Why do people study mathematics? In fact, many people are not clear about it, and there are even many misunderstandings.
Some students think that "mathematics is a little useful except when shopping, but it is a little useful when taking exams, and it is of little practical use."
Some students also think that "learning mathematics is for the college entrance examination." Without the college entrance examination, no one will learn these useless things. "
In fact, mathematics is a meaningful field.
1. 1 characteristics of the times
Mathematics has always been the main force in the formation of human culture, and the characteristics of an era can be understood through the mirror of mathematics. For example, ancient Greek mathematicians emphasized strict reasoning, so they were not concerned about the practicality of these achievements, but about educating people to make abstract reasoning and inspiring people to pursue ideals and beauty. So ancient Greece created beautiful literature, rational philosophy, and idealized architecture and sculpture that later generations could not surpass. China ancient mathematics advocated practicality, but its biggest shortcoming was the lack of strict proof. It is not difficult to understand why ancient China lacked rational thinking, and it is not difficult to explain Needham's puzzle: Why didn't modern natural science happen in China? In fact, the key to the problem lies in mathematics. Because, "Mathematicization of mathematics and various scientific hypotheses has become the pillar of modern science" [1].
The characteristics of an era are closely related to the mathematical activities of this era. Since17th century, due to the establishment of calculus, the success of seeking natural laws with the help of calculus tools has gone far beyond the field of astronomy. /kloc-in the 9th century, due to the perfection of calculus as a strict analytical system, the powerful theory of mathematical physics became possible, which eventually led to the birth of quantum mechanics and relativity, and made people have a deeper understanding of the basic properties of matter and space. In 1950s, the development of mathematics created the computer. Mathematics has gone from the background of science to the stage, and digitalization has penetrated into almost all human activities. Human history has entered a brand-new information age.
1.2 wonderful movement
Mathematics is a steep mountain with beautiful scenery hidden behind it. Mathematics, like music, can give people great spiritual shock. Russell wrote in his autobiography: "When I was 1 1, I began to learn Euclidean geometry, and my brother was my teacher. This is a great event in my life, as intoxicating as my first love. I never imagined that there were such wonderful things in the world. " [2] As we all know, Gauss put mathematics at the top of science, while Hilbert regarded mathematics as "a surprisingly beautiful and harmonious building".
In people's impression, mathematics and art have little in common, although they are both the crystallization of human wisdom. However, mathematics has been silently accompanying art, providing a rich source of inspiration and a solid creative pillar for art. We can easily find that mathematics can inspire art, and art can also inspire mathematics. From Fibonacci series and decimal places of pi to tetrahedron and Mobius belt, it can be used as inspiration for artists' creation.
Music is the pleasure that human spirit obtains through unconscious calculation. The French mathematician Fourier even proved that all sounds, whether noise or sounds made by musical instruments, complex or simple sounds, can be described comprehensively in a mathematical way. Fourier's proof has profound philosophical significance. Wonderful music is described by mathematics in an unexpected and wonderful way, which transforms the most abstract field in art into the most abstract science; The most rational knowledge is closely related to rational music. Therefore, mathematics is music in reasoning, and music is mathematics in feeling.
The close relationship between mathematics and architecture should not be surprising. Mathematics has always been an inexhaustible creative source for architects and a valuable tool for architectural design and innovation.
1.3 From Queen to Partner
Mathematics is known as the "queen of science" because of its outstanding intellectual achievements. Mathematics created Plato's philosophy, and Aristotle advocated that all scientific discourses should be reduced to syllogism in Post-analysis. Descartes believes that mathematics can be the form of all knowledge. The progress of Descartes' thought did not start from the principle of "I think, therefore I am", but from ordinary mathematical concepts and ideals. His ideal led to the establishment of analytic geometry, a branch of mathematics.
Galileo believes that in the field of mathematics, human beings can reach the apex of all possible knowledge, which is no less than the knowledge of divine reason. Condorcet, a French thinker, believes that algebra is the only truly accurate analytical language that exists so far, which contains some universally applicable principles and can be applied to the combination of all concepts. In Critique of Pure Reason, Kant tried to prove the foundation of establishing mathematics and mathematical natural science. He said that any natural science can only be regarded as a real science with gradual improvement if it can be studied with mathematical tools.
In fact, mathematics is not only the "queen" of science, but also the "servant" of science. This is because mathematics, as a tool, is widely used in other sciences and serves their functions. Mathematics plays an indispensable role in the development and perfection of almost all major scientific theories, and the achievements of mathematical research are often the catalysts for major scientific inventions.
Not only natural science, but also various social sciences are constantly turning to mathematics. With the further revelation of the relationship between mathematics and other sciences, mathematics has gained a new title-partner. Steen, an American mathematician, makes an analogy between mathematics and other disciplines: many learned people, especially scientists and engineers, imagine mathematics as a tree of knowledge, and formulas, theorems and conclusions are like ripe fruits hanging on the tree, which can be picked by passing scientists to enrich their theories. Mathematicians, on the other hand, regard mathematics as a rapidly growing tropical rain forest, which needs to absorb nutrients from the world outside mathematics, and at the same time devote itself to the rich and changeable wisdom of human civilization.
Mathematics has made a lot of contributions to other disciplines. At the same time, these disciplines are challenging mathematicians with some interesting new problems, resulting in new applications, and the more basic mathematics is, the more useful it is. It is conceivable that with the development of human society, mathematics will become the most basic subject and the framework of all sciences. If the post-modern proverb is adopted, it is that there is almost nothing that can avoid the "text" of mathematics. It can be said that if mathematics is suddenly taken away from our world, human society will collapse in an instant; If mathematics is frozen in our world, human civilization will go backwards immediately. Civilization without mathematics is unthinkable.
2. 1 Mathematics-the basic quality of people
Mathematics, as a basic quality of human beings, is particularly obvious in ancient Greek society. Greek philosophers regard knowledge as good, and the pursuit of truth, goodness and beauty is the purpose of Greek education. Plato believes that mathematics is a prerequisite for becoming a citizen. He thinks that if he forgets the fact that the ratio of diagonal to side length of a square is incommensurable, he doesn't deserve someone's name. Plato compared the essence of educated people and uneducated people to "cave illusion". If a person wants to know the universe, his soul must be tempered and saved first. Mathematics is an ideal means, especially geometry, which is a bridge from darkness in caves to shining light. Only when the human soul is cultivated by mathematics can it be extraordinary, return to the holy ideal world and be saved. People who have been trained in logic and mathematical reasoning will be more likely to escape from the cave of ignorance.
Mathematics is not only the basic quality of people, but also can improve intelligence and talent. Plato believes that those who are naturally good at arithmetic are often sensitive to learning all other subjects; And those who are slow to respond, if they have been trained in arithmetic, their responses will always improve. For soldiers, calculating and counting are essential skills for a soldier. What about philosophers? Plato believes that philosophers must get rid of the changeable world and master the truth, so they must learn the truth, otherwise they will never become a real calculator.
Plato particularly emphasized that abstruse things in geometry can help people to grasp good ideas more easily. The world of ideas is the origin of all true knowledge and the highest good. For Plato, mathematics is not only the basic quality of human beings, the king of philosophy, but also the mathematical quality beyond ordinary people. The development of society requires people to have higher mathematical quality. People who don't know basic mathematical language, basic mathematical symbols, basic mathematical reasoning and basic statistical charts will not be able to adapt to the rapid development of modern society. In the information society, mathematics, as the basic quality of modern people, is increasingly recognized by people. Mathematics has become a basic part of today's social culture with its thinking, rational spirit and aesthetic feeling. If a person doesn't know what mathematics is and lacks rational thinking and aesthetic consciousness, his comprehensive quality, insight, judgment and creativity will be greatly affected.
Mathematics is not a fashion for a modern person, but a practical need in work, study and interpersonal communication. For the peace and welfare of the country, the role of mathematics in labor training is crucial. Scientists and engineers depend on mathematics, and they need a solid mathematical foundation to succeed. For ordinary citizens who want to acquire modern citizenship, it is absolutely necessary to have at least a middle school level of mathematics foundation. Mathematical illiteracy is as harmful as illiteracy. It can be said that without mathematics, we can hardly live well; Without mathematics, it is difficult for us to do a good job; Without mathematics, it is difficult for us to think hard; Without mathematics, it is difficult for us to communicate well; Without mathematics, we can hardly appreciate it well.
2.2 Mathematics-Promoting Human Development
Through appropriate knowledge carriers, people's quality can be continuously and consciously improved, and people's excellent quality can be cultivated. Mathematics is such an important carrier. Because, when we are faced with a series of mathematical symbols used for calculation and reasoning, on the surface, we are operating the symbols, but in fact, calculation and reasoning are guiding our spirit. Therefore, mastering mathematics knowledge means understanding a modern scientific language and tools, learning a rational way of thinking and cultivating an aesthetic taste. Mathematics is a treasure house of wisdom and a garden for cultivating people's excellent character. Through the study of mathematics, "it can promote the development of students' learning attitude, thinking habits, thinking patterns and thinking strategies, so that every student can make an appropriate response to the new situation" [3].
The traditional positivist view of knowledge describes knowledge as linear accumulation and value neutrality, ignoring human activities in knowledge creation and the ethical significance of knowledge. However, knowledge is a kind of social construction in essence, which inevitably embodies people's value choice and shows people's ethical concern. Mathematics is no exception. For mathematics, it can promote the formation of the following excellent qualities.
First, honesty and integrity, advocating truth. Calculation and proof are not a simple operation step or a formal process, but a series of viewpoints and opinions. Mathematical conclusions are the same for anyone and must be accepted by the rational court. What is right is right, and what is wrong is wrong. Mathematical calculation, mathematical derivation and mathematical proof cannot rely on opportunism, but only on gradual calculation and reasoning. Through the study of mathematics, we can cultivate the good character of honesty and integrity, convincing people by reasoning, upholding the truth and correcting mistakes.
Second, be diligent in thinking and be brave in innovation. There is nothing better than mathematics to stimulate this unique and noble innovation ability of human beings. No subject can concentrate, accelerate and strengthen people's attention like mathematics. Facts have proved that the success of mathematicians lies not in talent, but mainly in diligence and innovation.
Third, persevere and dare to climb. There is no king in geometry, and mathematical research needs strong perseverance. Because the proof of mathematical proposition is like climbing a mountain, only those who persevere and dare to explore can reach the other side of victory. Mathematics is an excellent school of thinking, a training subject of wisdom and an abstract way of thinking. Accurate mathematical language allows us to think about complex decisions in an orderly way, rather than relying solely on anecdotes, guesses and eloquence.
Mathematics has been inextricably linked with thinking since its birth. Mathematics should be embodied by thinking, and mathematics is a tool of thinking. People who study mathematics can think more effectively. Developing people's thinking ability is an important cultural function of mathematics. Without mathematics, there is no organized logical thinking. Many famous philosophers have undergone rigorous mathematical training, such as Socrates, Plato and Aristotle in ancient Greece, Descartes, Spinoza, Leibniz, Locke, Hume, Becquerel and Kant in modern times, and Russell, Wittgenstein and Husserl in contemporary times. Mathematics is a way of thinking. Mathematics can make people's way of thinking rigorous and gradually form the habit of reasoning. Mathematical thinking can help us transition from daily thinking to formal thinking. The contribution of mathematics to our thinking lies in the great adaptability of its concepts, which is difficult for other non-mathematical models to achieve.
Ernst? Cassirer defined man as a symbolic animal and thought that "symbolic thinking and symbolic behavior are the most representative features in human life" [4]. An important feature of mathematics is its symbolic language. Mathematics uses symbols to express quantitative relations and spatial forms. With the help of the rigor and conciseness of mathematical language, people can express and study mathematical thoughts. If you express these ideas in common language, it will be cumbersome, and this simplicity will help improve the efficiency of thinking.
Beauty is a symbol of goodness, and beauty is bound to be connected with people's hearts. The beauty of mathematics lies in the elegance of mathematics, which is the harmony, symmetry and ingenious cooperation of different parts. Beauty is the first touchstone of mathematics, and there is no deformed and ugly mathematics in the world. Where there is mathematics, there is beauty. There is beauty everywhere in mathematics, not only the beauty of mathematical knowledge, the beauty of mathematical methods, but also the beauty of mathematicians' hearts. Art can beautify people's mind, but no art can beautify and decorate people's mind more effectively than mathematics.
Mathematics has aesthetic value, as clear as the value of music and poetry. Many mathematicians have discussed the influence of mathematical beauty on people. Russell has a famous saying: Mathematics, if viewed correctly, has supreme beauty-just like the beauty of sculpture, it is a cold and serious beauty. This beauty is not the weak aspect that attracts our nature. This beauty has no ornate decoration of painting or music. It can be pure to sublime, and it can reach a perfect state that only the greatest art can strictly express. A real spiritual pleasure, a spiritual excitement, a sense of superiority-these standards of perfection and beauty can be obtained in poetry and mathematics.
Poincare pointed out that it is also reasonable to pursue the truth for the beauty of the truth itself without selfishness, which can make people more perfect. Hardy once said that mathematics, like poetry or music, can promote and maintain the noble habits of the mind, thus increasing the happiness of mathematicians and even others. Therefore, it is difficult to find an educated person who is quite dull about the charm of mathematics.
Mathematics is the key to the door of opportunity. Mathematics is not only a scientific language, but also contributes to business, finance, economy and national defense in a direct way, opening the door for students' career. The more mathematics a person knows, the more open the door to his career will be. Today, people who know math and know math will get more opportunities than those who don't. From insurance company statisticians, system analysts, marketing experts, network managers to financial analysts, and so on. In fact, mathematics has been playing an important role in helping education authorities to determine which students should be paid by society. To some extent, the difference of mathematics level and ability determines a person's future career and development prospects.
In the future world, the best job hunting and promotion opportunities will be provided to those who have the confidence to cope with mathematics. As the foundation of science and technology, mathematics provides the key to success. The information age is the age of mathematics. Just as future scientists and engineers need a wide range of mathematics, future citizens will need extremely diverse mathematics to deal with a large number of tools, equipment and technologies based on mathematics in their work. When students leave school and enter the working life, mathematics largely determines what one can and cannot do.
In all countries of the world, the contents of mathematics courses in primary and secondary schools are relatively consistent, with outstanding similarities. Specifically, the content of mathematics courses chosen by countries is closely related to the needs of society, the development of mathematics and the development of students. Mathematics occupies a central position in the curriculum. No subject has been taught for so long in different countries or cultures. We seldom see students who are good at math but not good at other subjects. It is rare for a student to be the best in mathematics, but the worst in other subjects. On the contrary, those so-called "poor students" often can't learn mathematics well at first, and mathematics has become a "sieve" for these students. Screen out their employment opportunities and their development opportunities. Mathematics really opens the door to the future, and everyone's development depends on the success of mathematics education. In all civilizations, generation after generation of children learn mathematics in order to get a better life.
Human survival is an endless process of improvement and learning, and anyone is an unfinished person. Mathematics is very beneficial to a person's lifelong development. In fact, mathematics, as a basic course to cultivate citizens' quality, not only provides necessary preparation for students' further study, but also plays an irreplaceable role in students' lifelong development. Through the study of mathematics, the sustainable development of students is constructed, and then the lifelong development of students is promoted. Because even if students forget the knowledge of mathematics, the spirit, ideas and methods of mathematics will be deeply engraved in their minds, and they will be active in daily life for a long time, playing a role anytime and anywhere, benefiting students for life.
Science is the art of the universe, the tool to unlock the world, and the origin of all laws.