According to the website of the General Administration of Market Supervision on the 29th, the General Administration of Market Supervision, the Ministry of Human Resources and Social Security, the Ministry of Commerce, the General Administration of Customs and the State Administration of Taxation issued the announcement of the Guidelines for Enterprise Cancellation (Revised in 2021). The full text is as follows:

　　Guidelines for Enterprise Cancellation (revised in 2021)

　　First, the basic procedures for enterprises to withdraw from the market

　　Usually, when an enterprise terminates its business activities and withdraws from the market, it needs to go through three main processes: resolution dissolution, liquidation distribution and cancellation of registration. Take a company as an example. According to the Company Law, before the company withdraws from the market and formally terminates, it must declare its dissolution, set up a liquidation team to carry out liquidation, clean up the company’s property, pay taxes, pay employees’ wages and social insurance fees, etc. After the liquidation, it should make a liquidation report, cancel the company registration and announce the company’s termination.

　　Second, dissolution

　　The dissolution of an enterprise is a legal act in which an enterprise stops its business activities and begins to enter liquidation procedures until it terminates its legal personality when there are legal reasons for dissolution.

　　(1) voluntary dissolution.Refers to the dissolution of the company based on the will of the enterprise or shareholders. Take the company as an example, including: the business term stipulated in the articles of association expires or other reasons for dissolution stipulated in the articles of association appear; The shareholders’ meeting or the shareholders’ meeting decides to dissolve; Dissolution due to merger or division of the company, etc. Among them, the resolution of the shareholders’ meeting of a limited liability company on the dissolution of the company must be passed by shareholders representing more than 2/3 of the voting rights; A resolution on the dissolution of the company at the shareholders’ meeting of a joint-stock company must be passed by more than 2/3 of the voting rights held by the shareholders present at the meeting. The dissolution of a wholly state-owned company must be decided by the state-owned assets supervision and administration institution; Among them, the dissolution of an important wholly state-owned company shall be audited by the state-owned assets supervision and administration institution and reported to the people’s government at the same level for approval.

　　(2) Compulsory dissolution.It refers to the dissolution based on the decision and order of the relevant government organs or the court’s ruling, which is not based on the company or shareholders’ own wishes. It is usually divided into administrative decision dissolution and judicial decision dissolution. Administrative decision to dissolve, the company is ordered to be dissolved by the administrative authority ex officio because its behavior violates laws and regulations and harms social public interests or public order, including its business license revoked, ordered to close down or revoked according to law. If the judicial decision is dissolved due to serious difficulties in the company’s operation and management, and the continued existence will cause great losses to shareholders’ interests, which cannot be solved by other means, the shareholders holding more than 10% of all shareholders’ voting rights of the company shall file a lawsuit to the people’s court to dissolve the company and request the people’s court to dissolve it.

　　Iii. liquidation

　　After the company makes a resolution of dissolution, it shall be liquidated. The important content of company liquidation is to clean up the company’s assets, settle all debts and end all existing legal relationships. The purpose of liquidation is to protect the interests of creditors, shareholders and public interests. Except for dissolution due to merger or division, the company shall be liquidated at the time of dissolution.

　　(1) Establish a liquidation group.The Company shall set up a liquidation group within 15 days from the date of dissolution, which shall be responsible for cleaning up the company’s property, creditor’s rights and debts. The liquidation group of a limited liability company is composed of shareholders of the company (if the shareholders of the company are legal persons, relevant personnel may be appointed to participate in the liquidation), and the liquidation group of a joint stock limited company is composed of directors or personnel determined by the shareholders’ meeting. If a liquidation group is not established for liquidation within the time limit, the creditor may apply to the people’s court to appoint relevant personnel to form a liquidation group for liquidation.

　　(2) Publish the information of the liquidation group and the creditors’ announcement.Within 10 days from the date of establishment of the liquidation group, the applicant shall announce the information of the liquidation group through the national enterprise credit information publicity system. At the same time, the liquidation group shall notify creditors within 10 days from the date of its establishment, and publish creditors’ announcements through newspapers within 60 days according to law, or publish creditors’ announcements to the society free of charge through the national enterprise credit information publicity system for 45 days.

　　(3) Carrying out liquidation activities.The liquidation group is responsible for clearing the company’s property and preparing the balance sheet and property list respectively; Handle the unfinished business of the company related to liquidation; Pay fines and penalties of administrative organs and judicial organs; Pay the taxes owed to the customs and tax authorities and the taxes generated in the liquidation process, and go through relevant procedures, including late payment fees, fines, payment of taxes that need to be paid in advance for the cancellation of customs supervision of goods with tax reduction or exemption, submission of relevant licenses that need to be reissued, cancellation and liquidation of enterprise income tax, settlement of land value-added tax, settlement of export tax refund (exemption), cancellation of invoices and tax control equipment, etc. Taxpayers who have tax-related violations shall accept punishment and pay fines; Clearing creditor’s rights and debts; Dispose of the company’s remaining property after paying off debts.

　　(4) distributing the company’s property;After clearing up the company’s property, preparing the balance sheet and property list, the liquidation group shall formulate the liquidation plan and report it to the shareholders’ meeting, shareholders’ meeting or the people’s court for confirmation. After paying the liquidation expenses, employees’ wages, social insurance fees and statutory compensation, paying the taxes owed and paying off the company’s debts, the remaining property of the company shall be distributed according to the proportion of shareholders’ capital contribution in a limited liability company and the proportion of shares held by shareholders in a joint stock limited company. During the liquidation period, the company shall survive, but shall not carry out business activities unrelated to liquidation. The company’s property shall not be distributed to shareholders before it is paid off in accordance with the provisions of the preceding paragraph.

　　(5) Making a liquidation report.After the liquidation, the liquidation group shall prepare a liquidation report, submit it to the shareholders’ meeting, the shareholders’ meeting or the people’s court for confirmation, and submit it to the company registration authority to apply for cancellation of company registration and announce the termination of the company.

　　Iv. cancellation of registration

　　(1) Ordinary cancellation process

　　The general cancellation process is applicable to all kinds of enterprises. After the liquidation, enterprises need to cancel tax registration, enterprise registration and social insurance registration respectively. Companies involved in customs declaration and other related businesses also need to handle matters such as filing and cancellation of customs declaration units.

　　1. Apply for cancellation of tax registration.

　　When a taxpayer applies to the tax department for cancellation, the tax department conducts a pre-inspection of tax cancellation to check whether the taxpayer has outstanding matters.

　　(1) If taxpayers who have not handled tax-related matters take the initiative to go to the tax authorities for tax clearance, the tax authorities can immediately issue tax clearance documents according to the business license provided by the taxpayers.

　　(2) Taxpayers who meet the conditions for immediate handling of vacancies, when handling tax cancellation, have complete information, and the tax authorities immediately issue tax clearance documents; If the information is not complete, the tax department can immediately issue a tax clearance document after making a promise. Taxpayers should complete the information and settle related matters according to the promised time limit. The specific tolerance conditions are:

　　(1) taxpayers who have handled tax-related matters but have not received invoices (including invoices issued on behalf of them), have no tax arrears (late fees) and fines, and take the initiative to go to the tax authorities for tax clearance;

　　② Taxpayers who are not in the state of tax inspection, do not owe taxes (late fees) and fines, have paid off special VAT invoices and tax control equipment, and meet one of the following circumstances:

　　● Taxpayers with tax credit rating of A and B;

　　● M-level taxpayers whose tax credit rating of the holding parent company is Grade A;

　　● Enterprises founded by the provincial people’s government to introduce talents or industry leaders recognized by industry associations at or above the provincial level;

　　● Regular fixed individual industrial and commercial households that are not included in the tax credit rating evaluation;

　　● Taxpayers who have not reached the VAT tax threshold.

　　(3) If the conditions for the immediate handling of the commitment system are not met (or if the conditions for the immediate handling of the commitment system are met, but the taxpayer is unwilling to commit), the tax department will issue a Notice of Tax Matters to the taxpayer (informing the taxpayer of the outstanding matters), and the taxpayer can apply for tax cancellation only after handling all the outstanding matters first.

　　(4) If the manager of an enterprise declared bankrupt by a ruling of the people’s court applies for tax cancellation with a ruling of the people’s court to terminate the bankruptcy procedure, the tax department will immediately issue a tax clearance document.

　　(5) Before the taxpayer handles the tax cancellation, it is not necessary to apply to the tax authorities for terminating the "Entrusted Deduction Agreement". After the tax authorities complete the tax cancellation, the entrusted deduction agreement will be automatically terminated.

　　2. Apply for cancellation of enterprise registration.The liquidation group shall submit an application for cancellation of registration, resolutions of shareholders’ meeting, liquidation report and tax clearance certificate to the registration authority to apply for cancellation of registration. If the registration authority and the tax authority have shared the enterprise tax clearing information, the enterprise does not need to submit paper tax clearing documents; Those who have received the original and duplicate of the paper business license shall return the original and duplicate of the business license. When a wholly state-owned company applies for cancellation of registration, it shall also submit the decision of the state-owned assets supervision and administration institution. Among them, the approval documents of the people’s government at the same level shall also be submitted for the important wholly state-owned companies identified by the State Council. When an enterprise with a branch applies for cancellation of registration, it shall also submit the certificate of cancellation of registration of the branch.

　　3. Apply for cancellation of social insurance registration.An enterprise shall, within 30 days from the date of cancellation of enterprise registration, submit an application for cancellation of social insurance registration and other relevant cancellation documents to the original social insurance registration institution, and go through the formalities for cancellation of social insurance registration. Before the cancellation of social insurance registration, the arrears of social insurance premiums shall be paid.

　　4. Apply for the record cancellation of the customs declaration unit.Enterprises involved in customs declaration-related business can submit applications for cancellation of customs declaration units to the customs through the "single window" of international trade (http://www.singlewindow.cn) and "internet plus Customs" (http://online.customs.gov.cn), or through the cancellation "one-net" service platform networked by the market supervision department and the customs. For taxpayers who have filed with the customs and have tax arrears (including late fees) and fines and other tax-related matters that have not been settled, they should apply to the market supervision department for cancellation of enterprise registration after the customs declaration unit has filed for cancellation.

　　(2) Simple cancellation process

　　1. Applicable objects

　　Market entities without creditor’s rights and debts or having paid off creditor’s rights and debts (except listed companies). When applying for simple cancellation of registration, market participants should not have debts such as unsettled liquidation expenses, employees’ wages, social insurance expenses, statutory compensation, and taxes payable (late fees and fines).

　　In any of the following circumstances, the simple cancellation procedure is not applicable to an enterprise: it involves a foreign-invested enterprise that implements special access management measures as stipulated by the state; Being included in the list of abnormal business operations of enterprises or the list of serious illegal and untrustworthy enterprises; The stock right (investment interest) is frozen, pledged or mortgaged by movable property; Being under investigation or taking administrative enforcement, judicial assistance or being given administrative punishment; The unincorporated branch of the enterprise has not gone through the cancellation of registration; The summary cancellation procedure has been terminated; Laws, administrative regulations or the State Council decisions require approval before cancellation of registration; Other circumstances that do not apply to the simple cancellation of registration of enterprises.

　　If an enterprise is "listed in the list of abnormal business operations", "its equity (investment interests) is frozen, pledged or mortgaged by movable property", and "the unincorporated branch of the enterprise has not cancelled its registration", it is not necessary to cancel the simple cancellation of registration. After the abnormal state disappears, it can apply for simple cancellation of registration through publicity again. If the letter and form of the letter of commitment are not standardized, the market supervision department will accept its simple cancellation application after the market subject makes corrections, and there is no need to re-publicize it.

　　Taxpayers who meet the conditions of simple cancellation by the market supervision department, have not handled tax-related matters, have handled tax-related matters but have not received invoices (including invoicing), have no tax arrears (late fees) and fines, and have no other tax-related matters that have not been settled, are exempted from going to the tax department for tax clearance certificates, and can directly apply to the market supervision department for simple cancellation.

　　2. Handling process

　　(1) Enterprises that meet the applicable conditions log in and cancel the "One Network" service platform or the column of "Simple Cancellation Announcement" of the national enterprise credit information publicity system actively announce to the public the information such as the proposed application for simple cancellation registration and the commitment of all investors, and the publicity period is 20 days.

　　(2) During the publicity period, relevant interested parties and relevant government departments can raise objections and briefly state the reasons through the function of "Objection Message" in the column of "Simple Cancellation Announcement" of the national enterprise credit information publicity system. After the publicity period, the publicity system will no longer accept objections.

　　(3) After the tax authorities obtain the information pushed by the market supervision department to apply for simple cancellation of registration through information sharing, they should check the tax information system to verify the relevant tax-related situation in accordance with the prescribed procedures and requirements, and the tax authorities will not raise any objection to taxpayers who are shown by the inquiry system as follows: First, taxpayers who have not handled tax-related matters; Second, taxpayers who have handled tax-related matters but have not received invoices (including invoices), have no tax arrears (late fees) and fines, and have no other tax-related matters that have not been settled; The third is the taxpayer who has completed the tax clearance procedures such as paying off the invoice and settling the tax payable at the time of inquiry.

　　(4) After the expiration of the publicity period, if there is no objection within the publicity period, the enterprise shall handle the simple cancellation of registration with the registration authority within 20 days from the date of the expiration of the publicity period. If it is not handled at the expiration date, the registration authority may extend the time limit according to the actual situation, and the maximum extension period shall not exceed 30 days. After publicity, enterprises shall not engage in production and business activities unrelated to cancellation.

　　3. Simple cancellation of individual industrial and commercial households

　　Individual industrial and commercial households registered after the implementation of the "integration of two certificates" reform of business license and tax registration certificate need not submit a letter of commitment or publicize it if they cancel their registration through summary procedures. After the individual industrial and commercial households submit the application for simple cancellation of registration, the market supervision department shall, within one working day, push the relevant information about the individual industrial and commercial households’ application for simple cancellation of registration to the tax authorities at the same level through the provincial unified credit information sharing and exchange platform, government information platform and inter-departmental data interface (collectively referred to as the information sharing and exchange platform), and the tax authorities will give feedback on whether they agree to simple cancellation within 10 days. If there is no objection to the tax authorities, the market supervision department shall handle the simple cancellation of registration in time. For details, please refer to the Notice of State Taxation Administration of The People’s Republic of China, General Administration of Market Supervision on Further Improving the Simple Cancellation Registration and Convenient Market Exit of Small and Medium-sized Enterprises (Guo Shi Jian Zhu Fa [2021] No.45).

　　V. Guidelines for handling special circumstances

　　(1) There are problems such as shareholders’ loss of contact and non-cooperation.If it is difficult to cancel the limited liability company due to the loss of shareholders’ association or non-cooperation, all shareholders shall be notified in writing and in newspapers (or the national enterprise credit information publicity system), and a shareholders’ meeting shall be held to form a resolution in accordance with the voting ratio stipulated by laws and articles of association, and a liquidation group shall be established, and then an application for cancellation of registration shall be made to the enterprise registration authority.

　　(2) There is a problem that enterprises cannot organize liquidation by themselves.For a company that has been dissolved, but the investors with liquidation obligations refuse to perform the liquidation obligations or cannot set up a liquidation group for liquidation due to the inability to get in touch, the relevant shareholders or creditors may apply to the people’s court to appoint relevant personnel to form a liquidation group for liquidation in accordance with the provisions of the Company Law. After clearing up the company’s assets, compiling the balance sheet and list of assets, the liquidation group finds that the company’s assets are insufficient to pay off debts, and shall apply to the people’s court for bankruptcy according to law. If the people’s court ruled that compulsory liquidation or bankruptcy was declared, the enterprise liquidation group and the bankruptcy administrator may directly apply to the registration authority for cancellation of registration with the ruling of the people’s court to terminate the compulsory liquidation procedure or the bankruptcy procedure.

　　(3) The business license and official seal are lost.For enterprises that have lost their business licenses, they can apply to the enterprise registration authority for cancellation with the announcement of the loss of licenses publicized by themselves in the national enterprise credit information publicity system, without applying for a new business license. Where the official seal is lost, it shall be signed and sealed by all shareholders or signed and confirmed by the person in charge of the liquidation group. For an unincorporated enterprise as a legal person, the legal representative of the superior competent unit shall sign and affix the official seal of the superior competent unit for confirmation, and the relevant cancellation materials may not be affixed with the official seal.

　　(4) The shareholder (investor) has been cancelled.For an enterprise whose shareholders (investors) have cancelled but failed to clean up the foreign investment, and the invested enterprise cannot cancel, if its shareholders (investors) have a superior competent unit, the superior competent unit of the cancelled enterprise shall handle the relevant cancellation procedures in accordance with the regulations; If the cancelled enterprise has a legal successor, the successor may apply for it in accordance with the relevant provisions; If the cancelled enterprise has no legal successor, the shareholder (investor) registered at the time of cancellation of the cancelled enterprise shall apply for handling.

　　(5) Other issues.

　　1. For enterprises whose business licenses loaded with unified social credit codes have been revoked without replacement, the market supervision department has assigned codes to such enterprises, and enterprises can use their unified social credit codes to handle cancellation business in relevant departments without replacing their business licenses loaded with unified social credit codes.

　　2. A taxpayer whose business license is revoked by the registration authority or whose registration is revoked by other authorities shall, within 15 days from the date when the business license is revoked or its registration is revoked, apply to the original tax registration authority for tax cancellation.

　　3. Before going through the tax cancellation, taxpayers in abnormal tax state need to remove the abnormal state and go through the tax declaration formalities. In case of any of the following circumstances, the tax authorities may print the corresponding tax types and the relevant additional Confirmation Form for Batch Zero Declaration, which will be processed in batches after being confirmed by taxpayers:

　　(1) During the abnormal state, the value-added tax, consumption tax and related additional declarations that need to be reissued are all zero declarations;

　　(2) During the abnormal state, the monthly (quarterly) advance payment of enterprise income tax required to be reissued is zero, and there is no situation to make up for the previous losses.

　　VI. Prompt for Cancellation of Legal Liability

　　(1) When the company is liquidated, the liquidation group fails to perform the obligation of notification and announcement in accordance with the regulations, resulting in creditors’ failure to declare their claims in time and not being paid off, and the members of the liquidation group shall be liable for the losses caused thereby. (According to Article 11 of the Supreme People’s Court on Several Issues Concerning the Application of the Company Law of People’s Republic of China (PRC))

　　(2) If the liquidation group’s execution of unconfirmed liquidation plan causes losses to the company or creditors, and the company, shareholders or creditors claim that the members of the liquidation group shall be liable for compensation, the people’s court shall support it according to law. (According to Article 15 of the Supreme People’s Court on Several Issues Concerning the Application of the Company Law of People’s Republic of China (PRC))

　　(3) If the shareholders of a limited liability company, the directors and controlling shareholders of a joint stock limited company fail to set up a liquidation group to start liquidation within the statutory time limit, resulting in the depreciation, loss, damage or loss of the company’s property, and the creditors claim that they are liable for the company’s debts within the scope of losses, the people’s court shall support them according to law. (According to the provisions of the Supreme People’s Court on Several Issues Concerning the Application of the Company Law of People’s Republic of China (PRC) (II), Paragraph 1 of Article 18)

　　(4) If the shareholders of a limited liability company, directors and controlling shareholders of a joint stock limited company fail to perform their obligations, resulting in the loss of the company’s main property, account books, important documents, etc., and the creditors claim that they are jointly and severally liable for the company’s debts, the people’s court shall support them according to law. (According to the provisions of the Supreme People’s Court on Several Issues Concerning the Application of the Company Law of People’s Republic of China (PRC) (II), Paragraph 2 of Article 18)

　　(5) If the shareholders of a limited liability company, the directors and controlling shareholders of a joint stock limited company and the actual controller of the company maliciously dispose of the company’s property after the dissolution of the company, causing losses to creditors, or defrauding the company registration authority to cancel the registration of a legal person with a false liquidation report without liquidation according to law, and the creditors claim that they should bear corresponding liability for compensation for the company’s debts, the people’s court shall support them according to law. (According to Article 19 of the Supreme People’s Court on Several Issues Concerning the Application of the Company Law of People’s Republic of China (PRC))

　　(6) The company shall apply for cancellation of registration after liquidation according to law. If the company cancels its registration without liquidation, which makes it impossible for the company to liquidate, and the creditors claim that the shareholders of a limited liability company, the directors and controlling shareholders of a joint stock limited company, and the actual controller of the company shall be liable for paying off the debts of the company, the people’s court shall support it according to law. (According to the provisions of the Supreme People’s Court on Several Issues Concerning the Application of the Company Law of People’s Republic of China (PRC) (II), Paragraph 1 of Article 20)

　　(7) If the company goes through the cancellation of registration without liquidation according to law, and the shareholders or the third party promise to be liable for the company’s debts when the company registration authority goes through the cancellation of registration, and the creditors claim that they should bear corresponding civil liabilities for the company’s debts, the people’s court shall support them according to law. (According to the provisions of the Supreme People’s Court on Several Issues Concerning the Application of the Company Law of People’s Republic of China (PRC) (II), Paragraph 2 of Article 20)

　　(8) When the company’s property is insufficient to pay off the debts, if the creditors claim that the shareholders who have not paid their capital contributions, and other shareholders or promoters at the time of the establishment of the company shall bear joint and several liabilities for paying off the debts of the company within the scope of unpaid capital contributions, the people’s court shall support them according to law. (According to the provisions of the Supreme People’s Court on Several Issues Concerning the Application of the Company Law of People’s Republic of China (PRC) (II), Paragraph 2 of Article 22)

　　(9) If a member of the liquidation group violates laws, administrative regulations or the company’s articles of association and causes losses to the company or creditors, the people’s court shall support him according to law. (According to the provisions of the Supreme People’s Court on Several Issues Concerning the Application of the Company Law of People’s Republic of China (PRC) (II), Paragraph 1 of Article 23)

　　(10) If an enterprise conceals the real situation or practices fraud in the cancellation of registration, the registration authority may cancel the cancellation of registration according to law, and at the same time, the enterprise will be included in the list of enterprises that are seriously illegal and untrustworthy, and will be publicized through the national enterprise credit information publicity system. Relevant interested parties can claim their corresponding rights through civil litigation. (According to Article 64 of the Regulations on the Administration of Company Registration and Article 10, paragraph 2, of the Measures for the Administration of the List of Serious Violations and Dishonesty in Market Supervision and Management)

　　(eleven) the taxpayer fails to declare the cancellation of tax within the prescribed time limit, and the tax authorities shall order it to make corrections within a time limit and may impose a fine of less than two thousand yuan; If the circumstances are serious, a fine of not less than two thousand yuan but not more than ten thousand yuan shall be imposed. (According to Paragraph 1 of Article 60 of the Law on the Administration of Tax Collection)

　　(12) A taxpayer who forges, alters, conceals or destroys account books and vouchers without authorization, or overstretches expenditures or omits or understates income in account books, or refuses to declare or makes false tax returns after being notified by the tax authorities, and fails to pay or underpays the tax payable, is tax evasion. If a taxpayer evades taxes, the tax authorities shall recover the taxes and late fees that he fails to pay or underpays, and impose a fine of not less than 50% but not more than five times the taxes that he fails to pay or underpays; If a crime is constituted, criminal responsibility shall be investigated according to law. (According to the first paragraph of Article 63 of the Law on the Administration of Tax Collection)

Several main statistics of the results of the second national population census

(1964)

　　 (1) Total population

　　　 At 24: 00 on June 30, 1964, the national population was 723,070,269. The population of 28 provinces, municipalities and autonomous regions (Tianjin was then affiliated to Hebei Province) and active servicemen was 694,581,759, including 356,517,011 men, accounting for 51.33%; There are 338,064,748 women, accounting for 48.67%. The population of Taiwan Province, Hong Kong and Macao compatriots and overseas Chinese is 28,488,510.

　　　 The population of each province, city and autonomous region is as follows: (unit: people)

　　　 Beijing 7,568,495
　　　 Hebei Province 45,687,781
　　　 Inner Mongolia Autonomous Region 12,348,638
　　　 Shanxi Province 18,015,067
　　　 Liaoning Province 26,946,200
　　　 Jilin Province 15,668,663
　　　 Heilongjiang Province 20,118,271
　　　 Shanghai 10,816,458
　　　 Jiangsu Province 44,504,608
　　　 Zhejiang Province 28,318,573
　　　 Anhui Province 31,241,657
　　　 Jiangxi Province 21,068,019
　　　 Fujian Province 16,757,223
　　　 Shandong Province 55,519,038
　　　 Guangdong Province 42,800,849
　　　 Guangxi Zhuang Autonomous Region 20,845,017
　　　 Hunan Province 37,182,286
　　　 Hubei Province 33,709,344
　　　 Henan Province 50,325,511
　　　 Sichuan Province 67,956,490
　　　 Yunnan Province 20,509,525
　　　 Guizhou Province 17,140,521
　　　 Xizang Autonomous Region 1,251,225
　　　 Shaanxi Province 20,766,915
　　　 Gansu Province 12,630,569
　　　 Qinghai Province 2,145,604
　　　 Xinjiang Uygur Autonomous Region 7,270,067

　　 (2) Population of all ethnic groups

　　　 On June 30, 1964, there were 651,296,368 Han people in 28 provinces, municipalities and autonomous regions, accounting for 94.22% of the total population. The population of ethnic minorities is 39,883,909, accounting for 5.78%.

　　　 Ethnic groups with a population of more than one million are: Mongolian 1,965,766; 4,473,147 Hui people: 2,501,174 Tibetans; 3,996,311 Uighurs; 2,782,088 Miao people; 3,380,960 Yi people; 8,386,140 Zhuang people; 1,348,055 Buyi people; 1,339,569 Koreans; There are 2,695,675 Manchu people.

　　 (3) Population age

　　　 On June 30, 1964, the working-age population in China (men aged 16 to 59 and women aged 16 to 54) was 341,491,424, accounting for 49.17% of the total population.

　　　 The population under the age of 1 to 14 is 280,671,035, accounting for 40.4% of the total population. Among them: 114,287,925 school-age children aged 7 to 12; There are 135,422,127 children under 6 years old. The population over 61 is 38,171,010, accounting for 5.5% of the total population. There are 4,900 people over 100 years old (2,134 men and 2,766 women). The highest age is 150 years old, and there is one person.

　　 (4) Education level of the population

　　　 On June 30, 1964, among the population of 28 provinces, municipalities and autonomous regions, there were 2,875,401 people with university education, 9,116,831 people with high school education, 32,346,788 people with junior high school education and 195,824,459 people with primary school education.

　

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I. Literature sources

Taubenberger J　K, Morens D　M. 1918 influenza: the mother of all pandemics[J]. Emerging infectious diseases, 2006, 12(1):15-22.

The literature was published in the American CDC academic journal Emerging Infectious Diseases, January 2006, Volume 12, No.1, with the title "1918 Influenza: Mother of All Pandemic Diseases". （ www.cdc.gov/eid）

II. Introduction to the author

Dr. Taubenberger: Director of Molecular Pathology, United States Army Pathology Institute, Rockville, Maryland. The research direction is the molecular pathophysiology and evolution of influenza virus.

Dr Morens: epidemiologist, working for the American institute of allergy and infectious diseases. His research interests are emerging infectious diseases, virology, tropical medicine and medical history.

foreword

From 1918 to 1919, Spanish influenza caused about 50 million deaths in the world, and it is still an ominous haze of public health. There are still many unanswered questions about the origin, such as unusual epidemiological characteristics and main pathogenic factors. Although we are now trying to overcome the spread of pandemics such as H5N1 or other viruses, the impact of the 1918 influenza on public health is still uncertain. The information of the 1918 influenza is still being updated, such as sequencing the whole genome from the autopsy in the archives, but the virus genome alone cannot answer the key questions. To understand the 1918 flu and its impact on the future, we need detailed experiments and in-depth historical analysis. Tip: The number of words in the full text is 7279, and it takes an average of 15 minutes to finish reading.

background

During the 1918-1919 flu, about one third of the world’s population (about 500 million people) was infected and developed clinical symptoms. The pandemic is more serious than expected. Compared with the mortality rate of other pandemics (< 0.1%), the mortality rate of influenza in 1918 was > 2.5%. It is estimated that the total death toll is about 50 million, and the pessimistic view is as high as 100 million.

The influence of 1918 influenza was not limited to 1918-1919. Since then, almost all influenza A (except avian influenza virus, such as H5N1 and H7N7) in the world are descendants of 1918 influenza virus, including drifting H1N1, recombinant H2N2 and H3N2. The latter is the integration of the key genes of the 1918 influenza by the later avian influenza, thus expressing new proteins. It can be said that the 1918 flu is the mother of all pandemics.In 1918, it was unclear how human influenza was related to avian influenza and swine flu. Although the clinical and epidemiological characteristics are similar to those of influenza pandemics in 1889, 1847 or even earlier, the high mortality rate makes many people wonder whether it should be called influenza. This problem was not solved until 1930, when the influenza virus (now called H1N1) was isolated from pigs, and later it was also isolated from humans. Seroepidemiological studies soon linked the virus with the 1918 flu. Subsequent research shows that the offspring of 1918 virus has always existed in pigs, and may still appear in humans continuously, experiencing the continuous iteration of antigenic drift, and leading to an annual epidemic outbreak until the 1950s. In 1957, a new H _ H2N2 epidemic (namely "Asian influenza") began to appear, and the H1N1 virus, the offspring of the 1918 virus, completely disappeared from the human circulation, although the related pedigree was still attached to pigs. But in 1977, it suddenly "reappeared" from the laboratory freezer and began to be popular among humans.
In 2006, two natural lineages and two recombinant lineages of the offspring of 1918 virus became popular: human H1N1, swine H1N1 (swine flu), recombinant human H3N2 and recombinant swine H3N2, but none of the offspring was close to the pathogenicity of 1918 virus. Swine strains H1N1 and H3N2 rarely infect humans, while the morbidity/mortality of human strains H1N1 and H3N2 are lower than that of 1918 virus.In fact, the fatality rate of natural H1N1 is even lower than that of H3N2 (prevalent since 1968). The H1N1 and H3N2 viruses originated from the 1918 influenza have been prevalent all over the world for 29 years, and there are almost no signs of extinction.

First, try to understand what happened?

By the early 1990s, 75 years of research had failed to answer the most basic question of the 1918 flu: Why was it so deadly? People didn’t isolate any virus from the 1918 influenza epidemic, but their descendants continued to invade humans slightly. A follow-up survey of influenza epidemic in the 1920s showed that in the years after 1918, influenza epidemic became an annual epidemic with low mortality due to gene drift. Did one genetic event greatly reduce the pathogenicity of the 1918 virus, and then another genetic event turned the 1918 virus into a weaker H1N1 virus?

In 1995, a scientific team determined the autopsy materials of influenza in the autumn of 1918 from the archives, and began a long sequencing experiment on small RNA virus fragments, so as to deduce the whole genome of the 1918 virus. At present, the whole genome of one virus and partial gene sequences of four other viruses have been determined. The above experiments and a series of other articles related to 1918 virus have confirmed that 1918 virus is most likely the ancestor of human/pig H1N1, H3N2 and extinct H2N2. No mutation related to the genome of 1918 virus has been found in other highly pathogenic influenza viruses of human or animals, but the continuous study on virulence factors has produced some interesting results. Nevertheless, the 1918 gene sequence data can not answer the origin and epidemiological characteristics of the virus.

Second,When and where did the 1918 flu begin to spread?

Before and after 1918, most influenza pandemics originated in Asia and spread all over the world.During the 12-month period from 1918 to 1919, the 1918 flu spread more or less simultaneously from three regions: Europe, Asia and North America (the first wave is thought to have started in the United States in March 1918). Historical and epidemiological data are not enough to identify the geographical origin of the virus, and the recent 1918 gene system research can not analyze the geographical origin.

Although there was no national influenza disease reporting system in 1918, and the diagnostic criteria for influenza and pneumonia were not clear, since December 1915, there was an epidemic of respiratory diseases in the United States, and the mortality rate of influenza and pneumonia rose sharply in 1915 and 1916, and then decreased slightly in 1917. The first wave of influenza pandemic appeared in the spring of 1918, and the second wave and the third wave of influenza pandemic with higher mortality rate appeared in the autumn of 1918 and the winter of 1919 respectively, as shown in Figure 1.

Is it possible that the weak-adaptability H1N1 virus had spread in 1915, and although there were some serious diseases, it had not caused a pandemic?At that time, data consistent with this was also reported from European military camps, but the opposite conclusion was given: if the virus strain with new hemagglutinin (HA) affected the mortality rate of influenza and pneumonia in the United States, it should have caused a pandemic long ago, and someone should be immunized or at least partially immunized by 1918. It is difficult to determine that the "pioneer" events of the 1918 flu came from 1915, 1916 or even early 1918.

Figure 1 Three waves of epidemics: the weekly mortality rate of influenza and pneumonia in Britain from 1918 to 1919.

Another unique feature of the 1918 influenza pandemic was that people and pigs were infected almost at the same time.The 1918 virus probably expressed a new subtype of antigenicity, which led to the low immunity of most people and pigs. Recently published genetic studies show that hemagglutinin (HA) and neuraminic acid (NA) expressed by the 1918 virus gene were probably derived from the avian influenza virus shortly before the start of the pandemic, and the precursor virus failed to spread widely in humans or pigs for decades. More recent reports of the virus gene sequence and phylogenetic analysis of the virus also support this conclusion. Regression analysis of human/swine flu sequences from 1930 to the present shows that the precursor of 1918 virus first spread in humans from 1915 to 1918. Therefore, the precursor of the 1918 virus may have spread widely among humans before 1918, and so far no research has directly indicated the transition from any bird. In a word, its origin is still confusing.

Are the three waves of epidemics from the same virus?

Historical records since the 16th century show that a new influenza pandemic may occur at any time of the year, which is not necessarily the regular pattern in winter every year, because the behavior pattern most likely from the new influenza has been found among infected people. After that, these pandemic viruses began to drift in the face of the selective pressure of population immunity, and eventually the pattern of annual epidemic recurrence was triggered by drifting virus mutants.

During the 1918-1919 pandemic, the first spring tide began in March 1918 and spread to the United States, Europe and even Asia in different degrees in the next six months. The prevalence rate was very high, but the mortality rate in most areas was not significantly higher than the normal value. The second wave of autumn tide began in September-November, 1918, and it spread rapidly around the world and was fatal. The third wave of epidemic began in early 1919. According to the clinical similarity, some contemporary observers have come to the conclusion at the beginning that the three epidemics should be caused by the same disease: the mild symptoms in the three epidemics are the same, and they have the typical flu characteristics of the 1889 pandemic and earlier pandemics. However, in retrospect, there are few cases in which the first wave of spring tide developed rapidly from simple influenza to fatal pneumonia, and fatal pneumonia is the symbol of the last two waves of epidemic tide; Comparatively speaking, the frequency of complex, serious and fatal cases in the last two waves will be higher.

It is unprecedented for three large-scale epidemics to occur in a year. To some extent, the antigenic drift of the virus is the reason why it keeps recurring every year, and an antigenic virus variant appears about every 2 ~ 3 years. If there is no drift characteristic, once the immunity of human/livestock reaches the critical threshold, the influenza virus may disappear, and under this critical threshold, the further spread of the virus is limited. For decades, people have been speculating about the time and space between influenza pandemics. In addition to human/livestock immune restrictions, the factors of virus transmission include low ambient temperature, nasal cavity temperature (which is beneficial to heat-labile viruses, such as influenza), suitable humidity, indoor congestion and poor ventilation.
However, none of the above factors can explain the three waves of epidemic in 1918-1919, which occurred in spring and summer, summer and autumn and winter respectively. The first two waves occur at the time of unfavorable influenza transmission every year; The second wave broke out in the northern hemisphere/southern hemisphere from September to November; In addition, the period between epidemic tides is so short that it is almost impossible to detect in some areas. It is difficult for epidemiology to explain the sharp decline of cases between the first wave and the second wave, and the sharp rise of cases between the second wave and the third wave. Even assuming that the acquired immunity after infection is short-lived, there are too few susceptible people to maintain the spread at one point. How can a new explosive pandemic be triggered in a few weeks? Will the virus mutate completely at the same time in almost a short time around the world?
However, according to scientific experience, it takes several years for influenza virus to spread globally, not just a few weeks. Moreover, even the mutant that has drifted will take several months to spread around the world. Other influenza pandemics have not been reported continuously within one year. For example, the 1889 flu began in the late spring of 1889, and it took several months to spread around the world, reaching its peak in northern Europe and the United States in late 1889 or early 1890; The second recurrence occurred in late spring of 1891 (one year late) and the third in early 1892. Like the 1918 flu, more people died when the second epidemic wave recurred, but the spread time of the three epidemics in 1889-1892 was more than three years, while the spread time of the successive epidemics in 1918-1919 was compressed to August-September.The ability of the 1918 influenza to rapidly develop a continuous pandemic is still unknown. Because the autopsy materials we identified only came from the second wave of 1918 influenza, it is inconclusive whether the first wave or the third wave also came from the same virus or mutant. The experimental data show that the second wave of infected people may have obtained immune protection during the third wave of epidemic, but the data is not enough to support whether the second/third wave of infected people obtained immune protection from the first wave of epidemic, nor can they answer the question whether the three waves of epidemic came from the same virus or mutant. Only by getting the RNA positive samples of infected people before 1918 and the three waves of epidemic in 1918 can we answer this question.

4. Did the 1918 virus host come from animals?

The data of 1918 virus gene sequence shows that the whole genome may be new to human beings in 1918 or not long ago. It was not produced by recombining one or more new genes from previous viruses (unlike the 1957 or 1968 epidemic). On the contrary, the 1918 virus seems to be derived from an unknown source of avian influenza virus (eight gene fragments are different from the current avian influenza genes). The gene sequence of influenza virus collected from wild bird specimens around 1918 is not much different from that of today’s avian influenza virus, which indicates that even for a long time, the antigenic changes of avian influenza virus may hardly occur in natural reservoir.

For example, the sequence of 1918 nucleoprotein (NP) gene is similar to the virus in wild birds in amino acid level, but it is very different in nucleotide level, which indicates that the source of 1918 nucleoprotein is far from the virus nucleoprotein in wild birds at present. One way to check the evolutionary distance of genes is to compare the ratio of synonymous nucleotides to non-synonymous nucleotides. Synonymous substitution means that the nucleotide change in the sequence will not lead to amino acid substitution; Non-synonymous substitution means that nucleotide changes will lead to amino acid substitution. Generally speaking, viruses under immune drift pressure or adapting to new hosts show a larger proportion of non-synonymous mutations, while viruses under minimal pressure mainly accumulate synonymous substitutions, which are considered to reflect the evolutionary distance.

Because the 1918 influenza virus gene fragments known from wild birds have more synonymous substitutions than expected, they are unlikely to come directly from viruses similar to avian influenza virus. One of them is particularly obvious. When people check the 4-fold degenerate codons (a subset of synonymous substitutions), they find that the third codon can replace any of the 4 nucleotides without changing the amino acids. At the same time, although the 1918 virus has been adapted to the intermediate host of human/pig for many years, the amino acid level of its sequence is still very small compared with that of wild birds. One possible explanation is that these abnormal gene fragments were obtained from an unidentified influenza virus database.All these findings lead to a question: Where did the 1918 virus come from?

Contrary to the 1918 virus, the gene fragments of the recombinant viruses of 1957 and 1968 influenza were from Eurasian avian influenza virus. Both human viruses are produced by the same mechanism: it is the recombination of Eurasian avian influenza virus and the previously popular human H1N1 virus. To prove the origin of the 1918 virus, samples more similar to the 1918 virus sequence are needed: samples before the 1918 virus epidemic and wild epidemic samples.

5. What is the biological basis of the pathogenicity of the 1918 virus?

Single gene sequence analysis can not provide the cause of pathogenicity of 1918 virus. Through a series of in vitro/animal model experiments, the researchers tried to model the virulence of the virus constructed by reverse gene.

Influenza virus infection requires HA protein to bind to sialic acid receptors on the surface of host cells.However, the configuration of HA receptor binding site of influenza virus suitable for avian infection is different from that of influenza virus suitable for human infection. Avian influenza virus preferentially binds sialic acid receptor with α(2-3) linked sugar; Human influenza virus is considered to preferentially use α(2-6) linked sugar. This avian receptor configuration can be transformed into infection only by changing one amino acid, while the HA protein of five sequenced 1918 viruses has this change, which is probably a key step to adapt to human hosts. There is also a second possibility that three of the five sequenced 1918 viruses have another change in their HA sequence that enhances the binding of human receptors.

This means that at least two H1N1 receptor-binding mutants spread in 1918: one shows high affinity with human receptor and the other shows mixed high affinity with avian/human receptor. But there is no geographical or chronological indication that one of the variants is the precursor of the other.Did these viruses have the same transmission ability in 1918, did they have the same replication pattern in the respiratory tree, and did they spread the same virus in the first and third epidemics? Are unknown.

In a series of in vivo experiments, recombinant genes containing gene fragments 1 and 5 of 1918 virus have been produced. These recombinants with 1918 HA/NA showed high pathogenicity in mice. In addition, the microarray analysis of gene expression in lung tissue of these mice showed that cell apoptosis, tissue damage and oxidation were all related to the expression of such genes. These findings are unexpected, because the virus with 1918 gene has not adapted to mice; The control group (mice infected with other modern human viruses) showed little pathogenicity and virus replication. Mice infected with 1918 HA/NA recombinant showed necrosis of bronchial and alveolar epithelium and obvious inflammatory infiltration in their lungs, which indicated that 1918 HA (and possibly NA) contained pathogenic factors for mice. It is not clear whether the pathogenicity of mice can effectively simulate the pathogenicity of humans, and the potential role of other 1918 single or combined proteins is not clear. The researchers plan to further draw the genetic basis of the toxicity of the 1918 virus on other animal models. These experiments may help to determine the pathogenic components of the 1918 virus, but it is impossible to determine whether it is the main factor in the death pattern of the 1918 influenza.

Why did the 1918 virus kill so many healthy young people?

From the historical experience, the flu death curve by age has been U-shaped for at least 150 years (Figure 2), which shows the peak of death in childhood and old age, and the death rate in the middle age group is lower. On the contrary, the 1918 flu showed a unique pattern, a "W-shaped" curve that had never been recorded, and there was another death peak among people aged about 20-40.During 1918-1919, the mortality rate of people aged 15-34 suffering from influenza and pneumonia was more than 20 times higher than in previous years. Nearly half of the 1918 flu deaths came from people aged 20-40, which was unique to the 1918 flu.

Another unique point is that the mortality rate of people under 65 years old is much higher than that of people over 65 years old, and it accounts for 99% of the flu deaths in 1918. In comparison, the mortality rate of people under 65 years old accounted for 36% of the 1957 H2N2 influenza and 48% of the 1968 H3N2 influenza.

　

Figure 2 Mortality rate of influenza and pneumonia per 100,000 population of all ages in the United States from 1911 to 1918.

Further dividing the influenza mortality curve by age, we can clearly see that the prevalence rate of people under 35 years old is very high (Figure 3-a), but there is still a W-shaped death peak among young people, which is obviously different from the U-shaped curve of influenza in 1928-1929 (Figure 3-c). The same 1918 flu, the prevalence rate of 5 ~ 14 years old is also high, but the mortality rate is much lower (Figure 3-a/b). In order to explain this model, we must jump out of the host and environmental factors and look further, which may include immunopathological factors (such as increased antibody-dependent infection associated with virus exposure) and other risk factors (such as concurrent infection, drugs used and environmental factors). See figure 3.

Fig. 3 Community survey results of American public health institutions in 8 states in 1918.
Note: Figures A, B and C show the prevalence rate, mortality rate and mortality rate of influenza and pneumonia in different age groups respectively.

There is a theory that can partially explain these findings. The 1918 virus is highly toxic, but for patients born before 1889, that is, people who are over 35 years old and have been exposed to the virus at that time, they have obtained partial immune protection against the 1918 virus. But there is a paradox in this theory: this nameless virus precursor must have appeared before 1889, and then reappeared 30 years later, but no trace has been found today.

Epidemiological data collected from 1900 to 1918 provided good evidence for the emergence of a new antigenic virus in 1918. It shows that from 1900 to 1917, the age group of 5 to 15 years old accounted for 11% of the total number of influenza cases, while the age group over 65 years old accounted for 6% of the total number of influenza cases. However, in 1918, the age group of 5-15 years jumped to 25% of the total number of influenza cases, while the age group over 65 years accounted for only 0.6% of the total number of influenza cases. This is consistent with the results of protective immunity obtained by previous exposure to the same or related viruses, and the mortality data is also consistent. In 1918, the number of deaths from influenza and pneumonia in the age group over 75 was less than that in 1911-1917 before the pandemic. At the other end of the age group (Figure 2), the infant mortality rate in 1918 was similar to other pandemic patterns.

Will the 1918 flu reappear? If so, what should I do?

As far as the course of disease and pathology are concerned, the 1918 influenza pandemic is different from the historical pandemic only in degree, not in species.Despite the large number of deaths worldwide, most infected people (> 95% from industrialized countries) are mild, which is not much different from today’s influenza. In addition, the experimental results of recombinant influenza virus containing 1918 virus gene show that 1918 virus and 1918-like virus are as sensitive to the anti-influenza drugs rimantadine and oseltamivir (approved by FDA) as other typical influenza viruses.

However, the 1918 flu has some characteristics of its own: in particular, the mortality rate is 5 ~ 20 times higher than expected. From the clinical and pathological point of view, these high mortality rates seem to be caused by many factors, including a higher proportion of severe respiratory infections (organ failure not caused by influenza); In addition, death cases are concentrated in an unusually young age group; Finally, in 1918, three influenza epidemics appeared one after another at an unusually rapid speed. Each feature may reflect the genetic characteristics of the 1918 virus, but to understand them, it is necessary to check the host and environment.

Until we can’t determine which factors lead to the influenza pandemic and high mortality rate, these can only be guesses. We can only come to the conclusion that since it has happened before, similar conditions may lead to the same serious pandemic.

Like the virus in 1918, H5N1 is an avian virus, although it is a distant relative. The reasons for the evolutionary path of the 1918 pandemic are completely unknown, but it seems to be different from the current H5N1 situation in many aspects. No matter the 1918 pandemic or any other infectious disease pandemic, there is no historical data showing the existence of a pandemic "precursor virus", which led to the outbreak of highly pathogenic infection in poultry; There is no historical data to prove that highly pathogenic avian influenza (HPAI) virus, including other virus subtypes such as H5N1, can cause human epidemics, let alone pandemics.

Effective human-to-human transmission is the main prerequisite for the emergence of pandemic.Although the adaptation of influenza viruses to human cells (such as receptor binding) has begun to be understood at the molecular level, how various influenza viruses adapt to humans is not completely clear at present. In 1918, the virus acquired the characteristics of adapting to human beings, but at present, we have no way to know whether the H5N1 virus will acquire the ability of human-to-human transmission in a parallel process. Although the data about the 1918 virus has increased geometrically in the past ten years, we don’t know much more about the 2006 influenza pandemic than about the risk of the 1976 H1N1 "swine flu" epidemic.

Even with modern antiviral drugs, vaccines, and knowledge of infectious disease prevention, if there is another virus like 1918, it may still kill more than 100 million people all over the world. An outbreak of a pandemic virus with high pathogenicity potential, such as the recent H5N1 virus, may cause more deaths.

No matter the virus, host or environmental factors, the virus of the first wave in 1918 had nothing to do with the abnormal pathogenicity of the second and third waves. And more, identify the virulence models of the first wave of influenza RNA positive cases from different gene sequences; Identification of human influenza RNA samples before 1918 is helpful to understand the time when the 1918 virus appeared; The observation and sequencing of a large number of animal influenza viruses will help us to understand the genetic basis of adapting to the host and the natural reservoir range of influenza. Generally speaking, it is necessary to have a comprehensive understanding of the 1918 influenza from the aspects of history, epidemiology and biology in order to answer many unsolved mysteries.

Acknowledgement:This article was reviewed by Dr. Zhu Xun, a famous immunologist and an expert of the former National New Drug Advisory Committee. I sincerely thank Mr. Zhu for his careful guidance!

Translation: Shi Junxin　

Editor: Ginger

CCTV News:What you are looking at now is the Yunnan Huangguo Abies forest located in Chayu County, Linzhi City, southeast Tibet. These firs are very tall, and the tallest one is 83.2 meters high, which is equivalent to the height of 28 floors. Chayu has a warm climate and lush vegetation, with a forest area of more than 1.696 million hectares. A large number of rare wild animals and plants inhabit and grow here, and biodiversity is effectively protected.

　　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"

Read the original text

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.

In the first three quarters, the gross domestic product (GDP) was 87,026.9 billion yuan, up 3.0% year-on-year, 0.5 percentage points faster than that in the first half of the year, and the economy as a whole showed a recovery trend. Among them, GDP in the third quarter increased by 3.9% year-on-year, 3.5 percentage points faster than that in the second quarter.

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.

According to the Shandong Food and Drug Administration, for more than five years, Pangmou and her daughter bought 25 kinds of vaccines for human use, such as influenza and hepatitis B, at low prices from salesmen or vaccine dealers of pharmaceutical companies, and sold them to 24 provinces and cities at a higher price without strict cold chain storage and transportation, valued at 570 million yuan. On the evening of March 19, 2016, Shandong Food and Drug Administration announced that it had sorted out 107 online clues to provide vaccines and biological products to Pang and others, and 193 offline clues to purchase vaccines and biological products from Pang and others, involving 24 provinces and cities across the country.

Suitable target: products of 0-2 years old.

Reading duration: about 5 minutes.

Banner refers to banner advertising, which is the most common form of mobile advertising. It generally appears at the top or bottom of the APP interface, including static pictures, GIF pictures, text chains, and animated pictures with multi-frame pictures scrolling.

• Formally, Banner can be divided into static banner, animated banner and interactive banner.
• From the content, Banner can be divided into: pure pictures, graphics and text, and pure text.

Generally, the billing method is mainly based on CPC (cost per click), and the unit price is about 30 cents, and the price fluctuates greatly. It is more common for pure tool apps to use the bottom banner. For example, the air quality APP below.

On the homepage of e-commerce or community-based apps, there are a lot of advertisement spots in the form of announcements. The following picture is a screenshot of the homepage of JD.COM Mall APP, and that JD.COM Express is an announcement, sometimes called a trumpet. The advertising information is continuously scrolled and played.

Screen advertisements are more common in game or video apps, such as the Defending Radish APP in the picture below. Screen-inserted advertisements are also divided into static pictures and GIF pictures, which are generally accurate advertising promotion forms with stronger visual impact and better advertising effect. Advertising effect is generally negatively correlated with user experience. Screen-inserted advertising is better and more profitable than banner’s advertising, but it affects user experience.

Generally, CPA (such as user download and registration) is the main charging method, and there are also CPM (cost per thousand people) and CPC (cost per click) payment methods.

Full Screen Ads have been used by almost every APP. When the user opens the APP, it appears in full screen mode for about 3 seconds (generally it can be skipped), which can be a static picture, a multi-frame animation or a Flash effect.

At that time, the flash advertisement of No.1 car and Uber really surprised me, and Airbnb also used flash-style open-screen advertisements. However, the full-screen advertisement in Flash mode will make the APP installation package too large, so it is generally not used.

In addition to the open-screen advertisement when entering the APP, sometimes there will be full-screen advertisements due to misoperation in the game. When Shanghai Metro is connected to Peanut Metro wifi, there will also be full-screen advertisements that are forced to stay for 3 seconds.

Full-screen advertising charges are high, mainly in the form of CPM (thousand-person display cost).

Rich Media is relative to pictures, because it has the way of animation, sound, video or interactive information dissemination. Summary in a word: rich media is a way of information dissemination, and rich media advertising refers to the form of advertising expressed in this way of communication.

Rich media advertising, for users, means that the advertisements they see are cool, for advertisers, they can better display their products, and for Internet companies, they just need to load more advertising materials.

Feeds Ads are often mixed with normal information on timeline, which is not easy to be recognized, and users unconsciously finish reading the ads. Common in social apps, such as friends circle, Weibo, Instagram, and information apps, such as today’s headlines and Netease News.

The integration wall is common in some game apps. By giving players free game coins, players are encouraged to download and register other game apps, so as to achieve the purpose of profit or mutual diversion.

In addition, some third-party platforms encourage users to download the promoted APP in the form of points or phone bills for high advertising revenue.

Generally, the integrating wall is paid by CPA (such as registered download) for advertising effect, and the unit price is between 0.6 and 4 yuan. As long as you are willing to spend money, it is easy to get to the APPStore ranking version, and many apps are promoted and brushed through the integral wall.

On mobile video platforms such as iQiyi Youku, there are two common forms of advertising: patch and corner sign.

1) Patch:If you are a non-member, you will usually see a short video advertisement pushed accurately before the video starts. The following picture is a screenshot of the patch advertisement of iQiyi APP.

It is a smart choice to allow viewers to skip the patch advertisement after watching it for a few seconds. The audience forces them to watch it even if they don’t like it, which leads to poor user experience and no benefit to advertisers. It is better to allow users to skip, and judge which kind of advertisements this user is more interested in by marking the skipping time point, so as to achieve more accurate advertisement push.

2) Angle mark:Advertising forms that appear next to the video playing window in a transparent style generally have dynamic effects so as to attract users’ attention during viewing. The corner marker is allowed to be turned off by the user.

There are different opinions on the definition of Native Advertising. My understanding is that the content of advertising is native advertising.

The best example is Qipa’s program: "A fashion APP with a house and a car, money and power is not as good as a fashion app", "Yaha coffee that can only be chatted happily after drinking", and the international brand "More cereals and oats" …

The audience who like to watch Qipa’s story will be able to recite it, and these fancy slogans even become jokes between friends.

Content-oriented advertising can maximize revenue.

Bidding ranking is generally paid according to CPC (cost per click), and the most famous cases are Baidu and Taobao’s search results.

Bidding products will appear in the top position of search results, and are highly related to the content retrieved by users, which increases the accuracy of advertising promotion and easily attracts users’ attention and clicks, so the delivery effect is more obvious.

I received an advertising leaflet at the company gate after work yesterday, as shown below. Nowadays, leaflets are all changed to red envelopes, and the same paper size has different advertising effects. Life is full of creativity.

　

Author: pmwiki (WeChat official account: pmwiki), a product dog in business. I write articles to urge myself to think independently and to see how long I can persist. The content is mostly product sentiment, reading notes and life thinking.

This article was originally published by @pmwiki (Everyone is a product manager. Reprinting is prohibited without permission.