The Outline of New World History, edited by Qian Chengdan, a professor of Peking University History Department, is the final result of a major special research project of humanities and social sciences of the Ministry of Education. This project aims to explore China’s knowledge system of world history and build a framework for writing China-style world history textbooks. "Outline" is equivalent to the curriculum standard, which provides ideas, expands the connotation on the basis of "Outline", and can form a rich and comprehensive knowledge system of world history, thus spreading the correct view of world history to Chinese people and providing complete knowledge of world history. This article is taken from the Outline of New World History and reprinted by The Paper with authorization.

With the arrival of the mercantilist period, the expansion process of the west began. Mercantilism theory holds that precious metals are the embodiment of wealth, so seeking gold and silver overseas has become the main policy goal of western European governments. They encouraged their nationals to explore the sea, to explore overseas trade and to rob colonies. Colonies are of special significance to the mercantilist policy. Colonies bring markets as well as commercial profits, gold and silver to the home country.

Portuguese navigators first entered the Atlantic Ocean, and they opened a sea passage from Europe to eastern Asia in a century. In 1415, the Portuguese captured the Arab city of Ceuta in northern Morocco, which marked the beginning of European exploration and control of overseas territories. In the 15th century, most of the gold that arrived in Europe came from West Africa and the Ashanti black community near Ghana today. Muslim merchants brought gold from Africa and then took it north across the Sahara to Mediterranean ports. Portugal intervened in this gold business by force. Under the rule of King Joao II (reigned from 1481 to 1495), the Portuguese established trading ports and border trading posts on the coast of Guinea, and entered the mainland directly to Timbuktu. Portuguese ships arrived in Lisbon loaded with gold and controlled the circulation of gold in Europe by 1500.

Portugal established more than 50 trading ports between Africa and East Asia, and established the earliest commercial port empire. In San Giorgio da Mina, they engaged in the slave trade in West Africa; In Mozambique, they tried to control the gold trade in South Africa; In the Strait of Hormuz, they controlled the entrance to the Persian Gulf; In Goa, they sell Indian pepper; In Malacca, they supervise cargo ships from the South China Sea of China to the Indian Ocean; Through Ternat Island, they also controlled the clove and nutmeg trade in Maluku spice islands. Alfonso de Abuquiki, commander of the 16th century Portuguese Indian Ocean Corps, led the fleet to capture Hormuz in 1508, Goa in 1510 and Malacca in 1511, thus controlling the trade in the Indian Ocean, forcing all merchant ships to buy safety passes before they could dock at Portuguese trading ports. Ships without passes will be confiscated together with the goods. Like Portugal, British and Dutch businessmen also set up commercial ports on the coast of Asia, seeking to establish trade routes through commercial ports, but they have not yet thought of controlling freight on the high seas. In 1565, the Spanish army came to the Philippine Islands and named it after King Philip II of Spain. During 1603-1819, Spanish colonists had six large-scale conflicts with Filipinos and China businessmen in Manila, killing thousands of China businessmen.

The original purpose of European navigation was to find a new route to the East. Columbus, an Italian navigator, loved sailing adventures since he was a child. He read The Travels of Marco Polo and longed for India and China. At that time, the theory of the earth circle was very popular, and Columbus believed it. He successively asked the kings of Portugal, Spain, England, France and other countries for funding to realize his plan of sailing westward to the eastern countries, but all of them were rejected. Finally, he persuaded the Spanish king on the grounds of oriental products such as silk, porcelain, tea and spices, and was able to make it. In 1492, under the orders of Spanish King Isabella and Ferdinand, Columbus took the credentials to Emperor China, led three ships and 87 sailors to sail from Barros Port and crossed the Atlantic Ocean, but ended up in Bahamas, Cuba and Haiti. In the next three voyages, I visited Jamaica, Puerto Rico and the coastal areas of the American continent. He crossed the Atlantic four times and "discovered" America, becoming a famous navigator in history. The Spanish immediately entered these areas for early colonization. They conquered South America, robbed local wealth, slaughtered local residents, and sent a large number of blacks from West Africa to America to engage in slave labor, thus developing America. These activities quickly wiped out the Indians in South America. When Columbus came to Hispaniola in 1493, the population there was nearly 100,000. By 1570, there were only 300 people left.

In 1519, the navigator Ferdinand Magellan (1480-1521) sailed westward, hoping to find a route to the southeast coast of Asia. Magellan traveled from San Roca to Brazil, passed through the strait between the South American continent and Tierra del Fuego, and crossed the Pacific Ocean, Guam and the Philippines in 1521. He was killed by local residents for interfering with the infighting on the island. After Magellan’s death, the voyage continued. In 1522, the Victoria returned to Spain via the Indian Ocean, the Cape of Good Hope and the Atlantic Ocean, completing the first voyage around the earth in human history. This voyage verified the theory that the earth is spherical and brought back a huge amount of information about the Pacific Ocean.

The above-mentioned exploration activities triggered the competition between Portugal and Spain for overseas colonies. In 1494, Spain and Portugal signed the Tolde-silas Agreement, which demarcated the north-south boundary 370 leagues west of Cape Verde Islands. It was stipulated that Spain’s sphere of influence was to the west and Portugal’s sphere of influence was to the east, which was the first time that western countries divided up the world.

Colonization opened the way for primitive accumulation of capital in Europe. According to statistics, from 1493 to 1600, the Portuguese plundered more than 270,000 kilograms of gold in Africa alone. From 1521 to 1600, Spain plundered more than 200,000 kilograms of gold and 18 million kilograms of silver from America. Most of the capital in western Europe comes from gold and silver in America, which is related to Spain’s overseas colonization and monopoly of trade with the East to some extent. During 1519-1521, Spain conquered Mexico and Peru, began to plunder gold and silver there in 1531, and began to organize mining in America with new technology in 1540. In the trade with the East, the king of Spain levied a 20% trade tax, so Spain gained huge wealth from overseas trade. However, Spain did not keep this wealth. On the contrary, gold and silver flowed into other European countries, which promoted the development of capitalism in other regions.

Later, British and Dutch businessmen also came to Asia to set up commercial ports on the coastline and establish maritime trade lines through these commercial ports. The activities of the colonists promoted commercial development and established a global trading system in a real sense. Before that, the world’s commercial trade was regional, but the expansion of European countries at sea connected the world in the same trading system. The products made in Europe crossed the Atlantic Ocean westward in exchange for silver from Mexico, minerals from Peru and agricultural products such as sucrose and tobacco in the Caribbean. European textiles, guns and other manufactured goods went south to West Africa in exchange for African slaves and then transported them to work in tropical and subtropical plantations in the Western Hemisphere. China’s silk and porcelain are directly transported to Europe, and are warmly welcomed by the courts and upper classes of various countries; Tea and spices were shipped to Europe and America and eventually became mass consumer goods. Through the establishment of the global trading system, "the transformation from history to world history" has begun.

In early modern times, the trade routes in Europe were basically the same as those in the previous two centuries. Northern Italy and Flanders are the most developed cities and industrial centers in Europe, and they are both suppliers of woolen clothes in the European market. Northern Italy is also a producer of silk and other valuable clothing materials, while Flanders produces linen, ribbons and carpets. These two regions also have advanced shipbuilding and metal processing industries. Venice monopolizes the eastern trade through the eastern Mediterranean countries and islands. The goods from the east are mainly spices and other luxury goods, which are sold in Europe by Italian and German businessmen. They can go southwest to France and Spain and northeast to Germany and Baltic countries via the Italy-Flanders axis. The British route on the Italian-Flemish axis is mainly responsible for transporting the semi-finished clothes from Britain to Flanders and brabant for processing.

Gold and silver from America entered the northwest of Europe through Spain, making these places eventually become the most developed economic centers in Europe, including low-lying countries, northwest France and southeast Britain. The "lowlands" used to be the commercial meeting place between Italy and the Hanseatic League, but Spain’s tight financial situation and huge trade deficit made businessmen and bankers in the lowland countries, Italy and Germany become the actual leaders of international trade. The low-lying countries were the bridge between the North and the South in the Middle Ages, so Antwerp became the trade center of Spain, Portugal and Germany. In the 16th century, Antwerp was the largest international financial market in Europe, and every move here affected the whole European economy. The delay of Spanish and Portuguese cargo ships can cause commercial chaos in Antwerp, and even lead to bank failures in augsburg and Ulm. After gaining independence, the Netherlands followed Portugal and Spain and rapidly expanded its overseas trade. It monopolized the spice trade and controlled the eastern routes by crowding out Portugal’s forces in the East through war. In the Atlantic, it can also squeeze into Spain’s sphere of influence and insert a foot in trade. The 17th century became the "century of Holland", and Holland was the "sea coachman" at that time. Britain and France also rapidly expanded overseas after the reunification of the country. They successively established colonies in America, Asia and Africa, and replaced the Netherlands in the second half of the 17th century, becoming the protagonists in the struggle for world commercial hegemony in the next century.

　　China Youth Daily, Beijing, February 19th (reporter Zhao Limei, trainee reporter of Zhongqing.com, reporter Zhang Junbin) After the Hong Kong stock market closed at 16: 30 today, Meituan announced that it would pay social security for full-time and stable part-time riders nationwide, which is expected to be implemented in the second quarter of 2025.

　　Following the launch of the anti-fatigue mechanism and the cancellation of overtime deduction, this is another measure taken by Meituan to improve the social security of new employment groups in recent years. Since July 2022, Meituan has taken the lead in paying new occupational injury insurance premiums for new employment groups. At present, Meituan has invested 1.4 billion yuan to pay occupational injury protection for riders in seven pilot provinces and cities. In the future, this measure will further cover all riders in all provinces and cities.

　　Industry sources said that with the steady development of take-away and other industries, at present, a relatively clear division of "professional" and "part-time" groups has been formed among new employees such as take-away riders. Many riders have become stable practitioners after accumulating relevant experience and skills. Providing all kinds of security for stable employment is not only in line with the real interests of workers, but also conducive to the long-term development of the industry and the formation of a relatively stable and professional distribution group.

　　It is worth noting that since the beginning of the year, Meituan has continuously introduced heavy measures to strengthen the protection of new employment groups, including canceling overtime deductions and online anti-fatigue mechanisms, and has built 16,000 rider communities in conjunction with all sectors of society to help riders smooth the distribution path. The relevant person in charge of the US Mission said: "We will continue to increase resources and capital investment, continue to improve the rider welfare treatment system, and strive to contribute more positive forces to building harmonious labor relations."

Author | Xi Nanhua

Source | Mathematical Translation Forest

Quantity and shape are the basic attributes of matter and things. They are the objects of mathematical research, which determines the value and significance of mathematics.

Mathematics is actually concerned with the mathematical laws of quantity and shape, which is a reflection of the real world. The law of mathematics is the law of the basic attributes of matter and things, and it is the most essential part of the laws of nature and society.

The meaning and value of mathematics seems needless to say, but the language of mathematics is abstract, and the abstract face is basically that people don’t like it, and it is often mistaken for being far away from the real world and human fireworks, which is quite unjust. The abstract value will be mentioned later.

1. What was mathematics like in the distant past?

Mathematics has a long history. It is generally believed that mathematics, as an independent and theoretical discipline, appeared between 600 BC and 300 BC, and Euclid’s Elements (about 300 BC) is a brilliant model.

It systematically sorts out the mathematical achievements of ancient Greeks by using axiomatic system, and its system, the expression of mathematical theory and the way of thinking embodied in the book have far-reaching influence on the development of mathematics and even science. Throughout the history of mathematics development, The Original is the most influential mathematics book.

Another great mathematical work in ancient Greece was apollonius’s "Conic Curve", which was later than "The Original" in time. In addition to synthesizing the achievements of predecessors, this book has unique innovation, excellent material organization and flexible writing. This book can be called the pinnacle of conic curve, and later generations can hardly say anything new on this subject, at least geometrically.

Almost at the same time, there was a study of the history of mathematics. Eudemus (about 370-300 BC), a student of Aristotle (384-322 BC), wrote books on the history of mathematics.

The history of human civilization is much longer. About 10 thousand years ago, human beings began to settle in a region and live by agriculture and animal husbandry. Writing appeared much later, around 3200 BC. Before that, the progress of human beings in mathematics was extremely slow, because the level of development was low, the demand for mathematics was extremely low, and it was very difficult to form abstract mathematical concepts from scratch.

The most basic concepts of mathematics, numbers and straight lines, took a long time to form.

At first, people’s concept of logarithm was associated with specific objects, such as a tree, a stone, two people, two fish, and so on. Time, constantly passing, … Gradually, people realized the common numerical attribute of a tree, a stone and other concrete objects, and the abstract concept of number was formed.

Similarly, at first, people’s concept of line was associated with specific line shapes such as trees, branches, ropes and edges of objects. Time goes by … gradually, people realize the common shape attributes of concrete objects such as straight trees, taut ropes and straight edges of some objects, and the abstract concept of straight lines is formed.

The formation of the concepts of number and straight line is a leap for human beings to understand nature.

The emergence and development of mathematics is driven by real life. Arithmetic and geometry were first produced.

Realistic needs have led to the calculation between numbers (such as distributing food, exchanging goods, the number of days before the specified date, etc.). So you need to give the number a name and write it down and tell others.

Digital symbols introduced from the beginning of writing have played a great role in the development of arithmetic.

This is the first step to introduce general mathematical symbols and formulas. In the next step, the introduction of arithmetic operation symbols and unknown symbols was completed very late, and it was constantly improved. For example, the familiar symbols of addition, subtraction, multiplication and division were not used until the 15th and 18th centuries.

Arithmetic was first developed in Babylon and Egypt, due to the practical needs of taxation, land measurement, trade, architecture, astronomy and so on. But here is mainly for the calculation and answer of specific problems. This form of arithmetic is not a mathematical theory, because there is no general property (or law) about numbers.

The transition to theoretical arithmetic is gradual. Ancient China, Babylonia and Egypt already knew the possibility of millions. Here has shown the possibility of infinite continuation of the series. But people didn’t realize this clearly soon.

Archimedes (287-212 BC) pointed out the method of naming the number of a large number of sand grains in the Sand Counting Law. This is a matter that needs to be explained in detail at that time. It’s not an easy thing today.

In the third century BC, the Greeks clearly realized two important ideas: the sequence of numbers can continue indefinitely; We can not only use specific numbers, but also discuss general numbers, and establish and prove the general properties of numbers.

For example, there are infinitely many proofs of prime numbers in the elements, and this conclusion and proof will be mentioned later. Arithmetic thus developed into theoretical arithmetic.

Theoretical arithmetic is actually the theory of numbers, and the calculation of specific local problems is not its main content, but the establishment of the laws and general properties of numbers by concepts and reasoning is its main content. Of course, this will, in turn, be helpful to specific calculations at a higher level.

The convincing source of theoretical arithmetic: its conclusion is drawn from the concept by using logical methods, and both logical methods and arithmetic concepts are based on thousands of years of practice and the objective laws of the world.

The concepts and conclusions of theoretical arithmetic reflect the nature and relationship of the quantity of things, summarize a lot of practical experience, and show the relationships that are often encountered everywhere in the real world in an abstract form. The objects can be animals, agricultural products and planets.

Therefore, the abstraction of arithmetic is not empty, but through long-term practice, it summarizes some universal properties, which has wide application. The same is true for all mathematics and any abstract concepts and theories. The possibility of wide application of the theory depends on the extensiveness of the original materials summarized in it.

Abstraction has its own limitations: when applied to specific objects, it only reflects one aspect of the object, and often only quantity is not enough. You can’t apply abstract concepts everywhere indefinitely. A sheep and a wolf are added together, and a liter of water and a handful of soil are not the place where arithmetic plus one is applied. Truth is concrete and mathematics is abstract. The application of abstraction to concreteness is often an art and technology.

The development of numbers is also very interesting. At first, it is a number associated with a specific object, then an abstract number, and then a general number. Each stage relies on previous concepts and accumulated experience. This is also one of the basic laws of the formation of mathematical concepts.

The origin and development of geometry is similar to that of arithmetic. The actual needs of measuring and calculating the area of land and the volume of containers, the volume of barns and water conservancy projects have led to the emergence and development of geometry, including the concepts of length, area and volume. For farmers, knowing the area of land is very beneficial to predict the harvest. For water conservancy projects, it is important to know how long the earthwork volume will take to complete the project.

Babylonians and Egyptians were the leaders in the initial years of geometric development (about 3000 BC to 700 BC). At first, geometry is some formulas summed up from experience, including the formulas for finding the area of triangles, rectangles, trapezoid, circles, cuboids, spheres, etc.

The formula A=(8d/9)2 used by the Egyptians to calculate the area of a circle was surprisingly good at that time, where d was the diameter. This formula is equal to taking π=3.1605 from the area formula of a circle. Geometric problems are also arithmetic problems in calculation.

Babylonians and Egyptians should not have realized at that time that their algorithms and rules needed to be based on, or could deduce some conclusions from others through deduction. The formulas or laws they get are not related to each other, so they are not systematic.

At this time, the Greeks appeared. They went to Egypt and Babylon to do trade, travel and study math and science. In this way, the arithmetic and geometry of the Egyptians and Babylonians spread to Greece around the seventh century BC. Then came the era when the stars shone and there were many schools of thought. Interestingly, China was roughly in the Spring and Autumn Period and the Warring States Period, with a hundred schools of thought contending, and many thinkers came forth: Laozi, Confucius, Mozi, Mencius, Zhuangzi, Xunzi and Han Feizi.

The influential schools in the classical Greek period (from 600 BC to 300 BC) are: Ionian School, Pythagorean School, Ernian School, Clever School, Plato School, Aristotle School, etc.

The most important ideological contributions of the ancient Greeks to mathematics include: mathematics studies abstract concepts, and all mathematical results must be deduced by deduction according to the axioms clearly defined in advance.

Geometry thus develops in the direction of geometric theory; Introduce concepts, draw conclusions from experience, clarify the relationship between them, and find new conclusions. In this process, abstract thinking plays an extremely important role. In the spatial form of real objects, geometric concepts are abstractly generated: points (without size), lines (without width and thickness), surfaces (without thickness).

Like arithmetic, geometry comes from practice and gradually forms mathematical theory. Geometric theory studies the abstract forms and relationships of space.

This is different from other sciences that study the spatial form and relationship of objects, such as astronomy and measurement, or art such as painting and sculpture. It is impossible to do experiments in abstract space form, and only logical reasoning can be used to establish the connection between conclusions and derive new conclusions from known conclusions.

The obviousness of geometric concepts, the method of reasoning and the convincing conclusion are all based on thousands of years of practice and the objective laws of the world, just like arithmetic.

When we emphasize the importance of interdisciplinary to scientific development today, looking back at history, we will find that it is a specious formulation.

The intersection of disciplines has been very active in history, which is an important source of further general concepts, methods and theories, and has a great impact on the development of human civilization and science. The greatest scientists, such as Archimedes, Newton, Leibniz, Euler, Gauss and Einstein, have made great contributions in many aspects.

Let’s say that arithmetic and geometry, the earliest two branches of mathematics, were inseparable and influenced each other from the beginning. Simple length measurement is already a combination of arithmetic and geometry. When measuring the length of an object, put a single position of a certain length on the object, and then count how many times it is put together. The first step (placement) is geometric, the geometric concept behind it is congruence or coincidence, and the second step (number) is arithmetic.

When measuring, it is often found that the selected unit cannot be placed on the measured object for an integer number of times. At this time, the unit must be divided, so that a part of the unit can be used to measure the object more accurately, that is to say, not only the integer, but also the fraction can be used to represent the length of the measured object.

The score is thus generated. This is the result of the cooperation between geometry and arithmetic, which produces an important new concept-fraction, and causes the popularization of the concept of number from integer to fraction.

The discovery of irrational numbers also comes from the combination of geometry and arithmetic, but the discovery of irrational numbers cannot be realized by measurement, because the accuracy is always limited in actual measurement, and irrational numbers are infinite acyclic decimals.

Pythagorean theorem tells us that the diagonal length of a square with unit side length is the square root of 2, which is an irrational number. In this way, the concept of number is further developed. Moreover, people gradually understand the number as the ratio of a certain quantity to the quantity taken as a unit.

The discovery of irrational numbers is a typical example that reflects the power and profundity of mathematical theory in revealing natural laws and phenomena. Without mathematics, many phenomena and laws can’t be understood.

The further development of number is the concept of real number, and then the concept of complex number. Then there is the algebraic structure.

Hua Luogeng, the late great mathematician, made an incisive comment on the relationship between logarithm and form: when the number is missing, it is less intuitive, and when the number is missing, it is difficult to be nuanced.

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1. The original poem: number and shape are interdependent, so how can they be divided into two sides? When the number is missing, it is less intuitive, and when the number is missing, it is difficult to be nuanced; The combination of numbers and shapes is good, and everything is separated; Don’t forget, the unity of geometry and algebra is always connected and never separated! See Selected Poems of Hua Luogeng, China Literature and History Publishing House, 1986.

2. number (sh) number (sh)

Speaking of it, mathematics should start with numbers (sh) and numbers (sh). Who among us can’t count? Soon after we can talk, our parents will tell us to count, and our ability to count will definitely be greater when we get to kindergarten. We usually count

1, 2, 3, 4, 5, 6，……

It seems that most people don’t think of counting all the integers with positive integers. In fact, this is possible, and a number method is:

0, 1，-1, 2，-2, 3，-3，……

In this way, all the integers are counted with positive integers.

Ordinary people should not even think of counting rational numbers (fractions) with positive integers. Intuitively, this seems impossible. Surprisingly, this is also possible.

Fractions can be written as the ratio of integers: 0, p/q, where p and q are positive integers not equal to 0, and there is no common factor greater than one.

First, according to the size of the value of p+q, it is divided into several parts to sort, and each part is counted again, so one number method is:

0，1，－1，1/2，2，－1/2，－2，1/3，3，－1/3，－3，

1/4，2/3，3/2，4， －1/4，－2/3，－3/2，－4，……

In this way, we also counted the rational numbers with positive integers.

Curiosity certainly can’t end like this. We may wonder how to count real numbers with positive integers. This time there is really nothing to do: positive integers can’t count real numbers clearly. This can be strictly proved, but we won’t talk about it here, although it is not difficult.

The story is not over yet.

A question arises here: Is there a set of numbers between the whole of natural numbers and the whole of real numbers, which can’t be counted by positive integers (that is, it can’t establish a one-to-one correspondence with natural number set), and real numbers can’t be counted by this set?

Cantor, the founder of set theory (a branch of mathematics), suspects that such a set does not exist. This is the famous continuum hypothesis. Hilbert gave a report at the International Congress of Mathematicians in 1900, and listed 23 problems, the continuum hypothesis being the first one. This shows the importance of this issue. These 23 problems have a great influence on the development of mathematics in the future.

Godel is a great mathematical logician. In 1940, he proved that there is no contradiction between the continuum hypothesis and the axiomatic system we usually use. Just because there is no contradiction doesn’t mean it is right.

In 1963, Cohen established a powerful method-the forced method. By this method, he proved that there is no contradiction between the hypothesis of continuum and the axiomatic system we usually use. That is to say, in our commonly used axiom system, adding this assumption will not produce contradictions; If this assumption is not added, there will be no contradiction.

This is obviously beyond the expectation of ordinary people. An important and natural question cannot be judged true or false in our commonly used axiomatic system. This shows the strangeness of logic. Cohen won the Fields Prize in 1966 for his work on the continuum hypothesis.

The continuum hypothesis seems to have been understood, but in fact, the thinking on this issue has not stopped, and profound mathematics is still being produced.

We can compare the continuum hypothesis with the parallel axiom of plane geometry. The thinking and research on parallel axioms leads to the emergence of non-Euclidean geometry such as hyperbolic geometry. Riemannian geometry is a kind of non-Euclidean geometry and a mathematical framework of general relativity.

Curiosity, simple good questions can always take us far, far away.

3. Know infinity

In our limited life, it seems to be a difficult thing to know infinity, and it may even be a disturbing thing. The ancient poem "Born less than 100 years old, always worried about being a thousand years old" shows that we are not willing to be confined to our limited time and space.

But infinity is awesome. Pascal said, "When I think of my short stay in life, swallowed up by the eternity before and after, and the small space I occupy, submerged by the infinite and vast space that I know nothing about, I feel scared. The eternal silence of these boundless spaces scares me. "

There are infinite integers and infinite real numbers. In the game of counting, we know that these two infinity are essentially different.

Only mathematics can study the infinite, reveal the magical infinite world, and use the infinite to study the limited. Examples include limit, series, infinite set …

The following two equations can make people feel the infinite magic of mathematical utilization:

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2.When I consider the short duration of my life, swallowed up in an eternity before and after, the little space I fill engulfed in the infinite immensity of spaces whereof I know nothing, and which know nothing of me, I am amazed. The eternal silence of the infinite spaces frights me. Blaise Pascal, in "pensé es" (originally in French, meaning meditation), 1670.

Hilbert, a great mathematician, has a profound understanding of infinity: "No other problem has ever touched people’s hearts so deeply;" No other thought can stimulate people’s logical understanding of thinking so fruitfully; However, there is no other concept that needs to be clarified more than the concept of infinity. "

4. Some opinions

Great people never skimp on their awe and praise of mathematics:

Mathematics is the core of reality.

-Pythagoras School, Plato School

We often hear the view that "everything is number" comes from Pythagoras, and he has a similar expression: number rules the universe; Number is the essence of everything. Plato School was deeply influenced by Pythagoras School and put mathematics in the highest position: the highest form of pure thought is mathematics.

On the gate of Plato’s Academy, it is written that "those who have no knowledge of geometry are not allowed to enter this gate".

In the seventh chapter of Plato’s Republic, there is a long dialogue to discuss the importance of arithmetic and geometry. The conclusion is that arithmetic forces the soul to use pure reason to lead to truth, geometry is to know eternal things, and arithmetic and geometry are the first and second courses that young people must learn.

Mathematics is the true essence of nature.

-ancient Greece

With this understanding, it seems not surprising that ancient Greece can make epoch-making achievements in mathematics.

Physics is written in the big book of the universe, and it keeps opening before our eyes. But we can’t read this book until we learn to write the characters and language of the universe. It is written in mathematical language, and the characters are triangles, circles and other geometric figures. Failure to understand these means that it is impossible for human beings to understand every word of this book. Without these, people can only wander in the dark maze.

-Galileo

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3.“Das Unendliche hat wie keine andere Frage von jeher so tief das Gemüt der Menschen bewegt; das Unendliche hat wie kaum eine andere Idee auf den Verstand so anregend und fruchtbar gewirkt; das Unendliche ist aber auch wie kein anderer Begriff so der Adfkl?rung bedürftig.” David Hilbert: In address (4 Jun 1925), at a congress of the Westphalian Mathematical Society in Munster, in honor of Karl Weierstrass. First published in Mathematische Annalen (1926), 95, 161-190 with title über das Unendliche.

Galileo was one of the founders of modern experimental science and mechanical materialism. He established the law of falling body, discovered the law of inertia, and determined the "Galileo relativity principle". He is a pioneer of classical mechanics and experimental physics. He was also the first person who made great achievements in observing celestial bodies through telescopes. Galileo’s view of mathematics can be regarded as a development of the view of the ancient Greeks.

Mathematics is the queen of science.

-Gauss

Gauss is known as the prince of mathematics in the 19th century, the greatest mathematician in the 19th century, and an outstanding physicist, astronomer and geodetic scientist. His words are often quoted, but I don’t know where Gauss took the emperor.

In natural science, mathematics is incredibly effective.

-eugene wigner

Wigner put forward the theory that the nucleus absorbs neutrons and discovered the Wigner effect, so he won the Nobel Prize in Physics in 1963.

This introduction was the topic of Wigner’s report in Courand Institute of Mathematics of new york University on May 11th, 1959. The article was published in the journal Communications in Pure and Applied Mathematics sponsored by Courand Institute of Mathematics in February, 1960. This view of Wigner has a great influence, and the discussion and extension of this view have never stopped since it came out.

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4.Philosophy (i.e. physics) is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the letters i n which it is composed. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these, one wanders about in a dark labyrinth.” Galileo Galilei, The Assayer (Il Saggiatore (in Italian)), as translated by Stillman Drake (1957), Discoveries and Opinions of Galileo pp. 237-8.

5. "Die Mathematicist Die Knigin der Wissenschaft en und Die Zahlen Theorist Die Knigin der Mathematik", Wolfgang Sartorius von Waltershausen: Gauss Zum Ged Chtnis (Biography of Gauss), 1856.p.79. 。

God is a mathematician of very high rank. He used very advanced mathematics when he built the universe. Our attempt to be weak in mathematics enables us to understand a little bit of the universe. As we continue to develop more and more advanced mathematics, we can hope that we can better understand Universe 6.

-Dirac

Dirac discovered a fruitful new form of atomic theory, so he won the Nobel Prize in Physics with Schrodinger in 1933. The Dirac equation he put forward was hailed as a groundbreaking work, which predicted the existence of positrons and was later confirmed by experiments. The δ function he proposed was very creative and shocking, which was unacceptable in the mathematical theory at that time, but it was very useful in physics.

Later, when the generalized function theory appeared, mathematical theory could explain and deal with the δ function, which turned out to be a generalized function.

Mathematics must control our rational flight; Mathematics is a crutch for the blind. Without it, it is difficult to move. Everything in physics is undoubtedly due to mathematics and experience.

-Voltaire

Voltaire was a French philosopher and writer in the 18th century and a leading figure in the French bourgeois enlightenment. His thoughts represented the thoughts of the whole Enlightenment, enlightened people’s minds and influenced a whole generation.

The strength of French mathematics is not only the achievement of French mathematicians, but also profound cultural factors.

The development and perfection of mathematics is closely related to the prosperity of the country.

-Napoleon

Napoleon was a great French strategist and politician in the 19th century, and the founder of the First Empire of France. People generally pay attention to his military and political achievements. In fact, his achievements in science and education are also crucial to the future development of France.

During the First Empire of France, France established a national education system that has been preserved to this day, and established public middle schools and French universities to train talents and encourage the rise of scientific research and technical education.

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6. “God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better.” P. A. M. Dirac: The Evolution of the Physic ist’s Picture of Nature. Scientific American, May 1963, Volume 208, Issue 5.

7. “Mathematics must subdue the flights of our reason; they are the staff of the blind; no one can take a step without them; and to them and experience is due all that is certain in physics.” Francois Marie Arouet Voltaire, Oeuvres Completes, 1880, t. 35, p. 219.

8. “The advancement and perfection of mathematics are intimately connected with the prosperity of the State.” Napoléon Bonaparte: Correspondance de Napoléon, t. 24 (1868), p.112．

Napoleon paid great attention to science and culture. After taking power, he regularly attended the meetings of the French Academy of Sciences, invited academicians to report on scientific progress, and awarded many awards to scientists, including foreign scientists.

Napoleon’s concern promoted the prosperity of French science, and a large number of dazzling scientific stars appeared, such as Laplace, Lagrange, Gaspard Monge, sadi carnot, Fourier, Gay-Lussac, Lamarck and Ju Weiye.

Mathematical science presents one of the most brilliant examples. Without the help of experience, pure reason can successfully expand its territory.

-Kant

Kant was a German philosopher in the 18th century and was considered as one of the greatest philosophers of all times. He has profound knowledge of natural science and a deep understanding of morality. His philosophy has a profound influence on German classical philosophy and western philosophy, and also on the birth of Marxist philosophy. Critique of Pure Reason is his most famous work.

Strange as it may sound, the strength of mathematics lies in its avoidance of all unnecessary thinking and its pleasant saving of mental labor.

-Mach

Mach was an Austrian physicist and philosopher from the 19th century to the early 20th century. The Mach number of high-speed flight is named after him. His most important achievement was that he found the shock wave when he was studying the high-speed motion of an object in gas. Mach’s Mechanics had a profound influence on Einstein. Mach has also been nominated by many people as a candidate for the Nobel Prize in Physics.

Mach’s above viewpoint is a specious truth, which will be explained later by the problem of the seven bridges in Konigsberg and the classification of crystals.

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9. “The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience Immanuel Kant and F. Max Mü ller (trans.),’ Method of Transcendentalism’, Critique of Pure Reason (1881), vol. 2, p.610. See also: Critique of Pure Reason, p.575, by Kant, translated by Wang Jiuxing, Commercial Press.

10. “Strange as it may sound, the power of mathematics rests on its evasion of all unnecessary thought and on its wonderful saving of mental operations.” Ernst Mach: in E.T. Bell, Men of Mathematics (1937), Vol. 1, l (Roman numeral ‘l’)).

If I feel sad, I will do math and become happy; If I am happy, I will do math to keep happy.

-Renee

Alfréd Rényi is an outstanding Hungarian mathematician in the 20th century. He mainly studies probability theory, combinatorial mathematics, graph theory and sequence. Renee told us how good it is to do math!

Pure mathematical structure enables us to discover concepts and laws that relate to these concepts, and these concepts and laws give us the key to understanding natural phenomena.

-Einstein

One reason why mathematics enjoys special respect over all other sciences is that his propositions are absolutely reliable and indisputable, while all other scientific propositions are debatable to some extent and are often in danger of being overturned by newly discovered facts. There is another reason why mathematics has a high reputation, that is, mathematics gives precision nature a certain degree of reliability. Without mathematics, these sciences cannot achieve this reliability.

-Einstein

Einstein is the greatest scientist in the 20th century, and is well known to all women and children. Its scientific achievements have changed people’s understanding of the world.

He is not only a great scientist, but also a great philosopher and social activist, deeply concerned about the fate of mankind. The profound understanding of nature, society and human beings makes people marvel at his superhuman intelligence and great heart.

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11. “If I feel unhappy, I do mathematics to become happy. If I am happy, I do mathematics to keep happy.” Alfréd Rényi: In P. Turán, ‘The Work of Alfréd Rényi’, Matematikai Lapok (1970), 21, pp.199-210.

12. “pure mathematical construction enables us to discover the concepts and the laws connecting them, which gives us the key to understanding nature.” Albert Einstein, In Herbert Spencer Lecture at Oxford (10 Jun 1933), ‘On the Methods of Theoretical Physics’. Printed in Discovery (Jul 1933), 14, 227. Also reprinted in Philosophy of Science, Vol. 1, No. 2, (Apr., 1934), pp. 163-169. For Chinese translation, please refer to the first volume of Einstein’s Collected Works, translated by Xu Liangying and others, Commercial Press, 2010.p.448. 。

13.“One reason why mathematics enjoys special esteem, above all other sciences, is that its propositions are absolutely certain and indisputable, while those of all other sciences are to some

extent debatable and in constant danger of being overthrown by newly discovered facts. … But there is another reason for the high repute of mathemati cs, in that it is mathematics which affords the exact natural sciences a certain measure of certainty, to which without mathematics they could not attain.” Albert Einstein: Geometry and Experience, Published 1921 by Julius Springer (Berlin), also reprinted in “The Collected Papers of Albert Einstein”, Translation Volume 7, Princeton University Press, 2002. For Chinese translation, please refer to the first volume of Einstein’s Collected Works, translated by Xu Liangying et al., Commercial Press, 2010.p.217. 。

The universe is big, the particles are tiny, the speed of rockets, the cleverness of chemical engineering, the change of the earth, the mystery of biology and the complexity of daily use, and mathematics is everywhere.

-Hua Luogeng

Hua Luogeng’s comments on the use of mathematics are extremely incisive.

5. the spirit of exploring the world

In practice, knowledge is gained through sensibility and thinking. Furthermore, through abstract thinking, the connection between knowledge is established and science is formed. At this point, reason and thinking have their own free kingdom.

In one’s own kingdom, thinking often goes far beyond actual needs. For example, some large numbers such as one billion or ten billion are generated on the basis of calculation, and the actual needs of using them are later; Imaginary numbers are generated by solving the equation x2+1=0, and then they are widely used.

Mathematics is concerned with the mathematical laws of quantity and shape, and it is an elf to explore the world. In the free kingdom of thinking, it is dexterous and has a lot of free space to fly, and many achievements will take a long time to be applied after completion. Famous examples include:

The study of conic curve by Greeks more than two thousand years ago was used to describe the motion of celestial bodies in the 17th century.

L Riemannian geometry is the mathematical framework of general relativity.

The role of fiber bundle theory in gauge field theory.

The role of l matrix and infinite dimensional space in quantum mechanics.

The application of probability theory in statistical mechanics, biology and finance.

l ……

Our country’s culture and tradition are pragmatic, focusing on immediate interests. Here, I would like to quote the philosopher Whitehead’s advice:

"For those who limit their knowledge and research to obvious usefulness, there will be no more impressive warning, such as the following example: conic curves have been studied as abstract science for 1,800 years, without any practical consideration except to satisfy mathematicians’ thirst for knowledge. However, at the end of this long abstract research, they were found to be essential keys to acquire knowledge of one of the most important laws of nature."

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14. Hua Luogeng: "Great use of mathematics", originally published in People’s Daily on May 28, 1959. Reprinted in "Great Mathematics for Use" (selected works of Hua Luogeng’s popular science works), Shanghai Education Press.

6. The wisdom of mathematics

Most people are willing to stay away from mathematics, but Mach said that mathematics can save brains pleasantly (see the previous section 4: Some opinions), which is really confusing. Maybe Mach is talking about the wisdom of mathematics. We use two examples to illustrate this point.

The first example is the problem of the Seven Bridges in Konigsberg. This problem occurred in the 18th century, when Konigsberg was the city of Prussia, and now it is Kaliningrad, Russia. There is a river crossing the city, which divides the city into four parts, and there are seven bridges connecting these four parts, as shown in Figure 16 below.

It is said that a popular pastime of the citizens at that time on weekends was whether a route could be designed to cross each bridge just once. No one has ever succeeded, but that doesn’t mean it is impossible. In 1735, the mayor of Danz Creek (about 140 axioms west of Konigsberg) was entrusted by a local mathematician to find Euler. Euler was the greatest mathematician in the 18th century. At the age of 28, he was already famous.

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15. “No more impressive warning can be given to those who would confine knowledge and research to what is apparently useful, than the reflection that conic sections were studied for eighteen hundred years merely as an abstract science, without a thought of any utility other than to satisfy the craving for knowledge on the part of mathematicians, and that then at the end of this long period of abstract study, they were found to be the necessary key with which to attain the knowledge of one of the most important laws of nature.” A. N. Whitehead, Introduction to Mathematics, London WILLIAMS & NORGATE, pp110-111.

16. Source: https://plus.maths.org/content/bridges-k-nigsberg

Euler thought about the problem like this. The river divides the city into four parts, and the size of each part is not important. What matters is the route design of crossing the bridge. Thus, the land can be abstracted into points, and the bridge can be abstracted into connecting lines 17 between points.

So the problem becomes to design a route on the right picture above, which passes through each connecting line (bridge) exactly once.

Suppose there is such a route. If a point is neither the starting point nor the end point, then the route to this point (that is, the bridge) is different from the route to leave this point. This requires that the number of lines connecting this point must be even.

The picture above has four points, and the starting point and ending point of a line add up to at most two. That is to say, no matter how the route is designed, at least two of the four points are neither the starting point nor the end point, and the number of routes connecting such points must be even. However, the lines (bridges) connecting the four points in the above picture are all odd numbers, namely, 5, 3, 3, 3. This means that it is impossible to design a route for the above picture, passing through each connecting line (bridge) exactly once.

Euler’s way of solving this problem shows the abstract value and the wisdom of mathematical thinking. Euler’s work also marked the birth of a branch of mathematics-graph theory. Graph theory is very useful in information science, including network and chip design.

The second example is the classification of crystals. Diamonds and snowflakes are crystals, which are very beautiful. Crystals have good symmetry. In fact, the symmetry of crystals has a strong constraint on the types of crystals. The branch of mathematics that studies symmetry is group theory. So mathematics has played a great role in the study of crystals. In 1830, German hessel (1796-1872) determined that there were 32 symmetrical forms of crystal shape (called 32 point groups).

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17. Two sources: https://plus.maths.org/content/bridges-k-nigsberg

After determining the symmetrical form of the shape, people turn to the internal structure of the crystal. Frangen Heim (1801-1869), a 19th century German, proposed that the internal structure of crystals should take points as the unit, and these points are arranged periodically in three-dimensional space.

Later, the French Blavy (A. Bravais, 1811-1863) put forward the theory of spatial lattice, which holds that the center of mass of the material particles in the crystal is distributed at the vertex, face or body center of the parallelepiped unit of the spatial lattice, and the particles are periodically arranged repeatedly in the three-dimensional space. They identified 14 forms of space lattice.

Abandoning all the physical properties of crystals and considering crystals only from the perspective of geometric symmetry, Russian crystallographer Fedorov determined that there were 230 kinds of microscopic symmetry forms of crystals, that is, there were only 230 kinds of spatial (symmetry) groups inside crystals.

Fedorov’s work was the mathematical theoretical basis of the later crystal experiment, which played a great role in determining the internal structure of the crystal. All these 230 symmetries were found in the experiment. In 1912, M．V．Laue, a German, revealed the periodic structure inside the crystal for the first time through X-rays, and confirmed the geometric theory of crystal structure.

Since then, the British father and son Prague (William Henry Bragg, 1862-1942; William Lawrence Bragg, 1890-1971) and Russian Ulf (георгий (юрий) викт). In particular, they measured some crystal symmetries that Fedorov thought were imaginary (that is, symmetries that existed only in theory).

Laue and Prague won the Nobel Prize in Physics in 1914 and 1915 respectively. In the future, there are many works about crystal research that won the Nobel Prize.

7. The beauty of mathematics

Mathematicians, as well as some physicists, have a strong feeling for the beauty of mathematics, and their pursuit for it is endless:

My job always tries to unify truth and beauty, but if I can only choose one or the other, I often choose beauty 18.

-Waier

Weil is probably the greatest mathematician after Poincare and Hilbert in the 20th century, and he also put forward the gauge field theory in physics. His book Group Theory and Quantum Mechanics was first published in 1928.

It is said that theoretical physicists at that time would put this book on the shelf, but they didn’t read it because the mathematics in it was too difficult. Wail seems to believe that beauty is a higher level of truth, because what we see and understand should be only a part of truth.

And beauty can often bring us to a more comprehensive truth.

Beauty is the first test: ugly mathematics has no place in this world.

-hardy

Hardy was an outstanding analyst in the 20th century and the most outstanding mathematician in Britain in his time. His Monologue of a Mathematician expresses his views on mathematics and has a wide influence.

God created the world with beautiful mathematics. When trying to express the basic laws of nature by mathematics, researchers should mainly strive for the beauty of mathematics.

-Dirac

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18. “My work has always tried to unite the true with the beautiful and when I had to choose one or the other, I usually chose the beautiful.” Hermann Weyl, In Obituary by Freeman J. Dyson, ‘Prof. Hermann Weyl, For. Mem. R.S.’, Nature (10 Mar 1956), 177, p. 458. Dyson notes that this was told to him personally, by Weyl who was “half joking”.

19.Beauty is the first test: there is no permanent place in the world for ugly mathematics. — G. H. Hardy: In it A Mathematician’s Apology (1940) . First Electronic Edition, Version 1.0, March 2005, Published by the University of Alberta Mathematical Sciences Society, Available on the worldwide web at http://www.math.ualberta.ca/mss/. has a Chinese translation: A Mathematician’s Pleadings.

20. “God used beautiful mathematics in creating the world.” “The research worker, in his efforts to express the fundamental laws of Nature in mathematical form, should strive mainly for mathematical beauty.” Paul A. M. Dirac: in Paul Adrien Maurice Dirac: Reminiscences about a Great Physicist (1990), Preface, xv; p.110.

Dirac’s feeling of mathematical beauty is unique. Dirac’s equation is the perfect combination of experiment and mathematical beauty. In Dirac’s view, the equation derived from the experimental results only at that time does not have mathematical beauty, so he modified the equation according to his own understanding of mathematical beauty, and predicted the existence of positrons according to the modified equation, which was later confirmed by experiments. Dirac’s view seems to have something in common with Weil’s.

Dirac should like his equation very much. He first met Feynman at a meeting. After a long silence, Dirac said to Feynman, "I have an equation. Do you have one?". I guess Feynman was very depressed at that time.

Mathematics, if viewed correctly, not only possesses truth, but also possesses supreme beauty.

-Bertrand Russell

Russell, a mathematician and philosopher, won the Nobel Prize in Literature. The History of Western Philosophy, written by him, looks at the history of western philosophy from the perspective of a philosopher rather than a philosopher historian. It has a unique perspective, clear context, smooth writing and no lack of humor. His understanding of beauty naturally has a very broad background.

………

There is no doubt that the meaning of mathematical beauty has some similarities with other beauties such as art in formal beauty, but it is more a beauty of thinking and logic, wisdom and has its own characteristics. Everyone’s understanding of the beauty of mathematics is different, but the following views are helpful to grasp some meanings of the beauty of mathematics:

W form: clear, concise, simple, original, novel, beautiful, the connection between different objects.

W connotation: profound, important, basic and rich in meaning.

W proof: clear, neat and ingenious

Let’s illustrate the above point with some examples.

The first example is Pythagorean theorem, which is called Pythagorean theorem in the west. Hooking three strands, four strings and five is a special case of this theorem, which was put forward by Shang Gao in the early Western Zhou Dynasty. This theorem says that the sum of the squares of two right-angled sides of a right-angled triangle is equal to the square of the hypotenuse:

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21. “Mathematics, rightly viewed, possesses not only truth, but supreme beauty.” Bertrand Russell, Essay, `The Study of Mathematics’ (1902), collected in Philosophical Essays (1910), pp.73-74.

The proof is simple. The area of the big square in the above figure is the square c2 of the hypotenuse, which is equal to the sum of the areas of the four right triangles inside and the area of the small square:

Simplify, expand and gain.

So a2+b2=c2.

The form and proof of this theorem can reflect the meaning of the form and proof part of the mathematical beauty mentioned above. This theorem is basic, and its connotation is profound and rich.

An application of Pythagorean Theorem: On the plane coordinate, the coordinate (x,y) of a point satisfies the equation.

If and only if this point is on the circumference with radius r and the center of the circle is on the origin.

Pythagorean theorem is widely used, which is a manifestation of its basicity. Its profound connotation also lies in that many problems can be derived from it, such as:

What positive integers A, B and C can be the sides of a right triangle?

Is the area of a right triangle with integer sides an integer?

If the sides of a right triangle are all rational numbers, when is the area an integer (for example, 3/2, 20/3 and 41/6 are the three sides of a right triangle, and the area is 5. ) Such integers are called harmonious numbers or congruences.

The third question is closely related to the BSD conjecture of the Millennium problem. Who can solve the BSD conjecture, in addition to honor, can get one million dollars. 157 is a harmonious number, and the length of the three sides of the "simplest" rational right triangle with 157 as the area is:

The complexity and difficulty of the third question and BSD conjecture can be seen from this.

When talking about the meaning of beauty in mathematics, one of them is "the connection between different objects". This seems to have nothing to do with beauty, but it is actually a very important point of thinking, logic and wisdom. We look at Pythagorean theorem from this point of view.

Generally, people look at Pythagorean theorem as follows: knowing the length of two sides of a right triangle, we can find the length of the third side. This pragmatic thinking hinders our exploration and innovation. Looking at it from another angle, Pythagorean theorem reveals the relationship between the three sides of a right triangle.

This angle gives us a broad view at once. For example, the square of three numbers can be related to Pythagorean theorem or higher power:

This is the famous Fermat equation in number theory. Whether they have integer solutions without zero (that is, A, B and C are integers, but none of them are zero) is a problem that has puzzled mathematicians for more than 300 years.

In order to solve this problem, a great mathematics, algebraic number theory, has emerged, and now it is a very active research direction, with many famous scholars. The Fermat equation problem was finally solved by Wells in the 1990s, which was a great mathematical achievement in the last century. It was a sensation and the story behind it was unusually wonderful.

The second example is from Euclid’s Elements, which asserts that there are infinitely many prime numbers. There is a beautiful proof in Euclid’s book: If the conclusion is incorrect, then there are only a limited number of prime numbers, which are set as p1, p2, …, pn. Multiply them all and add 1 to get a number.

m＝1＋ p1p2 …pn

Then p1, p2, …, pn are not factors of M, so the prime factors of M are different from those N prime numbers. This is a contradiction, so there are infinitely many prime numbers.

This proof is neat and ingenious, which can make people feel happy mentally. Prime numbers seem easy to understand, but they are probably the most mysterious and elusive objects in mathematics. For prime numbers, it is easy to ask some questions that primary school students can understand, but the most intelligent mathematicians for hundreds of years can’t solve them.

For example, how much prime number occupies in natural numbers?

Goldbach conjecture: Every even number greater than 2 is the sum of two prime numbers.

Twin prime conjecture: There are infinitely many prime numbers P, so that p+2 is also a prime number.

The formulation of the first question is not clear enough. We can make the question more clear: how many prime numbers are there between 1 and n for any natural number n. Nobody can answer this question. But mathematicians have made a lot of progress.

At the beginning of 19th century, German mathematician Gauss and French mathematician Legendre put forward a famous conjecture about the proportion of prime numbers in natural numbers. At the end of 19th century, Adama and Dellavalle-Posen first proved this conjecture respectively, which is the famous prime number theorem. In 1949, Selberg and Erdis respectively gave elementary proofs of the prime number theorem. This is part of Selberg’s important work of winning the Fields Prize in 1950.

The second question is easy to understand, and it is easy to give examples, such as

12=5+7, 88=5+83=17+71=29+59=41+47， ….

So far, the best work on Goldbach’s conjecture is still the result of Chen Jingrun. His paper published in 1973 proved that every sufficiently large even number can be written as a prime number plus another number, and the number of prime factors of the other number does not exceed 2 (for example, prime numbers and 6=2×3 are such numbers, but 12=2×2×3 has three prime factors, which is not satisfactory).

Chen Jingrun’s result is known as Chen’s theorem in the world. In China, it has a misleading name: Chen Jingrun proved that 1+2 is a by-product of Xu Chi’s influential reportage "Goldbach conjecture".

Xu Chi’s reportage inspired a generation’s enthusiasm for mathematics and respect for Goldbach’s conjecture. Chen Jingrun also received a huge amount of letters of admiration and affection. This grand occasion never happened to mathematicians again.

Someone once told me about Chen Jingrun’s work, and he understood 1+2 completely literally. I tried to explain to him the meaning of 1+2 in Chen Jingrun’s work. He gave me an oblique look and said, "You don’t understand". I cried speechless and sighed deeply that it was not easy to do popular science.

At the same time, it is also found that sometimes people are obsessed with their own unrealistic understanding, which seems to be inseparable from their self-esteem and mental security.

The third question is also easy to understand. For example, 3, 5 and 41, 43 are all prime pairs with a difference of 2. The question is whether there are infinite such prime pairs.

In 2013, Zhang Yitang, a Chinese mathematician, made a great breakthrough in this issue. He proved that there are infinite pairs of prime numbers, and the difference between each pair of prime numbers is less than 70 million. Zhang Yitang’s result was a sensation, and the story that he kept pursuing his ideal in adversity was also very inspiring and touched the world.

Prime numbers are one of the most basic objects in mathematical research. So far, it seems that human beings have not shown enough intelligence to fully understand them. The most famous problem in mathematics is Riemann hypothesis, which is closely related to the study of prime numbers. In fact, Riemann put forward this conjecture at that time in order to study prime numbers. It is not surprising that Riemann’s hypothesis has not been solved yet.

The third example is the irrationality of the root number 2, which was a number that brought many troubles in ancient Greece. Theorem: If x2 = 2, then x is not a rational number.

We can also give an aesthetic proof. If the conclusion is incorrect, there will be integers a and b so that x = a/b. It can be assumed that a and b are coprime. Square both sides of XB = A, and you get X2B2 = A2. That is 2b2 = a2, so a is even and a = 2p.

So 2b2＝4p2 and b2 = 2p2, so b is an even number. Therefore, A and B are even numbers, and there is a common factor of 2, which is contradictory. So x is not a rational number.

Here, maybe we will suddenly think of whether pi, which was learned in primary school, is irrational? It seems that no one in primary school or middle school has talked about it. In fact, this is a good question, which is closely related to the famous problem of turning a circle into a square in ancient Greece.

This question says whether a square can be made only by ruler (without scale) and compass, and its area is the area of a given circle. It was not until Lin Deman proved the transcendence of π in 1882 that the answer was no.

Lin Deman’s work tells us that π is actually an extremely unreasonable number, called transcendental number, which is much more unreasonable than root number 2. The study of transcendental numbers is also very interesting and an important part of number theory. In the last century, Becker won the Fields Prize in 1970 for his research on transcendental numbers.

It is impossible to fully understand the beauty of mathematics without talking about its formal beauty. There are many important geometric objects in geometry that are extremely beautiful and amazing.

(1) Minimal surface: Minimal surface is very important in differential geometry. Minimal surface is the main tool in Qiu Chengtong’s proof of positive mass conjecture in general relativity.

(2) Fractal geometry: Fractal was discovered in the study of coastline in the last century, and later became an important branch of mathematics.

(3) Power system: Power systems are everywhere. The study of dynamic system in mathematics originated from Poincare’s study of three-body motion in astronomy, and now it is a very active branch of mathematics, and many people have won Fields Prize for the study of dynamic system.

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22. The following four color maps and the graphics in the next section are all from the Internet.

(4) Karabi-Chueh Manifold: Karabi-Chueh Manifold is a very important manifold, which has many researchers and plays a basic role in string theory.

There is no doubt that we can show the beauty of quality and form in mathematics indefinitely, but due to the limitation of space, we should give up this idea and leave more mathematical beauty to readers to explore.

8. Mathematicians

Mathematicians are a group of people with special talents, and their personalities and anecdotes are also colorful.

Weiner, the founder of cybernetics, is moving. On the day of moving, his wife repeatedly told him to go to the new address after work. Of course, as usual, Weiner forgot to return to the old site after work and found something different. I found a girl next to me in the dim light and asked, "I’m sorry, maybe you know me." I’m Norbert Weiner. We just moved. Do you know where we moved? " The girl replied, "Yes, Dad, Mom knew you would forget."

Wiener visited China in 1930s and gave lectures in Tsinghua. He appreciated Hua Luogeng very much.

Deligne was brilliant and won the Fields Prize for proving Wei Yi’s conjecture. He said: Whether you can do math problems is just a psychological problem. This is quite a bit like saying that I can do it, and saying that I can’t do it. This statement also echoes a widely circulated story.

One day, a student was late for a class in a cow university, and the class was over when he got to the classroom. There are seven topics left on the blackboard, which he thinks are homework. He will do these homework when he goes back. A week later, it was time to hand in homework. The student felt very painful. He only worked out two questions. Although he had a good idea for the third question, he had no time to finish it. When he threw his partially finished homework on the professor’s desk in frustration,

Professor: What is it?

Student: Homework.

Professor: What homework?

Only then did the students understand that what the professor wrote on the blackboard last week was the seven most important unsolved problems in this direction. It is said that this student has never done such an excellent job since he became a professional mathematician.

Hungarian mathematician Erdis is legendary, has no fixed residence, always travels, and cooperates with mathematicians there whenever he arrives, so the number of his collaborators is amazing. He believes that mathematicians are devices that turn coffee into theorems.

Siegel, a German mathematician, won the first Wolff Prize. He is a very smart and hardworking mathematician. Hiroyuki, a Japanese mathematician, won the Fields Prize. He often said that he was not talented, but he was meticulous and devoted himself to his work. When he first learned Algebra written by Vander Waals, he almost didn’t understand it, so he began to copy books until he understood it.

A mathematician talked about his late colleague: "He made many mistakes, but they were all made in a good direction. I tried to do this, but I found it difficult to make good mistakes. "

Physicist Kelvin (after whom Kelvin temperature is named) looks at mathematicians like this: Mathematicians are people who think the following formula is obvious:

Descartes was a mathematician and philosopher. Mathematically, he founded analytic geometry. Philosophically, he put forward "I think, therefore I am", which caused people to think deeply about the relationship between consciousness and existence.

There is a rumor that he is in love with Princess Christina of Sweden, and the writing communication is blocked by the royal family, so he uses the equation r=a(1-sinθ) to express his passion. The princess quickly understood this unique love letter after reading it. This equation is a polar coordinate equation, and its image is

It seems that mathematics is not only a language to describe nature, but also a language to describe love.

This paper is based on the author’s report of the same name. Most of the materials in this paper are well known. The main reference materials for the historical part are as follows:

1. Mathematics, its contents, methods and significance, Volume I, A.D. Alexandrov et al., Science Press, 2001.

2. Ancient and modern mathematical thoughts, Volume I, by M. Klein, Shanghai Science and Technology Press, 1979.

Other references are quite complicated, including network resources, some of which are listed in the notes in the article, and there are still many references that are difficult to list one by one.

Welcome attention

Popularization of science Liaoning

Original title: "Academician Xi Nanhua: The Meaning of Mathematics"

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CCTV News:According to the data released by the National Bureau of Statistics on October 24, in the third quarter, the national economy continued to recover, production demand continued to improve, employment prices were generally stable, and people’s livelihood security was effective and effective, and the overall operation was in a reasonable range.

In the first three quarters, the GDP increased by 3.0% year-on-year.

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Policy measures have made remarkable progress, and industrial production has rebounded significantly.

In the third quarter, the supply chain of industrial chain recovered steadily, and the added value of industrial enterprises above designated size increased by 4.8% year-on-year, up by 4.1 percentage points from the second quarter. The leading role of new kinetic energy was highlighted. In the third quarter, the added value of high-tech manufacturing increased by 6.7% year-on-year, which was 1.9 percentage points higher than that of industries above designated size in China. The output of new energy products such as charging piles, wind turbines and photovoltaic cells increased rapidly. The rapid recovery of the automobile manufacturing industry has played a significant role in stimulating the industrial economy.

Zhang Liqun, a researcher at the State Council Development Research Center:This shows the strong growth potential of China’s economy and the obvious expected effects of our macroeconomic policies, which are enough to enhance our confidence.

The employment situation is generally stable, and the unemployment rate drops in urban surveys.

In the first three quarters, the average urban unemployment rate was 5.6%, of which the average in the third quarter was 5.4%, down 0.4 percentage points from the second quarter. From the main population of employment, 25-mdash; The average unemployment rate of the 59-year-old labor force in the third quarter was 4.4%, which was significantly lower than the average level of 4.9% in the first quarter and 5.0% in the second quarter. Under the influence of a series of policies to stabilize employment and protect people’s livelihood, in the first three quarters, the per capita disposable income of the national residents actually increased by 3.2% year-on-year, 0.2 percentage points faster than that in the first half of the year, and the income growth of residents was basically synchronized with economic growth.

In the first three quarters, China’s import and export increased by 9.9% year-on-year

The General Administration of Customs announced on the 24th that in the first three quarters of this year, China’s total import and export value was 31.11 trillion yuan, up 9.9% year-on-year. Among them, the export was 17.67 trillion yuan, an increase of 13.8%; Imports reached 13.44 trillion yuan, up 5.2%. In the first three quarters, China imported and exported 4.7 trillion yuan, 4.23 trillion yuan, 3.8 trillion yuan and 1.81 trillion yuan to ASEAN, the European Union, the United States and South Korea, up 15.2%, 9%, 8% and 7.1% respectively. In the same period, China’s total import and export to countries along the "Belt and Road" was 10.04 trillion yuan, an increase of 20.7%.　

China-Europe train "Zhongyu" added new categories to the export goods.

On the afternoon of 24th, a China-Europe train (Zhongyu) loaded with new energy vehicles left Zhengzhou, passed through Alashankou, Xinjiang, and headed for Moscow, the Russian capital. This was the first time that China-Europe train (Zhongyu) exported new energy vehicles to Europe, which also marked the addition of new categories to the export goods of China-Europe train (Zhongyu).

Lu Lei, Chief of Customs Supervision Section II of Zhengzhou Station:We shorten the overall customs clearance time and port stay time of automobile export by means of immediate reporting and immediate inspection, and realize seamless and zero waiting at port clearance.

After nearly ten years of development, the business scope of China-Europe Train (Zhongyu) covers more than 140 cities in more than 40 countries, with special trains such as postal trains and timber trains, and more than 6,000 domestic and foreign partners.

　　Lead: Send off the keyboard man of New York Fashion Week, get ready for ammunition and wait for London Fashion Week. About London, I really want to see adjectives other than "unconstrained style", because there are also bare breasts and dragon and phoenix dancing! (Editor: Du Mingwei)

　　The following is a group chat record that took place after 11 noon. After that, I completely gave up the idea of sleeping on weekends.

　　The background of the dialogue is after Pam Hogg’s spring and summer 2019 show in London Fashion Week, which has just been "bombed".

　　I just want to say one thing to you: Eat, drink and be merry!

　　I don’t know if you big V bloggers who flew to London from new york are prepared psychologically. After all, this is the place where the design ghosts of Alexander McQueen, Vivienne Westwood and John Galliano, with the titles of "British fashion hooligan", "mother of punk" and "hopeless romantic master", get rich.

　　Fine, at the end of the story, can you please explain that this spinning and jumping dancer suit can still shake your rock sexy disco?

　　If new york is a city with high acceptance, then London is trying to show us how unlimited people are. Or in other words, ask the anti-vice inspection team to find out.

　　In addition to yo-yo color matching and fried crispy Pipi shrimp, Pam Hogg’s show sign is more like a masquerade ball in the old design era.

　　As the song goes: "I wore a veil and a headpiece with fake diamonds to attend this long-awaited masquerade ball." I know this will be my only chance, to be familiar with you but unfamiliar with you … You finally came to me gently and drove away Cinderella’s inferiority complex. "

　　Almost completely changed the shape of the body and the appearance of the face, which may really give Cinderella some courage and look at the prince in the eye. Anyway, you can’t recognize me, so what if it’s a fire.

　　Yes, this understanding must be a standard textbook answer.

　　Ps: The kind that can only appear in old magazines and never appear in real life.

　　Compared with other famous designers in London Fashion Week, she started her own fashion industry in the 1980s, and she is a young designer. At about the same time, Japanese designers broke into the European fashion circle and dismantled the fashion with various tricks that challenged the physical limits, which must have had a profound impact on Pam Hogg.

　　At the same time, she has the dual identity of a designer and a musician. From 1990 to 2000, Pam Hogg made many achievements in the music industry, not only formed the band Doll and Hoggdoll to write lyrics for this band, but also held a roving art exhibition to show the fashion films she directed.

　　It is said that Rhianna (Rihanna), Kylie Minogue (kylie minogue), rock women Alison Mosshart and Siouxsie Sioux, who are friends in the music circle, all love her clothes very much.

　　Everyone loves the clothes she designed. ……

　　I love the clothes she designed. ……

　　Love the clothes she designed ……

　　However, no matter how you recite the scriptures, there is no doubt that China Keyboard Man will never buy it.

　　@ Fanxi: Just fashionable orchid

　　@ Go to Qian Shan to see the setting sun.

　　@ Meng always loves art: I don’t understand the ninth picture.

　　The one on the first floor, if I guess correctly, must be from Zibo. But is it really appropriate for you to describe it as "fashionable"?

　　But there is also a very bad point. Will this give many cutting-edge designers the idea that no matter how much I go too far, there will always be countless fashion editors to give me a round trip?

　　With a strong heart that has seen Pam Hogg, I can finally watch all the shows and spit in London Fashion Week today.

　　On MATTY BOVAN’s runway this year, we finally breathed a sigh of relief about the world’s environmental protection problems, and finally we don’t have to worry about the transition and waste of garbage storage, because no matter how many surplus resources there are, they will be piled up on his clothes in the new season.

　　@ Ayu Xiao Bao: I don’t understand, after all, I’m not an artist.

　　@ Not in the search range: This ….. I don’t understand.

　　Contrasting colors, piling up, modern Superman or Contra, it is really easy to gradually adapt to all kinds of shameful and abnormal elements in London. I even feel that I want to try it, just for a moment.

　　Well, congratulations, it’s about to start to be very BIAN TAI.

　　Britain, of course, it is one-sided to use a country’s design to hold a certain type in place. But from the usual London Fashion Week, there are really few cool or flat designs. If we have to explain, the post-war material shortage more than 50 years ago and the rationing system that was not enough for anything really had a great influence on the designers at that time.

　　However, this kind of London, which is often called "creative", has always proved to be beneficial, always bringing fresher elements to fashion. When these elements are gradually integrated with the actual clothing structure, it will become more and more forward-looking.

　　Soon, I’ll get used to the rhythm of galloping cars on the runway of London Fashion Week.

　　@ 京京京京京京: This series is good.

　　@ Strawberry is just beautiful: it’s really beautiful.

　　@ Xiaobai Meets Cat: Good-looking

　　　　　　 After watching several "accidents" in London Fashion Week all day, RICHARD MALONE finally showed us creativity and fashion, not tit for tat.

　　How about it? Are you getting closer and closer to your ideal street style?

　　Has London Fashion Week just started seen something exciting to look forward to?

　　　Click on the link to review the previous fashion porridge:

　　Fashion porridge Vol.7 | new york’s final article: Laoganma of new york and Lin Yongjian female model who hit her face.

　　Fashion porridge Vol.6 | After watching several shows in new york, it is particularly difficult to turn off the lights when sleeping.

　　Fashion porridge Vol.5 | Black Naomi on the first day after the catwalk? Hack her? Hack her?

　　Fashion porridge Vol.4 | These "shut-up stunning" have seriously caused physical discomfort.

　　The three A-share indexes collectively closed down today. At the close, the Shanghai Composite Index fell by 0.4%, the Shenzhen Component Index fell by 1.13%, the Growth Enterprise Market Index fell by 1.54%, the North Stock Exchange 50 rose by 3.39%, and the turnover of the Shanghai and Shenzhen stock markets was 692.6 billion yuan. More than 4300 stocks in the two cities fell. The net purchase of northbound funds was 2.727 billion yuan.

　　On the theme of the plate, a few plates such as port shipping and non-metallic materials rose against the market; Tourism, hotels, cloud games, education and other sectors were among the top losers.

　　On the disk, shipping concept stocks rose sharply against the market, with the daily limit of (), (), (), (), and many stocks such as (), () and () rising by over 5%. In the news, due to the conflict between Palestine and Israel, the tension in the Red Sea has further escalated, and the four major shipping giants have suspended transportation in the Red Sea, and the Suez Canal, the shipping "artery", is facing the risk of closure; Longzi generation stocks are active again, () 3 consecutive boards, (), (), () daily limit, () intraday daily limit; Tourism and hotel stocks were depressed all day, (1) falling more than 7%, (2) falling more than 5%; () In the afternoon, the daily limit again recorded 13 days and 7 boards, and went out of the quasi-"ground board" market.

　　Plate analysis:

　　Straight flush hot stock list:

　　Transaction review:

　　At 09:25 A shares opened, the Shanghai Composite Index opened 0.2% lower, the Shenzhen Component Index opened 0.41% lower, the Growth Enterprise Market Index opened 0.5% lower, and the port shipping sector was among the top gainers.

　　At 09:27, the shipping concept stocks were active at the beginning of the session, Ningbo Ocean Shipping Bidding approached the daily limit, COSCO Haineng and () opened higher than 6%, and China Merchants Steamship and () opened higher in succession. In the news, global shipping may be blocked again due to the tension in the Red Sea. With the escalation of the conflict, the four major shipping giants suspended the Red Sea transportation, and the Suez Canal, the "artery" of shipping, faced the risk of closure, and the shipping cost faced the risk of jumping in the short term.

　　09:33 yuan Dream Star concept stocks continue to be active, with () and () 2 consecutive boards, () and () rising.

　　At 09:35, the initial trading of pork stocks rose, () rose more than 7%, followed by (), (), (), (), () and so on.

　　09:37 Data element concept stocks were active at the beginning of the session, with () and () daily limit, () and () rising by more than 5%, and () and () followed suit. In the news, the National Development and Reform Commission publicly solicited the opinions of the "Three-year Action Plan for Data Elements ×" (2024-2026) (draft for comments). According to the opinion, by the end of 2026, the average annual growth rate of the data industry will exceed 20%, and the scale of data transactions will double.

　　At 09:42, traditional Chinese medicine stocks rose, () went up, (), (), (), () and so on.

　　At 09:44, FTSE China A50 index futures rose in the short term, and once fell by 1%.

　　At 09:46, the trading of the securities sector rose, () rose by more than 7%, followed by Pacific, (), () and Founder Securities. In the news, Guolian Securities announced that the controlling shareholder Guolian Group was allowed to become the major shareholder of Minsheng Securities. The specific integration of Guolian Securities and Minsheng Securities still needs to be communicated with relevant parties, and related work has not yet been carried out.

　　At 09:53, the real estate development sector bottomed out and rebounded, () rose by over 5%, followed by (), (), () and ().

　　10:00 According to () iFinD data, the turnover of Shanghai and Shenzhen stock markets reached 215 billion yuan within half an hour of opening.

　　At 10:07, Longzi’s stocks were active again, with the leading shares being 3 consecutive boards, () and Longzhou’s daily limit, and Longjiang Communications, Shenglong, () and Longgao’s shares rose more than 5%.

　　At 10:21, the memory chip sector fluctuated and fell. Baiwei Storage fell by more than 5%, () fell by more than 4%, and Puran shares, Dongxin shares, () and Hengshuo shares followed.

　　At 10:25 (), the floor board was staged, and the turnover exceeded 500 million yuan. The stock had three consecutive boards and once fell in early trading.

　　At 10:41, the short play game board oscillated lower, () and () fell more than 6%, () fell more than 5%, and () and () followed.

　　At 10:42, Huawei’s auto concept stocks rose, and Shenglong shares and () rose daily, while (), () and () rose more than 5%.

　　At 10:45, the whole vehicle plate moved up, () pulled up linearly and went up by the daily limit, (), (), (), () and so on.

　　At 10:50, the main contract of 2404, the contracts of 2406, 2408, 2410 and 2412 of the European freight forwarding index all hit the daily limit, reporting 9.99%, 10%, 10%, 9.99% and 9.99% respectively.

　　10:52 According to the data of the straight flush iFinD, according to the balance scale, the net inflow of southbound funds has exceeded 3 billion yuan up to now, of which the net inflow of Hong Kong stocks through Shanghai is 2.052 billion yuan and the net inflow of Hong Kong stocks through Shenzhen is 949 million yuan.

　　At 11:27, the main contract of lithium carbonate dived in a straight line, and turned down in the day. Now it has fallen by more than 2% and is now quoted at 103,000 yuan/ton.

　　At 11:28, the growth enterprise market index fell to 1%, the Shanghai Composite Index fell by 0.12%, the Shenzhen Composite Index fell by 0.7%, and () fell by more than 4%.

　　At 13:13, the increase of shipping concept stocks further expanded in the afternoon. Jinjiang Shipping and Haitong developed daily limit in the afternoon, and COSCO Haineng hit the daily limit. (), Ningbo COSCO had a daily limit, and Phoenix Shipping and COSCO Haikong rose by more than 5%.

　　At 13:15, Contemporary Amperex Technology Co., Limited fell more than 5% in intraday trading, with turnover exceeding 3.8 billion yuan.

　　At 13:26, the Beizheng 50 Index rose more than 3% in the afternoon. Among the constituent stocks, Air China COSCO once hit a daily limit of 30CM, Junchuang Technology rose more than 20%, and Yoshioka Precision rose more than 14%. The three major indexes of the main board continued to fall, and both the Growth Enterprise Market Index and the Shenzhen Component Index hit new lows in the year.

　　At 13:28, the net purchase of southbound funds reached 5 billion yuan.

　　At 13:31, the Shenzhen Component Index fell to 1%, the Shanghai Composite Index fell by 0.34%, the Growth Enterprise Market Index fell by 1.33%, and more than 4,300 shares in the two cities fell.

　　13:34 According to the straight flush iFinD data, up to now, the turnover of Shanghai and Shenzhen stock markets has exceeded 500 billion yuan, of which the turnover of Shanghai stock market is 218.6 billion yuan and that of Shenzhen stock market is 281.4 billion yuan.

　　At 13:49, the tourism and hotel stocks continued to be in a downturn. Lingnan Holdings fell over 6%, Qujiang Wenlv and () fell over 4%, and (), (), () and () followed.

　　At 13:51, Haizhi hit the daily limit in the afternoon and stepped out of the quasi-"ground-sky board" market, with a turnover of nearly 900 million yuan.

　　At 14:35 (), he dived at the end of the day, once falling by nearly 7%, and the turnover exceeded 400 million yuan.

　　News:

　　1. Oriental Selection: Dong Yuhui was promoted to senior partner of Oriental Selection.

　　Dong Yuhui’s identity became "Senior Partner of Oriental Selection" after the announcement of the live broadcast of the account selected by Dongfang. Earlier, Yu Minhong said in the live broadcast that Dong Yuhui would definitely have the right to speak in the future.

　　2. Relevant responsible comrades of the Central Finance Office explained in detail the spirit of the 2023 Central Economic Work Conference.

　　According to Xinhua News Agency and the responsible comrades of the Central Finance Office, at present, China’s real estate market is in a transitional period. Although it has encountered some difficulties, there are still broad prospects and solid support for sustainable development. With the continuous implementation of the major decision-making arrangements of the CPC Central Committee and the effective implementation of various tasks, I believe that it will be able to effectively resolve risks, build a new model of real estate development, and promote the stable and healthy development of the real estate market.

　　3. At the end of the year, the integration and reorganization of state-owned enterprises is a good show, and the layout of strategic emerging industries has become a trend.

　　According to the China Securities Journal, from the end of the year, the wave of mergers and acquisitions of state-owned enterprises surged. The industry believes that the meeting of heads of central enterprises and the meeting of heads of local state-owned assets supervision and administration commissions to be held in the near future will further deploy the reform of state-owned enterprises in 2024, and the reorganization and integration of state-owned assets is expected to accelerate, and the layout of strategic emerging industries will become a new trend of professional integration of central enterprises.

　　4. CITIC Securities: "Data Element X" plans to release new kinetic energy opportunities.

　　CITIC Securities said that on December 15th, the National Bureau of Data solicited opinions from the society on the "Three-year Action Plan for Data Elements ×" (Draft for Comment), aiming to launch key actions in 12 major areas, and strive to show the multiplier effect of data elements in 2026 and create more than 300 typical application scenarios. The average annual growth rate of the data industry exceeded 20%, and the scale of data transactions doubled. "Data Factor ×" is another important policy after "Data 20", which provides specific direction and path guidance, and the scene landing is more feasible, which helps to guide the government and social forces to participate extensively. We believe that the construction of data element system has been continuously improved and deepened, and its potential has been continuously released. It is suggested to focus on investment opportunities in data collection, confirmation, trading and application, and the Internet, publishing and other sectors are expected to fully benefit.

　　5. The US Department of Commerce removed four China enterprises from the "unverified list".

　　According to the information released by the U.S. government in the Federal Gazette, a document to be released by the Bureau of Industry and Security of the U.S. Department of Commerce on December 19th shows that the Bureau of Industry and Security revised the U.S. Export Administration Regulation (EAR) and removed four China companies from the "UVL". Including Chengde Oscilloscope Electronic Technology Co., China No.2 Heavy Machinery Group, Ningbo Daai Laser Technology Co., Ltd.) and Xinjiang east hope New Energy Company Ltd., this revision will take effect on December 15th. (Interface News)

　　6. This year, the central government will issue 1 trillion yuan of treasury bonds, and the budget for the first batch of treasury bonds is 237.9 billion yuan.

　　According to CCTV news, this year, the central government issued 1 trillion yuan of national debt, which is specially used to support post-disaster recovery and reconstruction and enhance disaster prevention and mitigation capabilities. Not long ago, the working mechanism for the implementation of additional national debt projects established by the National Development and Reform Commission and the Ministry of Finance in conjunction with relevant departments has determined the first batch of projects. The reporter recently learned from the Ministry of Finance that the budget of the first batch of national debt funds of 237.9 billion yuan has been issued.

　　7. Huawei nova joins the Pioneer Program or indicates that the series will be sold in advance.

　　According to the science and technology innovation board Journal, Huawei said that the nova series will soon join the Pioneer Program. Some people in the industrial chain told reporters that the Ultra or Pro version of Huawei’s nova12 series may be equipped with Kirin chips.

　　8. National Symposium on Public Security Economic Investigation: Focus on key areas such as securities and continuously improve the level of combating crime.

　　According to the official news of the Economic Investigation Bureau of the Ministry of Public Security, the national symposium on public security economic investigation was held in Suzhou, Jiangsu Province on December 15th. The meeting called for continuous efforts to protect people’s happiness and peace and economic and financial security, focusing on key areas such as counterfeit money, fake cards, fake invoices, money laundering, tax-related, securities, finance, etc., constantly improving the level of combating crime and actively responding to the expectations of the people and various business entities.

　　9. Zeng Congqin, Chairman of Wuliangye: Eight generations of Wuliangye will choose the opportunity to adjust the ex-factory price and appropriately reduce the dosage.

　　According to 21st Finance, () Zeng Congqin, chairman of Wuliangye Group (shares), said that Wuliangye will fully promote channel profits in 2024, and will appropriately adjust the ex-factory price of the eighth generation Wuliangye at the same time, and appropriately reduce the input. The reporter had previously learned that the contract signed by Wuliangye and its dealers in the coming year will be reduced by 20%.

　　10. Evergreen Shipping and ONE suspended the booking operation of Red Sea container transportation.

　　According to Cailian, we learned from several freight forwarders today that there is a freight forwarder who has received the notice from Evergreen Shipping: due to the international situation, all booking operations in the Red Sea are suspended, and new bookings will not be accepted for the time being. In addition, some freight forwarders revealed that Ocean Network (ONE) informed that it would stop receiving Israeli goods in January, and also considered the substantial price increase of European routes. According to the information provided by another freight forwarder, All ONE including AR1/MD1/MD3 (routes) have been stopped, and the containers that have been reserved but have not been picked up have been stopped. Please arrange for customs clearance and further notice on the parts that have been picked up.

　　11. Shenzhen plans to relax the license plate application conditions.

　　According to the "Shenzhen Release" WeChat WeChat official account news, the Shenzhen Municipal Bureau of Transportation recently released the "Detailed Rules for the Implementation of Incremental Regulation and Management of Cars in Shenzhen (Draft for Comment)". According to its contents, Shenzhen will appropriately relax the scope and conditions for the application of incremental indicators for ordinary cars, and add special incremental indicators, which will be configured by means of ladder lottery. This means that the lottery winning rate is expected to increase. The "Draft for Comment" proposes to add special incremental indicators on the basis that the amount and allocation method of conventional incremental indicators in the current regulatory policies remain unchanged. That is, the conventional incremental indicators take one natural year (12 months) as a configuration cycle, and the allocation quota of ordinary car incremental indicators in each cycle is 80,000, which is allocated on a monthly basis and cannot be allocated across cycles; There is no configuration quota limit for the increment index of hybrid car and the increment index of pure electric car. There are 40,000 incremental indicators for ordinary cars in lottery mode and bidding mode, with individual indicators accounting for 88% and unit indicators accounting for 12%. The incremental indicators of hybrid cars and pure electric cars are directly configured after application and qualification examination.

　　12. Xiaomi responded that "the intelligent door lock automatically opens the door": only when the door is left unlocked does there exist the theoretical possibility of "unexpectedly opening the door automatically".

　　Xiaomi spokesperson issued a document in response to "Intelligent door lock automatically opens the door". After investigation, the products appearing in the relevant videos adopt semi-automatic lock bodies with in-line C-class lock cores, and do not have the function of automatically retracting the lock tongue. Its physical structure determines that the door will not open automatically when it is locked normally, and the product also does not support network remote unlocking. Only when the door lock is not completely closed and the installation tolerance of the door frame is too large, the door is in an unexpected "left unlocked" state, and there is a theoretical possibility of "unexpected automatic door opening". The after-sales engineer of Xiaomi products has come to the door to complete the inspection of the products, and has not reproduced the situation in the video. After communication, the doubts have been solved for the relevant users. We will also invite third-party appraisal institutions to conduct appraisal tests on this product to ensure the public’s right to know about safety and security. Thank you for your attention from users and the media.

　　13. Merchant ships in the Red Sea are frequently attacked by the United States or organized alliances to launch escort operations.

　　According to CCTV news, several merchant ships were recently attacked by Houthi armed forces in Yemen in the Red Sea waters, which aggravated the tension in the Middle East and affected international shipping. Sources said on the 17th local time that US Defense Secretary Lloyd Austin will announce a Red Sea escort operation when he visits the Middle East this week, and several Arab allies are believed to participate. Sources who did not want to be named told the British Guardian that the United States intends to form a naval task force with other countries to patrol the Red Sea, the Mande Strait and the Gulf of Aden. Austin will announce this escort operation this week and draft the code name "Guardian of Prosperity".

　　14. COSCO Shipping, OOCL, etc. have notified to suspend cargo loading on the Red Sea route.

　　According to The Paper, it is learned exclusively from freight forwarders that COSCO, OOCL and EMC have verbally notified to suspend the cargo delivery on the Red Sea route due to the international situation. ONE Ocean Network Shipping Co., Ltd. has also verbally notified the suspension of cargo pick-up on the Red Sea route. Maersk and CMA CGM informed in the morning of December 18th that the cargo receiving situation in the direction of the Red Sea would wait for the notice from the head office, and the news is expected later today. It should be noted that CMA, COSCO Shipping, Evergreen Shipping and OOCL have previously cooperated to form an alliance. In addition, a freight forwarder said that at present, mediterranean shipping company (MSC) only notified the Cape of Good Hope at the southern tip of Africa, and did not suspend cargo pick-up in relevant directions. Hapag-Beurotte has informed that, except VIP guests, the Middle East route, the Red Sea route and the west and east coasts of the Mediterranean route are suspended from accepting booking until further notice.

　　15. Ningbo Ocean Shipping, China Merchants Steamship, COSCO Haineng and many other shipping companies responded to the impact of the Red Sea crisis.

　　According to Yinshi Finance, the Red Sea crisis caused concern about navigation deviation, and many shipping companies responded to the impact of the Red Sea crisis. A person from Ningbo Ocean Shipping Securities Department said: "It may cause changes in the relationship between supply and demand to a certain extent and affect shipping prices, but it is hard to say to what extent." A person from COSCO Haineng Securities Department said: "Our company has no ships going to the Red Sea now, and the company’s main route is to return to China from the Middle East." Regarding whether the above incidents have an impact on international shipping prices, the above-mentioned person said: "The company cannot comment now." A person from the Securities Department of China Merchants Steamship said that there are no ships passing through the Red Sea route at present. She said that ocean transportation is affected by many factors such as supply and demand, shipping prices, oil prices and geopolitics. She said that it is not clear whether the above incidents will cause shipping prices to rise, but the company’s operation is relatively stable.

Phoenix Technology News On October 27th, in response to the recent media concern about the problem of "mobile phone traffic running fast", the relevant person in charge of China Mobile said: the relevant reports are not true, and mobile phone traffic will not "run fast".

China Mobile said that the billing system has a strict inspection and verification mechanism, and has passed the continuous inspection and testing by competent departments at all levels and independent third parties. The efficiency, stability and accuracy of the system are at the leading level in the world. If the traffic is not cleared in the current month, it changes the charging rules, which realizes the rolling function of traffic and does not affect the traffic measurement. For the same picture or video, there is no change in the traffic measurement before and after the traffic is not cleared in the current month.

In response to relevant reports, China Mobile said that it had specially organized a traffic billing test, and found no problem of "mobile phone traffic running fast", and promised that "billing error will be returned twice".

At the same time, Mobile said that with the continuous improvement of the 4G network, more intelligent terminals were launched, and richer mobile phone applications stimulated and improved customers’ traffic consumption to some extent. In addition, many applications in smart phones "inadvertently" generate online traffic without customers’ knowledge. For example, the weather forecast program automatically updates the weather data regularly; Mobile phone antivirus software automatically downloads virus database; In order to ensure the timely receipt of mail, the mobile phone mail receiving and dispatching software regularly visits the mail server for inquiry; The software regularly checks the version, upgrades or downloads patch software; Free games with advertising banners or advertising pop-up content updates. There is also a part of traffic consumption caused by viruses and Trojans in mobile phones.

In order to avoid unnecessary data traffic, China Mobile advises customers to pay attention to the following items when using smart phones:

1. When quitting the application software on the smart phone, try to use the "Quit" option in the software menu instead of simply quitting the operation interface.

2. Regularly clean up background running programs. According to the operation method of the used smart phone, enter the task manager, find the application that has been used but is still running in the background, and forcibly stop the application to ensure complete exit.

3. Turn off the functions of data push and automatic update in the settings of various application programs, use manual update control, and then manually update when you need to query.

4. Turn off the automatic sending and receiving function of mobile email.

　　CCTV News:Pangolin is a kind of animal covered with scales from beginning to end. Hard scales are pangolin’s protective clothing, but they also bring heavy pain to pangolin.

　　Recently, Shenzhen Customs seized pangolin scales weighing 11.9 tons. A pangolin has about 0.4 to 0.6 kilograms of scales. These 11.9 tons of pangolin scales mean that about 20,000 to 30,000 pangolins have been brutally killed. On the morning of the 29th, Shenzhen Customs announced the seizure process of the largest pangolin scale smuggling case to date.

　　Shenzhen Customs seized 11.9 tons of pangolin scales.

　　On July 1st this year, Shenzhen Customs, which belongs to Dapeng Customs, found that one of the containers was abnormal when checking and releasing dozens of containers. Customs officers immediately conducted a thorough investigation of this container. After taking out more than 100 bags of charcoal, they found some different packaging bags inside.

　　Chen Ken, a member of Shenzhen Customs Inspection Department of Dapeng Customs, said: "After opening the packaging bag, it was initially suspected that it was pangolin scales."

　　After on-site counting and weighing, 239 packages of pangolin scales were found, with a total weight of 11.9 tons.

　　The suspect’s profit is as high as ten times or even dozens of times.

　　Who is smuggling these pangolin scales? Finding suspicious people has become the key to solving the case.

　　After combing the massive information, the customs anti-smuggling personnel finally found a Chinese name pinyin Xia Mou on the sea waybill. By expanding the scope of information to investigate Xia and Xia’s social circle, a man named Li Moujun entered the sight of anti-smuggling personnel.

　　According to Li Moujun’s account, he bought pangolin scales from many places in Africa at a price of about 150 yuan RMB per kilogram in an attempt to transport them to China for profit, and the profit was as high as ten times or even dozens of times.

　　11.9 tons of scales equals 20,000-30,000 pangolins killed.

　　The reporter saw the pangolin scales seized this time at Shenzhen Dapeng Customs inspection site. Judging from the packaging bag, the appearance was covered with many unknown bugs, and there was still a strong fishy smell at the scene. The pangolin scales seized this time are as big as shells and as small as fingernails.

　　According to experts in the protection of endangered animals and plants, a pangolin has about 0.4 to 0.6 kilograms of scales. The smuggling of 11.9 tons of pangolin scales seized by Shenzhen Customs this time means that about 20,000 to 30,000 pangolins have been brutally killed.

　　Pangolin scales are no different from human nails.

　　Pangolin, as an endangered wild animal, has a strong armor, but it is difficult to be greedy by enemies. Because pangolin scales can be used as Chinese herbal medicines in ancient China, they have become a tool for criminals to make profits. But in fact, modern western medicine says that the composition of pangolin scales is no different from that of human nails.

　　In China, pangolin belongs to the national second-class protected animals. Species and their products without import and export certificates are prohibited from trading, carrying or mailing in and out of our country. Illegal import, export or smuggling of such articles by other means will bear corresponding legal responsibilities. If the circumstances are serious enough to constitute a crime, criminal responsibility will be investigated according to law. At present, Li Moujun and others involved in the case have been arrested by the procuratorate, and the case is under further investigation.

　　Pangolin is the most hunted mammal in the world.

　　Pangolin is the only mammal covered with scales; It has no teeth, so it can’t chew; They feed on ants and termites; Pangolin mothers carry their babies with their tails; Pangolin moves at night in most cases, and its eyesight is poor, which will not pose a threat to any other mammal. When it encounters enemy harm, pangolin will shrink into a ball and protect its weak abdomen with scales, thus protecting itself from predators. However, it is this interesting and harmless animal that has become the most hunted mammal in the world.

　　Two of the four pangolins in Asia — — Chinese pangolin and Sunda pangolin — — It has been listed in the red list of the World Conservation Union as an extremely endangered species, which is only one step away from extinction in the wild. In addition, the conservation level of eight species of pangolins in the world has been upgraded to "VU", which means that no pangolins are safe.

　　Lenovo’s "magic" effect became the cause of the massacre.

　　Because pangolin is good at making holes, the ancients thought pangolin had the effect of "getting through". Therefore, pangolin unfortunately became a member of the prescription when it encountered diseases that needed to be "getting through" such as carbuncle, sores, amenorrhea and milk obstruction. In recent years, the domestic market has severely cracked down on the sale of endangered animals, but some people even "eat more as they get more endangered" in order to show off their identity, which has also become the reason for pangolins to die at the table.

　　However, does pangolin, which has been slaughtered so wantonly, really have those magical effects? The scales of pangolin are just keratinized skin appendages, and its main component is β -Keratin is not essentially different from hair, nails and other ingredients.

　　Refuse to eat pangolin and refuse to use pangolin products

　　Under the double pressure of being used as medicine and cooking, it is estimated that the demand for pangolins in China is as high as 200,000 each year, of which 50% are used as medicine and 50% are used as food. Due to a large number of catches, the number of pangolins in China has dropped sharply. According to a survey in 2008, the number of pangolins in China is roughly between 25,100 and 49,450, which is less than one-fifth of the annual consumption, so smuggling is rampant.

　　It is necessary to strengthen the crackdown on pangolin smuggling activities, and at the same time establish relevant protected areas to protect pangolin’s living environment. The most important thing is to refuse to eat pangolin and refuse to use pangolin products.

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　　Zuo is a tile percussion instrument in ancient China. The picture shows 2008 actors singing at the opening ceremony of the Beijing Olympic Games, welcoming friends from all over the world.

　　Rites and music civilization is an important part of ancient civilization in China. As early as the Xia, Shang and Zhou Dynasties, ancient sages formed a set of quite perfect ritual and music system through system of rites and music, and promoted it as a moral and ethical ritual and music education to maintain human harmony in social order. Rites and music civilization has had a great and far-reaching impact on the development history of Chinese civilization for thousands of years, and it still has its strong vitality.

　　The emergence of ritual and music civilization

　　China’s ancient "rites" and "music" originated from ancient primitive worship. The Book of Rites says, "At the beginning of a husband’s ceremony, he began to eat and drink, and he burned the porpoise. Respect and respect? If you drink, you will feel like a drum, and if you can make it respect ghosts and gods. " Its contribution to the gift, beating the earth drum and having fun, is the earliest ritual music ceremony. In the legendary Five Emperors’ period, although the emperor’s leading position and surrender had produced the consciousness of "ceremony", the system of ceremony had not yet been produced. It was only in the Xia Dynasty that the etiquette system was gradually established, because "the world is home, and each family is close to its relatives", so "adults think of etiquette" and "etiquette thinks of discipline". Due to the lack of written records and archaeological materials, it is difficult to know the details of Xia Li. Due to a large number of archaeological discoveries in Yin Ruins and more records in Historical Records of Yin Benji, Shang Li has been well documented. In the Zhou Dynasty, the ritual system was the epitome of the previous generation, and gradually became complete and mature. There were many songs and dances before the Zhou Dynasty. Zhuangzi Tianxia said, "The Yellow Emperor has Xianchi, Yao has Dazhang, Shun has Dashao, Yu has Daxia, and Tang has Da? 》。” By the Zhou Dynasty, the content of "Yue" was constantly enriched, and a corresponding system was formed. At that time, in addition to the representative "Dawu", according to the records of the twenty-nine years of Xianggong in Zuo Zhuan, there were dozens of Zhou Le. In the Zhou Dynasty, there was also a special organization "Spring Official" to regulate and manage music and dance, and under the Spring Official, there was a senior music teacher to teach the sons of the country "music virtue", "music language" and "music and dance" (Zhou Li Spring Official).

　　The ancient ritual and music civilization in China was formed and perfected in the Zhou Dynasty, because at that time, not only a systematic ritual and music system was formed, but also the ritual and music were endowed with rich humanistic connotations. The etiquette, ritual system and etiquette meaning formed in the Zhou Dynasty, such as crown, marriage, funeral, sacrifice, court, employment, township, shooting and official system, are mainly preserved in the Confucian classics "Yili", "Zhouli" and "Book of Rites" which have been handed down to this day. The "six generations of happiness" and the contents of music morality, music language, music and dance that flourished in the Zhou Dynasty were recorded in Yue Jing, but Yue Jing was "lost in Qin fire"; Fortunately, "Rites and music should be considered as useful", and the contents of many music systems can be seen in the etiquette system of "Three Rites", and the Music Book, which specializes in music meaning, is also preserved in the Book of Rites. In addition, the ancient "music" is a trinity of song, music and dance. According to Mr. Yang Xiangkui’s textual research, Zhou Le’s lyrics can be found in the Book of Songs, such as Zhou Song.

　　The Great Biography of Shangshu said that "Duke Zhou was a regent" and "system of rites and music for six years". "Zuo Zhuan" recorded in the eighteenth year of Wengong: "Zhou Gong, the former monarch, made the rites of the week, saying," Look at morality and do things with morality. " Duke Zhou was an important figure in the process of the formation of ritual and music civilization. He system of rites and music not only transformed and developed the rites and music from ancient times to the Shang Dynasty, forming a systematic system of laws and regulations and norms of behavior, but also injected the factor of "virtue" into it, which made it have profound connotations of morality and ethics. Confucius is another important figure in the development of China’s ancient ritual and music civilization. His first contribution is to inherit, popularize and publicize the ritual and music civilization, and to sort out and spread the Confucian classic "Six Classics" which records the ancient ritual and music civilization. Second, he took rites and music as the object of explanation, focused on highlighting the essence of rites and music civilization, and emphasized the ethical education and the function of governing the world.

　　The essence of etiquette and music civilization

　　The expression of rites and music needs to have certain forms, such as jade and silk, advance and retreat; Huang Zhong-Da-Lu and Gan Qi-Yu are the beauty of ceremony and music, but appreciating the ceremony of beauty is not only to satisfy the eyes and ears, but more importantly, to understand the original meaning of ceremony and music civilization leading people to be good. Confucius said: "Li Yun Li Yun, jade and silk clouds? Le Yun Le Yun, Zhong Gu Yun? " (The Analects of Confucius, Yang Huo) The Book of Rites and Music says: "It is the system of rites and music made by the late king, which is not based on the desire to hear and hear, but will teach the people to be like and hate, but also against humanity." These discourses aim to show that the form of civilized beauty of rites and music is to express the content of goodness, in which beauty is secondary and goodness is the main one. Confucius once said, "What is the courtesy of being unkind? People are heartless, so what are you happy about? " ("The Analects of Confucius, Eight Shu") Here, he put forward benevolence as a goal of leading people to be good through rites and music. Therefore, it is important to grasp the essence of etiquette and music civilization.

　　There are several meanings of "ceremony" in ritual and music civilization. First, "courtesy" is the foundation of human nature. "Book of Rites Quli" says: "Parrots can talk and stay with birds; Orangutans can talk and stay with animals. Today’s people are rude, although they can speak, is it not as good as the heart of an animal? ….. It is made by a sage, to teach people for courtesy, to make people polite, and to know themselves from animals. " "Rite" is regarded as the standard to distinguish people from animals, civilization from barbarism, so "Rite" is one of the most important characteristics of human civilized society. Secondly, the important role of "ceremony" lies in regulating people’s position and relationship in society. Etiquette makes people clear their position in society and know how to respect and be humble; Make people distinguish between right and wrong things or behaviors and know what to do and what not to do. As a code of conduct, "ceremony" maintains social order and justice. Third, "courtesy" is also a moral norm, which guides people to be kind and self-disciplined. Confucius said: "When the Tao is governed by politics, it is punished by qi, and the people are exempt and shameless; The Tao is virtuous, and it is courteous, shameful and qualified. " ("The Analects of Confucius is Politics") Therefore, the ritual and music civilization emphasizes the internalization of social rules into people’s inner yardstick through ethics. Fourthly, we can achieve the realm of social harmony by knowing and observing the ceremony. "The Analects of Confucius Learn": "There is a Confucius saying: the use of courtesy, harmony is precious. Wang Zhidao first, Sri Lanka is beautiful. It’ s not feasible to be small and big, but to know and be harmonious, not to be polite. " It not only emphasizes the desire of "harmony is precious", but also points out that "harmony" cannot be achieved simply for the sake of harmony, nor can it be unprincipled. This principle is propriety. It is the most beautiful state to achieve harmony while observing social order.

　　The essence of "music" in ritual and music civilization also has several ends. First, the social function of "music" focuses on the spirit of harmony. "The Book of Rites and the Book of Music" said: "Therefore, musicians should judge one thing to make peace, compare things with decorations, and combine the rhythm with writing, so they can make peace with their father, son, monarch and minister, and attach relatives to all the people. It’s the first way to make fun of Wang Li. " "Therefore, the musicians, the fate of heaven and earth, the discipline of neutralization, human feelings can not be avoided." It is pointed out that "music" is the discipline to coordinate all things in the world, and its function is to make people live in harmony. Second, "music" pays attention to orderly coordination. Yue Ji said: "The palace is the king, the business is the minister, and the horn is for the people. For things, feathers are things. If the five are not chaotic, then there is no? ? Voice. " It uses the five-tone metaphor to describe various characters, indicating that it is necessary to be orderly and coordinated in order to play harmonious music. Third, "music" also has the function of cultivating sentiment and changing customs. Yue Ji said: "If you treat your mind with joy, you will feel the need to forgive.". Yi Naoko is happy when he forgives, happy when he is happy, and peaceful for a long time. " "The Book of Filial Piety" also said: "It is not good at fun to change customs." That is to say, music education can cultivate the mind, make people happy and peaceful, and live a long life. Therefore, Confucius asked people to listen to elegant music and stay away from obscene sounds.

　　"Music, the sum of heaven and earth. Rites, the order of heaven and earth is also. " (The Book of Rites and the Book of Music) Order and harmony are the main themes of the ceremony and music civilization. Yue Ji said: "The musicians are the same, but the proprietors are different." It means that the function of music is to coordinate up and down, and the function of ceremony is to distinguish the order. However, although ceremony and music are different in form and function, they complement each other. In ancient tradition, "ceremony" is humanity, which covers everything, including "music". In the Zhou Dynasty, although the ceremony and music had their own systems, music was still an aspect of the ceremony system, and the harmony of music was also auxiliary and subordinate to the ceremony in order to realize it. The Book of Music says that when people are lured by foreign things, they will lose their nature and have evil thoughts such as greed, cruelty and fraud, so the first king made rituals and music to regulate people’s hearts. "Etiquette is popular with the people, and music is in harmony with the people’s voice", which is to bridge the psychological gap caused by the division of "ceremony" with the harmony of "music". Confucius and other Confucians often compare "ceremony" and "music" because the combination of the two can play a role of balance and reconciliation.

　　Modern significance of ritual and music civilization

　　The pre-Qin ritual and music civilization has experienced generations of evolution, with the specific content changed but the theme unchanged. It is of practical significance for China and the world to abandon the distinction between nobility and inferiority in the old ceremony and absorb the concept of order and harmony in the ceremony and music civilization.

　　In contemporary China, where a harmonious society is being built, the theme of ritual and music civilization is worth exploring and absorbing. The concept of order and harmony of ritual and music civilization has both internal moral norms derived from conscious consciousness and external binding behavior norms. Regulating people’s behavior with certain etiquette forms can strengthen social affinity and exert positive influence on people’s socialization. The inner moral cultivation of rites and music can achieve the balance and sublimation of human nature, and develop the sentiments of "reciprocity", "sincerity", "trust" and "righteousness", thus realizing the harmony between the subject and the outside world, the harmony of the group and the harmony of the society.

　　China, with its reform and opening-up, is opening its mind to the world and working together with the people of other countries to safeguard world peace and promote common development. The concept of order and harmony of ritual and music civilization is undoubtedly conducive to promoting the establishment of a just and reasonable new international political and economic order and realizing the pursuit of building a peaceful, stable and prosperous new world for people of all countries.

　　The fine tradition of etiquette and music civilization will also complement the Olympic spirit of "making sports serve the harmonious development of people" through the concept of "humanistic Olympics" in the 2008 Beijing Olympic Games. The ceremony, music and dance of China’s ancient ritual and music civilization are actually similar to the ancient Greek Olympic movement and ceremony. The "rural shooting ceremony" and "big shooting instrument" in the "ceremony" are sports meetings held by the countryside and governors respectively. Naturally, there are rules and competitions in these archery competitions. However, we have to salute each other before the competition and drink together after the competition. Therefore, Confucius said, "If you are humble, you will rise and drink, and you will be a gentleman" ("The Analects of Confucius"). This is a friendly and harmonious competition. Music and dance in ritual music are similar to gymnastics now. People sing and dance in music, marching and jumping, thus pursuing the harmony between body and soul, between people and between people and nature. "People’s Olympics" is the Olympics of cultural exchange, and the 2008 Beijing Olympic Games is a great handshake between the Olympic Games with a long history and the Chinese culture with a long history. The concept of order and harmony in China’s ritual and music civilization is a valuable idea dedicated to the world through the People’s Olympics. It will show the oriental charm of Chinese culture and convey to the world the beautiful wish of the people of China to maintain peace and develop together with the people of other countries.

Editor: Liu Li