Number theory is a vast and fascinating field of mathematics, sometimes called "higher arithmetic," consisting of the study of the properties of whole numbers. Primes and prime
factorization are especially important in number theory, as are a number of functions
such as the divisor function , Riemann
zeta function , and totient function . Excellent
introductions to number theory may be found in Ore (1988) and Beiler (1966). The
classic history on the subject (now slightly dated) is that of Dickson (2005abc).
The great difficulty in proving relatively simple results in number theory prompted no less an authority than Gauss to remark that "it is just this which gives the higher arithmetic that magical charm which has made it the favorite science of the greatest mathematicians, not to mention its inexhaustible wealth, wherein it so greatly surpasses other parts of mathematics." Gauss, often known as the "prince of mathematics," called mathematics the "queen of the sciences" and considered number theory the "queen of mathematics" (Beiler 1966, Goldman 1997).
See also Abstract Algebra ,
Additive Number Theory ,
Algebraic Number Theory ,
Analytic Number Theory ,
Arithmetic ,
Computational Number Theory ,
Congruence ,
Diophantine Equation ,
Divisor
Function ,
Elementary Number Theory ,
Gödel's First Incompleteness
Theorem ,
Gödel's Second
Incompleteness Theorem ,
Multiplicative
Number Theory ,
Number Theoretic Function ,
Peano's Axioms ,
Prime
Counting Function ,
Prime Factorization ,
Prime Number ,
Quadratic
Reciprocity Theorem ,
Riemann Zeta Function ,
Totient Function Explore this topic in the MathWorld classroom
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Cite this as:
Weisstein, Eric W. "Number Theory." From
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