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I think there are two types of learning, one is general knowledge, including various common sense, life principles, etc., and the other is ability.
Leaving aside general knowledge, the purpose of the latter is to acquire a certain ability, and existing knowledge is a shortcut. But the premise is often ignored, that is, you must be able to walk by yourself. The result of putting the cart before the horse is that knowledge has become a mountain that hinders us.
When I was in school, I was very confident in learning data, why? Because I learned a formula when I was in elementary school, and deduced another formula by myself. I felt that I had made a big discovery, and I excitedly told the teacher. The teacher told me that I could learn it next year, but he still suspected that I had read the textbooks for the senior grades. I was very frustrated because the formula I discovered had been discovered by someone else, but I was also very happy because the first person who discovered it was a mathematician. If I was born earlier than him, this formula should have my name on it. Already—a childhood thought.
Of course, this incident discouraged my interest in deriving mathematical formulas, because I don’t know if the formulas I deduced have been discovered by others. But this kind of self-confidence has always been with me, and I have never doubted my ability to learn. Until high school, my mathematics, physics and chemistry have always been very good.
In my opinion, the exploration of human beings in the field of mathematics is like walking a path. When you first started on the road, you only need to do addition and subtraction, and you can get negative numbers when you do subtraction. Moving forward, you need to do multiplication and division. When you have decimals and fractions, you will find that some are indivisible, and you will have infinite decimals. Going forward, you need to calculate the area and volume, and you have the square, the cubic, the square root, and even a geometry. Going deeper, equations, mechanics, calculus and so on. These concepts or discoveries are like signposts, recording the footsteps of human exploration.
When we go to study mathematics, we are retracing this path. But the first thing we have to learn is how to walk, that is, the basic method of studying mathematics, and then we run along the road signs of our predecessors, quickly explore this road, and when we run to the end of the road, we can slowly explore it. What are the places to go. Even on the way, you can also pay attention to the open spaces beside the road without road signs.
For those who are not interested in mathematics, it is enough to learn how to calculate. More complex calculations can be learned after use, or directly use a computer.
I am not interested in pure theoretical research, I prefer to study and research purposefully. Because I believe that the actual needs of social life promote the development of science and technology, and dragon-slaying skills that have nothing to do with social life needs will disappear no matter how advanced they are, while related skills will continue to develop.
In addition to the fun of learning itself, I went to school to enter the university, and the purpose of the university was to find a job. Studying at work is because of work needs, and restarting study after the age of 30 is to solve my life problems.
There is no need or problem, and learning aimlessly is just another way to pass the time. To pass the time, we must find the way we like, just like when we get tired of playing a game, we will naturally change it.
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