I am a second-year girl, in a good junior high school, her grades are not bad, she has not fallen in the top fifteenth grade, twice first. Chinese is now above 135, Mathematics English is above 145, and the total score of eight subjects is first in the basic grade.

When I was in elementary school, I was like most of my classmates. Although I was excellent in mathematics, I was afraid and bored with “Olympics” and never showed any talent for mathematics. It wasn’t until the summer vacation of Xiaoshengchu that I came into contact with geometric proofs at home for seven times. From then on, I was obsessed with mathematics and became a class representative at school. In the first year of junior high, I was very passionate about geometry. The small dining table was chaotic. I sat on the stone steps diagonally opposite the school at noon in the name of arriving early to prove the theorems I learned before. The sum of the inner angle and 180, the sum of the two sides. Greater than the third side.. These seemingly naive properties have given me an initial understanding of mathematics research and established the dream of pure numbers. Thinking about it now, I really miss the mood at that time, calm, quiet, innocent, warm and beautiful.

The physics teacher in our class in the second grade is my most respected. He is not limited to taking exams, he has a deep understanding of mathematics and physics, he also deeply influenced and inspired me, and cultivated my initial academic thinking. He also appreciated my seriousness, hard work and passion, and explained obtuse-angle trigonometric functions to me. Later, I wrote some creative ideas as my first thesis. I also learned about the SCI paper division, the four major journals and PRL, and heard about arXiv, and I personally logged in to experience it. Last winter vacation, I first came into contact with number theory and proved a theorem a few nights. When I showed the process to the mathematics teacher expectantly, I was overturned by a few words. At that moment, I was really uncomfortable, but still resisted crying and nodded silently. That is the difficult and vast side of mathematics, presented to me for the first time.

This semester, I will have more in-depth exposure to mathematics, study high school mathematics in class, and understand complex numbers, derivatives, non-Euclidean geometry, and group theory outside class. I also started to study a mathematics monograph “Modern Euclidean Geometry”. Some friends may have heard of it. . Going farther and farther on the road of mathematics, I started to feel powerless. To be honest, in our school, as a girl, I don’t think there are a few boys who can completely crush me in mathematics. But what really left me at a loss was the sense of insignificance when faced with the huge peak of mathematics. I used to have unrealistic fantasies about mathematics because I only saw the tip of the iceberg.

The article I stumbled across a month ago, “Being an Ordinary Man in Peking University School”, also completely pushed my dream of mathematics into the cold valley, and also removed the climbing ladder.

I began to doubt myself. On the surface, everything was business as usual, and my grades did not decline, but my heart became sensitive, fragile, and confused. I even dreamed that I couldn’t solve the problem. I cried and woke up in the second half of the night. Until the last monthly exam, I only took 142 due to copying the wrong number. Fortunately, my Chinese was super-normal and saved me on the edge of the top ten. A classmate of our class took the 150 test, and then a math weekly test was not completed in the whole class. When the math teacher asked me, I casually replied that xx (the 150) did not finish. That day, I suddenly realized that this small monthly test failure made me subconsciously put myself in a position worse than others. I suddenly woke up and felt that my state was wrong.

I have always believed that mathematics is not for examinations. My dream has always been to become a mathematician like Galois. In my heart, he is a person who can really understand mathematics. He died in a duel at the age of 21, but he achieved a mathematics achievement that will be remembered forever: he founded group theory and proved that there is no general solution to equations of degree five or more.

But I also began to faintly, and more and more clearly know that I am not a genius, I have no extraordinary talent, and no keen sense of number. I suspect that I shouldn’t fall in love with mathematics, and it’s not suitable to take the road of research. But I was not reconciled to give up. After all, I vowed to devote my life to mathematics on the night of completing the trigonometric function thesis, without any regrets. And now, looking back on my naive belief two months ago, I feel like a world away.

I just want to know, without outstanding talent, can I grow into an ordinary mathematics researcher? Is it possible to realize the sincere expectation of physics teachers: I hope you can become an excellent researcher and let knowledge and ideas become our beliefs.

Mathematics has always been my belief, but the belief in “I can handle mathematics” has gradually dimmed. what do I do?

Such a sincere question deserves a sincere answer. Due to my limited proficiency, I cannot comment on mathematics research, but I can still express some opinions on mathematics learning and the problems mentioned by the subject. First of all, I am envious of the subject’s literary talent, and here are some responses to the subject’s article: Until the summer of Xiaoshengchu, I was exposed to geometric proofs at home for seven times. I was obsessed with mathematics and became a class representative in school. In the first year of junior high, I was very passionate about geometry. The small dining table was chaotic. I sat on the stone steps diagonally opposite the school at noon in the name of arriving early to prove the theorems I learned before. The sum of the inner angle and 180, the sum of the two sides. Greater than the third side.. These seemingly naive properties have given me an initial understanding of mathematics research and established the dream of pure numbers. Thinking about it now, I really miss the mood at that time, calm, quiet, innocent, warm and beautiful. Very good, I can see that you really like it. Regardless of the future outcome, these beautiful memories are also worthwhile. Later, I wrote some creative ideas as my first thesis. I also learned about the SCI paper division, the four major journals and PRL, and heard about arXiv, and I personally logged in to experience it. Last winter vacation, I first came into contact with number theory and proved a theorem a few nights. When I showed the process to the mathematics teacher expectantly, I was overturned by a few words. At that moment, I was really uncomfortable, but still resisted crying and nodded silently. That is the difficult and vast side of mathematics, presented to me for the first time. It is a good thing to have innovative ideas and want to do research. But unfortunately, junior high school students, high school students, and most college students in mathematics departments do not have the ability to do valuable mathematical work. Generally speaking, if you have selected the field you are interested in, have completed most of the graduate courses in this field, and read some classic papers in this field, you will be considered to have passed the threshold of research in this field. This is very different from biology, chemistry, computers, and physics. So my suggestion to the subject is to study as much as possible now, so that you can study ahead, but you can temporarily dispel the idea of research. But what really left me at a loss was the sense of insignificance when faced with the huge peak of mathematics. I used to have unrealistic fantasies about mathematics because I only saw the tip of the iceberg. The mathematical system that was gradually established after the beginning of the 20th century was too grand, and each of us was too small in front of this system. It’s normal to have this feeling. In fact, after four years of undergraduate studies, it is possible to browse through the framework of this field. The article I stumbled across a month ago, “Being an Ordinary Man in Peking University School”, also completely pushed my dream of mathematics into the cold valley, and also removed the climbing ladder. I also read this article. In fact, this article is more about how to adjust your mentality as a very good but not talented mathematics student in a place where experts gather at Peking University. The school the subject will go to in the future may not be as fierce as the Peking University School of Mathematics. For example, many foreign universities are far easier than Peking University, but the mathematics department is also very good. However, this article is still valuable, that is, the main topic is to recognize the fact that oneself is likely to be an ordinary person, and then work hard with a calm mind and down-to-earth. I began to doubt myself. On the surface, everything was business as usual, and the grades did not drop. But my heart became sensitive, fragile, and confused. I even dreamed that I couldn’t solve the problem. I cried and woke up in the second half of the night so that I wouldn’t be awake…this article It just tells that there are a bunch of mathematics geniuses in a school in Beijing who do not know the subject. Their excellence does not deny the effort and value of the subject. If you are sad because of the fact that there are people better than yourself in the world (this is an inevitable thing that everyone needs to face), it is really unnecessary. I have always believed that mathematics is not for examinations. My dream has always been to become a mathematician like Galois. In my heart, he is a person who can really understand mathematics. Unfortunately, this dream is unlikely. One dream with a much higher success rate is to become a mathematician. Galois is a genius once in a century. Even among the best mathematicians in the world, few people dare to say that they have the talent and spirituality of Galois. As mentioned earlier, most of us are destined to be ordinary people, so it is normal not to be the next super genius like Galois, and there is no shame. In addition, how to define a “person who really understands mathematics”? There are also many unknown mathematicians in the world who have worked hard in their fields for a lifetime and made contributions. In my opinion, these people are also people who really understand mathematics. I wonder if the subject agrees with my idea? But I also began to faintly, and more and more clearly know that I am not a genius, I have no extraordinary talent, and no keen sense of number. I suspect that I shouldn’t fall in love with mathematics, and it’s not suitable to take the road of research. But I was not reconciled to give up. After all, I vowed to devote my life to mathematics on the night of completing the trigonometric function thesis, without any regrets. And now, looking back on my naive belief two months ago, I feel like a world away. Not a genius, no talent is a fact that 99.9999…% of people in the world need to accept, because by definition, only a handful of people are geniuses. It is not shameful to admit that you are not a genius and to reconcile with yourself. On the contrary, this is a very courageous thing. But for this reason, you should not feel that you should not fall in love with mathematics and not suitable for the road of research. Love this kind of thing is beyond all rational interpretable categories. So if the subject feels that he is in love with mathematics, it can only be said that it is your inner decision, then just follow your heart and let the flow go. If you give up mathematics because of this little setback, it is really not suitable for research, because the difficulties you encounter on the research road are much greater than this, and you may not be able to bear it. I just want to know, without outstanding talent, can I grow into an ordinary mathematics researcher? Is it possible to realize the sincere expectation of physics teachers: I hope you can become an excellent researcher and let knowledge and ideas become our beliefs. It is possible that, in fact, the group of “ordinary mathematics researchers” is much larger than the subject imagined. But becoming a mathematician is more difficult than you think. And this difficulty comes not only from the difficulty of the subject and the limitation of one’s own ability. The competition in the academic circle is too cruel, and the front is too long. You may question your choices because of many unexpected things: lifestyle, money, family, career… If you find yourself hesitating in your heart, or your thoughts have changed in the middle of the process, hope that the main topic will be honest with yourself. . Mathematics has always been my belief, but the belief in “I can handle mathematics” has gradually dimmed. what do I do? The belief that “I can handle mathematics” is not true, and it should not be the belief of the subject. No mathematics learner has the guts to say “I can do mathematics”. No matter how smart people are, no matter how talented they are, with the deepening of mathematics learning, they will inevitably encounter a frustrating moment. At this point, your intuition is no longer accurate, your brain starts to tire, and your logical chain begins to break. You will find that you have no way to easily control an abstract mathematical concept, just like riding an untamed wild horse. difficult. In many cases, you need to spend hours, or even days, to fully understand the content of one or two pages of a math textbook. No one can escape this node, although some people may encounter it later than others. But this is inevitable: mathematics is not easy for anyone. Then with your repeated derivation, your brain is constantly running at a high speed unconsciously, considering the logic between theorems, you will crush your original incorrect intuition, and your understanding of these objects and logic will deepen, suddenly At a certain moment, you will suddenly realize that all the pieces start to combine and become a beautiful work of art, and you finally understand this theorem. After that, you will build up new intuitions, and then continue to turn to the next page of the math book and repeat the same process… So my advice to the subject is not to think so much, because no one can learn from yourself Early performance predicts performance after ten years, and there is no way to predict whether one can achieve the goal within time (proof: not a Nash equilibrium). So the decision to embark on the path of mathematics research is actually an incomplete information game, which can only be said to be a pony crossing the river. But given that the subject likes mathematics so much, I think no matter how talented you are, you will unconsciously embark on the road of mathematics, so you have not many choices because you have already made a decision in your heart (laughs). In this case, follow your heart, but ask for no regrets. Finally, I hope the subject will give up the fantasy and prepare to fight.