First of all, you should like mathematics and regard mathematics as your lifelong pursuit. This is easy to say, but it is actually a very difficult thing. Unamuno said in The Tragic Consciousness of Life: "When people believe that they can pursue truth for the sake of truth itself, they are actually pursuing life in truth". Math is boring. You need to find beauty, experience beauty and feel the truth in the pursuit of mathematics. If a person can regard mathematics as his life, he will certainly become a mathematician and a great mathematician.
Secondly, you need to stick to it and don't get distracted. You are still young, you are only in junior high school, you have to take the college entrance examination when you enter the university, and you are facing graduation ... all these may make you change your mind under various pressures. As Marx said, people can only engage in politics, religion, philosophy, science and education if they have a material foundation. It is not enough for children to have beautiful dreams, but also to be practical and make such dreams become ideals. When I graduated from high school, I gave up my choice of mathematics major under various pressures. After I entered the university, I entered the computational mathematics major by mistake. But after graduation, I have to go to work to earn money to support my family, so I took part in the work and did some work unrelated to mathematics. After work, I will continue to study and study math very hard. Although I have written some papers, I obviously feel that my level is declining and I lag behind my classmates. Therefore, if you want to become a mathematician, you must always stick to your original choice, be willing to be poor and lonely, resist the pressure from all sides, and don't let external forces destroy your inner world.
Third, only the first two are not enough. Mathematicians must be good at mathematics. So you should have a good math foundation. At the same time, under the secondary education system in China, you must get good grades, otherwise you can't continue studying, go to college or go to graduate school. After all, the possibility of self-study is very small, mainly relying on school education to lead you to the forefront of mathematics.
Fourth, regarding the study of mathematics, we should learn the thinking mode of mathematics, read more, see more and do more. It is necessary to do math problems by hand. Hua said that "learning mathematics without doing problems is equivalent to going to Jinshan without gold." But don't always solve problems according to the problem-solving mode of textbooks when doing problems. The whole mathematical system consists of some mathematical definitions and rules. Therefore, we should deeply understand each definition and express it in our own language. When solving problems, we should start from the definition we understand and complete it according to our own ideas, and don't apply patterns. You should know why.
Fifth, we should have a broad vision of mathematics. Don't confine yourself to a theorem, a deduction or something. The formation of every concept and the acquisition of every conclusion are based on the historical background. Every mathematical conclusion has a background process: phenomenon-problem-guess-proof-conclusion (or new mathematical concept). After the conclusion is reached, it is a deductive process: conditions for establishment-scope of application-accuracy (no requirement for qualitative conclusion)-theoretical position-modern development-application-new conclusion (theoretical deduction) When learning mathematics, we should pay attention to expanding our knowledge and try our best to understand the mathematical background. This is also necessary for an excellent mathematician.
Sixth, plan your own academic path. This point is aimed at the actual situation. Now that you are in junior high school, I think you may want to study mathematics as much as possible, or even start from high school or even college. This idea is normal for people your age. When I was in junior high school, I learned high school knowledge. When I was in high school, I had finished the basic college courses such as calculus and linear algebra. But still, it's best not to be so eager for success. The urgent task is to learn all subjects well, and try not to let the achievements of other subjects hinder you from continuing to study mathematics. First, make sure that you can be admitted to the university. If you are excellent in all subjects, you can expand appropriately. But we must lay a good foundation in mathematics and exercise our ability of calculation and reasoning. In 1949, Hua gave a direct proof of the theorem that any normal sub of an object must be contained in its center, which is called CARTAN-BRAUER-HUA theorem in the literature. Before working in China and RICHARD BRAUER, H.CARTAN used the complex technique of subdomain extension of GALOIS theory to prove that this result is only applicable to divisible algebra. In contrast, Hua's proof is only half a page, relying only on an elementary identity, which is very long, but only junior high school knowledge. Therefore, we must lay a good foundation, which is good for the future road of mathematics.
When waiting for the college entrance examination, it's best to take a math major (if you have strong self-study ability, you don't have to take it). It's even better if you take a math major in some universities with very high math level (such as Zhejiang University, Peking University, China University of Science and Technology, etc.). ). and then continue to study for master's and doctor's degrees without interruption. This will make your road as a mathematician very smooth.
Well, that's a lot of verbosity.