As one of the four ancient civilizations in the world, our great motherland has made many outstanding contributions in the long history of mathematics development. These brilliant achievements are far in the forefront of the world and enjoy high honors in the history of world mathematics.

First, the location value system was first used.

The so-called position value system means that the same number has different values because of different positions. For example, in 365, the number 3 means 300 and 6 means 60.

Using this method to represent numbers is not only concise, but also convenient for calculation. Decimal numeration system is adopted, which is the earliest in China. The number 13 was found in the archaeological excavation of Oracle Bone Inscriptions in Yin Ruins. They are:

Tens of thousands of natural numbers can be expressed by symbols of 9 numbers and 4 position values, and the position value system has sprouted. By the Spring and Autumn Period and the Warring States Period, our ancestors had generally used calculation to calculate. It is not only more convenient than the 60-bit value system of ancient Babylon, but also more advanced than the decimal non-bit value system of ancient Greece and Rome. This advanced counting system is one of the important milestones of human civilization and an unparalleled brilliant achievement in the history of mathematics in the world.

Second, the earliest use of scores

During the Western Han Dynasty, Zhang Cang, Geng Shouchang and other scholars sorted out and deleted the mathematical knowledge since the Qin Dynasty and compiled Nine Arithmetic Chapters. In the chapter of Tian Fang, a mathematical classic, a complete scoring algorithm is proposed.

From Liu Hui's Nine Chapters Arithmetic Notes, we can know that in Nine Chapters Arithmetic, the operation rules of reduction, combination (fractional addition), subtraction (fractional subtraction), multiplication (fractional multiplication) and reduction (fractional division) are exactly the same as our current fractional operation rules. In addition, it also records the knowledge about scores, such as class scores (comparing the size of scores) and equal division (finding the average of scores), which is the earliest book in the world to systematically describe scores.

Fractional operation became popular in Europe around15th century. Europeans generally believe that this algorithm originated in India. In fact, India began to have fractional arithmetic in the works of Brahman Gupta in the seventh century, and these laws are the same as those introduced in Nine Chapters of Arithmetic. Liu Hui's Notes on Arithmetic in Nine Chapters was written in Wei Jingyuan's fourth year (263), so even compared with Liu Hui's time, we are about 400 years earlier than India.

Third, the earliest use of decimal places

Liu Hui introduced in "Notes on Arithmetic in Nine Chapters" that the infinity of a square is approximated by decimals (emblem number, that is, decimals) and put forward the concept of decimals for the first time. During the Song and Yuan Dynasties, Qin and he were expressed as 1863.2 inches, which was basically consistent with the current notation. By about 1300, 1338+02 had been written in Liu Jin's Law Poetry in Yuan Dynasty.

Write the decimal part on the line after the integer part. However, it was not until 1585 that the concept of decimal appeared in the west, and his expression method was far less advanced than that of China. For example, he recorded the above decimal as 106368. Therefore, we can proudly claim that China is the first country in the world to use decimals.

Fourth, the earliest use of negative numbers

The concept of negative number and the principle of addition and subtraction of positive and negative numbers have been introduced in Nine Chapters of Arithmetic. Liu Hui said: "The gains and losses are relative, and the positive and negative numbers should be named." This is a clear definition of positive and negative numbers. The addition and subtraction rules of positive and negative numbers given in the book are exactly the same as those introduced in textbooks now.

These contents appear in the equation chapter of the book and play a role in solving equations (groups). For example, the eighth question in this chapter is:

Today, we sold two cows and five sheep to buy thirteen tapirs, leaving a thousand dollars. Selling three cows and three tapirs and buying nine sheep is enough money; Selling six sheep, eight tapirs and buying five cows cost less than 600 yuan. What are the prices of cattle, sheep and tapirs?

The solution is:

Technically, if the equation holds, two cows and five sheep are positive, thirteen cows are negative, and the rest of the money is positive: three cows are positive, nine sheep are negative, and three cows are positive; The second time, the cow is five negative, the sheep is six positive, the tapir is eight positive, and the lack of money is negative. Deceive people with positive and negative techniques.

What this means here is that if the price of each cow, sheep and tapir is represented by X, Y and Z respectively, the following equations (groups) can be listed:

Then use positive and negative numbers to calculate the result. All the coefficients and constant terms of the equation have negative numbers, which is the first one in the world to apply negative numbers to calculation.

In foreign countries, negative numbers have been regarded as an "absurd number" for a long time and have been abandoned outside the big family of numbers. It was not until the 7th century that Gupta, a Brahman in India, began to understand negative numbers. Fibonacci was the first person in Europe to give a correct explanation of positive and negative numbers, but they were more than 700 years later than our ancestors, about 1000 years later.

The earliest discovery of binomial coefficient law

After learning polynomial multiplication, it is not difficult to know:

Wait a minute. So, what is the law of the coefficient of the right-hand term in the above formula?

126 1 year, Yang Hui, a mathematician in the Song Dynasty, gave an origin diagram of the root-seeking method in his book "Detailed Explanation of Nine Chapters" (see the figure below), and divided the indexes respectively.

The binomial coefficient of 0-6 is listed, and it is pointed out that "the method of solving this problem originated from the book of unlocking calculation, and Jia Xian used this technique." Jia Xian was a mathematician in the Northern Song Dynasty, life is unknown, who lived in the first half of 1 1 century. That is to say, China has known the binomial coefficient law as early as 1 1 century. Now, we call this rule "Jia Xian Triangle" for short.

Abroad, it was not until the15th century that Arab mathematician Al Cassie used right triangles to represent triangles with the same meaning. 1527, German Appian also printed this binomial coefficient table on the cover of an arithmetic book he wrote. In the 16 and 17 centuries, many mathematicians in Europe also proposed Jia Xian-like triangles, among which Pascal was the most famous. Europeans call this binomial coefficient table "Pascal Triangle", but that was 1654 years ago, more than 600 years later than Jia Xian, and even nearly 400 years later than Yang Hui.

Of course, in the history of world mathematics development, China's mathematics is "the best in the world" far more than the above five aspects. However, we can see that our motherland is an ancient civilization with a long history, and our Chinese nation is a great nation, which has made many contributions to the development of world civilization. The brilliant achievements made by our ancestors in mathematics will be immortal and praised by people all over the world.