I study mathematics experience
Qiu Chengtong Academician
June 9, 1997
Department of Applied Mathematics, Hsinchu Jiaotong University
Moderator Lin Songshan speech:
Today, we are very happy to be able to give a speech to the academician of Qiu Chengtong, not to speak the math of the Olympic, how to do it.
Deep math, good mathematics. This question is "I studied the experience of mathematics", is the study of mathematics
Inspection, we welcome academicians.
Today, Lin Song Mountain told me to tell me about the application of mathematics. I think I want to think about learning. because I
It's almost five years in Taiwan. I think many researchers do the best ways to study, especially
I think many young people can read abroad? This is very worth thinking. So, I want to tell
Speaking my own experience, or my opinion on mathematics, let everyone refer to it.
I think the first saying is the most important thing, of course, I have to be enthusiastic, the most important thing is to ask the truth, it is always necessary to cultivate
of. We have learned to seek truth, whether it is for nature or from mathematics, we have
Different concepts, but true to beauty is the most important. The enthusiasm of pursuing true and beautiful, because
We have to encounter a lot of different difficulties on the road to do the knowledge. If we don't have a dedication, there is no way.
The law continues. So the highest lounged goals of the pursuit of learning, nothing is true, the goals pursued, enthusiasm
It will not be extinguished. We don't want to cultivate your enthusiasm for your pursuit of learning. I am going to see my father in a few days.
The legacy, where Qu Yuan:
The road is long and the road is long, and the rest will come up and down.
The road to learn is very far away, we must see very far, so we have to go up to ask for, try to do something
Go seek. How to find true and beautiful, you can continue to stick to it, this is a very important cause of success.
If there is no enthusiasm, you will never do a clip of university. We will give another example of foreign countries.
Son, in a organized system, our competition is very powerful, especially in physical or other experimental science
Aspects of research, is really seconds; if there is a topic, everyone knows others will do
This problem, many post doctor or faculty together often work late at night, even the whole
Don't sleep at night. There is of course a competitive in this, it is hope to reach a goal, it is better than people.
One thing; but on the other hand, it is also because of the truth, it is very enthusiastic, stimulating us to relax. no
If you have a number of Tenure's Faculty, there is no need to desperate this, but many faculty is still
It is important to be enthusiastic like this. We have to know that the road to study is far away, we have to be in the middle
It is also possible to do it when you are low. Many people doing research, he often thinks if it is not in the center,
He dare not go. Some people go to the best place, and he does not dare to go to the topic. This has a lot of different
Reason, wait for us to talk slowly, but one of the most tight, I think it is necessary to do it. Basic skill
There will be the above problems when you don't do it. At the time of secondary school, when college, or at the institute as a graduate student
At the time, many basic kung fu must cultivate, many students do not do the basic kung fu when they are young.
The study is very difficult.
Jiaotong University focuses on mathematics, but we know that the main tools for applying mathematics are from pure math; a lot
The student people think that since the application mathematics does not have to learn pure mathematics or the application physics does not have to learn basic things.
It is a big mistake. Many basic efforts are not learning when they are students, why? we
To do exercises, and to do a lot, this is the necessary process of learning basic kungfu. I think a lot of people who have taken a doctorate now have a book when they look at a book. I have encountered some complicated calculations.
It is often unwilling to count, but a lot of basic ideas is to come from the calculation. What we did
Proposition, the last time may leave a very simple and beautiful result, but the middle often spends a lot of calculation
They know how this result is obtained. Doing a good job is not a good evening, often do one hundred
The time, ninety-nine times is wrong, and the last time is success. But when I succeed, I only tell you success.
If you don't tell you about the experience of ninety-nine failed. Wrong experience is often very funny, because often
Obvious mistake, you have to know when you finish it. But when you listen to people, you will have a little wrong with others.
The part of the mistake, the result of doing the wrong mistake, let your eyes bright, it helps you, let you go forward. In fact, you can
The result of doing the wrong, it is already very good, because many beginners don't even make this topic, you can't
Squire. For example, you gave me a chemical problem, I don't know where I started to do it.
Because I don't have this basic effort, I don't know where to start from.
A good mathematician must be able to master two basic efforts than two doors. Basic kung fu is not a grand opening
Come. For example, however, the method of algebra, has a method of analyzing, and there is a different method such as a geometric method.
We started learning in secondary school. Some people like geometries, I feel that the algebra doesn't mean, or I don't want to learn, or
People who have the number of schools don't want to learn geometry, all kinds of ideas are all, but we finally find really studying.
It must be used all. Some people say that I only do a special topic, I will only do this on this aspect, the result is
The problems in this area are not good. Because the development of mathematics is constantly changing and constantly changing.
The natural world can provide us, will not continue to provide geometric aspects because you are geometrists
The problem is often a problem with geometry. When you come to the topic, you should use other workers.
With, I can't understand, I will suffer than others. For example, a very important "group representation theory",
Generally speaking, many places do not teach this course, but in application science or theoretical science, "group expressed theory
"It is also used in physics. Some good mathematicians can use the" group representation theory "to analyze many problems.
We may not have these methods because we have not made good things. I want to "group
"Probably in the study institute or the second half of the university. Chinese mathematician training in this area is not
Enough, it is not as good as foreign scholars, and some basic disciplines must learn well, and they will learn very early. We learn
The mathematics is not allowed to learn the basic skills of mathematics, and in physical basic kung fu, this is at the university.
It is necessary to learn. Mechanics, electromagnetic us must have a certain understanding, because physical and mathematics have been issued in the decades of mathematics.
The exhibition is getting closer, many problems are physically provided. If we do not recognize these basic ideas
If we have to see the topic, you can't mention other mathematicians who know this, you can quickly integrate.
In this year, many mathematics issues are often from other learning such as theoretical physics, application mathematics or
Its science comes, they even provide intuition and methods. We think about some problems for a long time, often
So I have been solved, and if we never touch other scientific, it is completely out of date. for example
In terms of algebraic geometry have long-term development in these twenties years. But it has been classic in these years.
Or the method of the fiber bus, there is no way to solve the problem, and the result is from the theoretical physics to help us see it.
Not possible. Due to the limitations of its own knowledge, many algebraic geometers have no time to meet this difficulty.
The law accepts the views of these experts, and if you encounter theoretical physics, you will not dare to touch it. But the physics is provided, solving me.
The direction of the basic problems, algebra geometry, I feel very difficult, because they have no way to understand, so
This is a very troublesome problem. If you don't know how to learn physics, you will be difficult to accept this new
Challenge. I remember that I have seen a book, and the author is very grateful to Albert, why is he grateful?
What about him? He said that Albert teach my algebra, making me sit down, seeing the number of people will not panic, so that I can
Sit down and treat the problem of algebra. That is to say that we can basically do this, I sit down
Come, see geometric issues or apply mathematics, you can't sit down and want to have a way to deal with him, I think
This is very important. We often see problems, when sitting down, what is panicked, therefore
Forget it, I think everyone has this experience. You must do the basic kung fu must do you to see a topic, obviously
Unknown, unsolved problem, you can still sit down, then work hard to solve it. Even if you can't
Solve it, but you know how to think about how to think, and you will not panic, give up, I think this is the most important
of. It is often because of the basic kung fu, when a deep question or opinion occurs, we refuse
Conventionally accept, think that these topics are not important, this is to explain why you can't do something
The most natural method is the most natural way. Training Basic Kung Fu should be in graduate students, college students or middle school students. Basic kung fu
How to learn? Sometimes I look at one side, I'm looking at the two, I think it will be understood after three books.
Single reading book is not enough, the most important thing is to do exercises, because you can know if you are doing exercises.
Did you not understand, you also understand the difficulties encountered in the ancients. The exercise is not only looking for textbooks, in class and
You can also find Seminar. Many students don't want to write notes when they are in class, they don't make a note.
It is impossible to demonstrate any discipline. Especially sometimes the topic of the speech is not in the book, or
It is not yet published. I often feel very strange, why do students don't make notes? He thinks he understands, in fact
I don't understand. Because people who may even have a lecture, they have not understood, but people who listen to people are not willing to make notes.
I will not talk to the speech, and I will not discuss with other teachers. I often spend an hour on the side.
Listening, I forgot all after listening. Because you don't have a note written, how can you happen?
Forget? Another training basics is where to find out where you don't work. Let's see "group"
When we show theory, we have a big set of theory. Single view Theory is not enough, often know the group
How to decompose, you can't write it down, the theory is not good for you. Another example in an equation
Estimation of the style, do you have a way to explain it, you will rely on your actual calculation experience, don't read one
Two books are sufficient. For example, my son has recently decomposed this problem due to the study, and teachers teach him a big
How to break up the problem of integer equation. He learned. I have learned very well, and I learned how to find the root. but
An exam is that he doesn't know how to decompose it. I told him that you know how to find the root, why not
Can you decompose due to Mainly, he did not expect to find the root with factorial decomposition to find the same thing. In the issue
When training is basically kungfu, you must want to know the relationship between mathematics life, and understand why you want to solve these
Proposition. We went to see many people wrote the past, wrote a lot of very beautiful introductions and criticism. However, you have not experienced this road, you don't understand what is difficult, why people will be like this?
The child thinks. To get this experience, don't just do your exercises, but also to do more difficult exercises. Doing difficult exercises
What is the benefit? Difficult exercises are often a combination of several basic problems. When I read a book, I'm reading a book.
Often it will read a book, I feel very happy, because I'm finished; but again, but
Don't understand. I think everyone has this experience, what is the main reason? We didn't learn this discipline,
When you are more difficult, you will find difficulties. Especially when we do some topics
Waiting, often thinking is like, thinking in the mind, thinking that I have already understood, can solve, just love
I hope to solve it quickly, soon after reading that book, in fact, this is deceived, nor training basics
Method of Kung Fu. A good topic, you should sit down with a pen to write down step by step, and you will send
There are many basic steps that you are not figured out. When you get clear, you go to see your previous needs.
Where, how can I, I think you will slowly understand where the essence of the whole study. So say, pat
It is very important to do the topic. When we are doing college students, I am willing to do this, often when they are graduate,
Just thinking about it, you will not use it after graduation, you won't write it. One topic is there, we are very
It is very obvious that it is very obvious, but some are almost not, it seems to be almost.
Yes, there are a lot of clever inside. We must do it, when you are in a class, basic Kung Fu
After you have made it very clear, you will find a lot of books in the book. When you find the mistake in the book, your basic
Kung fu is also good. Our students don't look at the class books, and even the textbooks of themselves don't look at it.
Disappointed. To do research, I know, I am going to find my own ideas. Listen to class in order, don't read it after listening
, Do a few exercises, how to do it well. Because you didn't think about how you think about it. I
When college students just started the first and a half, I felt very happy because I started strictness. because
From the entire logic, you can derive it at a point, from the previous geometric or analytical problems, I think
I am very happy to connect it slowly. What is the reason I am talking about this? I feel a lot now.
College students or postgraduates are not enthusiastic about macro mathematics. I want to have the topic on the class, I can do it.
It, you feel very happy. You don't want to think all the whole mathematics, or the whole geometry, or the entire generation
Number, what do we need to study? What objects do we have to pursue? I want to consider these things.
Love doesn't spend too much time, but you have an integral idea. Integrity idea is right
There are basic skills, even if you are very trivial, you have to know, you can have a basics for the entire science.
View, a wide range of views. Talk now about my personal experience, I remember that I learned when I met.
The plane geometry. Everyone knows that the plane is very beautiful, I think it is interesting. The flat geometric on the book
I know how to do it. But I think it is still not enough, so I will connect a lot of basic questions.
Together, I will start slowly. I have found some questions that have nothing, what can I want to think about the book?
Use place, is it possible to solve most of the planar geometries? I want to find some propositions that these methods are not
There is a way to solve. I remember that I thought of a question in junior high school, I found that there was no way to solve it. I spent a lot of work to think, I have seen a lot of extracurricular books to help, I am very happy to find a book telling the question.
The question is impossible to solve it with a compass and a ruler, and can be proved with an algebra. Because there are many different ideas
Law, half a year of work, I don't know that the compliance and the ruler I can't solve this problem, so I will see people will
This question is clear, I feel very happy; At that time, I didn't know the theory of Galois, so
Still don't know how to prove. But I at least knowing that there is a problem that I can't use conjunction with a ruler.
of. Also because of a long thinking, I started to know more about this type of problem. I also started appreciation
Go to the essence of mathematics. I think we do an exercise or study, we best spend some work to think about the whole question.
The question of the dragon, and more about some reference books, this is very helpful to you. Because mathematics is nothing more than many ways
Put together to solve a lot of different problems. This is a tool, we understand the limitations of this whole method,
There is a big help for basic skills. Basic Kung Fu is a tool, not a end point, is a start. base
If you don't know what you have, there is no way to talk about a certain study, a certain study is not good. Remember in Hong Kong
When I met a university, the environment at the time was much better than now, and there is no book at all, there is nothing.
Very good tutor, but still read a lot of extracurricular books, and also read a lot of articles. But it seems that there is a lot of waste.
Energy, this is too shallow in the eyes, sitting on the well, does not know the development and direction of mathematics. I will go to Berkeley in the future.
I have read a lot of articles, I have to know much. On the one hand, the local library has rich collection, on the one hand
Yiyou's interaction, the heart began to establish a view of mathematics. When I was secondary, the teacher told us: a good book
It is also necessary to see it. I also look at the bad book in mathematics. You may be strange why I am not good.
Also see; I think this, you must know what is a good book, what is a bad book, so you look
When the article is, be sure to figure out that this author writes the article and does not see it. Some autists, you know
His work is great, but you can see many modern times from a bad article.
development of. Because sometimes, from a simple way to write, you can see more easily, but you must
To know that the proposition he talks is not intentionally, you must go through your own brain.
. However, the organization inside him is often there, and there is often a famous article in the ordinary art.
It will also introduce something that is talking about in a famous article, and it is often written more easily. because
Its level is relatively low, it can learn some big mathematician articles, you have seen it, soon, I know how to enter
Different places, compared to good articles. This is my own experience, you don't have to do this like this.
My suggestion is for most of the time to see the works of mathematicians, small time to browse the general work, and
Comparison. When I graduate, I sometimes see the journal in the library from morning to night. At the time because
There is no research room in Berkeley, and the graduate students have no research room, sitting in the library all day. Almost mainly
I have seen the articles of journals, I have seen it, but at least some main theorems have seen. when
Most of you can't understand. I don't know how there is nothing. Often you have to spend a lot of works in the details of the details
A good article. Because the first article you can understand is too good. Not talking about
Not good, simple articles sometimes have found, seeing more articles, let you know that people are interested in which direction is interested, it is very helpful to you. There are many students run to ask me, I tell him who is doing a certain year.
After that, what stage, they have been surprised, why do I know? No one talks to me, I am my own
See it on the article. This is very important, because when you study, what do you know?
Question, great help to you. Because often doing research, you must know who is only done, in
Where you can find this document, you think that you have this help, you can run back to find this
file. Even if you know who has touched this issue in that year, it also has a lot of benefits. Have a lot of names
The articles of the family are often more step more than others, just because he knows who has done this thing, he can go find this
The article, or to find a mathematician help, otherwise, more than 100,000 people doing mathematics, you don't
Know who has done this problem, no one has done. So learning more about someone else in this area.
Question, no matter the famous articles, poor articles are good, look at it. Of course, I suggest you look more
The name of the article, because the poor article is equal to the essay, watching the martial arts novel, put it on one side after reading. you have
After the pursuit of enthusiasm, slowly put different views together. After this first step, I think
You can start looking for your own topic. Because you have begun to know what problems are mainly seen throughout the mathematics. A good
What is the problem with mathematician finds your own problem. Of course, there are different findings, some people want to develop a set
On some people to solve the problem, the theory's goal is still to solve the problem, so solving important issues is
A very important ring in the general theory of development. For example, it is three-dimensional, it is three-dimensional control.
The most important guess in the topology, we know that the former people have spent a lot of effort to solve it, now there are many different
The trial method is each a climate. This proposition has become a discipline rather than an independent question.
question. This is the structural problem of three-dimensional space, and it is necessary to completely solve this conjecture. On the other hand, some people are
What is interested in Poincare Conjecture, is not interested in other problems, because it is recognized
problem. I want everyone to have different views. I have many friends being a very famous mathematician, they
I just want to solve the problem, I think this is a wrong choice method. In mathematics, we should have the whole
There is a systematic idea, thinking about what kind of problem should be solved throughout the mathematical purpose.
You may have read the three stages of the kingdom of university, the first stage is Yan Shu, "Western wind last night
Delivery tree, alone in the West Building, looking for the end of the earth. "This is the first stage of King Guodi to make a university asked, to explain
This paragraph, I have to explain the importance of basic kungfu. If the basic kung fu is not done well, you don't look at it.
far. Your call is a middle school student to see the end of the world, it is impossible, and finally tells some empty talks. Mathematics
Or if you have a scientific history, you are not qualified to talk about things. It's not to call you all.
Solution, at least a certain understanding. Many students now, especially postgraduate, I think it is more headache, teach him to do
A small question, after doing it, I don't want to put it in my life. Keep writing a small article, I have written the article. Of course you can send
Table, speaking to some young people, he thinks it is very good, don't want important questions, today can write one
Xiaobu, you can write a small article tomorrow, you can upgrade, if you don't write, life will be flexible. This is right, but you really want to be a good topic, but it is not so difficult. Some research
Sheng's papers are famous writings in history. Why can they spend three, four years of work, make such a
Color work? They never understand, and then go forward. Said that I really want to do a good top question, not
It is like you think a lot of time to spend a lot, the problem is what your determination is. Western wind last night
Delivery tree, that is, if you want to look far, you have to remove the small tree in front to see the far. If our eyes
It is a small topic in the world, and you will always see it. We must know how to give up some slag, can we do one
Some good questions, I think this is a very important thing. You don't want to give up, you know that you will not have a future.
The problem will never do a good problem. This is a difficult choice, because you feel graduated, upgrade
Question, and don't want to give up, you know that you will not have a future problem, then you will never make a university asked.
. I remember that when I just learned geometry, the popular metrics were geometric, all tools were triangle comparative theorem.
Come, I always feel that it is not deep enough to the geometry, and I will start a series with my friends and students.
In the geometric study of the tool to the differential equation, I am also very glad that I will give up some small results, take a self
His road. When we have questions, you can follow the famous mathematicians, follow the tutor or from the book, but
The final thinking must have your own ideas to make an university asked. Because you don't have your own ideas,
You always follow people, there is no way to learn. However, you may not qualify for this thing.
Because you don't understand this. I told a lot of pile at first, because I hope you want to think about it.
I want to be basically doing well, I want you to know the different propositions in this study. Just like you buy goods, you want
I know what is possible in the department store, you pick it up. The second stage of the kingdom of the kingdom is Liu
Yong's poem: "The belt is gradually widened, and it is awkward." Finding the enthusiasm of the truth is like a young love person.
It is very important to pursue your own object. In the middle of the pursuit of a good proposition, there are many
Working, sometimes even very painful. But as long as we know, the final result is worth it, we will
I will spend a lot of work, just like love. Many young people are looking for an object, thinking about it, as a learning
There is no such attitude. If you have no enthusiasm for learning, you can't make a university.
ask. In fact, Qu Yuan said, "There is also a good thing, although nine death is especially true." More is more complete than Liu Yong. Next
It is a third stage of Wang Guowei to know that Wang Guowei's third stage is: "Dream is looking for him thousands of Baidu, he looks back, but the man is in the light
Sands. "Of course, this is the new poem, not what I said, but basically we have this feeling. You really
When you have a good article, you have this feel. We spend a lot of work to make a good proposition, there is
When you think about it, you consider this idea to sleep well, sometimes you can't sleep well, think hard. Sometimes
Hard work, just sleep for a long time, if you do this, you will solve a lot of unexpected.
problem. I don't think people are particularly smart, but you spent a lot of work, you can enter traffic or Tsinghua University,
It should not be too bad. I think you spent so many indentations, I must have some results. I
They don't have the same relationship with love, sometimes it does not necessarily see a goal, but see other. Just like I just
Speaking, we have to solve the Poincare Conjecture, and finally did not solve it, but solved other propositions, which is often in the history of math. Everyone has this experience, you must solve this problem clearly.
The results were found to solve other problems. This is because we do this topic, I don't know how to walk.
Yes, but you will do this tool all, the basic idea, interesting ideas you know
Once, you can solve a lot of problems. When walking on this road, don't be too stubborn. You have to know
Have other interesting questions. It is a new set of ideas, often there is other problems, you can just
solve. However, you have to know, you have a study throughout the study, your eyes are open, how
What is it? Many students don't want to listen to Colloquium, and I don't want to listen to other people's seminar. Do not listen
Seminar does not know what is doing. Obvious you can solve the problems they are doing, but you
It's a big difficult to see it. Many students, especially Chinese students, tell me
Wen is this, this seminar has nothing to do with my paper, I don't want to listen, don't want to see, don't want to go
Come with others, don't want to talk to others. As a result, your paper may not be the problem you can solve, maybe
Your way is just to solve people's problems. Because you don't want to listen, go, you can't solve it.
question. A person's thinking is limited, the ability is limited, you can't help but help. What is the help of people?
worry? On the one hand, it is to read articles, listen to seminar, on the one hand, please ask the famous family. When you go to ask others
Waiting, 95% people don't know what you are doing, or you can't provide you with direct opinions. If
Directly provide you with your questions directly, your problem is not necessarily a problem.
It can be seen that you haven't figured out how important this problem is not figured out. But don't matter. Ask others to always be good,
At least know how good this problem is, still bad. If you are afraid, just in seminar or colloquium
When you want to listen more, you can listen to you. If you don't understand in seminar, at least
You are watching the words he wrote, you know what you are doing recently. You may feel inexplicable,
But in fact you can get the benefits, this is very important. So you can have the opportunity to try to listen to different classes.
There is a great advantage for you; the pure mathematics should also go to the application of mathematics or physical classes. Listen to Seminar
Even if Relax has no relationship, anyway, it is better than boring or watching TV. How
An isolated place can also be a good study. I will give an example, fourteen years ago, Fudan University
There is a student, he is coming to me, I promised to collect him. As a result, the principal of Fudan University was afraid of studying students.
All walks away, so it is not allowed to go abroad, so he has no way to come with me. But he wrote me 80 years
Set, there is about one hundred questions, choose one of the topics to do, desperately doing. I don't know that he fights.
Life is doing this topic, although he is in a relatively isolated place, but only for more than ten years.
Type, finally made a very important result last year. I feel very happy, because this topic is a very simple
The problem. It can be seen that you only have to find the topic, and you don't work hard, even if you don't come to visit.
If you can't do it. Of course, I don't know if he doesn't have it, because Fudan is big.
There are also some very good mathematicians in school. I don't think I will not be with others. But in Jiaotong University
The Tsinghua is not a place that is all isolated. Under this condition, I think it is definitely able to learn, as long as we will make it clear about the whole idea, the whole question is clear.
Today, I said that I think it is five years. I want to tell me the experience of my book, I hope you can refer to, I
It is the practice of this. But it is not seen that everyone has such a practice because every mathematician is
There is a different view of learning. You can follow different routes, but I want the basic work that I want to start.
Doing well, it will never fall. Then we must try to develop your own field, and the topic must do important. Rear
It may be a relatively small result. But I always want to do an unimportant problem than when I start.
Great. After solving the entire major problem, your opinion or the views of the whole study are different, you will
Have different ideas. Tell this today, thank you.
