Chapter 263 Is it Lin’s conjecture again?

"Atoms can form connections. To put it simply, it is the connection formed between electrons."

"Covalent bonds, ionic bonds, and metallic bonds, although these bonds are just the interaction between electrons, if we look at them in terms of wave functions, they can still be seen as a line, and these atomic nuclei can Look at each one..."

"Kink!"

In Yan Beiyuan's house, Lin Xiao was hunched over his desk, looking at the atomic models and extremely complex mathematical formulas drawn on the draft paper.

And Lin Xiao's eyes gradually became brighter.

A month passed, and the direction he was studying was full of hardships.

After all, how to abstract these microscopic physical phenomena into mathematical formulas is full of difficulties.

What's more, he also needs to find a theory that can be used to control the formation of chemical bonds, and then discuss the bonding principle of silicon.

This is what basic scientific research is like. The more you need to understand the principles, the more involved you will get. Just like Lin Xiao’s photolithography machine, from the optical system, you need to follow the mechanical arm, to the servo motor, and then to the encoding. If the sensor is further subdivided, we have to continue to study the material of the sensor and other things.

However, fortunately, he was superior in skills, and now, he finally found a key point.

"Just think of these chemical bonds as lines, and then think of these nuclei as the kinks in those line segments."

“Through the topological method, we first realize the analysis from one dimension to two dimensions, and then realize the analysis from two dimensions to three dimensions.”

"In this way, we can understand the basic reasons that control the bonding patterns of these atoms."

"At that time, let alone the bonding mechanism of silicon, the bonding mechanisms of all other elements will be perfectly explained."

Lin Xiao's eyes lit up.

The nature of chemical bonds is easy to understand. It is the electromagnetic interaction between atoms. Electrons are negatively charged and atomic nuclei are positively charged. These bonds are formed due to mutual attraction.

The bonding mechanism he discussed can be used to explain why the microstructure of a substance has this structure.

For example, why does carbon 60 become a spherical structure instead of an elliptical structure during its formation?

Another example is why the diamond structure in crystallography is such a structure.

Knowing why, he can then start from why to find the silicon crystal lens to prepare them.

Having established such principles and understanding in his mind, the next step is to use the knowledge he possesses to solve this problem.

Of course, this step is not simple either. How to use mathematical methods to explain this process is also a very difficult process.

Because before taking action, Lin Xiao currently does not know what knowledge he will use in the future besides knowing the methods that need to be used in topology.

This is the difference between scientific research and problem solving.

It is easy to see what knowledge is needed to solve the problem. To solve a conic section problem, you need to use number theory knowledge, and to solve an algebra problem, you need to use algebra knowledge.

But this kind of scientific research is different. The methods to be used are not clear. In addition to sufficient knowledge reserves, it also requires a comprehensive understanding of the knowledge reserves.

This brings us to Maxwell's equations again. What Maxwell did was just combine the four equations of Gauss's law, Gauss's magnetic law, Maxwell-Ampere's law and Faraday's law of induction. Of course, it cannot be said to be that simple. , in fact, the Maxwell equations originally created by Maxwell had a total of 20 component equations. It was only after a physicist named Heaviside simplified them that they were reduced to four incompletely symmetric vector equations.

And this is where Maxwell's genius lies. He made a wonderful summary of so many equations, and then successfully completed "On Electricity and Magnetism", which brought huge development to the development of the physics world, even at that time Maxwell has every chance to come up with the theory of relativity based on this thing, because Maxwell's equations are perfectly consistent with the special theory of relativity.

Unfortunately, the special theory of relativity was not developed until decades later by Einstein. Of course, Einstein came up with this thing because of his genius in summarizing and organizing past theories, coupled with his own It took a lot of thinking to come up with this thing. Just like Hilbert commented at the beginning: If you pick a random kid on the street in Göttingen, he will know more about four-dimensional geometry than Einstein. However, it was physics who discovered the theory of relativity. Einstein, not a mathematician.

As for Lin Xiao's current research, he is not just like this, because the work he has to do now is not only to summarize the old theories of the past, but also to complete a new theory. The challenge here is even more Huge, like his multidimensional field theory.

Turning the pen in his hand, he raised his eyebrows: "Of course, at least I know now that this thing requires multi-topology."

"Then add in the basic principles of chemical bond formation, and from there, I can establish the first steps."

"Well...then we have to start with the three principles of bonding."

The three principles of bonding are: orbital symmetry matching, orbital energies similar, and maximum orbital overlap.

Whether it is the formation or breaking of chemical bonds, it can be explained by these three principles.

And if he wants to discuss the bonding mechanism, he must be inseparable from these three principles.

"Then...then we can start taking action."

After thinking for a moment, Lin Xiao found a way to start, which is to calculate the molecular orbital wave function using the linear combination approximation of atomic orbitals:

【ψj=∑Cijχi】

…

As time passed, Lin Xiao gradually got better. Although he didn't know what the final form would be, due to his control of knowledge, he could easily make the calculation direction toward the goal he wanted.

So just like that, time passed quietly.

Although this New Year's Day holiday is a holiday, it is the same for him, except that it is better that he does not have to go to class. Of course, it is January and it is the exam week of the university. His classes have already been completed, so You don’t even need to go to class.

Until the third day of the New Year's Day holiday.

"Why did the mold form appear again?"

Lin Xiao frowned slightly as he looked at the mathematical symbols and numbers on the papyrus paper that represented modular forms.

Why do you come up with the modular form? In Lin Xiao's calculations, this is a matter of course. In other words, the modular form must appear in his calculations.

But the key question is, what will he do next?

Last time, when he was demonstrating that the diffraction and interference of light are related to strings, he used the modular form. At that time, it was because it was related to string theory. After all, the modular form has been used in string theory.

And now it is used in topology, but this still surprises him.

Of course, these are not problems. The most important thing is that if he wants to continue going down now, he will face the same two choices as before, or try to choose another direction, like last time he made a sub-model form, and then proved the original purpose from another direction. In addition, he had to try to prove his Lin's conjecture!

Using this modular form as a springboard to communicate the relationship between functions and layer forms, he can then convert the functional form of any atomic structure into a layer form, and then use the role of the layer form in the topological field to help him solve the current atomic problem. Structural topology issues will play a very huge role.

"Layer" is a theory in topology, algebraic geometry, and differential geometry. You can use layers whenever you want to track the algebraic data that changes with each open set in a given geometric space.

Its application in topology is very important.

After a moment of confusion, Lin Xiao finally became convinced.

"Whatever, fuck him."

Then, prove Lin's conjecture!

His Lin's conjecture is of great significance to the development of mathematics.

Since the emergence of Lin's conjecture three years ago, it has caused many people around the world to study Lin's conjecture.

The realization of transforming functions into layers will be of great significance to promote the development of algebraic geometry. After all, this is to directly draw an equal sign between functions and topology, thereby providing a huge role in communicating algebra and geometry.

In the end, it will also bring great help to the unification of the Langlands program.

Because of this, the status of Lin's conjecture in the mathematical world has also become higher and higher, although it cannot be said that it has a higher status than those conjectures that have been accumulated for decades or hundreds of years, such as Riemann's hypothesis, or P=NP Problems, etc. However, the mathematical community basically believes that it is only a matter of time before the importance of Lin's conjecture is raised to the level of these conjectures.

It is probably equivalent to "qualifications" in mathematical conjecture.

For example, the Riemann Hypothesis is feasible because there are thousands of propositions based on its establishment. As long as it is proved, these propositions can be upgraded to theorems. And these thousands of propositions have been developed over hundreds of years. accumulated by mathematicians.

In fact, assuming that Lin's conjecture is established, many propositions have already appeared, and there will definitely be more in the future.

Therefore, it is important to prove the significance of Lin's conjecture.

not to mention--

The conjecture I came up with was finally proven by myself a few years later. This sounds like a story.

You know, the International Congress of Mathematicians is also held this year.

Four years ago, he proposed Lin's conjecture at the International Congress of Mathematicians, and four years later, he completed its proof at the International Congress of Mathematicians.

"It sounds very interesting... Then let me bring another interesting story to the history of mathematics."

Lin Xiao's eyes moved, and then he stopped the pen in his hand and started to go online to find some current research on Lin's conjecture.

After all, before doing the project, you need to conduct a literature review.