Before entering fully into the clarification of the meaning of the term arithmetic, let us analyze what its etymological origin is. Specifically, we can say that it is a word that comes from the Latin noun “arithmetica”. However, this, in turn, derives from the Greek, exactly from “aritmetikos”, which is the result of the sum of two different parts:
-The name “arithmos”, which can be translated as “number”.
-The suffix “-tikos”, which is used to indicate “relative to”.
According to DigoPaul, the arithmetic is the area of mathematics focused on numbers and the operations carried out with them. It should be remembered that numbers are the signs that allow us to express a quantity.
The formal emergence of arithmetic took place in Ancient Greece from an increase in the rigor of mathematics and the development of proofs. Thus the four elementary operations of this branch were established: adding, subtracting, multiplying and dividing.
Advancing in the complexity of arithmetic, one can move from elementary operations to others such as root extraction and power calculation. It is also possible to include letters next to the numbers in order to achieve the representation of different variables.
Among the most important figures in arithmetic in Ancient Greece, we can highlight some such as the following:
-Euclid (325 BC – 265 BC), who is considered the father of Geometry. He made numerous works that have become pillars of the aforementioned arithmetic, such as “The elements”.
-Nicomaco de Gerasa, who is classified as a neopythagorean mathematician. One of his most important and recognized works was “Introduction to arithmetic”, where, among other things, he comes to the table and explains number theory well. So important was this work that it became manual in the Platonic schools.
The arithmetic can develop differently. If it is simple operations, they can be performed mentally or with the help of the fingers of the hand. In ancient times the abacus was also used, a device with small balls that move to do the calculations. Nowadays arithmetic operations are usually carried out with a calculator, either physical or virtual.
Although it is true that the abacus is one of the best known instruments that have been used to carry out calculations within arithmetic, in history there have been many others with the same objective. We are referring to the counting sticks, the Babylonian tablet, the Inca abacus, the adding machine…
It is known as high arithmetic to the study of the properties and functions of numbers. In this framework, one can speak of binary arithmetic (which appeals to zero and one to represent values), modular arithmetic (which works with modules) and ordinal arithmetic (oriented to ordinal numbers), among others.
The arithmetic second order, moreover, is composed of different axiomatic systems allowing formalization of natural numbers and subsets formed by them.