The first mathematical thinking, which originated from probability theory, is called "seeking certainty from uncertainty"
We often say "doing the right thing over and over again" is actually a popular expression of probability theory. The so-called "right thing" refers to something that can be successful with a high probability. And what is the so-called "repetition"? In fact, after learning probability theory, we have a quantitative understanding of the matter of repetition.
Although there is no 100% probability of success in this world, as long as you repeat the things with high probability of success, your probability of success will be close to 100%. This is to find certainty from uncertainty. This is the most important way of thinking taught by probability theory.
The second kind of mathematical thinking, which comes from calculus, is called "looking at problems with a dynamic eye"
Newton invented differential and used the concept of infinitesimal to help us grasp the law of moment. Integral is just the opposite of differential, which reflects the cumulative effect of instantaneous variables.
The way of thinking of calculus is essentially to look at problems from a dynamic point of view. The result of one thing is not instantaneous, but a long-term cumulative effect. When something goes wrong, don't just look at that moment. Only by tracing the source from the macro to the micro can we find the root of the problem.
The third mathematical thinking, which comes from geometry, is called axiomatic system.
There is no right or wrong justice, and there is no need to prove it. Axiom is choice, knowledge and benchmarking principle.
The fourth mathematical thinking, which originated from algebra, is called "the directionality of numbers"
Before learning fractions, in our cognition, numbers are discrete, and they are points. With scores, the numbers begin to become continuous. Just like in life, at first you look at things, right or wrong, big and small. Slowly, you realize that the world is not that simple, and you begin to look at things in gray.
In fact, numbers have a direction. In mathematics, we call a directed number a vector. A negative number is a positive number.
The fifth mathematical thinking, derived from game theory, is called "global optimization * * * win".
In the zero-sum game, you should always stay awake: you want the global optimal solution, not the local optimal solution. Non-zero-sum games are about winning.
I: Learning mathematical thinking can help us understand the laws of some things. There are five kinds of mathematical thinking that we need to remember. One is probabilistic thinking. We should look for constant factors in a rapidly changing society, such as Musk's first principle. The second is calculus, which can not only decompose problems, but also think about them systematically, from both macro and micro perspectives; Third, the axiomatic system, mathematics can be self-consistent because its theorems are all derived from kilometer logic. Without exception, axioms are the essence of society and need to be divergent, and we also need to establish the principles of our lives according to axioms; The fourth is algebra. Algebra can be divided into positive and negative directions. The second is that algebra can be discrete or continuous, rational or irrational. This is not the definition of duality, but let us think from multiple angles and gray levels. Fifth, game theory, we should look at the problem in the long run and win.
A: Actually, there are more than these kinds of mathematical thinking, including many functions, which can also help us understand the world. Combine perceptual knowledge with rational mathematics, and you have Ge.