Author | More people are righteous
Source | Know zhuanlan.zhihu.com/p/338826476
Yue Minyi, a famous mathematician and pioneer and leader of Chinese operations research, has achieved a number of important research achievements at the international leading level in queuing theory, nonlinear optimization and combination optimization. He was the deputy director of the Institute of Applied Mathematics of the Academy of Mathematics and Systems Science of the Chinese Academy of Sciences, and the chairman of the Chinese Operations Research Society. Born in June 1921 in Guiyang, Guizhou Province, he graduated from the Department of Mathematics of Zhejiang University in 1945. Since then, he has taught at Guiyang High School, Zhejiang University and Guizhou University. He was initially taught by Professor Chen Jiangong and Professor Su Buqing to study function theory, and later became an assistant to Professor Hua Luogeng, engaged in number theory research. In 1951, he was transferred to the Institute of Mathematics of the Chinese Academy of Sciences to engage in mathematical research. He has successively served as assistant researcher, deputy researcher and main research. In 1958, in accordance with the needs of the country, it was transferred to a new subject area - operations research. His research achievements in operations research are remarkable, and he is a well-known expert in operations research in mainland China. For his outstanding achievements in the field of operations research, he has won the National Science Conference Award (1978), the first prize of the Natural Science Award of the Chinese Academy of Sciences twice (1981, 1987), the third prize of the National Natural Science Award (1987), and the first Science and Technology Award of the Chinese Operations Research Society (2008), etc., making outstanding contributions to the development of operations research and mathematical planning in mainland China and the cultivation of talents.
It is mainly engaged in the research of number theory, queuing theory, sorting theory, mathematical planning and other aspects. In terms of number theory, it solves the new problem proposed by Gross Walder in the United States, and makes significant improvements to the three-dimensional divisor problem. In terms of queuing theory, the analytical expression of the instantaneous state of M/M/s of multiple queuing systems is given for the first time, and the existence nature of the smooth distribution of this system is studied. In terms of sorting theory, the optimal conditions for differential order are derived for the Flow-Shop sorting problem, and a new efficient algorithm for seeking the optimal order is designed. In terms of mathematical programming, the non-convergence problem of Wolfe's reduced gradient algorithm for nonlinear optimization problem is solved, and a new dependent gradient complacency with global convergence is designed to solve non-convex programming. He has published more than 20 papers and several other works in the fields of Fuers' analysis, number theory, queuing theory, combinatorial mathematics, mathematical planning and other subjects. He was the editor-in-chief of operations research, the deputy editor-in-chief of the Journal of Applied Mathematics, and the editor-in-chief of the operations research sub-volume of the Encyclopedia of China.
Most of the people who like to introduce their learning experiences are people who think they have achieved something but are not willing to drown out. Since I am willing to write this short article, it is difficult to exclude myself from these people. But I am a man who works all day and has nothing to do. If there is some "experience", it is mainly in the aspect of failure. Although the experience of failure cannot guide the "direction" of the later generations, it is not without the use of pointing out the "lost".
Mathematics is a fascinating subject, but it is not as accessible as literature. When an author creates a literary and artistic work, he often unconsciously thinks of the vast number of readers in his heart, hoping to get resonance from them and arouse some kind of admiration or sympathy from them. When most mathematicians create a certain result, they mainly think of a part of his colleagues who are higher than him, hoping to arouse the admiration or admiration of those people in a winner's posture (except for those who write "papers" for upgrading or other purposes). Not attaching importance to the evaluation of peers, but only hoping to get the sympathy and admiration of the majority of the masses in society, such mathematicians, I think, can not say no, but the number will not be many. Therefore, mathematical theorems, from the process of their emergence, it is difficult to say that they have the desire to take the initiative to win the admiration of the broad masses, and people cannot talk about approaching them naturally.
A young man begins to like mathematics, often because, consciously or unconsciously, after a period of effort, long or short, he feels superior to those around him, and makes him feel that he has a certain degree of superiority in this subject, which is generally regarded as difficult to deal with, and moves forward with a sense of a winner. At this time, he will have fun solving mathematical problems, and mathematics will "fascinate" him. The more he is fascinated, the more he will study hard, his grades will naturally improve significantly, and his interest will become greater and greater. Therefore, the hobby (or interest) in mathematics is acquired, produced through hard work, not innate.
Some people, in their infancy, were higher in their recognition or imagination of mathematical calculations or of certain simple geometric images than those around them of the same age, and later he made mathematics a profession. This situation often made him feel that he had a natural mathematical talent, and even was born to engage in the field of mathematics. We think that certain talents born only help him to be easily interested in mathematics, and his love of mathematics is acquired. Except for a few people, the talents of ordinary people are not much different.
When I was in high school, I began to divide the liberal arts and science classes from the second grade, and due to the large number of people requiring science students, I needed to pass the exam to get to the science class. I learned math very poorly and barely passed. But in the monthly exam, I only took the fifty-odds test, failed, and was scolded by the teacher. In my dormitory, there was a classmate who was in the bunk next to me, and everyone called him Mr. Zheng, but he scored seventy points and was praised (at that time, it was not easy to get more than seventy points). I was not convinced, thinking that I was smarter than him, at least people did not call me boss, thinking that he just happened to meet. At that time, several classmates came to ask Mr. Zheng for advice, and he replied with a straight face. I couldn't help but secretly admire him, so I asked him how he came to be. He told me that every day when we went to bed after lunch, he went to the classroom to do exercises. His words inspired me a lot. After that conversation, I stopped taking a nap every day after lunch and rushed to the classroom to do exercises. Soon I also achieved good grades and started my career in mathematics.
Yue Minyi won the first Science and Technology Award of the Chinese Operations Research Society
I am not a person who follows the rules and does learning, and if I have gained a little, I am very ambitious and hope to ascend to the heavens one step at a time. I always try to learn something deeper and harder than in class. For example, while the teacher was teaching plurals and quadratic equations, I was desperately trying to do the exercises in the chapter on equation theory (Fan's large algebra). Because it is self-study, the text is half-understood, and when the teacher teaches a chapter of equation theory, because most of the content I am already familiar with, I have no intention of listening to the lecture, I do not have the heart to study the places that are not clear, and I am interested in calculus and differential equations all the time, and the result is that most of what I have learned is "sandwich rice", and then I have to return to the pot, and I have to do half the work. Although I have come to realize from my friends' work that step-by-step is a good way to learn, I have wasted a lot of time after all. Moreover, the habit of being ambitious and far-sighted and seeing different thoughts is difficult to eradicate.
The so-called step-by-step means that when the first step has not been learned thoroughly, or even seems to understand, do not enter the second step. Mathematics is a discipline that is very logical, and the later parts often use the knowledge of the previous parts, or the methods of dealing with problems. Sometimes although theorems or methods are not used directly, some kind of training is needed, and without this knowledge, methods and training, the further you go, the more confused you will feel. What is written, specious, replaces strict mathematical reasoning with intuition, and is full of fallacies. In terms of learning, because the things encountered are more and more complex, they will feel chaotic, do not know how the problems in the article are solved, and even what to say. As a result, you will feel more and more unable to learn, and you will lose interest. If you develop a gradual habit, you will sort out what you have learned. A complex proof of which parts are original to the author and which are "high", it is estimated that they cannot be made. From this, I found the gap between myself and the author. "Shun people also, I also people", we must look up to those talented authors. Deficiencies, quickly make up for them, and try to catch up. Generally speaking, in the same article, "high" is generally not much. For this kind of "high", we must make efforts to learn, experience, and find a way to use it. More on this point.
When you develop a habit of analyzing problems and pondering articles, you accumulate over time; You will feel that something complex is also made up of a few large parts. The reasons for the emergence of these parts and the interrelationship between them are also understandable. At the same time, because of the more things to read and the higher the skill of calculation, you will find that some complex deduction process is mostly composed of some inevitable steps, and it is easier to grasp the new key part. And when you want to create and write articles yourself, you can see the big layout and easily know where the difficulties are. This is like playing chess, a good chess player, every time he plays a piece of chess, he must go all out, not easy to fall, and consider every possible situation to the best of his ability. After practicing for a long time, he found that every time he wanted to make a son, only a few situations had to be considered, and the rest could be ignored, and the scope of consideration could be reduced to a few possibilities, and the analysis of the problem would be deepened. A good chess player can see ten, twenty, or even more, and that's where kung fu lies. On the contrary, some people do not pay attention to cultivating themselves, casually, relying on intuition, not going deep, one son goes down, it becomes a big mistake, the number of plates is a lot, but it is a piece of.
Hua Luogeng was listening to Yue Minyi talk about the research work he had done
For learning, it is necessary to take it step by step to avoid sandwiching raw rice. But it is not enough to just take it step by step. A book or an article, it is always written in some logical order. According to the content it contains, according to the interrelated relationship, the content is arranged in a certain order, so that the things mentioned earlier will not be used in the later words, which is called logical, otherwise it will be chaotic. It is impossible to imagine that a secondary school textbook would put quadratic equations in front of a primary equation. Because the knowledge of primary equations is used when solving quadratic equations. A decent book is always written in a step-by-step spirit.
We read a book in order to learn something useful. That is, this knowledge may be used in some occasion in the future. When we need to use them, we know that these things exist, and we don't have to learn them temporarily. The knowledge here can be a theorem or conclusion, some technique for dealing with problems, or some kind of compound of them. To make our work run smoothly, rather than running into walls everywhere, we are required to be able to master this knowledge skillfully. When it is used, some are easy to come by hand, some need to be transformed, and some need to be created in some way. To do this, teachers and students must have higher requirements for themselves.
When teaching people to practice boxing, boxing teachers generally always teach students a set of boxing techniques first. After the student has learned these sets, when he actually meets an opponent, if he shows them one by one in the order taught by the teacher, it will become a funny play. If he doesn't get beaten, he has to be flexible and flexible with what he has learned. He should know which hand to apply under what circumstances, under what circumstances to put the unrelated hands together, sometimes need to change, sometimes need to create, and so on, this is called disassembly, convergence. The difference between a good teacher and a bad teacher is first of all whether each action he teaches is correct, but the more important difference is that a good teacher focuses on how the student uses what he has already learned. He confronts his students, sees his flaws, makes him suffer a loss, and then points him out and teaches him how to overcome his shortcomings. The method of Wang Jin teaching Shi Jin mentioned in the second episode of the Water Margin is a good example. Shi Jin's earlier teacher, Li Zhong, seemed to be a less intelligent teacher. Although Shi Jin was taught by seven or eight "famous masters," the sticks that came out were "just flaws, and they can't win really good men" and "good is good, they can't get into battle." When fighting with Wang Jin, it was only after one round that Wang Jin was "only provoked, and the stick of the later life (Shi Jin) was thrown aside, and he fell backwards." ”
Of course, this is not to say that the seven or eight "famous masters" are all mixed meals. Shi Jin did learn a lot from them, so "more than half a year before and after, Shi Jin learned the eighteen martial arts very skillfully from the new, and Wang Jin taught them wholeheartedly, and every piece of the point was mysterious." "What those seven or eight masters lack is that they can't point out this mystery."
However, there are many capable people in the rivers and lakes, each with its own expertise and its own tricks. How to deal with these tricks, even the best master can't point them out to the students one by one. This requires you to learn, experience, and strive for excellence in practice.
The content of mathematics is much more complicated than the art of fist. How to apply the knowledge learned is generally achieved by doing exercises (here, I would like to say that I am not in favor of solving problems). However, exercises are generally related to the content of the chapters in which they are located, and therefore have their limitations in terms of training human abilities and applying the knowledge already acquired. Students should be trained to have a habit of trying out when they see a biased problem, a strange problem, and a difficult problem, and not to give up without making it happen. Students are required to use all their strength to take out the "strength to eat milk". A problem, if you can't do it yourself, and others do it, it shows that you are a "bad egg", you need to redouble your study and try to catch up; if you do it yourself, others have not yet made it, indicating that you still have some merits, playing a role in boosting morale. By doing some informal exercises, students can develop the ability to flexibly use the knowledge they have learned.
Teachers should be encouraged to work with students on assignments. It is normal for teachers to sometimes inevitably lose to students. "Threesomes, there must be my teacher", not to mention that there are dozens of students in a class, and naturally some of them will be talented. The teacher may have more knowledge than the student, but it cannot be said that his intelligence also exceeds that of all the students in the class. This is logical reasoning. Therefore, there is no shame in losing to them. From failure, teachers can learn certain ways of thinking about problems from students, certain things that they don't know. With these, when teaching the next class, you will increase your ability and gradually win the trust of students, which is called teaching and learning.
Let us now turn to the question of the purpose of learning. We say that learning is a means, not an end. We always learn for a purpose. Learning endlessly is nothing more than a waste of time and energy. The purpose of learning is to use the acquired knowledge and ability to solve problems. Here, we would like to emphasize the word "ability" in particular. It is gradually cultivated in the process of learning, invisibly, and I often hear some people say: "I don't use what I learned in the classroom in my work." "This kind of reference is not comprehensive, and the knowledge in the classroom may not be used directly for some people, but the ability cultivated through learning plays a role there." This ability includes the way of thinking about problems, the logic of thinking, and the ability to analyze and absorb new things as a result of having a wider range of knowledge, and so on. Even for these people, I believe that as long as he is willing to study, rather than deal with the work at hand, what he has learned will come in handy.
The purpose of learning is to solve problems. What kind of problems to solve? In terms of mathematics, there are roughly three sources for the problem. A class of problems arises from within mathematics, the so-called purely mathematical aspects of problems. For example, would any sufficiently large even number necessarily represent the sum of two prime numbers? This problem arises from the structure of mathematics. The second type of problem is a universal mathematical problem that arises in order to solve practical problems. Most of the problems in operations research and mechanics fall into this category. For example, the organization of transportation. Such problems can be reduced to a specific form of mathematical problem. This comes the study of how to solve, and the nature of the solution in various cases, and so on. What is being studied here is not a specific transport problem, but a study of a common and representative transport problem. The results of the study are then applied to a variety of practical problems with similar structures. We call this kind of mathematical problems based on the study of natural and social phenomena as applied mathematics. The third type of problem is how to use mathematical methods to solve a specific practical problem. It is also a transport issue, but the specific circumstances are different. For example, some goods are easily broken, some goods are flammable, and some goods, such as chemicals and food, cannot be transported together. When applying the methods of applied mathematics to specific problems, certain modifications must also be made according to the situation. We call this kind of work an application of mathematics. Whatever kind of problem it is, it requires us to apply the knowledge we have learned flexibly, and it requires us to create a new one on the basis of the old. Here, I would like to say a few words to young readers. The development of things always comes first, and the later people always surpass the predecessors. This is an inevitable law of historical development. Otherwise, it would be impossible for human beings to progress from the burrowing wilderness to the current situation of life. But who will surpass the predecessors, that is another matter. Although it is not necessarily better than the predecessors through hard study and hard work, it is inevitable that it will not be better than the predecessors without doing so. Victory belongs only to those who are not afraid of hardships and hard work, and here perseverance is extremely important, I have had this experience more than once, when I studied a problem, after some "effort", I felt cornered and decided to give up. But it didn't take long for someone else to do it. Taking a look at what others are doing is entirely within your own reach. My failure was a lack of perseverance. Whether we can sort out some intricate and tangled things in an orderly and clear way, clarify their mutual relations, and draw the necessary conclusions require perseverance; when encountering difficulties and feeling helpless, can we consider from various different channels, carefully read and analyze relevant materials, draw useful things from them, and apply them to our own problems, which require perseverance; when we want to open up a new topic or field, we must read a large amount of literature. Learning something that you have never encountered before, you have a long way to go, and whether you can implement it consistently requires perseverance. In short, perseverance is an essential factor for completing a career. Confucius said, "Fortitude mu ne near ren", raising perseverance to the height of near benevolence (the highest virtue of Confucianism). It is not unreasonable that it is also listed abroad (fortitnde) as one of the four basic virtues.
The purpose of learning is to use. Use what you have learned to create spiritual or material wealth. The idea of asking only about hard work and not about harvest cannot be considered a good idea, a thought of being responsible to the people. "Use" is for a certain goal. With a goal, there is a choice of what to learn, not endless. In time, you also know how far you should learn, and you can also measure whether you really understand what you have learned, integrate it, and know what knowledge you need to master for your own purposes. At this time, you will also feel that although some knowledge is already very familiar and can even be memorized, it has not really been mastered, because it will not be used, and then re-learning, the experience is very different from before.
Here arises the question of how to find a "goal". For comrades engaged in practical work, the goal often comes from the practical subjects on which they were engaged at that time. For example, a designer, when designing a certain project, if he wishes to create something, he should understand the latest methods and latest achievements in this field in the international arena, and then put forward opinions on what should be done according to the specific conditions of the mainland and after careful analysis. For a comrade engaged in theoretical work, things are more complicated. The requirements of theoretical topics are not as specific as those of practical problems, and the degree of freedom is greater. How to choose an appropriate subject, even for experienced people, is not so easy. In this regard, although there is no shortage of self-taught people, if you can get the help of good teachers and friends, you can take fewer detours.
In the selection of a theoretical topic, at least two aspects must be considered: first, the topic should have a certain theoretical value; second, it should be competent within one's own ability. Beginners are prone to extremes, or choose problems very difficult, greatly exceeding their own ability, and the result is to run into walls everywhere, unable to do anything, and waste a lot of time. For example, many people regard the Goldbach problem or the Fermat problem as a research topic, and they have no idea about the development of research work on these topics and the reasons why previous generations have not succeeded, that is, the difficulties of the problem. Others choose things that can only be used as simple exercises as research topics. Articles cannot be published when they are written, and even if they are published, it is difficult to be elegant. To choose the right topic, you must be familiar with the literature related to the topic, know what is called "one step forward", and then establish the goal of your own efforts.
Professor Yue Minyi attended the Second (Expanded) Meeting of the 8th Council of the Sorting Branch of the Chinese Operations Research Society and the National Ranking and Portfolio Optimization Academic Forum held in Rizhao in July 2014
Finally, I would like to touch upon the issue of "fundamentals". The basis referred to here refers to the knowledge and training necessary to engage in a discipline. Without the necessary knowledge, one does not know what others are talking about and does not understand the meaning of the questions and conclusions. Without the necessary training, it will feel difficult everywhere and difficult to move forward. Therefore, a certain foundation is necessary. But the foundation is only relative to a certain subject. Those who study algebra have different requirements for mathematical analysis than those who study differential equations. And a person often changes his views and topics according to objective needs or the development of disciplines, at this time, the original foundation can not adapt to new needs, and it is necessary to learn from the new. Even if you always work in the same discipline, with the development of the discipline and the expansion of your work scope, you need to learn new basic things. Therefore, the foundation is a bottomless pit. Although a certain foundation is necessary, you can't wait until everything is ready before you start working, you can only expand and deepen your basic knowledge by doing and learning at work.
For the training of basic training to talk about, it is important to do more different types of problems to do brain work. Wide thinking. A good writer always has a wide and varied way of thinking. Shakespeare is a good example, and his thirty-seven plays have their own characteristics in terms of themes and treatments. The main characters in "Water Margin" also have their own unique faces. But a clumsy author tends to be the same when dealing with the subject matter, so that people know who it is from at first sight. Such a person to engage in mathematics, in the best case, is just a cheng bite gold, that is, so three axes. When there is a problem, it happens that his hand can be controlled, and it is counted as a collision; if it is not right, there is nothing to do. The shortcoming of Cheng Biting Jin is not that he is incompetent, because he also has a three-plate axe, but that he is conformist, satisfied with the status quo, unwilling to learn new things, nor do he want to learn from other people's strengths.
Above, I wrote some of my own experiences in the process of learning mathematics. Talking about this does not mean that I have learned well; on the contrary, I have all the shortcomings mentioned above, comparing my shortcomings with the advantages of others, feeling a lot, and writing about some feelings. On the other hand, for learning, each person has his own experience, which naturally carries many prejudices and limitations, please forgive the reader.