Junxin asked Zhao Zhen to answer this question by name, which was an opportunity for Zhao Zhen, but it was also a challenge for him who was introverted.

Influenced by Grotendieck's letter some time ago, Junxin also began to take a certain interest in the philosophical problems of mathematics. Later, when he was a student at Princeton University, he thought of the textbook "Princeton Mathematical Guide", which was edited by Professor Gowers to introduce the study of mathematics in the world, and Junxin decided to bring a certain philosophical reference to his research direction, so as to improve his own views on mathematics.

"Teacher, I think mathematics is the foundation of other natural subjects, as long as you learn mathematics well, then there is no problem at all in learning other subjects." Zhao Zhen thought about it for a long time, and finally came up with something that he thought was very stylish.

Junxin nodded, and praised with a flat face, "Okay!" He felt that the answer was too standard. There is a very famous saying in this era: learn mathematics, physics and chemistry well, and you will not be afraid to go all over the world. Zhao Zhen's answer just changed this sentence, which was not very incisive.

"Anyone else to say?" Jun Xin glanced around and continued to ask.

"Teacher, I think mathematics is a subject, and its usefulness is like a tool that can be used to solve real problems."

"Well, that's a good point."

"Teacher, I think mathematics is a science used to construct human cognition, no matter what kind of cognitive facts, in the end, it is necessary to establish its absolute mathematical model mathematically."

"Yes, yes, anything else?"

"Teacher, I think mathematics is a discipline that purely studies the relationship between numbers, and its purpose is to study numbers..."

"Teacher, I think ......"

The answers, of course, are varied. Some people say it is one-sided, some people say it is a bit narrow, some people say it is a bit realistic, and some people say it is a bit big and generalized. For these answers, Junxin just listened calmly, and did not make any specific comments, at most only a thumbs up, and in most cases, Junxin only nodded slightly.

What is Mathematics? What can mathematics do is actually a problem that everyone who studies mathematics will face, and it is also a problem that must be faced.

Professor William Thurston, one of his math mentors, asked him this question. However, Junxin at that time only answered with a very standard answer, and as for whether the answer was what he thought in his heart, even Junxin himself couldn't be sure.

However, in the past six months, Junxin has quietly done his own research in a turbulent environment, and at the same time exchanged his mathematical thinking and research methods with some famous mathematicians in the world, and gradually formed his own set of views, or rather, his own set of philosophies on mathematical research.

His dream was to build a school comparable to the Göttingen, Copenhagen School, and so on. Whether it is the Göttingen School or the Copenhagen School, the ideas of its founders have profoundly influenced the future development of their schools.

The Göttingen School was founded by Gauss and successively flourished by such almost omnipotent mathematicians as Riemann, Klein, and Hilbert. The Copenhagen School, on the other hand, was founded by Niels Bohr, and the ideas of the school are closely related to Bohl, upholding openness, enthusiasm, etc., just like the character of the goalkeeper Bohl.

Now that he has come to Junxin, since he hopes to establish a new school with great influence, he naturally has a strong interest in spreading his ideas. And the students in Hua Luogeng's class in front of him have become the best targets for him to promote his ideas.

"Some time ago, Mr. Alexander-Grotendick suddenly wrote me a letter because of the proof of Mordell's conjecture on this question." Junxin waited until the surrounding voices were quieter, and finally spoke. However, Junxin did not directly answer the questions he began to ask, but Satoshi Rotten Dick wrote a letter to himself and began to talk.

"In the letter, Mr. Grotendick gave me the question: What does mathematics mean to mankind?"

"That's the question I started asking you, because only when you know the answer to that question will you know what math can do. As for the question of the gentleman, I just had a little idea very simply. ”

"I think mathematics is an important tool for human survival!" Jun Xin said this, obviously raising his voice, "This is my opinion on mathematics, the mother of natural science. ”

Jun Xin's eyes were a little solemn and glanced at the students of Hua Luogeng's class who were gathering around him with high concentration, and said in a solemn tone: "I don't know what Mr. Grotendieck's views on mathematics are, but it is obvious that his ideas have a great influence on IHES and the entire French mathematical community, because Mr. Grotendick has not only established an IHES, but more importantly, he has established a cognition of mathematics. He made his students and his followers understand the direction of the study and direction of the mathematics they were studying, which was the most important point. ”

"That's what we're missing the most. We have always said that we must work hard to catch up with the world's most advanced level and the world's top research standards. But this direction of research is a political goal, not a scientific goal. ”

"Catching up with the world's top level, this is a goal, in terms of the development of mathematics itself, it may have its benefits, but it has no practical significance."

"So in my mind, mathematics is a tool for human survival, not to catch up with a certain level. Unfortunately, the vast majority of us will and will be given the task of raising the level of scientific research in our country as a whole. And to do that, you will have a hard time making breakthrough research. Junxin seems to have seen the current situation of the Chinese mathematics community in the decades since.

Jun Xin shook his head and said: "The topic is far away, I just said that mathematics is a tool for human survival, so since it is a tool, where is it embodied in such a tool?" ”

Let's take a look at a few events like this:

The first is that Maxwell established the theory of electromagnetism and used the knowledge of calculus to create Maxwell's equations. This has led mankind into the era of electrification, and electricity has become the main energy source.

The second event is that in 1915, Einstein used tensor analysis tools to establish a mathematical model of the general theory of relativity, and the direct by-product of this theory was the atomic bomb.

Not to mention the law of gravitation, the Pythagorean theorem, which is a mathematical theorem that does not need to be explained at all. ”