Great Country Academician

On the podium, Zhou Hai stopped the chalk he was calculating 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 the time for more than ten minutes, and finally confirmed a road that didn't work.

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

However, after careful consideration and study of the topics in the notebook, he was relieved again.

It's normal that he can't solve this problem in a short time.

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

This kind of problem, even if he devotes himself to research, he may not be able to solve it. If he wants to find an idea or directly prove it in a test, the difficulty is no different from the sky.

"Where did you find this question?"

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

As an undergraduate student, he started to come into contact with things like world conjecture?

Or is it a topic he found on purpose, on purpose?

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

I have seen geniuses and mediocre talents, I have seen those who are down-to-earth and work hard step by step to move forward, and I have also seen opportunistic people who want their tutors to help write their graduation thesis.

This kind of asking the teacher for super-class questions and difficult questions, in order to get close to and gain a good impression in front of the teacher, so that the teacher feels that he is studying seriously.

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

But no matter what, a freshman who starts to come into contact with such things as world-class conjectures will make people feel surprised and suspicious.

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

But if this topic was conceived by himself in the process of learning, it would be too shocking and unbelievable.

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

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 into a certain field and have almost reached the end can do it.

Can a freshman make it this far?

impossible!

Absolutely impossible!

Zhou Hai didn't believe that a freshman could do this, so he asked Xu Chuan where he got this question from.

Hearing Zhou Hai's inquiry, Xu Chuan took out "Factorization of Linear Operators and Geometric Properties of Banach Space" from his schoolbag again, turned to the last three chapters, and handed it to him.

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

"If remember Nn(r)=#{(Q1,...,Qn)∈"|qi+...+q

"Starting from Theorem 3.1, when the second term of the Dirichlet spectral counting function is asymptotically extended to the adjacent connected branches of the special non-connected region, this problem in the notebook is encountered."

Xu Chuan briefly explained the source of the problem in the notebook, which attracted Professor Zhou Hai's shocked and surprised gaze.

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

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

"What's wrong? Is there any problem?" Xu Chuan raised his head and asked in confusion.

"Then do you know what this question is going to extend?" Zhou Hai asked eagerly.

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

Regarding the spectral asymptotic method and problems on connected regions with fractal boundaries, he has never studied in his previous life, and he is not quite sure what these problems correspond to when they are expanded.

"It's the Weyl-Berry conjecture!"

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

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

Xu Chuan asked suspiciously, he had never heard of this conjecture.

After all, the field of mathematics is too vast, and there are a lot of world-class conjectures and problems. He was not a major in mathematics in his previous life, so it is normal to not know about some mathematical conjectures.

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

"It mainly studies the spectral asymptotics of elliptic operators, the inverse spectral problem and the construction of spectral fractal regions such as fractal drum theory, and the conjectures of nonlinear analytical Gevrey-like micro-local analysis, which are world-class conjectures."

"Of course, it's normal for you not to know about this conjecture. It's not as well-known as top conjectures such as Fermat's conjecture, four-color conjecture, and Goldbach's conjecture, nor is it as difficult."

"If it is divided according to the difficulty of solving the conjecture, it should belong to the conjecture of the level between T2-T3."

"Teacher, can you explain this conjecture in detail?" Xu Chuan asked with interest.

He knows a little about the division of ranks mentioned by Zhou Haikou.

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

In mathematics, there are many conjectures and problems.

The most famous and common ones are the seven millennium mathematical problems such as the "Riemann Hypothesis", "Yang-Mills Gauge Field Existence and Mass Interval Hypothesis", and "P=NP Problem". These problems are basically at the T0 level.

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

If you solve any one, you can get the Fields Medal, and you can go to any university in the world to be a professor or even the director or dean of the mathematics department.

From the T0 level down, the T1 level is Goldbach's conjecture, the four-color problem, the Langlands reciprocal conjecture, and some of the questions in Hilbert's 23 questions.

Here I would like to mention the Goldbach conjecture that Minke focuses on. Its difficulty is actually worthy of the T0 level.

But in the year before last, that is, in 2013, Harold Hoofgot, a researcher at the Ecole Normale Supérieure de Paris, published two papers announcing that the weak Goldbach conjecture was thoroughly proved.

The 'weak Goldbach conjecture' has been proven, which makes Goldbach's conjecture lose the relative integrity of the conjecture, so it is downgraded from T0 to T1 level.

However, this does not mean that the difficulty of solving it has been reduced. In fact, if it is purely from the difficulty of solving it, its difficulty is still at the T0 level.

By the way, most of the research on Goldbach's conjecture is because they can only understand this. Other conjectures, even at the T2T3 level, they can't even understand the meaning of the title.

And if you solve a conjecture at the level of T1, you can also get the Fields Medal, and you can also go to any university in the world to be a professor or even the dean or dean of the mathematics department.

Further down, there are mathematical conjectures and difficult problems at the T2 level and T3 level.

There are many conjectures about this kind of ladder, and Xu Chuan can't name every one of them.

If you insist, the Model conjecture derived from the Poincaré conjecture, the weak Goldbach conjecture derived from the Goldbach conjecture, the twin prime number conjecture, and Hilbert's twenty-three questions can all be put into in this ladder.

As for Zhou Hai's Weyl-Berry conjecture, he really doesn't know about it, nor has he studied it.