Zhou Hai dragged a chair from the side and sat down, ready to communicate with Xu Chuan about this.

That's right, it's communication, not pointing.

In his opinion, Xu Chuan's mathematical ability, which can study the weak Weyl-Berry conjecture branch problem, has reached a certain level.

"The Weyl-Berry conjecture originated in 1966 when the mathematician Mark Carker, in a lecture of that year, asked a question that has left history of science to behold: 'Can anyone hear the shape of a drum from the sound?'"

"Hear the shape of the drum by the sound? Can this be done too? Beside Xu Chuan, a classmate who came over to listen asked curiously.

Zhou Hai smiled, not minding the students interrupting him, college and junior high school are two completely different learning environments.

In universities, some teachers often chat with students in addition to imparting knowledge during classes.

After all, students are young, and their thinking about problems can sometimes be very special and bring unexpected surprises.

Moreover, it is far more useful to promote students' curiosity about a certain field through some stories, and to get them into a learning state than if you force knowledge on them, which is also more in line with the university.

"Mathematically speaking, a membrane is stretched over a rigid bracket to form a two-dimensional drum."

"Different shapes of drums produce different frequencies of sound waves when struck, so they produce different sounds."

"With these different sounds, we can really determine the shape of the drum."

"This involves the work of two mathematicians, Alan Connors and Walter van Suellecombe."

"They extended the traditional framework of non-reciprocal geometry to deal with the ..... of spectral truncation of geometric space and the tolerance relationship of providing a coarse-grained approximation of geometric space at finite resolution, and used the spectral truncation of a circle to define a propagation number for the operator system, and proved that it is an invariant at stable equivalence and can be used to compare approximations in the same space."

"In this framework, we can describe the vibration of the 'drum' when it is struck by using the wave equation, and because the edge of the 'drum face' is firmly attached to a rigid shelf, we can consider the boundary conditions of the wave equation to be Dirichlet boundary conditions."

"With the data from these two pieces, and using methods such as the diffusion equation, we can calculate the shape of the drum from the sound of it, even if you haven't seen it."

Zhou Hai explained with a smile, but directly said that he was stunned and came over to listen to the lively students.

What is spectral truncation of geometric space? What is the meter of the spectrum truncation of the circle?

They all know what it means, but they have never heard of it.

Can math really go this far? It's not metaphysics!

You can know what's going on with a finger pinch, that's outrageous, right?

It was Xu Chuan who probably understood what Zhou Hai meant.

The so-called "listening to the drum to distinguish shapes" is actually the eigenvalue problem of the Laplace operator in a region.

To 'listen to the drum and distinguish shapes' through mathematics is related to another concept.

That's the 'diffusion imagination'.

We all know that if a drop of ink is dropped into clean water, the ink will spread over time.

This is the phenomenon of diffusion.

Over time, matter will spontaneously diffuse from a place of high concentration to a place of low concentration, whether it is called 'tangible' or 'intangible'.

For example, if you press a piece of copper and a piece of iron together, after a period of time, through the instrument, you will find that there is copper on the surface of the iron, and there is iron on the surface of the copper, which is also a diffusion, but the process is quite slow.

The same goes for the sound.

The sound of a drum can indeed be calculated by clarifying the Dirichlet boundary conditions and the initial vibration conditions, and then bringing in the equations of time and diffusion.

Mathematics is so magical, ordinary people think it is incredible and even metaphysical, but in mathematics it can be calculated for you step by step.

.......

Through Professor Zhou Hai's explanation, Xu Chuan probably understood the spectral asymptotic of the so-called elliptic operator and the Weyl-Berry conjecture.

To put it simply, you can see the Weyl-Berry conjecture in two dimensions.

Mathematicians in the past have confirmed this, but not the Weyl-Berry conjecture in three-dimensional or more complex conditions.

The need now is whether mathematicians can find a fractal framework in which the three-dimensional or more complex Weyl-Berry conjecture holds, and where the ∂Ω can be measured.

That's the purpose.

As for what it will do if it is confirmed, what will it do?

I guess it can be used to study the shape of the stars and the size of the universe in the universe, but as for the rest, there should be no conjecture that can be put into practice.

But mathematics, to be honest, modern mathematics is actually very far from the concept of "useful".

If one does not have a strong, intrinsic interest in mathematics on their own, it seems difficult to solve the question "why should I study mathematics?"

Richard Feynman, known as the 'all-round physicist' in the last century, considered a major in mathematics when he was young.

But when he went to the mathematics department for counseling, he asked, "What's the use of studying mathematics?" ”。

Then the old professor of the mathematics department told him, since you ask this question, then you don't belong here, you don't belong to the mathematics department.

Then, the big guy went to study physics.

The distance unit of 'nanometer', which we all know now, was proposed by him.

Mathematics is a product of pure abstraction, and definitions and logic are the cornerstones that make up the mathematical system.

Mathematicians are often not concerned with how mathematical concepts and derivations relate to the real world; Mathematical conclusions may not be found in the real world.

However, with the development of technology and society, some results that were previously thought to be meaningless will become meaningful.

For example, there is a certain connection between the "antimatter" he studied in his previous life and the negative roots of quadratic equations, which seem to be useless today.

It's like if you learn calculus, but you don't use it at all for grocery shopping and you don't think it's useful.

Kangxi, a historical celebrity, also asked the question of what calculus is for.

Later, he probably felt that none of the 'self-capture and worship, level the three feudal domains, collect WW, seize the heirs of the nine kings, govern the Yellow River, write eight strands, and cultivate crops' did not need to use calculus, so he felt that there was no need to promote it.

Over time, however, the development and application of calculus has influenced almost all areas of modern life.

From modern missile flight calculations to cold medicine, calculus is needed.

Because through the law of decline of drugs in the body, calculus can deduce the time of taking drugs.

So don't say that math is useless, if math is useless, you won't even be able to take medicine at the right time.

......