Chaos in mathematics -- mathematics as a mathematics

Running at night is boring.

Why is mathematics called mathematics? What is mathematics? Why study so many "technical" things? Why? Without thinking logically or wanting to do anything, running is too monotonous and too tired to stick to it.

I recently reviewed the beginning and end of the three mathematical crises. Today, people will laugh at the bidaras School. How can a group of stubborn, crazy, and "stupid" people stop killing people because they don't admit that they are irrational. Why is mathematics so hard to understand?

It suddenly seems that I understand why mathematics is "Mathematics. Because mathematics is a learning of "Number !...... Isn't it ?!!...... No.

In fact, there are some things we get used to, but we don't know that clearly. If you have stayed with a great person for a long time, you will feel that he is ordinary. "Number" is also a great thing that makes us feel ordinary (concept ?). The number is so common that we think it is "ordinary and simple ". "No count !" It means a dummies. Yes, the number is very simple, but it is also very powerful. Because people try to convert what they want to know into numbers. Many times, they have succeeded. Just like, when we describe a person, we use age to represent him, weight to represent him, height to represent him, and number to represent him. This is amazing, because originally, "There is no number in the world, and more people are used, it becomes a number ". A cow and a sheep are both animals. What a powerful abstract capability !! People may not realize how much progress this is for human intelligence. But we have been doing this and constantly expanding our abstract capabilities to convert everything we need to know into numbers: motion, we describe him with speed, time, we use the number of water drops to describe it. We use the number to indicate the number of our population, and then use the ratio to describe its growth. Everything is so natural. Until the people of the bildagos school realized that "everything in the universe can be summed up as an integer ". This kind of introspection capability is rare. It requires both IQ and intelligence. Whether it is wrong or not, but this recognition is the rise of the mathematical spirit. The bidaras school consciously recognizes that people have a powerful tool to understand nature, and strives to develop such a tool. In addition, it strives to use this tool to solve new problems. I have to respect them.

It's no wonder that when we discover irrational data, the bildagos school will be so scared (the first Mathematical Crisis) that we don't want to admit it, because this is the fundamental collapse of the world. This means that we have a world we don't know.

Today, it seems that the emergence and solution of the first mathematical crisis are nothing. People "naturally" acknowledge the existence of irrational data and continue to study data, on this basis, a complete set of methods has been developed. From arithmetic operations, to solving algebraic equations, to learning to use functions, and a series of methods (such as calculus) invented to process functions, they all aim to better process numbers, the Relationship Between the number and the number. We convert the same things that need to be studied into numbers (such as voltage, such as speed, such as force, or power). Once we express it with numbers, we have a complete set of mature and powerful methods to deal with it, get the results we want, and then map back to the real natural attributes. This "method" is so powerful and "concise" that people turn this method into a class called "Mathematics" (Chinese people call it so well ), this method is purely thinking, and uses the most powerful capabilities in people's thinking-abstraction and logic.

This reminds me of the Cartesian coordinate system. With the combination of numbers and shapes, people can associate the research on Graphs with the research on functions. This is equivalent to returning a lot of problems to the research on the relationship between numbers. This allows people to "reuse" a large number of research results, greatly develop research methods, and promote the advancement of mathematics as a tool. Really great. Perhaps finding a more "common" part for all tools and making it the most effective is one of the minds of mathematicians. There must be more common attributes between "Number" and "other basic tools. The final world will be described from a unified perspective. On the one hand, pursuing the unification of "root", the flourishing development of "branches" by one method is the driving force of the development of mathematics. People may also find that some attributes cannot be described by "Number" or are processed by "number, in this case, we need to introduce a new "basic tool" to describe it and establish a system for it. It can find a common logical-based tool between many seemingly different phenomena. This tool is called mathematics.

Suddenly, I seem to have stopped the tangle of the definition of "radians. In fact, no matter how you define it, the key is to find a good relationship and establish a strong and reliable method to solve the problem. This is the "radians" and the "Triangle" based on this. They are not necessarily the best, most reasonable, or most effective, but there is currently no "better, more reasonable, and more effective". Therefore, we need to appreciate this beauty and "accidental" and continue to move forward, find more natural fundamentals.

Really, I am very tired.