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).
Source:
Wolfram – Mathworld
COGNITIVE GEOMETRICS 