!
When the research and development direction is found, research can begin.
Wang Hao was not in a hurry to do research. He still cared about the students. Because he wanted to do research with the students and at least let them understand the Yang-Mills theory, he specially set aside half a month's homework.
'.
The assignment content consists of some difficult basic knowledge, and also includes a short paper on related research.
"You try to understand this information. Quantum mechanics covers a wide range of topics, but we only study it from a mathematical perspective, not physics."
"This is important."
"Mathematics is the foundation. You don't need to understand quantum mechanics in depth, or the more complex standard model of particles, but you need to understand the mathematical basis..."
Wang Hao explained patiently, and he also praised Ding Zhiqiang in particular, "Inspiration is very important when doing research. Ding Zhiqiang is very good in this aspect. Many of his ideas are sudden, but they are very important."
"When you do research alone in the future, you should also pay attention to every idea. Maybe an accidental idea can make a breakthrough in your research."
“In this regard, you need to have a discovery mindset. Don’t be limited by your knowledge, especially not by ‘correct knowledge’. You must dare to question.”
Wang Hao talked about some of his own experiences and then ended the course.
The students took the materials and left.
Ding Zhiqiang walked at the back. He looked at the information in his hand and felt very depressed.
Years ago, he completed the study of algebraic geometry, and his life was just like other first-year graduate students, studying in class normally.
Perhaps in the eyes of other students, it is not easy to understand the knowledge in class and it takes up most of the day.
Ding Zhiqiang felt very relaxed.
This has been the most relaxing time in the past three years.
Every night, he still has two or three hours of free time, which makes it even easier on weekends. Last weekend, he even slept until half past ten in the morning.
This is simply a dream-like life.
He found the sense of ease he once had, but now the ease was over again. The pile of information in his hands was enough to take up most of his free time.
"Life is so difficult!" Ding Zhiqiang thought depressedly.
Studying every day is not the most uncomfortable thing. The most uncomfortable thing is that others always urge him to study.
When he came home during the winter vacation, the first thing he heard from his mother when he entered the door was, "Why are you back? Didn't you say you were very busy? I thought you wouldn't come back this year."
The next step is, "Your father and I both know that your mentor is Wang Hao, Xiaoqiang. With such a good opportunity, you must give our family a voice and become a great scientist in the future!"
Ding Zhiqiang was filled with tears as he listened. He really didn't want to be a great scientist!
…
Wang Hao began to do research seriously.
The Yang-Mills equation is a nonlinear partial differential equation, but each type of nonlinear partial differential equation can be said to be a new research project, and the original research cannot be copied rigidly.
His research on the NS equation is very in-depth, but he can only use related methods to approximate the Yang-Mills equation.
"What's the point of approximate solution?" Wang Hao thought and shook his head.
If it is infinitely approximate to a certain set of exact solutions, the solution is still meaningful, but because it is an approximate solution after all, subsequent analysis of the physical properties is very difficult.
"However, it is difficult to analyze the physical properties of any set of solutions."
Wang Hao still feels that he is affected by the content of quantum physics. What he wants to do is to study it in a purely mathematical way and not be affected by the content of the physical direction.
He kept thinking.
This time I am not stuck in the office, doing research as if in retreat, my life is still normal.
Lin Bohan came over.
The new semester has begun, project funds have been allocated, and Lin Bohan has also received a bonus. Naturally, he is very active in research. He spent a lot of time thinking about the next step of research, and came to Wang Hao to express his views.
Lin Bohan entered the office, sat on the sofa and said, "We can start with something simple, for example, the simplest compound composed of two different atoms."
"The microscopic morphology created in this way is certainly much more complex than a single atom, but it can also be gradually improved."
"Our definition of semi-topology is also based on this basis, just like the new geometry we have studied."
"Let's discuss it step by step..."
This is what Lin Bohan thought of.
The new geometry content published by Wang Hao only targets single-element substances, such as aluminum, gold, copper, etc.
Because it only targets single-element substances, the new geometry is not suitable for more complex compounds.
Their research direction was to establish a semi-topological system to cover the microscopic morphological structure of complex materials, but the research encountered problems and they could not figure out how to proceed next.
If we just expand the difficulty a little bit and only discuss the simplest compound composed of two different atoms, the complexity will definitely increase a lot, but it will not reach the point where it cannot be solved.
Lin Bohan's proposal is still very valuable.
Wang Hao shook his head and said, "It would indeed become easier if it were only expanded to two different atoms, but the problem we are encountering now is not difficult or simple."
He continued, "The microscopic morphology can also be understood as the topological magnetic magnetic chain in condensed matter physics. The nodes of this topological morphology are not necessarily based on molecules."
"In other words, when forming a topological magnetic chain, the same molecule may be connected to other molecules at different points."
"This is the main reason for the complexity."
In fact, the explanation is very simple. For example, the microscopic structure of the molecule ab composed of 'a' and 'b' is not necessarily ab-ab-ab-ab..., it may also be aba-bba-abb-baa...
….
It is precisely because individual molecules may not be at the same node in the microscopic morphology that the shaping of the microscopic morphology becomes very complicated.
Even a microscopic form composed of only two elements may undergo countless changes.
Wang Hao continued, "Whether it is two elements, three elements, or more elements, there is essentially no difference."
"Because of this, I said that I would only do research from the direction of mathematics."
"Now I'm even more sure of it."
Wang Hao stood up and walked around and said, "I have a student named Ding Zhiqiang. You should have seen him, right?"
"He reminded me and made me realize that sometimes mathematics and physics need to be separated."
"If mathematics and physics are combined, then we should find one physicist to join the project, instead of several of us conducting research, and the problem will become very, very complicated."
"So for this research, we no longer consider physical issues, but only consider shaping new topological definitions, and only consider shaping a new topological system based on algebraic geometry."
"If we want to move to the study of microscopic morphology in the future, we will use the defined framework to conduct specific research on it."
"Mathematical theory is the most important."
"As long as we lay a solid theoretical foundation, no matter how complex the microscopic morphology is, it is just an application..."
Wang Hao explained his thoughts.
This statement will definitely be recognized by the mathematics community. Many mathematicians think so, especially mathematicians who do pure mathematics research.
Pure mathematics is the basis of mathematics.
Only with a large amount of pure mathematics research can we lay a solid foundation for applied mathematics and be closely connected to real applications.
From pure mathematics to applied mathematics, and then to real-life applications, between pure mathematics and real-life applications, there is 'applied mathematics'. Because of this, many people think that 'pure mathematics' is meaningless because it is closely related to real-life applications.
Decoupling.
Actually, this is not the case.
Without the research of pure mathematics, the development of applied mathematics would lack a foundation.
In fact, what Wang Hao said is not profound, it is just the basis of mathematical understanding.
Many people can say the same thing.
Lin Bohan can also say it.
But being able to say it and being able to think about it when doing it are completely different concepts.
Lin Bohan felt a sudden enlightenment. He had always understood this truth, but when he really devoted himself to research, he could not help but be connected to superconducting, continuous superconducting materials and other contents.
He found that he really should expand his thinking, and it was Wang Hao who really achieved "applying theory to research."
To be continued...