The influence and role of mathematics can be said to be ubiquitous

This article is a speech by academician Li Daqian at the orientation meeting for the freshmen of the School of Mathematical Sciences at Fudan University. The speech is then red-hot in the circle of friends. That's right, a speech about mathematics turned out to be so hot. You might have a look. Then take a look at how Academician Li Daqian used mathematics to answer your confusion...

For the vast majority of people, mathematics is the most learned course in life: from primary school to secondary school, from secondary school to university, to the graduate student's learning stage, all are studying mathematics. Why spend so much time learning math? Why must we try hard to learn mathematics?

If you think that this kind of learning is only for the purpose of implementing the rules of the school and the teacher, it is only for the purpose of dealing with the relevant examinations and achieving a good result. It is just to get a diploma and find a high-paying job in the future, or just to grasp more or less. Some related mathematics knowledge, even if it enters the School of Mathematical Sciences, will inevitably adopt a passive and coping attitude towards mathematics learning, and the effect of learning will inevitably be greatly affected. Therefore, this seemingly ordinary problem is actually worthy of serious consideration.

01 The influence and role of mathematics can be said to be ubiquitous

To find out why we must learn mathematics, we must first understand the importance of mathematics itself.

Everything in the world has its two sides: number and shape. Mathematics as a science to study the quantitative relationship and spatial form in the real world is to eliminate other specific characteristics of matter. It only studies the entire world from the perspective of number and shape. The role and status of mathematics now appears to be summarized as follows:

1. Mathematics is an evergreen knowledge

As an essential course for elementary schools and secondary schools, mathematics is an indispensable knowledge for human beings. There is no doubt about this. Many discoveries of mankind are like smokes. Many disciplines establish new theories by overturning the predecessors' conclusions; however, the development of mathematics in the past is not the result of later generations destroying predecessors, but each generation of mathematicians is in the original. Based on the building, add a new layer of building. Therefore, the conclusion of mathematics often has eternal significance.

Euclid was an ancient Greek mathematician more than 2,000 years ago. However, the Euclidean geometry he named is still playing an important role. The Pythagorean theorem is not only not considered old. Disregarding teeth, it is also known as the First Law of the Ages. It has been highly praised and applied repeatedly, which fully illustrates this point.

2. Mathematics is a scientific language

Galileo once said: "The book of nature is written in a mathematical language.... Unless you first understand its language,..., the book cannot be read." Math is a scientific language. It is very accurate. This is the characteristic of mathematics.

At the same time, this language is universal in the world. Addition, subtraction, multiplication, division, exponentiation, exponential logarithmics, differential calculus, constants, etc. These mathematical languages ​​and symbols may have been varied and varied in the beginning but they have long been unified as a fixed pattern. And it is very convenient to use.

3. Mathematics is a powerful tool

Mathematics has played an important role in people's daily life and production at any time and place. It is obvious to all. In modern times, mathematics as an important weapon of modernization has played a more crucial and even decisive role in many important fields. The outstanding achievements made by our country in the development of two bombs and one star have brought together the efforts of many outstanding mathematicians. This is an outstanding example.

4. Mathematics is a common foundation

Now, not only in the natural sciences, technical sciences, but also in the economic sciences, management sciences, and even the humanities and social sciences, mathematics has become necessary in order to accurately and quantitatively consider issues and obtain a well-founded regularity understanding. Important basis.

Without the support of mathematics, it has been very difficult for related sciences to make great progress. Many disciplines (especially many natural science disciplines) have even become mathematically trending in recent years.

5. Mathematics is an important science

Mathematics ignores the specific forms and attributes of matter, and studies the real world purely from the perspective of quantity relations and spatial forms. It is similar to philosophy and has characteristics that surpass specific disciplines and are universally applicable. It has guiding significance for all disciplines. The mathematical sciences nowadays have constituted a huge scientific system that includes many subdisciplines embedded in pure mathematics and applied mathematics and many new interdisciplinary sciences.

We must not think that mathematics that we have already studied, including already understood mathematics, is the whole of mathematics. Actually, the mathematics studied in secondary schools is largely in the category of elementary mathematics, and the advanced mathematics studied in undergraduate colleges is marked and started with the calculus created by Newton and Leibniz in the 17th century. There have been more than 300 years of history. Mathematics is far more colorful than what we have already seen. It is not too much to say that the connotation of mathematics is profound.

However, the more mathematics develops, it does not make things more and more complicated. On the contrary, it will become easier to deal with problems, and people’s ability to understand the world and transform the world will also become more and more, which will make us learn more and more mathematics. Charm, more and more learn to learn.

In the past mathematics class in the sixth grade of primary school, “chicken and rabbit sharing the same cage” was a top-level problem. It was said that some chickens and rabbits were placed in a cage, for example, the known number of heads was 10, the number of feet was equal to 28, and chickens were asked. How much is it? How much is the rabbit? Since the chicken has only two feet and the rabbit has four feet, the problem is complicated, and the requirement of the arithmetic class is to write the answer in one step, which will make it harder. However, if you learn algebra through high school, you only have to set up chickens for x and rabbits for y. According to the question, you can list a binary simultaneous equation for each question, and you can get the answer to the question at once. This is how easy it is!

The plane geometry studied in middle school is a challenge and test for intelligence in order to prove that it is necessary to dig out the auxiliary lines. However, we have learned analytic geometry, combined algebra and geometry, and the geometric problems that we have racked our brains to solve are All of a sudden became easy.

When I was in high school, I was interested in how to use mathematics to find the semi-circular center of gravity. I also spent a lot of time in my spare time. The result was nothing. Later, I heard the teacher say that this problem can only be solved by using calculus. Only when we know that there is still such an infinitely powerful knowledge in the world as calculus, it also stimulates my curiosity and motivation to further study mathematics. The really good mathematics is more and more in-depth, more concise, and more and more useful.

6. Mathematics is a key technology

The mathematics that can be done with a pen and a piece of paper can become a technology and it seems to be incredible. However, the combination of mathematical ideas and methods and highly developed computing technology has indeed formed a technology, and is a key and achievable technology, called "mathematical technology." The part that plays a central role in this technology is mathematics, and taking away it leaves only a pile of scrap metal.

The advanced technology we see in the hospital is an outstanding example. Its essence is the use of X-rays from a variety of flat images taken from various angles to recover the three-dimensional shape of objects in the body (such as tumors), which is entirely a matter of mathematics. In this way, the connotation of mathematics into computer software and hardware becomes an important part and key technology, which can be directly translated into productivity. Now, the saying that "high technology is essentially a mathematical technology" has been recognized by more and more people.

7. Mathematics is an advanced culture

Mathematics is an important foundation of human civilization. Its emergence and development have been accompanied by the progress of human civilization, and have played an important role in promoting and occupying a pivotal position. For the sake of time, the following is a simple example of counting and carrying.

Everyone knows that math began counting. The primitive people can only distinguish between 1 and more, and when they encounter 3, they feel that they have more, and the trio is "congregation". This is probably the case. Later, with a decimal system, using the ten numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0, plus every tenth (and one decimal point), you can represent any one of the world’s digital. This is a fact that people now know when they are young. It seems to be perfectly right.

However, this has gone through a long historical process and is an indelible and enormous contribution of mathematics to human civilization. Without it, a slightly larger number can be confusing, not to mention the huge astronomical numbers or the extremely small numbers. It is impossible to perform complex or high-precision math operations in the financial industry or scientific experiments. Can we still have such a highly developed civilized society?

There are many examples of this, but it is evident from this example that mathematics was, and is, and will be, an advanced culture in the future. It leads, promotes, and influences the progress of human civilization. It has profoundly changed the face of the world, and also changed the human's own thinking ability and level of understanding, and changed the human itself. Human beings are fully enjoying the grace of mathematics and culture, but they are often unaware and accustomed to it.

The ancients said: "The sky will not be born with Nepal, and it will last forever." Everyone thinks about it. If there is no mathematics or no progress in mathematics, people may still live in ignorance and lead a life that is “as long as night”. What are our reasons for not paying attention to mathematics and paying no attention to the guidance and cultivation of mathematics culture? What role?

To sum up, for a long time, mathematics, as an accurate language and a powerful tool, has played a pivotal role in people's understanding of the world and the transformation of the world.

Especially in the modern era, mathematics as an important weapon of economic construction, as an important foundation for science, and as an important pillar of human civilization, has played a key and even decisive role in many fields. Mathematical technology has become a prominent symbol of high technology. And the indispensable component, the influence and role of mathematics can be said to be ubiquitous, and its importance has been recognized by more and more people. In this way, mathematics is not only the most important compulsory course in primary and secondary schools, but also in many faculties of universities. It is a matter of course.

02 Mathematics education seems to be just a kind of knowledge education, but it is essentially a kind of quality education.

On the other hand, we must understand why we should study mathematics well, and we must also understand the important role of learning mathematics in the cultivation and growth of a person.

Since mathematics is so important, the purpose of learning mathematics is only to obtain a large number of theorems, formulas, and conclusions. If we understand a variety of mathematical methods and methods, we will have to solve a variety of exercises and even problems. no! ! !

If mathematics learning is only seen as accepting a lot of mathematics knowledge, then even if you know more about the theorems and formulas, you may still inevitably become a mass of deadly dogmas and hardly work. If mathematics learning is only understood as the number and speed of “brushing questions,” it can only be a skilled mathematics crafter at best.

Mathematics is a science that emphasizes thinking and understanding, rigorous training, and creativity. Only by mastering the way of thinking and spiritual essence of mathematics can we deduce the ever-changing vivid conclusions from a few formulas and show endless possibilities. power.

Many of our alumni who have successfully applied mathematics and achieved outstanding achievements in practical work have such experience: The specific mathematics sub-disciplines that need to be used in the work, and the specific mathematical theorems, formulas, and conclusions are not necessarily true. Many; many of the mathematics knowledge they have learned in school seem to be of no use, and some may even have forgotten, but they are trained in mathematics, the mathematical thoughts and spirit they receive, and the mathematics education they acquire. It plays an active role all the time and becomes the most important factor for success. In my opinion, this is a very worthwhile experience talk.

In fact, through careful mathematics study and rigorous mathematics training, students can have some unique qualities and abilities. These qualities and abilities are irreplaceable or difficult to achieve in the learning of other courses and other aspects of the practice. Moreover, even if the learned mathematics knowledge is forgotten (this is often the case!), these qualities and abilities as a person Mathematics education will not disappear, it will be accompanied by a lifetime and always play an active role. These qualities and capabilities, for example, are:

Self-conscious quantity concept. People will pay careful attention to the quantitative aspects of things and their patterns of change, rather than “numerous things in the chest,” rely on feelings, “shooting heads” to make decisions and do things.

Strong logical thinking ability. It enables people to maintain clear thinking, clear and orderly, and orderly handling various tasks.

Highly abstract thinking ability. In order to face the complicated phenomenon, people can distinguish between the primary and the secondary, grasp the main contradiction, highlight the essence of things, and solve the problems step by step, without being at a loss, unable to do anything at all, or with eyebrows and mustaches.

Mathematical derivation requires that every sign and every decimal point cannot be vague, which helps to cultivate careful, meticulous style and habits.

What mathematics pursues is the most useful (broad) conclusion, the fewest conditions (costs), and the most concise proof. Through rigorous mathematics training, the habits and styles of perfection and perfection will gradually be formed.

Paying attention to the ins and outs of mathematics and knowing the origins and processes of the development and development of mathematical concepts, methods, and theories will increase the awareness, beliefs, and abilities to establish mathematical models and use mathematical knowledge to deal with complex issues in the real world.

As a kind of ideological gymnastics and competition, mathematics will increase people's fighting spirit and resilience. Through continuous analysis of contradictions, they will shed light on difficult situations and eventually solve problems.

Learning and thinking in mathematics will open up a vast space of freedom for students to inspire their exploration spirit, innovation awareness, and innovative ability, so that they will be more flexible and active, and their intelligence and wisdom will be fully demonstrated and played.

It can be seen that mathematics education seems to be only a kind of knowledge education, but it is essentially a kind of quality education.

This quality education is not imposed from outside, but is inherent in mathematics education itself. By imparting and learning mathematics knowledge as a carrier, through rigorous and serious mathematics learning and training, it is possible to unconsciously and consciously transform the qualities and abilities of the above-mentioned aspects into an eye-catching, self-improvement, practice, engrave in mind, form habits, and gradually become oneself. Mathematics education.

If you truly learn mathematics, no matter which industry you are going to do in the future, it will make people smarter, more intelligent, more competitive, and will never be used for life. For most of our students, it will also be the place where they will most remember the future, and mathematics learning will give them the greatest benefit. Of course, if you do not study mathematics, or if you just learned everything through carelessly learning some mathematics, you will not be able to achieve this effect. This is undoubtedly "into Baoshan and empty back".

The above-mentioned, in principle, can apply to all students and even primary school students, and of course everyone is no exception. However, today everyone has come to Fudan’s School of Mathematical Sciences and is about to start studying mathematics as a professional system. When it is stepping into the hall of mathematics science and becoming a new army of mathematics, your task should not be just a routine sense. Under study, we must travel to the deep and beautiful mathematical kingdom, taste and explore the essence and mystery of mathematics science, and strive to contribute to it.

At the same time, we must also contribute to the magical and practical ideas, tools, and methods of mathematics, and strive to reveal the mysteries and laws of nature and human society, and have a better understanding and understanding of the world we live in. And then for the country, for the nation, for the benefit of mankind.

Because of this, it is hoped that the newly enrolled students at Fudan University of Mathematical Sciences have established a lofty aspiration from the outset and have a beautiful dream of using mathematics as their lifelong career and aspire to cultivate and build themselves into a future. The mathematicians have made their own contributions and contributions to the development and progress of mathematics and to the development and progress of human society. They have also added color to Fudan's mathematics.

This is a lofty and lofty ambition, but it is not an unreachable goal. We are pleased to see that the vast majority of the 121 undergraduates enrolled this year are admitted to the first choice. Conscientiously choose mathematics as their own volition, stating that everyone's love and pursuit of mathematics. Determined to become a mathematician, under the nurture and influence of Fudan's 100-year prestigious school, he took over the batons of senior mathematicians in the hands of professors Su Buqing and Gu Chaohao, and inherited and carried forward the Fudan School of Mathematical Sciences as a cradle for outstanding mathematicians. The fine traditions of the students should be the conscious pursuit of many students, and it is worth giving sufficient encouragement and support.

There may also be a considerable number of students. Although they are interested in mathematics and they are well aware of the importance of mathematics, they hope to lay a good foundation in mathematics and move to other industries in the future. It should be said that this is also a good way out and motivation for learning mathematics. Many graduates with good mathematics foundations and accomplishments will enter all walks of life. They will not only fundamentally change the appearance of these industries, but also provide good mathematical development itself. The external environment and bring about great promotion are also worthy of encouragement and support.

However, despite the fact that you will enter all walks of life in the future, your advantage over others is not in other places, but in your mathematical accumulation; whether you can stand out in a new environment in the future, you can only depend on yours. Mathematical advantage, not the other! Your future focus should be on the intersection of mathematics and other disciplines. This is what industry is now advocating and applied mathematics. Your goal should also be to become a mathematician and a real industrial and applied mathematician.

In this regard, I also want to say a few words to the female classmates present here. In recent years, the proportion of female students in undergraduate and graduate students of Mathematical Sciences is quite high. The proportion of female students in undergraduate students this year has slightly decreased compared with previous years, but it also exceeds 18%, and the proportion of female students in graduate students is close to 34%. Most female students are serious and have good grades. Some of them are also very good, but sometimes they may be somewhat less confident.

Can a female student become a mathematician in the end? The answer is yes.

There are no shortages of outstanding female mathematicians in history. In order to illustrate this point, I will ask the teacher in charge of the school to send you an e-mail to a booklet to be published by my editor in a series of books on mathematics and culture. The book is titled “Breaking through the fences of secularism and prejudice.” An outstanding female mathematician." The three female mathematicians are Germain of France, Kovalevskaya of Russia and Knott of Germany. They have made such outstanding contributions in the era of women’s lack of education’s basic rights, and thus they should be a great encouragement and an excellent model for our broad female students. I hope everyone can find time to read them well. Read it for the first time and think about it.

We believe that our female classmates will surely build enough confidence. Others can do it. We must be able to do it through our own efforts and efforts. Hu Shisheng, the only female science professor at the Chinese Academy of Sciences, is at the School of Mathematical Sciences. She has set an example for us and we should redouble our efforts.

In short, for all the students, to establish a lofty goal, strive to learn mathematics, and learn as much as possible, not only is the learning requirement for you at this stage, but also a strategic investment for your future development. Do it. We want Fudan's School of Mathematical Sciences not only to become a veritable cradle for the development of male and female mathematicians, but also to become a veritable cradle for the development of male and female industrial and applied mathematicians. It is hoped that everyone will work together to work hard to create a culture and promote the realization of this goal as soon as possible.

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