The most ancient mathematical activity was counting.
The account was necessary to monitor the livestock and conduct trade.
Some primitive tribes counted the number of objects by comparing them with various parts of the body, mainly fingers and toes.
A rock drawing that has survived to our times from the Stone Age depicts the number 35 in the form of a series of 35 finger sticks lined up in a row.
The first significant successes in arithmetic were the conceptualization of numbers and the invention of four basic actions: addition, subtraction, multiplication and division.
The first achievements of geometry are associated with such simple concepts as a straight line and a circle.
The further development of mathematics began around 3000 BC thanks to the Babylonians and Egyptians.
The prerequisites for the transformation of mathematics into a theoretical science first appeared in ancient Greece.
The Pythagorean school played an important role in the formation of ancient Greek mathematics.
For the Pythagorians, any number represented something more than a quantitative quantity.
For example, the number 2, according to their view, meant a difference and therefore was identified with an opinion.
The four represented justice, since this is the first number equal to the product of two identical multipliers.
The Pythagorians also discovered that the sum of some pairs of square numbers is again a square number.
For example, the sum of 9 and 16 is 25, and the sum of 25 and 144 is 169.
Such triples of numbers as 3, 4 and 5 or 5, 12 and 13 are called Pythagorean numbers.
They have a geometric interpretation: if two numbers from the triple are equated to the lengths of the legs of a right triangle, then the third number will be equal to the length of its hypotenuse.
This interpretation, apparently, led the Pythagorians to realize a more general fact, now known as the Pythagorean theorem, according to which in any right triangle the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
However, the question may arise: why, when investigating when and how mathematics as a science arose, do we turn to ancient Greek thinkers, while already before the Greeks, in Babylon and Egypt?
Indeed, mathematics originated in the Ancient East, apparently long before the Greeks.
But the peculiarity of ancient Egyptian and Babylonian mathematics was the lack of a unified system of proofs in it, which first appeared among the Greeks.
"The big difference between Greek and Ancient Eastern science is precisely that Greek mathematics is a system of knowledge skillfully constructed using the deductive method, while ancient Eastern texts of mathematical content contain only interesting instructions, recipes and often examples of how to solve a certain problem."
Ancient Eastern mathematics is a set of certain rules of calculation; the fact that the ancient Egyptians and Babylonians could perform very complex computational operations does not change anything in the general nature of their mathematics.
These features of ancient Eastern mathematics are explained by the fact that it was practically applied in nature; with the help of arithmetic, Egyptian scribes solved problems "about calculating wages, about bread or beer, etc.", and with the help of geometry they calculated areas or volumes.
In both cases, the computer had to know the rules by which the calculation should be performed.
In this respect, special texts are characteristic, intended for scribes who were engaged in solving mathematical problems.
The scribes had to know all the numerical "coefficients" they needed for calculations.
The lists of" coefficients "contain" coefficients " for "bricks", for "walls", then for "triangle", for "circle segment", then for "copper", "silver", "gold", for "cargo ship", for "diagonal", etc.
A very important task of mathematics was the calculation of the calendar, since the calendar was used to determine the timing of agricultural work and religious holidays.
It should be noted that in Ancient Greece, as well as in Babylon and Egypt, computing techniques were developed, without which it was impossible to solve practical problems of construction, military affairs, trade, navigation, etc.
But it is important to keep in mind that the Greeks themselves called the methods of computational arithmetic and algebra logistics (logistika counting art, number technique) and distinguished logistics as the art of calculation from theoretical mathematics.
The rules of calculation were developed in Greece in the same way as in the East, and, of course, the Greeks could borrow a lot from both the Egyptians and the Babylonians.
About the logistics of the Greeks, as well as about mathematical calculations in the East, we can say that it was practically applied.
The logistics included: counting, arithmetic operations with integers up to the extraction of square and cubic roots, actions on a counting device — an abacus, operations with fractions and methods of numerical solution of problems for equations of the first and second degree.
In logistics, the applications of arithmetic to land surveying and other tasks of everyday life were also considered.
The Greeks themselves distinguished logistics from theoretical arithmetic, which they called simply arithmetic.
The rules of logistics were stated dogmatically and, generally speaking, were not provided with evidence in the same way as was customary in the Egyptian papyri.
Thus, in Greece there was both practically applied mathematics (the art of numeracy), similar to the Egyptian and Babylonian, and theoretical mathematics, which assumed a systematic connection of mathematical statements, a strict transition from one sentence to another with the help of proof.
It was mathematics as a systematic theory that was first created in Greece.
It must be assumed that the formation of mathematics as a systematic theory was a long process: from the first Greek mathematicians (the end of the VI V century BC) to the III century BC, more than two hundred years of rapid development of Greek science passed.
However, already in the early Pythagoreans, i.e. at the first stages of the formation of Greek mathematics, we can find such specific features that fundamentally distinguish their approach to mathematics from the ancient Eastern one.
First of all, such a feature is a new understanding of the meaning and purpose of mathematical knowledge, a different understanding of the number: with the help of the number, the Pythagoreans do not just solve practical problems, but want to explain the nature of everything that exists.
Therefore, they strive to comprehend the essence of numbers and numerical relations, because through it they hope to understand the essence of the universe.
This is how the first attempt in history to comprehend the number as a world creating and meaning forming element arises.
What the Babylonians and Egyptians used only as a means, the Pythagoreans turned into a special subject of research, i.e., into the goal of the latter.
The Pythagoreans were the first to elevate mathematics to a previously unknown rank: they began to consider numbers and numerical relations as the key to understanding the universe and its structure.
For the first time, they came to the conclusion that "the book of nature is written in the language of mathematics."
It is not surprising that the thinkers who for the first time tried not just to technically operate with numbers (i.e. calculate), but to understand the very essence of a number, the essence of a set and the nature of the relations of various sets to each other, solved this problem initially in the form of explaining the entire structure of the universe with the help of a number as an initial.
Before mathematics appeared as a theoretical system, the doctrine of number as a certain divine beginning of the world arose, and this, it would seem, not mathematical, but philosophical theoretical teaching played the role of an intermediary between ancient Eastern mathematics as a collection of samples for solving individual practical problems and ancient Greek mathematics as a system of propositions strictly connected with each other by means of proof.
