It is simply impossible to imagine modern civilization without numbers. We encounter them every day, perform dozens, hundreds and thousands of actions on them using computers. We are so used to it that the history of the development of numbers does not interest us at all, and many simply never thought about it. But without knowledge of the past, you can never understand the present, and therefore you should always strive to comprehend the origins.
So what is the history of the development of numbers? When they appeared, how did man come to their creation? Let's find out about it!
Development
In mathematics, no component is more important. Despite this, the number as a concept has been developing for more than one thousand years, until the scientific minds of the whole world agreed on how to perceive it.
The first applied disciplines, which urgently required the appearance of this concept, were associated with agriculture, construction and observation of stars. In turn, the study of the starry sky and the classification of all dimensions were vital for the development of shipping and international trade, without which no state could develop.
A bit of philosophy
Even the most primitive figures were developed and reduced to a single form for many centuries. Many of them were formed as a result of creative rethinking of words or individual letters. The famous Pythagoras said that numbers are that mysterious, ephemeral substance from which the entire Universe is formed. In general, according to modern concepts of science, he was largely right.
The Chinese divided the numbers into two large categories (which have survived to this day):
- Odd, or Yang. In ancient Chinese philosophy, they symbolized heaven and auspiciousness.
- Accordingly, even (Yin). This concept symbolized the earth and instability.
Since ancient times ...
Surely you have already guessed that the history of the development of numbers begins its reckoning from the time of the most ancient times. At that time, mysterious symbols were accessible for understanding only to privileged priests, who became the first mathematicians in the history of our world.
Anthropologists and archaeologists have precisely established that man knew how to count already in the Stone Age. At first, the first numbers were indicated solely by the number of fingers on the hands and feet. They were used to count steps, booties, enemies ... At first, a person needed only a few simple numbers, but the development of society required an ever-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 whole of human civilization in general, since the bill required intense intellectual work.
So the history of the origin and development of the number is inextricably linked with the improvement of the mind and the desire of our distant ancestors for self-improvement. The more often 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 to compare the number of items with similar values ​​for the goods offered to him. The concepts of “more”, “less”, “equal”, “same amount” appeared. The knowledge quickly became more complicated, and therefore the need for an account system soon appeared.
It should be remembered that the history of the development of numbers in reality began with the appearance of the first intelligent person. On an intuitive level, he was able to compare the number of people, animals, objects, without even the slightest idea of ​​even the simplest mathematics. But this was the strange thing: any object can be touched, and some of them can be easily put together in a heap.
The numbers that describe the properties of these very objects exist, but it was impossible to touch or compare them. This property made people awe; they attributed magic, supernatural qualities to numbers.
Some evidence for 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 precisely three forms (in ancient Greek, for example): singular, dual and plural. A little later, a man learned to distinguish, for example, two bison from three. Initially, the account was associated with a specific set of items.
Until recently, indigenous Australians and Polynesians had only two numerals: “one” and “two,” and all the other numbers people got by combining them. For example, the number three is two and one, four is two and two. This is surprisingly reminiscent of the binary system of calculus, which now uses computer technology! However, the harsh life of those times forced to study, and therefore a primitive account quickly turned into a mathematical science.
Babylon and Mesopotamia
In ancient Babylon, mathematicians developed especially widely, since gigantic, extremely complex structures were created in this state, which without calculations could not be built. Strange as it may seem, the Babylonians did not have a special thrill for numbers, so the history of the development of the concept of number in the broad sense of the word began precisely with them.
The Babylonians went around all their contemporaries in that they could record the maximum number of objects, people or animals with a minimum set of characters. They first introduced a positional system, which assumes a different numerical value of the same digit, occupying different positions in a numerical context.
In addition, their system of calculation was based on the six-decimal measurement method, which the Babylonians, as scientists suggest, borrowed from the Sumerian civilization. Do not think that in this area the history of the development of the concept of number has stopped. We still use the concept of 60 minutes, 60 seconds, 360 degrees in the context of measuring the circle.
Anticipated Pythagoras
The ancient scribes in Babylon already knew quite well the properties of right-angled 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 could even solve problems with up to three unknown values ​​with their help!
In the recent past, modern mathematicians have been surprised to learn that their ancient predecessors succeeded in extracting not only square, but even cubic roots. They also came close to determining the number of Pi, roughly rounding it to three. It should be noted that the Egyptians subsequently managed to more accurately calculate its value (3.16).
Integers
No less ancient is the history of the development of natural numbers. At present, it is believed that the ancient Roman scientist Boethius (480-524) was the first to use this term in his writings, but long before him, Nikomakh from Gerasa wrote in his writings about the natural series of numbers.
However, in the modern sense, the term "natural number" was used only by D'Alembert (1717-1783). But do not quibble: the study of the account itself began with them. After all, the numbers 1, 2, 3, 4, ...
With their appearance, a major step was taken towards the emergence of mathematics and algebra in the form in which we know them today. Modern mathematicians speak with confidence about the infinity of a number of natural numbers. Of course, in ancient times, man did not know about this. The amount that people simply could not imagine was indicated by the words "darkness", "legion", "multitude" and so on. So the history of the development of the line of numbers is extremely ancient ...
Set theory
At first, the natural series 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 “Psammit”, which his contemporaries often called so: “Calculus of grains of sand”. He accurately calculated the number of tiny particles that theoretically could occupy the entire volume of a ball with a diameter of 15,000,000,000,000 kilometers.
The Greeks managed to reach Archimedes to the number of 10.000.000 myriads. Myriad, however, they called the amount of 10,000. The name itself comes from the Greek “miros”, which in Russian means “immeasurably large”, “incredibly huge”. Archimedes went further: he began to use the concept of "myriad myriads" in his calculations, which subsequently led him to create his own, author's system of calculus.
The maximum value that the scientist could describe contains 80,000,000,000,000,000 zeros. If you print this number on a long paper tape, then you can encircle the entire globe around the equator more than two million times.
Thus, all natural numbers have two important functions:
- They can describe the number of any items.
- With their help, signs of objects in a numerical series are described.
Real numbers
But what about the history of the development of
real numbers? Indeed, in mathematics they occupy an equally important place! First, refresh the memory. Any positive, negative number, as well as zero, can be called valid. They are many divided into rational and irrational.
If you carefully read the article, you could have guessed that the history of the development of real numbers begins with 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, this date can be noted as an intermediate.
As for the negative values, they were first described by Diophantus (Greece) in the third century AD, but they were “legalized” only in India, almost simultaneously with the concept of “zero”.
It should be remembered that the history of the development of numbers in mathematics assumed their existence in ancient Egypt, since as a result of calculations they often appeared. It was only at that time that they were considered “impossible” and “unrealistic,” although they were occasionally used as intermediate values.
Rational numbers
Recall that a rational number is a fraction. In the form of the numerator, an integer is used in it, and the denominator is a natural number. We will never know when and where this concept arose for the first time, but it was already actively used by the Sumerians several thousand years before our era. Their example was followed by the Greeks and Egyptians.
Complex numbers
But they were received relatively recently, immediately after identifying methods for calculating the roots of the cubic equation. The Italian Niccolo Fontana Tartaglia (1499-1557) did this around the beginning of the sixteenth century. And then he found out that to solve various problems it is far from always possible to use only real numbers.
It was possible to explain this strange phenomenon only in 1572. Rafael Bombelli was able to do this, with which begins the history of the development of complex numbers. But the results he obtained were considered “charlatan's fabrications” for a very long time, and only in the 19th century did the great mathematician Karl Friedrich Gauss prove that his distant predecessor was absolutely right.
Another theory
Some researchers say that imaginary values ​​were first mentioned back in 1545. This happened on the pages of the famous work “The 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 when multiplied give 10, and when multiplied, their value increases to 40.
For a long time, the question for mathematicians was whether their set could be completely closed. Let us explain: do operations on complex values ​​always lead to complex, real results, or further research can lead to the discovery of something completely new? However, the solution to this problem lies in the works of Abraham de Muavre (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 area.