History

Number theory is a branch of mathematics which deals with the natural numbers,

1, 2, 3, …,

often called the positive integers.

Archeology and history teach us that man began early to count. He learned to add numbers and much later to multiply and subtract them. To divide numbers was necessary in order to share evenly a heap of apples or a catch of fish. These operations on numbers are called calculations. The word “calculation” is derived from the Latin calculus, meaning a little stone; the Romans used pebbles to mark numbers on their computing boards.

As soon as men knew how to calculate a little, this became a playful pastime for many a speculative mind. Experiences with numbers accumulated over the centuries with compound interest, so to speak, till we now have an imposing structure in modem mathematics known as number theory. Some parts of it still consist of simple play with numbers, but other parts belong to the most difficult and intricate chapters of mathematics.

Numerology

Some of the earliest traces of number speculations can certainly be detected in superstitions concerning numbers, and these one finds among all peoples. There are lucky numbers to be preferred and cherished, and there are unlucky ones to be shunned like the evil eye. We have a good deal of information about the numerology of the classical Greeks, that is, their thoughts and superstitions in regard to the symbolic meaning of the various numbers.