Humans are the product of animal evolution, and there was no concept of quantity at first. However, the developed brain's understanding of the objective world has reached a more rational and abstract level. In this way, in the long life practice, out of the need to record and distribute daily necessities, the concept of number has gradually emerged. For example, a wild animal is captured, which is represented by 1 stone. If you catch three heads, put three stones. "Knotting knots" is also something that many close ancient humans have done. There is a record of "tying the knot to govern the country" in the book of changes. Legend has it that the ancient Persian kings tied knots with ropes to count the days of war. It is also a common method used by the ancients to carve or hide the bark with sharp tools or count it on the ground with small sticks. When these methods are used much more, the concept of number and the symbol of counting are gradually formed.

At first, the concept of numbers began with natural numbers, such as 1, 2, 3, 4 ... No matter where they are located, the symbols used for counting are the same size.

The figures in ancient Rome were quite advanced, and now many old wall clocks are often used.

In fact, Roman numerals have only seven symbols: I (for 1), V (for 5), X (for 10), L (for 50), C (for 100), D (for 500) and M (for 65438). No matter how the positions of these seven symbols change, the numbers they represent are the same. They can be combined to represent any number according to the following laws:

1. Repetition: How many times a Roman numeral symbol is repeated means several times this number. For example, "three" means "3"; "XXX" means "30"

2. Add right and subtract left: add a symbol representing big numbers to the right of the symbol representing small numbers, indicating that big numbers are added with small numbers, such as "VI" for "6" and "DC" for "600". A symbol representing a small number is attached to the left of the symbol representing a large number, indicating a number in which a large number is subtracted from a small number, such as "IV" for "4", "XL" for "40" and "VD" for "495".

3. Add a horizontal line: add a horizontal line to the Roman numeral, indicating that it is 1000 times that number. For example, ""means "15000" and "165000".

In ancient China, notation was also very important. The oldest notation is found in Oracle Bone Inscriptions and Zhong Ding, but it is difficult to write and identify, so it is not used by future generations. In the Spring and Autumn Period and the Warring States Period, production developed rapidly. In order to meet this need, our ancestors created a very important calculation method-calculation. The computing chip used for calculation is made of bamboo sticks and bones. Arranged according to the specified length order, which can be used for counting and calculation. With the popularization of calculation, the arrangement of calculation and preparation has become the symbol of calculation. There are two types of calculation and arrangement, horizontal and vertical, both of which can represent the same number.

It is clear from the absence of "10" in the calculation code that the calculation strictly follows the decimal system from the beginning. Numbers exceeding 9 digits will enter one digit. The same number, a hundred in a hundred, Wan Li has ten thousand. This calculation method was very advanced at that time. Because the decimal system was really used in other parts of the world at the end of the 6th century. But there is no "zero" in digital calculation, and there is a vacancy when it meets "zero". For example, "6708" can be expressed as "┴ ╥". There is no "zero" in the number, so it is easy to make mistakes. So later, some people put copper coins in the blank to avoid mistakes, which may be related to the emergence of "zero" However, most people believe that the invention of the mathematical symbol "0" should be attributed to Indians in the 6th century. They first used a black dot () to represent zero, and then gradually became "0".

Speaking of the appearance of "zero", it should be pointed out that the word "zero" appeared very early in ancient Chinese characters. But at that time, it didn't mean "nothing", just "bits and pieces" and "not much". Such as "odd", "sporadic" and "odd". "105" means that there is a score of 100. With the introduction of Arabic numerals. "105" is pronounced as "105", and the word "zero" corresponds to "0", so "zero" means "0".

If you look closely, you will find that there is no "0" in Roman numerals. In fact, in the 5th century, "0" was introduced to Rome. But the Pope is cruel and old-fashioned. He doesn't allow anyone to use "0". A Roman scholar recorded some benefits and explanations about the usage of "0" in his notes, so he was summoned by the Pope and executed the punishment of "Zn" so that he could no longer hold a pen and write.

But no one can stop the appearance of "0". Now, "0" has become the most meaningful digital symbol. "0" can mean "No" or "Yes". For example, a temperature of 0℃ does not mean that there is no temperature; "0" is the only neutral number between positive and negative numbers; The power of 0 of any number (except 0) is equal to1; 0! = 1 (factorial of zero is equal to 1).

In addition to decimal system, in the early stage of the germination of mathematics, there were many numerical decimal systems, such as five, binary, ternary, seven, eight, decimal, hexadecimal, twenty, hexadecimal and so on. In the long-term practical application, decimal has finally gained the upper hand.

At present, the internationally used numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0 are called Arabic numerals. In fact, they were first used by ancient Indians. Later, Arabs integrated ancient Greek mathematics into their own mathematics, and this simple and easy-to-remember decimal notation spread all over Europe, gradually evolving into today's Arabic numerals.

The concept of numbers, the writing of numbers and the formation of decimal system are all the results of human long-term practical activities.

With the needs of production and life, people find that it is not enough to express it only by natural numbers. If five people share four things when distributing prey, how much should each person get? So the score is generated. China's academic score is earlier than that of Europe 1400 years! Natural numbers, fractions and zeros are usually called arithmetic numbers. Natural numbers are also called positive integers.

With the development of society, people find that many quantities have opposite meanings, such as increase and decrease, advance and retreat, rise and fall, east and west. To represent such a quantity, a negative number is generated. Positive integers, negative integers and zero are collectively called integers. If you add a positive score and a negative score, they are collectively called rational numbers. With these digital representations, people find it much more convenient to calculate.

However, in the process of digital development, an unpleasant thing happened. Let's go back to Greece 2500 years ago, where there was a Pythagorean school, a group that studied mathematics, science and philosophy. They believe that "number" is the origin of all things and dominates the whole nature and human society. So everything in the world can be summed up as a number or a ratio of numbers, which is the source of world harmony. When they say numbers, they mean integers. The appearance of scores makes "number" less complete. But the score can be written as the ratio of two integers, so their faith has not wavered. However, a student named hippasus in the school, when studying the median term in the ratio of 1 2, found that no number written in integer ratio can represent it. Let this number be x, because the result of deduction is x2=2. He drew a square with a side length of 1 and set the diagonal as X. According to Pythagorean theorem x2= 12+ 12=2, we can see that the diagonal length of a square with a side length of 1 is the required number, and this number must exist. But how much is it? How to express it? Hippasus and others were puzzled and finally decided that this was a new number that they had never seen before. The appearance of this new number shocked the Pythagorean school and shook the core of their philosophical thought. In order to keep the math building that supports the world from collapsing, they stipulated that the discovery of new figures should be kept strictly confidential. And hippasus still can't help letting the cat out of the bag. It is said that he was later thrown into the sea to feed sharks. However, the truth cannot be hidden. People later found many numbers that can't be written by the ratio of two integers, such as pi, which is the most important one. People write them as π, and so on, and call them irrational numbers.

Rational numbers and irrational numbers are collectively called real numbers. The study of various numbers in the real number range makes the mathematical theory reach a quite advanced and rich level. At this time, human history has entered the19th century. Many people think that the achievements in mathematics have reached the peak, and there will be no new discoveries in digital form. But when solving the equation, you often need to make a square. If the square number is negative, is there any solution to this problem? If there is no solution, then mathematical operation is like walking into a dead end. So mathematicians stipulated that the symbol "I" was used to represent the square root of "-1", that is, I =, and the imaginary number was born. "I" became a fictional unit. Later generations combined the real number with the imaginary number and wrote it in the form of a+bi (A and B are both real numbers), which is a complex number. For a long time, people can't find quantities expressed by imaginary numbers and complex numbers in real life, so imaginary numbers always give people an illusory feeling. With the development of science, imaginary numbers have been widely used in hydraulics, cartography and aviation. In the eyes of scientists who master and use imaginary numbers, imaginary numbers are not "virtual" at all.

After the concept of number developed to imaginary number and complex number, for a long time, even mathematicians thought that the concept of number was perfect and all the members of the mathematical family had arrived. However, in June 1843+16 10, British mathematician Hamilton put forward the concept of "quaternion". The so-called quaternion is a number. It consists of a scalar (real number) and a vector (where x, y and z are real numbers). Quaternions are widely used in number theory, group theory, quantum theory and relativity. At the same time, people have also studied the theory of "multivariate number". Multivariate number has gone beyond the category of complex number, and people call it hypercomplex number.

Due to the development of science and technology, concepts such as vector, tensor, matrix, group, ring and domain are constantly produced, which pushes mathematical research to a new peak. These concepts should also belong to the category of numerical calculation, but it is not appropriate to classify them into super complex numbers. Therefore, people call complex numbers and hypercomplex numbers as narrow numbers, and concepts such as vectors, tensors and moments as generalized numbers. Although people still have some differences on the classification of numbers, they all agree that the concept of recognized numbers will continue to develop. Up to now, several families have developed greatly.