Radar constellation _leosat constellation

What interesting things did you experience in the college entrance examination?

Today, in my thirties, I look back on my experience so far (philosophy of mathematics in high school->; Enter Nanjing University to study business management-> Senior Professor of New Oriental GMAT/GRE/ TOEFL-> Studying abroad (Faesse Business School &; University of Chicago booth business school)->; Business &; Amgen Southern Europe Management Team; Financial analyst->; HSBC Hong Kong Stock Derivatives Trader (Co-Director)->; I think the experience of studying philosophy of mathematics in senior high school, though full of setbacks, is a very unique and interesting experience, which will benefit me for life. I will use my experience to answer this question and give some enlightenment that I personally think is very important.

Go back a little time. When I was 3 years old, my father taught me how to calculate 9+9. He focused on the carry in decimal operation, and then gave me a problem of 999+999 to solve. I solved this problem after mastering carry. Of course, I was praised by my parents and relatives, calling me "smart" because I can use the rounding rule flexibly. Since then, the word "smart" has been firmly combined with the word "flexible" in my mind, and since primary school, mathematics has become my favorite subject, without one, because it is flexible and beautiful. Because the topics in primary school and junior high school are not difficult enough, I can also do math easily with my own "feeling".

After entering high school, everything seems to have changed, and the amount of knowledge and the difficulty of the topic (especially the competition topic) suddenly increased. In view of this situation, my teacher (and most math teachers) suggest that you classify the math problems in each chapter and find out the common solutions of each kind of problems (such as translation method, complement method, direct method, three vertical theorems, etc.). ), and then familiarize yourself with these solutions by asking questions. Hearing such a suggestion, I was blinded at once. Isn't this inconsistent with the "flexibility" that I have admired since I was a child? In this case, doesn't mathematics become the same as rote learning? I hate this kind of study from the bottom of my heart, but the reality is cruel If I don't sum up all kinds of problem-solving methods of sea tactics in advance and encounter problems in various chapters, my "feeling" will often fail, let alone come up with a solution in the very limited time of the exam. However, logic tells me that this learning method is wrong-if you learn 1000 types of questions and memorize 1000 methods, what should you do when you encounter 100 1 types of questions? Take a long view. Can I only solve the problems that teachers have taught, books have introduced and I have been doing all my life? What about unprecedented problems? What about the so-called innovation ability? Why can those mathematicians explore all kinds of theorems and prove them in such a novel way? They have never seen these theorems before. Is it because they are gifted and I am stupid, or do they have their own unique way of thinking, and I just haven't found it? Although I am proud, I will never admit that I am more stupid than others, so I am determined to create a set of thinking that can solve all the problems in the world (not just math problems). /kloc-when I was 0/6 years old, I came across Mr. Jin Yong's novel the legendary swordsman and was ecstatic. Is my thinking not in conformity with the Nine Swords of Dugu? Everyone else is memorizing methods, just like the various swordsmanship of Huashan School and Songshan School, and I need to create nine swords of Dugu, and I can find flaws in every topic without winning!

So I resolutely started the research and development of "Nine Swords in Mathematics", but the ideal is beautiful and the reality is often cruel. I didn't listen to the teacher's lecture and taught myself the course. I found many problems, especially the competition questions with certain difficulty to learn. However, it is difficult to explore a new thing at any time, and you are bound to make all kinds of mistakes in the process. The "laws" I have summed up often apply to one topic, but not to another. At that time, the Internet and information technology were far less developed than now. My parents and I traveled all over the streets of Guiyang, and the library couldn't find a decent book introducing mathematicians' thinking. As a result, my grades fluctuated greatly, because I completely abandoned the tactics of asking questions about the sea and boldly practiced the immature "law" that I summed up in the exam. It seems nothing now, but for me at that time, the top students from small to large, their math scores could actually drop to 70 points of 100, while those diligent "back teachers" who I despise in my heart could get full marks, which was a bolt from the blue! I have also become an alternative in the eyes of teachers and classmates. I was arrogant and didn't attend classes, but my grades deteriorated. Even my parents and relatives can't understand it, which gives me a lot of pressure. I was unmoved, and even applied this way of independent thinking to physical chemistry and other disciplines. I still remember asking my physics teacher, "Mathematics is a wonderful axiomatic system. As long as the axiom is correct, all the theorems derived from it are correct, but physics seems to be different. You see, Newton's theorem textbook says that it is no longer applicable at high speed, but the momentum conservation theorem deduced from it is also correct at high speed. Isn't this illogical? " As a result, I was invited by my parents, saying that your children don't study hard and never forget it every day. Actually, this is a very good question. The logical basis of science is different from that of mathematics. Science is not a deductive system, but a logical system based on induction and causality, so mathematics is not a science. )

But now I am very proud that I have withstood all the pressures and persisted in my research. Maybe hard work will pay off, maybe luck. I finally summed up the first three tricks in my current mathematical philosophy before the college entrance examination, namely, translation, specialization and objectification. Enough to cope with any difficult college entrance examination questions and 70% competition questions. It was not until I entered the university that I found many books by great mathematicians in the university library. They actually explore the same as me-the nine swords in mathematics, such as Descartes. The core of his creation of analytic geometry is our first move "translation"-transforming all geometric problems into equations, and the steps of solving equations are fixed, so he can solve all geometric problems; Another example is Euler, a very prolific mathematician, whose problem-solving thinking (such as extensive use of analogical reasoning) is amazing; Another example is Paulia, a master of problem-solving thinking and eloquent reasoning, and so on.

All these efforts have begun to pay off. Whether it's mathematics in college, or specialized courses, or specialized courses after going abroad, such as some advanced financial courses, the philosophy of mathematics I have learned has made me comfortable-I don't need to do a lot of exercises at all, I can quickly cut into the essence of the subject and solve problems flexibly. Take my work in Amgen as an example. As an internal consultant, I was sent to Portugal, Spain, Belgium and other countries to help local management teams solve one problem after another. My philosophy of mathematics has also played a great role. In the process of consultation, many problems are new and unprecedented, and I can explore one solution after another. In the years that HSBC has been engaged in derivatives trading, mathematical philosophy has also played a vital role in exploring the laws of financial markets and finding out appropriate trading strategies. In starting a business, many ideas in mathematical philosophy, such as management by objectives derived from the third move, have become a part of our company's business strategy and corporate culture.

Seeing this, I believe many people already know my answer to the question "What is learning high school mathematics well?". -Learn the problem-solving thinking of first-class mathematicians, practice it in the study exam of high school mathematics, and continue to practice it in future life and work. Students or parents often ask me, is this mathematical philosophy helpful to improve my grades? Of course, the answer is yes. If the philosophy of mathematics can't even help the small college entrance examination, it doesn't deserve the word "philosophy". Students who have a solid grasp of basic concepts can reach the level of NMET 140 within 2 or 3 months by studying mathematical philosophy and integrating it through a lot of practice. It is also possible that students who work harder will win the first prize in the competition within 4 or 6 months. "Your philosophy of mathematics is too high. How should I learn? " In order to solve this problem and let the children in China really learn the essence of mathematics, I set up essential education, and spent a lot of time and energy to record all the chapters in high school. In each chapter, in addition to reviewing the relevant knowledge, I also explained in detail how I use mathematical philosophy, especially our first three tricks, to work out the answers step by step, so that students can learn the correct way of thinking to solve problems step by step. I hope to change China's rote learning education and really cultivate some real talents. This is my original intention of establishing essential education. Interested students/parents should read an article I wrote before, How to Become a Master of Solid Geometry.

Finally, I want to talk about the enlightenment of my unique experience:

If a person wants to achieve something, he can neither be superstitious about authority nor imitate others easily. He should stick to the road of logic, regularity and objective reality. There is a thing in this world called statusquo, which is a pattern that everyone does and gradually forms. For example, the mode of "classifying topics and memorizing methods". Learn to question the premises behind these models and assume that they are correct? Great scientists and companies in the world are often good at challenging these models (status quo). For example, Einstein challenged Newton's "model" and put forward general relativity. For example, Toyota challenged the mass production mode and finally proposed lean production. Such examples abound.

People should set long-term goals instead of always focusing on short-term goals. You know, most of the long-term happiness in this world is short-term pain. I am glad that I had this vision when I was in high school. I was not moved by the ups and downs of short-term grades and insisted on pursuing a mathematical philosophy that would benefit me for life. A few years ago, when I saw the same principle written by Mr. Radario (one of the most successful founders of hedge funds in the world), I couldn't help feeling a little proud. I hope our natural education students will keep this in mind and not be moved by short-term interests. SteveJobs's speech at Stanford, I hope students can have a good look and understand the true meaning of "follow your heart". To some extent, following your heart is to remind people to pursue long-term goals. Although there will be setbacks and pains in the short term, in the long run, these setbacks and pains are worthwhile. I can't help but sigh when I hear that all the top candidates in the college entrance examination in Hong Kong apply to medical schools and want to be doctors (doctors in Hong Kong earn much). If I pursue short-term comfort, I don't have to quit my job with an annual salary of several hundred dollars and start my own business.

People should be able to accept others' incomprehension and have indomitable toughness. Since you start to challenge the existing model (the status quo), you will certainly not be understood by most people, and it is normal to hear all kinds of questions. I hope students will remember that your task is not to be an actor, and your task is not to please others, so you don't need the approval of most people, especially short-term approval. Insist on doing things that are logical and realistic, don't be hit by mistakes, keep learning from them, and when your advantages appear, those doubts will slowly dissipate.

The mathematical philosophy I developed is more like a skill of swimming and cycling than a knowledge (such as what Newton's theorem is). Learning this skill requires a lot of practice. How can you learn to swim without diving, how can you learn to ride a bike without wrestling? In fact, many things in this world are easier said than done, such as the above three, 1) challenging authority, 2) pursuing long-term goals, and 3) being resilient. I believe that 99% people can understand them, but how much can they do? Or Mr. Wang Shouren summed it up very well, knowing but not doing it means not knowing. This is why many people disdain many good chicken soup articles, but they don't know that the problem lies with themselves.