaraghavan number Ravindran Kannan, Professor of Computer Science and Mathematics at Yale University ...
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... Heronian triangle Integer triangle Pythagorean triple Triangular number. ...
Multiple Zeta Function - References
... Dirichlet series related to the Riemann zeta function", Journal of Number Theory 19 (1) 85–102, doi10.1016/0022-314X(84)90094-5, ISSN 0022-314X, MR 0751166 Crandall ... and other multiple zeta-functions", Proceedings of the Session in Analytic Number Theory and Diophantine Equations, Bonner Math ... Number Theory 6 (3) 501–514 ...

### Famous quotes containing the words theory and/or number:

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Albert Einstein (1879–1955)

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