2. Mathematics is a science with strict logic. To put it bluntly, mathematics is a subject of scrutiny. What is censorship? Is to reason out reasonable results under certain conditions. And what we have to learn is to constantly sum up experience in this thoughtful process and make our thinking more acute.
Go back to your thinking of solving mathematical problems, and put aside the skills and methods purely for solving problems. Mathematical problems are actually abstractions of problems in life, that is, mathematical problems are a symbolic form of life problems.
Think about how you usually solve the problems in your life. Perhaps your elders have taught you this or that, but when you actually encounter problems, this or that method is often unsatisfactory, because each method has its own suitable person, and no golden key can make you once and for all. After experiencing such a thing, you will sum up the methods that apply to you. Slowly, with more experience, you will sum up a set of ways to deal with things, but this method is not omnipotent, because you can't guarantee that there will be no new problems tomorrow. So the only universal method is to keep trying and sum up experience.
What is mathematical thought? Give you an Olympic math problem, and you can solve it in two minutes. Is that called mathematical thinking? Maybe you just saw a similar problem two days ago and drew a gourd ladle. Mathematical thinking cannot be cultivated by solving hundreds of mathematical problems, and it is not what I said in these two or three sentences. Doing math problems is just one way. Thought should be cultivated in life. Besides mathematics, we should learn more other knowledge, such as literature, philosophy, computer science and so on. Think more and summarize more. When you have a unique view on a problem, others will think you are a thoughtful person. And this kind of thinking, in the field of mathematics, is mathematical thinking! ! You know, the originator of computers is not a professional computer researcher, but a mathematical expert. However, the so-called masters of mathematics are often not born in ordinary classes. They may be painters, philosophers, or even monks sweeping the floor ~ ~ Haha, just kidding.