On the podium, Zhou Hai stopped the chalk calculation on the blackboard, frowned at the white writing, turned around, picked up the blackboard eraser, and erased all the mathematical formulas and calculations on it.
He calculated for more than ten minutes and finally confirmed that there was a dead end road.
For the first time since teaching, he was stumped by a student's question. It was incredible.
However, after carefully thinking and studying the topics in the notebook, he felt relieved.
It's normal that he can't solve this problem in a short time.
Although the title was handwritten by Xu Chuan, it was actually part of a weakened form proof of a world-class mathematical conjecture.
Even if he devotes himself to research, he may not be able to solve this kind of problem. If he wants to find an idea or directly prove it in a test, the difficulty is as high as the sky.
"Where did you get this question?"
After confirming that he could not solve the questions 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 are starting to get exposed to things like world conjecture?
There are many people who ask teachers for super-syllabic and difficult questions in order to gain a good impression in front of the teacher and make the teacher feel that they are studying seriously.
But the year before last, that is, in 2013, Harold Hoefgot, a researcher at the Ecole Normale Supérieure in Paris, published two papers, announcing that he had completely proved the weak Goldbach conjecture.
"Of course, it's normal that you don't know this conjecture. It's not as well-known as Fermat's conjecture, the four-color conjecture and Goldbach's conjecture, and it's not as difficult as it is."
Or is it a question he found specially on purpose?
However, this does not mean that the difficulty of solving it has been reduced. In fact, in terms of the difficulty of solving it, its difficulty is still at the T0 level.
Zhou Hai dragged a chair over from the side, sat down and continued: "The Weyl-Berry conjecture, its full name is the spectral asymptotic of the elliptic operator and the Weyl-Berry conjecture."
"Weyl-Berry conjecture? Is it a problem in the field of functional analysis?"
In the world of mathematics, there are many conjectures and problems.
He did know a little bit about Zhou Haikou's classification of levels.
Not to mention a freshman, even the graduate students, doctoral students he teaches, and even a university professor may not have such ability.
There are currently about ten mathematical conjectures and problems at T0 level.
Here I would like to mention Goldbach’s conjecture, which Minke focuses on. Its difficulty is actually worthy of the T0 level.
“It mainly studies the spectral asymptotic and inverse spectral problems of elliptic operators and the construction of spectral fractal regions such as fractal drum theory and the conjectures of nonlinear analytic Gevrey-like microlocal analysis, which are world-class conjectures.”
By the way, most civilians study Goldbach’s conjecture because they can only understand it. For other conjectures, even at the T2T3 level, they can’t even understand what the title means.
Any problem is difficult to solve, and mathematics is no exception.
"This book contains some descriptions of spectral asymptotic methods and problems on connected regions with fractal boundaries."
"Then do you know what the extension of this problem will be?" Zhou Hai asked eagerly.
"It's Weyl-Berry conjecture!"
If you solve a T1-level conjecture, you can also win the Fields Medal, and you can also become a professor or even the director or dean of the mathematics department in any university in the world.
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.
Of course, he didn't think Xu Chuan was this kind of person.
"What's wrong? Is there any problem?" Xu Chuan raised his head and asked with some confusion.
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.
Zhou Hai lowered his voice, but there was a hint of trembling and excitement in his tone.
But no matter what, when a freshman begins to come into contact with such things as world-class conjectures, it will always make people feel surprised and doubtful.
He has been teaching for more than 20 years and has seen students one after another.
How can a freshman come 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.
“If we remember Nn(r)=#{(Q1,…,Qn)∈”|qi+…+q
"Starting from Theorem 3.1, when combining the second term asymptotically of the Dirichlet spectral counting function to expand the adjacent connected branches of the special non-connected region, we encountered this problem in the notebook."
I have seen geniuses and mediocre talents, I have seen students who study hard and move forward step by step, and I have seen people who are opportunistic and want their tutors to help them write their graduation thesis.
The 'Weak Goldbach Conjecture' has been proven, which caused Goldbach's conjecture to lose the relative integrity of the conjecture, so it dropped from T0 to T1 level.
Regarding the area of spectral asymptotic methods and problems on connected regions with fractal boundaries, he had never studied it in his previous life, and he didn't quite know what these problems would correspond to when expanded.
If you solve any problem, 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.
After all, the field of mathematics is too vast, and even if it is a world-class conjecture, there are a lot of conjectures and problems. He was not a math major in his previous life, so it is normal for him not to know some mathematical conjectures.
But if this topic was conceived by himself during the study process, it would be so shocking and incredible.
Xu Chuan shook his head. He really didn't know this. These questions in his notebook were all recorded by him while he was reading and studying.
"Is this question really something you developed through your own research?"
From the T0 level down, the T1 level includes Goldbach's conjecture, the four-color problem, Langlands' reciprocity conjecture, and some of Hilbert's twenty-three questions.
And it would be okay if he found the questions himself. After all, if many college students are interested in a certain subject, they will look for some questions on the Internet or in the library to try to solve.
Xu Chuan briefly explained the source of the problem in the notebook, which caused Professor Zhou Hai to cast a shocked and surprised look.
Xu Chuan asked doubtfully, he had never heard of this conjecture.
"Teacher, can you tell me more about this conjecture?" Xu Chuan asked with interest.
Zhou Hai opened his lips slightly, feeling that his mouth was a little dry. After swallowing hard, he asked in disbelief.
This is something that can only be done by top mathematicians or mathematicians who have studied extremely deeply in a certain field and have almost reached the end.
"If we divide it according to the difficulty of solving the conjecture, it should be a conjecture between T2 and T3."
Study old knowledge, integrate it, and then expand to new boundaries and new problems based on this.
Further down, there are mathematical conjectures and difficult questions at T2 level and T3 level.
There are many conjectures about this kind of staircase, and Xu Chuan cannot name every one of them.
If you insist on talking about it, Model's conjecture derived from Poincaré's conjecture, weak Goldbach's conjecture derived from Goldbach's conjecture, twin prime conjecture, Hilbert's twenty-three questions can all be put into
In this staircase.
As for the Weyl-Berry conjecture mentioned by Zhou Hai, he indeed did not know about it and had not studied it.