On the podium, Zhou Hai stopped the chalk that was performing calculations on the blackboard, frowned at the white handwriting, turned around and picked up the blackboard eraser to erase all the mathematical formulas and calculations on it.

He calculated for more than ten minutes, and finally confirmed that there was a road that did not work.

For the first time since teaching, he was stumped by a question from a student, which was incredible.

However, after carefully thinking about and studying the topics in his notebook, he was relieved.

It's normal for him to not be able to solve this problem in a short period of time.

Although the title was written by Xu Chuan, it was actually part of a weakened form of proof of a world-class mathematical conjecture.

This kind of problem, even if he concentrates on research, may not be able to solve it, and it is tantamount to climbing to the sky if he wants to find an idea or prove it directly in a test.

........

"Where did you get this question?"

After confirming that he couldn't solve the question on the notebook in a short time, Zhou Hai returned to Xu Chuan's seat, returned the notebook in his hand to him, and asked curiously.

As an undergraduate, you start to be exposed to such a thing as world conjecture?

Or is it a topic he deliberately found, deliberately?

He has been teaching for more than 20 years and has seen students class after class.

I have seen genius teenagers and mediocre assets, I have seen people who study hard step by step, and I have also seen opportunistic people who want to ask their tutors to help write their graduation thesis.

This kind of over-the-top questions and difficult topics are consulted by the teacher, in order to have a good impression of Hebo in front of the teacher, so that the teacher feels that he is studying a lot seriously.

Of course, he didn't think Xu Chuan was this kind of person.

But in any case, it is surprising and suspicious for a first-year student to start being exposed to such a thing as world-class conjecture.

And if he found the topic himself, it would be fine, after all, many college students who are interested in a certain subject will look for some problems on the Internet or in the library to try to solve them.

But if the topic was conceived by him in the process of studying, it would be shocking and incredible.

Not to mention a freshman, even the graduate and doctoral students he leads, or even a university professor, may not have such ability.

Study old knowledge, integrate it, and then expand new boundaries and new problems on this basis.

This is something that only top mathematicians or mathematicians who have delved so deeply into a certain field that they have almost reached the end of their life can do it.

Can a first-year student get this far?

No way!

When pigs fly!

Zhou Hai didn't believe that a first-year student could do this, so he asked Xu Chuan where he got this question.

......

Hearing Zhou Hai's inquiry, Xu Chuan re-found "The Factorization of Linear Operators and the Geometric Properties of Banach Space" from his school bag, turned to the last three chapters, and handed it to him.

"The book contains some descriptions of spectral asymptotic methods and problems on connected regions with fractal boundaries."

"Nn(r)=#{(Q1,...,Qn)∈"|qi+...+q

"Starting from theorem 3.1, I encountered this problem on a notebook when I combined the second term of the Dirichlet spectral counting function to asymptote to extend the adjacent connected branch of a special disconnected region."

Xu Chuan briefly explained the source of the problem in the notebook, and Professor Zhou Hai cast a shocked and surprised gaze.

"Is this question really developed by yourself through your own research?"

Zhou Hai opened his lips slightly, feeling that his mouth was a little dry, and after swallowing his saliva hard, he asked in disbelief.

"What's wrong? Any questions? Xu Chuan looked up and asked a little puzzled.

"Do you know what it is to continue to expand on this issue?" Zhou Hai asked urgently.

Xu Chuan shook his head, he really didn't know this, these questions in the notebook were all recorded by himself in the process of reading and studying.

As for the spectral asymptotic methods and problems on the connected regions with fractal boundaries, he really hadn't studied them in his previous life, and he didn't know what these problems would correspond to.

"It's the Weyl-Berry conjecture!"

Zhou Hai lowered his voice, but there was a hint of tremor and excitement in his tone.

"Weyl-Berry guess? Is it a problem in the field of functional analysis? ”

Xu Chuan asked suspiciously, he really hadn't heard of this conjecture.

After all, the field of mathematics is too big, even if it is a world-class conjecture and a lot of problems, he was not a major student of mathematics in his previous life, and it is normal for him not to know some mathematical conjectures.

Zhou Hai dragged a chair from the side, sat down and continued: "The Weyl-Berry conjecture, the full name is called the spectrum asymptotic of the elliptic operator and the Weyl-Berry conjecture. ”

"It mainly studies the spectral asymptotic and inverse spectral problems of elliptic operators and the conjecture of nonlinear analysis of Gevrey-like microlocal analysis of isospectral fractal regions such as fractal drum theory, which belongs to the world's conjecture."

"Of course, it's normal that you don't know this conjecture, and it's not as well-known as the top conjectures such as the Fermat conjecture, the four-color conjecture and the Goldbach conjecture, and it's not as difficult as it."

"If you divide the conjecture according to the difficulty of solving it, it should belong to the conjecture between T2 and T3."

"Can you elaborate on this conjecture?" Xu Chuan asked with interest.

He knows a little about the division of levels in Zhou Haihai.

Any problem is difficult to solve, and mathematics is no exception.

In the world of mathematics, there are many conjectures and problems.

The most famous and common are the seven millennial mathematical problems such as the Riemann conjecture, the Yang-Mills criterion field existence and mass interval hypothesis, and the P=NP problem, which are basically at the T0 level.

There are currently about ten mathematical conjectures and problems at the T0 level.

Solve any one, and you can get a Fields Medal, and you can go to any university in the world to become a professor or even the head or dean of a mathematics department.

Below the T0 level, T1 is the Goldbach conjecture, the four-color problem, the Langlands inverse conjecture, and some of the questions in Hilbert's Twenty-Three Questions.

Here is a mention of the Goldbach conjecture that focuses on the study of civil science, and its difficulty is actually worthy of the T0 level.

But the year before, in 2013, Harold Hoovgot, a researcher at the École Normale Supérieure in Paris, published two papers in which he announced that he had completely proved the weak Goldbach conjecture.

The 'weak Goldbach conjecture' has been proven, which makes the Goldbach conjecture lose its relative integrity and therefore it falls from T0 to T1.

However, this does not mean that its difficulty is reduced, in fact, if it is purely in terms of difficulty to solve, its difficulty is still at the T0 level.

By the way, most of the Goldbach conjectures in civil science research are because they can only understand this, and the other conjectures, even at the T2T3 level, they can't even understand what the question means.

And if you solve one of the conjectures at the T1 level, you can also win the Fields Medal, and you can also go to any university in the world to become a professor or even the head or dean of the mathematics department.

Further down, there are T2 and T3 mathematical conjectures and puzzles.

There are a lot of conjectures about this kind of ladder, and Xu Chuan can't say the name of each one.

If I have to say, the Moder conjecture derived from the Poincaré conjecture, the weak Goldbach conjecture derived from the Goldbach conjecture, the twin prime conjecture, and Hilbert's twenty-three questions can all be put into this ladder.

As for Zhou Hai's Weyl-Berry conjecture, he really didn't know about it and didn't study it.

.........