Zhou Hai dragged a chair from the side and sat down, ready to discuss this matter with Xu Chuan.
That's right, it's communication, not instruction.
In his view, Xu Chuan's mathematical ability, which can study branch problems of weak Weyl-Berry conjectures, has reached a certain level.
"The origin of the Weyl-Berry conjecture comes from mathematician Mark Kuck in 1966. In a lecture that year, he raised a question that will go down in the history of science: 'Can anyone tell the shape of a drum from the sound?'
'"
"You can hear the shape of a drum through the sound? Is this possible?" A classmate next to Xu Chuan who came over to listen asked curiously.
Zhou Hai smiled and didn't mind the students interrupting him. University and junior high school are two completely different learning environments.
In universities, some teachers not only impart knowledge during class, but also often chat with students.
After all, students are young, and sometimes their thinking on problems is very special and can bring unexpected surprises.
Moreover, it is far more useful to use some stories to prompt students to be curious about a certain field and get them into a learning state than to force knowledge onto them. This teaching method is also more suitable for universities.
However, with the development of technology and society, some results that were originally considered to have no practical significance will become meaningful.
This is the phenomenon of diffusion.
As for the specific use of this thing after it is confirmed?
"Through these different sounds, you can really determine the shape of the drum."
As time goes by, substances will spontaneously diffuse from places with high concentration to places with low concentration. This phenomenon will occur whether it is so-called 'tangible' or 'intangible'.
Then the old professor in the mathematics department told him that since you asked this question, then you don't belong here, you don't belong in the mathematics department.
We all know that if a drop of ink is dropped into clean water, the ink will spread over time.
As for the sound emitted by a drum, after clarifying the Dirichlet boundary conditions and initial vibration conditions, and then incorporating the time and diffusion equations, the shape and size of the drum can indeed be calculated.
It can probably be used to study the shape of stars in the universe and the size of the universe. As for other things, there are probably no practical applications of this conjecture at present.
But when he went to the mathematics department for consultation, he asked, "What is the use of studying mathematics?".
"Under this framework, we can describe the vibration of the 'drum' when it is struck through the wave equation. At the same time, because the edge of the 'drum head' is firmly attached to the rigid frame, we can think of the boundary of the wave equation as
The conditions are Dirichlet boundary conditions."
Zhou Hai explained with a smile, but directly confused the students who came to listen to the excitement.
"This involved research by two mathematicians, Alan Connors and Walter van Suilekom."
What is the spectrum cutoff of geometric space? What is the spectrum cutoff of a circle?
They all know what it means to distinguish the position by listening to the sound, but they have never heard of distinguishing the shape by listening to the sound.
When Richard Feynman, known as the 'all-round physicist' in the last century, was young, he considered majoring in mathematics.
To use mathematics to "listen to the drum and identify the shape" is related to another concept.
The current need is whether mathematicians can find a fractal framework, so that the three-dimensional or more complex Weyl-Berry conjecture can be established under this fractal framework, and can make Ω measurable under this fractal framework.
Mathematics is a product of pure abstraction, and definitions and logic are the cornerstones of the mathematical system.
For example, if you press a piece of copper and a piece of iron together, after a period of time, through instrument testing, you will find that there is copper on the surface of the iron and iron on the surface of the copper. This is also diffusion, but the process is quite slow.
Through Professor Zhou Hai's explanation, Xu Chuan roughly understood what the so-called spectral asymptotics of elliptic operators and the Weyl-Berry conjecture were all about.
But as for mathematics, to be honest, modern mathematics is actually very far away from the concept of "useful".
The unit of distance that we all know today as "nanometer" was proposed by him.
This is the purpose.
Mathematics is so magical. Things that ordinary people find incredible or even metaphysical can be calculated for you step by step in mathematics.
"Drums of different shapes produce sound waves of different frequencies when struck, and therefore produce different sounds."
It's like you learned calculus, but you don't use it when buying groceries and think it's useless.
Mathematicians usually do not care about how mathematical concepts and derivation are related to the real world; mathematical conclusions may not necessarily be able to find prototypes in the real world.
"Mathematically speaking, stretching a membrane over a rigid support creates a two-dimensional drum."
That is ‘diffused imagination’.
"With these two pieces of data, and using diffusion equations and other methods, we can calculate the shape of the drum from the sound it makes, even if you have never seen it."
You can tell what happened just by counting with your fingers. This is too outrageous, right?
The same goes for sound.
If a person does not have a strong and intrinsic interest in mathematics, it seems difficult to solve the question "Why should I study mathematics?"
Mathematicians in the past have confirmed this, but not the Weyl-Berry conjecture in three dimensions or more complex conditions.
For example, the "antimatter" he studied in his previous life has a certain connection with the negative roots of the quadratic equation that seem useless today.
The famous historical figure Kangxi also asked the question what is the use of calculus.
"They extend the traditional framework of non-commutative geometry to handle spectral truncation of geometric space and tolerance relations that provide coarse-grained approximations of geometric space at finite resolution, and exploit the spectral truncation of circles to define a system of operators.
A propagation number that is shown to be an invariant under stable equivalence and can be used to compare approximations in the same space."
Xu Chuan, on the other hand, probably understood what Zhou Hai meant.
Later, he probably felt that none of the tasks of "capturing Oboi, pacifying the three feudal lords, conquering WW, seizing the nine kings' direct descendants, regulating the Yellow River, writing eight-legged essays, and cultivating crops" required the use of calculus, so he felt that there was no need to promote it.
To put it simply, you can turn the previous "listening to distinguish drum shapes" into a two-dimensional Weyl-Berry conjecture.
The so-called "identifying the shape by listening to the drum" is actually the problem of the eigenvalue of the Laplacian operator in a region.
Then, this big guy went to study physics.
Can mathematics really do this? It is not metaphysics!
However, as time goes by, the development and application of calculus has affected almost all areas of modern life.
From modern missile flight calculations to taking a cold medicine, you need to use calculus.
Because based on the decay pattern of drugs in the body, calculus can deduce the regular medication time.
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.