In his representative works “The Rise of the Western World” and “Structure and Change in Economic History”, the famous economist North, based on the formation and change of property rights, believes that the system plus technology determines the transactions that constitute the total production cost. and switching (production) costs, thereby affecting the performance of the economy. Therefore, the efficiency of the market, the development of the economy and the rise and fall of the country can be said to be directly dependent on the design and structure of the institutional level.

The author here mainly wants to make some discussions on mathematics and the rise of the Western world.

The famous mathematician M. Klein has successively written works such as “Ancient and Modern Mathematical Thoughts” and “Mathematics – The Loss of Certainty”. Klein’s book “Mathematics in Western Culture” shows us the prominence of mathematics in Western civilization. In the preface, Klein first states his purpose for writing: “The purpose of this book is to clarify the idea that mathematics has always been a major cultural force in Western civilization. Almost everyone knows that mathematics is Engineering design has extremely important practical value. But few people understand the importance of mathematics in scientific reasoning and the central role it plays in important physical theories. As for mathematics, it determines the content of most philosophical ideas and research methods, destroyed and constructed many religious teachings, provided the basis for political and economic theory, shaped many schools of painting, music, architecture and literary styles, founded logic, and provided answers for the people and the universe. Even lesser known are the fundamental questions that provide the best answers. As the incarnation of the spirit of reason, mathematics has penetrated areas formerly ruled by authority, habit, and custom, and replaced them as a guide to thought and action. Above all, as a precious and incomparable human achievement, mathematics is comparable to at least any other cultural branch in pleasing the eye and providing aesthetic value.”

”Mathematics in Western Culture” on the one hand shows the development history of mathematics itself, and analyzes how mathematics developed into a great cultural force; on the other hand, it focuses on mathematics and philosophy, painting, music, architecture, religion The relationship between mathematics, economics, ethics, etc., describes the important influence of mathematics on the process of Western civilization.

Klein pointed out: “Mathematics is not only a method, an art or a language, but more importantly, a system of knowledge with rich contents, the contents of which are of great interest to natural scientists, social scientists, philosophers, and logicians. Very useful to artists and to influence the doctrines of politicians and theologians at the same time; to satisfy human curiosity to explore the universe and to contemplate beautiful music; and at times may even influence modern history in imperceptible but undeniable ways. process.”

How can mathematics influence the rise and fall of nations and the course of modern history? This is really surprising.

Mathematics is a representative of a country’s rational thinking and scientific development. In foreign countries, statistics is one of the most valued subjects in universities, and the development of statistics is a sign of measuring the academic level of a certain university. The United Nations recommends that a government that can stand in the modern international community must be able to provide 1,600 national statistics.

The current US President Bush pointed out that in order to maintain its leading position in the world economy, the United States cannot be complacent. Students should lay a solid foundation of mathematics and science knowledge, increase basic research and technological innovation, so as not to lose to emerging countries such as China and India. competitor.

In the minds of today’s Japanese, mathematical strength is equal to the competitiveness of individuals, and collectively, it is equal to the national strength of the entire country.

From ancient India to the present, mathematics has always been the driving force behind the logical thinking of Indians. It is as important as the religious philosophy of India. Mathematics, from definition, deduction of theorems, to solving problems step by step, is consistent with the analytical and logical abilities required for writing software. Students who have mastered mathematics can easily enter the door of information technology. India has invested a lot of manpower and material resources in mathematics education. The multiplication table of elementary school mathematics in India is no longer the ninety-nine multiplication table in primary schools in my country, but the multiplication table of 22 times 22 is recited. India requires students to memorize the multiplication of integers within 20 such as 18×16. Strict math proficiency tests are required for both liberal arts and science subjects upon graduation from high school and upon admission to universities and professional schools. In terms of class schedule, India has a lot of class hours in mathematics education, and the class hours used for mathematics education in middle schools reach about 200 hours per year. Both the Indian government and local governments have recognized the importance of mathematics education, and adopted a policy of allowing young people who shoulder important responsibilities in the future to receive adequate mathematics education, so that students have good mathematics knowledge, and have achieved results in the field of information technology industry, directly Or indirectly promote the development of the information technology industry. Even India’s “father of software” Kohli said: “India is poor and has no capital to make hardware, but we have the best mathematical minds, and we can definitely make the best software.”

Since the 1990s, Korea Tech High School The weight of the main courses such as mathematics, physics, chemistry and biology has been increased, many elective courses with certain difficulty have been arranged, and students have been encouraged to carry out scientific research, invention and innovation. Today, there is a high school of science and technology in every district of each city in Korea. The purpose of the school is to cultivate and educate students with outstanding scientific and mathematical talents, to maximize their creativity, and to improve and cultivate them as excellent students in the future. The basic quality of scientific and technological talents.

In 1992, the United Nations Educational, Scientific and Cultural Organization clearly stated in the Rio de Janeiro Declaration: “Pure and applied mathematics are the main keys to understanding the world and its development”.

When someone asked the first Nobel Laureate in Physics what kind of literacy a Roentgen scientist needed, his answer was “The first is mathematics, the second is mathematics, and the third is mathematics.”

In economics, mathematics is an important tool to improve the scientific and analytical level of economic theory. Among the Nobel laureates in economics, except for Hayek, who won the prize in 1974, almost all the award-winning achievements have used mathematical tools. More than half of the winners are economists with profound mathematical skills, and a few winners are famous mathematicians themselves.

Stuart, Fellow of the Royal Academy of Sciences, said: “Our world is built on mathematics. Mathematics is inevitably integrated into our entire culture. We do not feel how strongly our lives are affected by mathematics. The reason is mathematics. Always try to hide behind the scenes as much as possible.”

So, since mathematics is so important, why does Klein, in “Mathematics in Western Culture”, argue that mathematics has always been a major cultural force in Western civilization. Is it not in Eastern civilization, especially in Chinese civilization? Moreover, we all know that the ancient Chinese civilization is very developed in mathematics, and can even be called the teacher of Western mathematics in some respects.

Ancient Greek mathematics was good at logical reasoning and geometry, while ancient Chinese mathematics was good at arithmetic and algebra.

Confucius taught his disciples the six arts of propriety, music, archery, imperialism, calligraphy, and arithmetic. Some people also believe that ancient Chinese mathematics mainly appeared in the form of “management mathematics” and “woodworking mathematics”. During the construction and development of the Great Wall and the Grand Canal, our ancient ancestors accumulated a lot of knowledge in geometric measurement, numerical calculation and civil engineering.

As early as in ancient Greece, Plato hung a sign on the door of the school he founded, “Forbidden students who do not understand geometry to enter.” The Pythagoreans regarded number as the source of all things. Almost all the great philosophers of ancient Greece were great mathematicians. Aristotle said: “Although new thinkers study mathematics for other things, they regard mathematics and philosophy as the same.”

However, in modern times, it is difficult for us to see Chinese people at the peak of mathematics figure on the field.

Mr. Jin Kemu pointed out in the article “Mathematics Mulan Needham Problem” (“Dushu” 2000 No. 3): “This “Fermat’s Last Theorem” also reminds me of the so-called Needham problem. This British scientist is studying and writing Chinese In the history of science and technology, the question was raised more than once: Why did Chinese science and technology surpass Europe in the first place, but became inferior to Europe after the 15th century? This is to ask: Why did modern science happen in Europe but not in China? Many people look for the reasons and get There is no convincing answer. Why is this happening? So the problem is not China but Europe. It is not that China has suddenly slowed down, but Europe has suddenly changed, and there has been a Renaissance of the Great Leap Forward. “Fermat’s Last Theorem” talks about the history of mathematics There is a saying that solves this problem: The major turning point of Western mathematics occurred in 1453.”

Ancient Greek mathematics belonged to the axiomatic deductive system, and it used the mode of axioms, postulates, and definitions to prove a series of theorems; Zhang Shaofeng believes that Babylonian mathematics People and ancient Egyptians have accumulated a lot of mathematical knowledge, but they can only answer “how”, but can’t answer “why”. The ancient Greeks learned these experiences from the Arabs and carried out fine Thinking and rigorous reasoning gradually gave birth to mathematical science in the modern sense (Zhang Shaofeng, “Ancient Greece – The Cradle of Mathematical Science”). Therefore, from ancient Greece, the seeds of transcendence have been planted in Western mathematics.

In AD 529, Emperor Justinian of the Eastern Roman Empire ordered the closure of the Plato Academy and other schools in Athens, and the teaching of mathematics was strictly prohibited. This has dealt a heavy blow to the study of mathematics. In 641, Alexandria was occupied by the Arabs, the library was destroyed again, and Greek mathematics came to an end.

In the Middle Ages, Christian theology ruled. Most people tend to think that the rise of Christianity brought about a decade of downfall in mathematics. However, Wang Youjun, in “A Preliminary Exploration of the Role of Christianity in the Rise of Modern Mathematics”, believes that mathematics has always been regarded as a model of order and rationality. Under such a value orientation, it is natural for mathematics to be admired in a religious environment. The search for the mathematical laws of nature has become a very devout religious activity, the purpose of which is to reveal the greatness and splendor of God. After hundreds of years of accumulation and brewing in the Christian cultural atmosphere in the Middle Ages, this belief finally erupted with unprecedented vitality around the 16th century, which played a great role in promoting the emergence of modern mathematics and modern science.

At the climax of the Renaissance, the development of mathematics was closely combined with the innovation of science, and the significance of mathematics in understanding nature and exploring truth was highly emphasized by the representatives of the Renaissance. Mathematics, physics, including innovations in worldviews became the foundation of modern civilization. Leonardo da Vinci was not only a scientist, but an all-rounder with great interests in anatomy, art, aerospace, architecture, plants, engineering, geology, mechanics, philosophy and sculpture. Much of Leonardo’s work has to do with practical applications of mathematics and geometry. In any serious discussion involving mathematics, science and art, his name cannot be ignored. In terms of mathematics, the main contribution of this period was to absorb the achievements of ancient Greek mathematics and Arabic mathematics on the basis of the great translation movement in the Middle Ages, which prepared the conditions for the great development of mathematics in the next two centuries.

In the 16th and 17th centuries, European feudal society began to disintegrate and was replaced by capitalist society. Due to the development of capitalist machine industry, as well as the promotion of navigation and military affairs, the rapid development of science, technology and mathematics has been promoted. The emergence of Galileo’s experimental mathematical method shows a new combination of mathematics and natural science. The publication of Descartes’ important work “On Method” and its appendix “Geometry” led to the birth of analytic geometry. Newton and Leibniz realized that differentiation and integration are actually a pair of inverse operations, and thus gave the fundamental theorem of calculus, the Newton-Leibniz formula.

Ancient Chinese mathematics has been in a leading position in the world in many aspects since it was recorded in writing, but after the Ming and Qing dynasties, China has stagnated in mathematics, so that it lags behind as an import-oriented country. In traditional Chinese culture, the idea of emphasizing Taoism over art has always been prominent. Technology has long been a vassal of Confucianism. In addition, in the Yuan, Ming and Qing dynasties, the “barbarian invasion”, the corruption of the empire, and self-isolation have made thinking Culturally stagnant, too.

The famous historian Huang Renyu believes that capitalist society is a modern society that can manage the entire society in numbers. As a result, members of the society have become many parts that can be replaced with each other; moreover, the division of labor in society can be complicated. The law not only aims at the inviolability of private property rights, but can also divide and merge rights and obligations by adding, subtracting, multiplying and dividing numbers to support such division of labor. This has created an unparalleled advantage in promoting the development of science and technology. With the agricultural organization as the national backbone, it focuses on maintaining the old balance in everything; while the commercial organization as the national backbone focuses on accelerating exchanges. The more the times evolve, the more the latter can master technology, while the former’s weaknesses are more exposed, and its citizens are dissatisfied with the incompetence of its government. From the Ming and Qing Dynasties to the early 20th century, Chinese history has not been able to form a national social structure that can truly be managed by numbers.

Therefore, “the man who does not use mathematics to serve himself will find that mathematics is used by others against himself.” Therefore, Klein argues in “Mathematics in Western Culture” that in Western civilization, mathematics has been a major cultural force. As a result, mathematics has put China on the sidelines.

The development of mathematics is closely related to the progress of society. The main technologies of the three industrial revolutions in human history are inseparable from the development and innovation of mathematics. With the development of computers, mathematics has penetrated into various fields such as physics, biology, electronics, and commerce. From satellites to nuclear power plants, from weather forecasts to household appliances, the high-precision, high-automation, and high-efficiency characteristics of high-tech technology are all through mathematics. Models and mathematical methods are implemented with the help of computerized control.

Klein pointed out in “Mathematics in Western Culture”: “Mathematics is a spirit, a rational spirit. It is this spirit that inspires, promotes, inspires, and drives the human mind to its fullest extent. It is this spirit that tries to decisively influence the material, moral and social life of mankind; tries to answer the questions posed by human beings; tries to understand and control nature; tries to seek and establish the deepest and most profound knowledge that has been acquired Perfect connotation.”

In today’s world, the competition for comprehensive national strength has reached a fever pitch. Among them, the competition in the field of science and technology is even more intense. Mathematics, like other sciences, also has two values: material value and spiritual value. The famous American historian Stavrianos pointed out in “Global History” that traditional Chinese culture respects the elderly and despises the young; respects the past but despises the present; respects the established authority and despises the change. As such, it becomes an excellent tool for maintaining the status quo, which ultimately leads to an atmosphere of conformity and orthodoxy in everything that precludes further development of ideas. This helps explain why China, despite its initial success in inventing paper, printing, gunpowder and the compass, has since fallen behind the West in technology. It is mathematics that largely determines the backwardness of historical China and the rise of the Western world.