Number theory is the branch of mathematics concerned with the properties of the integers—that is, whole numbers and their negatives. Number theory also deals with a type of whole numbers called prime numbers. A prime number, such as 2, 5, or 71, is a whole number greater than 1 that can be divided without a remainder only by itself and 1.
About 300 B.C., the Greek mathematician Euclid discussed prime numbers in his book Elements. He proved that there are infinitely many prime numbers. Euclid’s Elements also stated a famous property of whole numbers called the fundamental theorem of arithmetic. This theorem states that every whole number greater than 1 can be written as a product of prime numbers in exactly one way.
The systematic study of number theory began with the work of the French mathematician Pierre de Fermat in the 1600’s. A landmark book in number theory was Disquisitiones Arithmeticae (1801), by the German mathematician Carl Friedrich Gauss. It developed a comprehensive theory of whole numbers, including a complete proof of the fundamental theorem of arithmetic.
