Zhang, known as the sweeping monk of mathematics, proved a weakened form of twin Mr. Zhou's conjecture a few years ago, which established his position as a first-class mathematician in mathematics, won the award invitation and so on, and reached the peak of his life.
Before that, I didn't find a suitable job after my Ph.D. graduation, and then I worked in various jobs in the United States for more than ten years, such as restaurant waiter and accountant.
Similarly, the late bloomer was Hiroyuki Hiroyuki, a Japanese mathematician, who received his doctorate at the age of 34.
Not to mention the first-class mathematicians, even all doctors, on average, are too late.
But that didn't stop him from seeking knowledge. Later, Fields and Wolff both won the Nobel Prize in Mathematics, and they made important contributions to harmonic integrals, algebraic geometry and complex manifolds.
The above two mathematicians are my favorite idols. Obviously, they are smart, but their circumstances and choices are somewhat different from those of their peers, thus giving the public a silly feeling.
This kind of "stupidity" is simply persistence!
Mathematics is difficult, and at the same time, appreciating the beauty of mathematics requires the appreciator to have certain mathematical ability. Unlike painting and music, God directly gave us accurate eyes and ears.
To understand the use of mathematics, there are certain requirements for your work scope.
For example, if you are a college English teacher, it is normal that you don't use math very much;
But if you are a college math teacher and you say you can't do calculus, it's definitely not possible.
For example, if you are an aerospace expert, you must be familiar with differential equations and dynamic systems.
If you are an expert in quantitative investment in derivatives, you must be familiar with stochastic processes and stochastic differential equations. ......
1. logic language
The difficulty of mathematics is that it relies on logical language to construct its content, in short, it does not talk about people.
But we are human beings, and the natural languages we use most are Chinese, English and so on. Every assertion in mathematics needs to be proved.
In life, if every time you say a word, you have to' wait a minute, let me think about whether your first sentence is right or not, and then we'll talk about the second sentence'. Do you think you can still find friends? Girlfriend Even a boyfriend? -Appropriate expressions are omitted here.
Let's look at the following statement:
There is a positive integer n. For any two people in the world, A _ 0 and A _ 1, N people can be found, so that these two people can get through the bridge of understanding, that is, A _ 0-B _ 1-B _ 2-...- B.
Do you think this expression looks comfortable?
N=6, which is the famous six-dimensional space theory.
It means that you can get to know anyone in the world through up to five strangers.
Does this vernacular feel much more comfortable?
2. Interest and seeking advice
Learning mathematics well mainly depends on two points:
One is my interest in logic and thinking.
For example, people who always like to ask why, or people with competitive IQ, are relatively easy to be interested in mathematics or natural science;
The second is to have a good teacher.
In fact, this is still relatively miserable in China, except for first-tier cities like Shanghai.
Many of our teachers are not self-educated. In fact, before high school, if all the questions were answered well, the mathematics involved was very extensive, and basically a doctor of mathematics was needed to be competent.
For example, why the circumference \pi of a circle is multiplied by the diameter, why the area of a straight line is 0, and why it is 0. \dot{9}= 1, and so on.
I believe many math teachers can't answer these questions that seem to have little effect on the usual exams.
Because they haven't seriously considered it themselves, and he thinks you just have to remember it.
So the common teaching method is that the teacher forces you to write it down with a harsh tone and its inviolable majesty, so you start to hate the teacher.
Although you can skillfully calculate the correct answer of every exam in a limited time regardless of the form, doubts still exist in your heart, and you feel that you are sitting on an empty building.
Students who can prove or completely answer the above questions are confident, and their existence is based on a solid foundation, safe and comfortable. Even though their grades are not so ideal because of an accidental carelessness, they are very practical and confident.
The former is different. As long as my test scores get worse, I hate not only math teachers, but also math.
Moreover, until I graduated from high school, even from college, married and had children, I still had a little knowledge about why the circumference of a circle is \pi times the diameter, and why the area of a straight line is 0 and why it is 0. \dot{9}= 1。
If you find that your teacher is like what I said above, you should either spend more time on self-study, or pay for a good teacher to give you extra-curricular tutoring, or find some good online resources.
Because mathematics has one advantage that other disciplines don't have, that is, it can prove its right or wrong. Generally, people who really understand are very clear about whether they are right or wrong. Just like time, it is 24 hours a day for everyone, and everyone's life expectancy is not much different.
Other sciences, even the physics closest to mathematics, often need experiments to verify. Only when others do experiments according to your same rules and get the same conclusions as you, your findings or conclusions will be recognized.