From Almighty Scholar to Chief Scientist

Chapter 266 Lin's Conjecture Again?

"Atoms can form a connection, to put it simply, it is a connection formed between electrons."

"Covalent bonds, ionic bonds, and metal bonds, although these bonds are just the interaction force between electrons, they can still be regarded as a line in terms of wave functions, and these nuclei can be Look at it one by one..."

"Kink!"

In Yanbeiyuan's house, Lin Xiao leaned over his desk, looking at the atomic models and extremely complicated mathematical formulas drawn on the draft paper.

And Lin Xiao's eyes gradually brightened up.

A month has passed, and the direction of his research has been full of hardships.

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

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

This is the case with basic scientific research. The more you need to find out the principle, the deeper you get involved. Just like Lin Xiao’s lithography machine, from the optical path system, you need to follow the mechanical arm, to the servo motor, and then to the coding. If you want to subdivide the sensor, you 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 the bonds as lines, and the nuclei as the kinks in those lines."

"Through the method of topology, first realize the analysis from one-dimensional to two-dimensional, and then realize the analysis from two-dimensional to three-dimensional."

"In this way, the fundamental reasons governing the bonding laws of these atoms can be ascertained."

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

Lin Xiao's eyes lit up.

The nature of chemical bonds is well understood, that is, the electromagnetic interaction force between atoms is at work, electrons are negatively charged, and atomic nuclei are positively charged. Under mutual attraction, these bonds are formed

And the bonding mechanism he discussed can be used to explain why the microscopic structure of a substance is such a structure.

For example, carbon sixty, why does it become a spherical structure instead of an elliptical structure during the formation process.

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

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

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

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

Because before doing it, apart from knowing the method of topology, Lin Xiao still doesn't know what knowledge he will use in the future.

This is the difference between scientific research and doing problems.

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

But this kind of scientific research is different. The methods to be used are not clear. In addition to sufficient knowledge reserves, it is also necessary to achieve a mastery of the knowledge reserves you have.

This brings us to Maxwell's equations again. What Maxwell did was to combine the four equations of Gauss' law, Gauss' magnetic law, Maxwell-Ampere's law and Faraday's law of induction. Of course, it cannot be said so simply. , in fact, the Maxwell equations that Maxwell first came up with have a total of 20 component equations, but after a physicist named Heaviside simplified them, they were summarized into 4 incompletely symmetrical vector equations.

And this is where Maxwell's genius lies. He summed up so many equations wonderfully, so he successfully completed "On Electricity and Magnetism", which brought great development to the development of physics, even at that time. Maxwell has every opportunity to come up with the theory of relativity based on this thing, because Maxwell's equations fit perfectly with the special theory of relativity.

Unfortunately, the special theory of relativity was not invented by Einstein until several decades later. Of course, Einstein came up with this thing because of his genius-like induction and arrangement of past theories, coupled with his own Just like what Hilbert commented at the beginning: Any child on the road in Göttingen can understand four-dimensional geometry better than Einstein, but it is physics who discovered the theory of relativity Einstein, not a mathematician.

For Lin Xiao's current research, he is not just like this, because what he has to do now is not only to summarize the old theories in the past, but also to complete a new theory. The challenges in this are even more important. Huge, like his multidimensional field theory.

Turning the pen in his hand, he frowned: "Of course, at least I now know that this thing needs to use multi-topology."

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

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

The three principles of bonding are orbital symmetry matching, orbital energy similarity, and orbital overlap maximum.

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... next, we can start to do it."

After thinking for a while, Lin Xiao found a direction to start with, which is to calculate the molecular orbital wave function by approximating the linear combination of atomic orbitals:
【ψj=∑Cijχi】

……

As time passed, Lin Xiao gradually became better. Although he didn't know what the final form would be, but because of his control over knowledge, he could easily direct the direction of calculation towards the goal he wanted.

So just like that, time passed quietly.

This New Year's Day holiday, although it is a holiday, is the same for him, but it is better that he does not have to go to class. Of course, the time has entered January, and when it is the exam week of the university, his classes have already finished, so You don't even have to go to class.

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

"Why did the modular form appear again?"

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

Why did the modular form come up? In Lin Xiao's calculation, this is a natural work, that is to say, the modular form must appear in his calculation.

But the key question is, what will he do next?
Last time, when he demonstrated that the diffraction and interference of light are related to strings, he used the modular form. At that time, it was because of the connection with string theory. After all, the modular form was originally used in string theory.

And now it is used in topology again, but this still makes him feel a little surprised.

Of course, these are not problems. The most important thing is that if he wants to continue to go down now, he will face the same two choices as before, or try to choose another direction. Form, and then proved the original purpose from another direction, and other than that, he had to try to prove his Lin's conjecture!

Using this modular form as a springboard to communicate the relationship between the function and the layer form, then he can 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 solve the current atomic structure. Structural topology problems will play a very huge role.

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

Its application in topology is very important.

After a moment of entanglement, Lin Xiao finally felt certain in his eyes.

"Never mind, fuck it."

Then, prove Lin's conjecture to it!
His Lin's conjecture is of great significance to the development of mathematics.

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

Turning functions into layers is of great significance for promoting the development of algebraic geometry. After all, this is to directly draw an equal sign between functions and topology, and then provide a huge role for communication between 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 mathematics world has become higher and higher, although it is not said that it can be compared with those conjectures that have accumulated for tens of hundreds of years, such as the Riemann conjecture, or P=NP However, the mathematics 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 roughly equivalent to the "seniority" in mathematical conjecture.

For example, Riemann's conjecture is because there are thousands of propositions that can work based on the premise of its establishment. As long as it is proved, these propositions can be raised to theorems, and these thousands of propositions are all developed for hundreds of years. accumulated by mathematicians.

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

So it is very important to prove the significance of Lin's conjecture.

not to mention--

The conjecture I put forward was finally proved by myself a few years later, which sounds full of storytelling.

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 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 surfing the Internet, looking for some current research on Lin's conjecture.

After all, before doing a project, a literature review is required.

(End of this chapter)