History of the development of numbers. History of the development of real numbers

Modern civilization is simply impossible to imagine without numbers. We encounter them every day, we make dozens, hundreds and thousands of actions on them with the help of computers. We are so accustomed to this that the history of the development of numbers does not interest us at all, and many people have never even thought about it. But without knowledge of the past, one can never understand the present, and therefore one should always strive to understand the origins.

So what is the history of the development of numbers? When did they appear, how did the man get to their creation? Let's find out about it!

Development

In mathematics, there is no component more important. Despite this, the number as a concept has evolved over several thousand years, until the scientists of the world have agreed on how to perceive it.

The first applied disciplines, which urgently demanded the emergence of this concept, were associated with agriculture, construction and observations of the stars. In turn, the study of the starry sky and the classification of all measurements were vital for the development of shipping and international trade, without which no state could develop.

A little philosophy

Even the most primitive figures were developed and brought to a single view over many centuries. Many of them were formed as a result of creative rethinking of words or individual letters. The famous Pythagoras said that the figures are that mysterious, ephemeral substance from which the entire universe is formed. In general, according to modern ideas of science, he was in many ways right.

The Chinese divided the numbers into two large categories (which have survived to this day):

• Odd, or Ian. In ancient Chinese philosophy, they symbolized the sky and auspiciousness.
• Accordingly, even (Yin). This concept symbolized land and instability.

Since ancient times ...

Surely you already guessed that the history of the development of numbers begins to count down from the times of the deepest antiquity. At that time, mysterious symbols were accessible only to the privileged priests, who became the first mathematicians in the history of our world.

Anthropologists and archaeologists have accurately established that man was able to count already in the Stone Age. At first, the first numbers were indicated solely by the number of fingers and toes. They used them to count the steps, the prey, the enemies ... At first the person needed only a few prime numbers, but the development of society required an increasing complexity of the system. This not only led to the development of the rudiments of mathematics, but also contributed to the development of the entire human civilization in general, since the account required intense intellectual work.

So the history of the emergence and development of the number are inextricably linked with the improvement of the mind and the desire of our distant ancestors to self-improvement. The more they looked at the stars, the more they thought about mathematical patterns (even at a primitive level) in the world around them, the wiser they became.

Intuitive concept of number

As soon as the first barter occurred, a person began to learn how to compare the number of items with similar values for the goods offered to him. There were concepts "more", "less", "equal", "as much". Knowledge quickly became more complicated, and therefore soon there was a need for an account system.

It should be remembered that the history of the development of numbers in reality began with the appearance of the first intelligent person. He intuitively knew how to compare the number of people, animals, objects, even without even the slightest notion of even the simplest mathematics. But this was the oddity: any object can be touched, and some of them can easily be put together in a heap.

Numbers, which describe the properties of these very objects, exist, but it was impossible to touch or compare them. This property brought people into awe, they attributed the numbers to magical, supernatural qualities.

Some evidence of hypotheses

Scientists have long assumed that initially people used only three concepts: "one", "two" and "many." This hypothesis is brilliantly confirmed by the fact that in many ancient languages there are exactly three forms (in ancient Greek, for example): single, dual and plural. A little later, a man learned to distinguish, for example, two bison from three. Initially, the account was associated with some specific set of items.

Until recently, the Indigenous Australians and Polynesians had only two numerals: "one" and "two", and all other numbers were obtained by combining them. For example, the number three is two and one, four are two and two. This is surprisingly reminiscent of the binary system of calculus now used by computer technology! However, the harsh life of those times forced them to learn, and therefore the primitive account quickly turned into mathematical science.

Babylon and Mesopotamia

In ancient Babylon, mathematics developed particularly widely, since in this state gigantic, extremely complex structures were created, which without calculations could not be built. Strange as it may seem, the Babylonians did not have a special trembling for the numbers, so the history of the concept of a number in the broad sense of the word began precisely with them.

Babylonians bypassed all their contemporaries in the fact that they could write the maximum number of objects, people or animals with a minimal set of symbols. They first introduced a positional system, which assumes a different numerical value of the same number occupying different positions in a numerical context.

In addition, their system of calculus was based on the sexagesimal method of measurement, which the Babylonians, as scientists suggest, borrowed from the Sumerian civilization. Do not think that the history of the development of the concept of numbers has stopped in this area. We still use the concept of 60 minutes, 60 seconds, 360 degrees in the context of measuring the circumference.

Anticipated Pythagoras

Ancient scribes in Babylon already knew well the properties of rectangular triangles. In addition, they performed the calculation of the volume of the truncated pyramid. Today it is precisely known that the history of the development of rational numbers originates precisely from those times: the mathematicians of Mesopotamia and Babylon not only actively used fractions, but even could solve with their help problems involving up to three unknown values!

In the recent past, modern mathematicians were surprised to learn that their ancient predecessors succeeded in extracting not only a square but even a cubic root. They also came close to determining the number Pi, roughly rounding it to three. It should be noted that the Egyptians subsequently managed to calculate much more accurately its value (3.16).

Integers

No less ancient is the history of the development of the natural number. At present, it is believed that the first to use this term in his works was the ancient Roman scientist Boethius (480-524), but long before him, Nikomach of Geraz wrote in his works about the natural, natural series of numbers.

However, in modern understanding the term "natural number" was used only by D'Alembert (1717-1783). But you should not quibble: the very study of the account began with them. After all, natural numbers are 1, 2, 3, 4, ...

With their appearance, the most important step was taken towards the emergence of mathematics and algebra in the form in which we know them today. Modern mathematicians with confidence speak of the infinity of a number of natural numbers. Of course, in ancient times a man did not know about this. The amount that people simply could not imagine was indicated by the words "darkness", "legion", "set" and so on. So the history of the development of the number line is extremely ancient ...

Theory of set

At first, the natural number of numbers was extremely short. But the famous Archimedes (III century BC) managed to significantly expand this concept. It was this legendary scientist who wrote the work Psammite, which his contemporaries often called it: "Calculus of grains of sand". He accurately counted the number of tiny particles that theoretically could occupy the entire volume of the ball with a diameter of 15,000,000,000,000 kilometers.

Prior to Archimedes the Greeks managed to reach the number of 10.000.000 myriads. Myriad, however, they called the number at 10 000. The very name comes from the Greek "miros", which means "immeasurably large", "incredibly huge" in Russian. Archimedes went further: he began to use in his calculations the concept of "myriad myriad", which subsequently led him to create his own, the author's system of calculus.

The maximum value that the scientist could describe is 80.000.000.000.000.000 zeros. If you print this number on a long paper tape, then you can gird the entire globe over the equator more than two million times.

Thus, all natural numbers have two most important functions:

• They can characterize the number of any objects.
• With their help, signs of objects in a number series are described.

Real numbers

But what about the history of the development of real numbers? After all, in mathematics, they occupy no less important place! First we'll refresh the memory. Any positive, negative number, and also zero can be called valid. Their set is divided into rational and irrational.

If you carefully read the article, you could guess that the history of the development of real numbers begins from the very dawn of mankind. Since the concept of zero was first (more or less reliable information) formulated in 876 from the Nativity of Christ and introduced in India, we can mark this date as an intermediate date.

As for the negative meanings, they were first described by Diophantus (Greece) in the third century AD, but they were "legalized" only in India, practically simultaneously with the concept of "zero."

It should be remembered that the history of the development of numbers in mathematics presupposed their existence even in Ancient Egypt, because as a result of the calculations they were often manifested. But only at that time they were considered "impossible" and "unreal", although occasionally they were used as intermediate values.

Rational numbers

Recall that a rational number is a fraction. In the form of a numerator, an integer is used in it, and the natural number is the denominator. We will never know when and where this concept originated for the first time, but it was actively used by the Sumerians for several thousand years before our era. Their example was followed by the Greeks and Egyptians.

Complex numbers

But they were obtained relatively recently, immediately after the discovery of methods for calculating the roots of the cubic equation. This was done by the Italian Niccolo Fontana Tartaglia (1499-1557) around the beginning of the sixteenth century. And then he found out that it is not always possible to use only real numbers to solve various kinds of problems.

It was only in 1572 that this strange phenomenon was explained. It was able to do this Raphael Bombelli, from which the history of the development of complex numbers begins. But the results obtained by him for a long time were considered "inventions of a charlatan", and only in the 19th century the great mathematician Carl Friedrich Gauss proved that his distant predecessor was absolutely right.

Another theory

Some researchers say that for the first time imaginary quantities were mentioned as far back as 1545. This happened on the pages of the famous at that time work "Great Art, or On Algebraic Rules," which was written by Gerolamo Cardano. Then he tried to find a solution to the problem of two numbers, which multiply 10, and multiply them to 40.

For a long time before mathematicians there was the question of whether their set could be completely closed. Let us explain: are operations on complex values always yield complex, real results, or can further exploration lead to the discovery of something completely new? However, the solution to this problem is in the works of Abraham de Moivre (they date back to 1707), as well as in the works of Roger Cotes, which were published in 1722.

That's the whole story of the development of the number. Briefly, of course, but the article nevertheless considers the main milestones of research in this field.