From Almighty Scholar to Chief Scientist

Chapter 292 Arriving at Hodge's Conjecture
For Oleyevich, he knew that Lin Xiao's report was of great importance to the study of Hodge's conjecture.

Both forms of integral Hodge conjecture in the past have certain errors, that is to say, mathematicians have found counterexamples, so mathematicians are still pursuing a new integral Hodge conjecture, which can perfectly combine Hodge Conjectures are summarized.

Now, in Lin Xiao's report, a very rigorous discussion process was used to propose this brand-new motivational cohomology person, and then he came up with this new integral Hodge conjecture. In this regard, it is enough to make Ole Jevic believed it very much, and Lin Xiao later used a counter-evidence method to prove that his integral Hodge conjecture was completely correct, and it carried all the information of the original Hodge conjecture.

"Loss of information" is a common situation that hinders the development of mathematics, and generally occurs in changes of form.

For example, Lin Xiao’s Lin’s Theorem solves the change from function to layer. In the past, not all functions could be transformed into layers, because some information would be lost during the transformation process, that is to say, some Information will be lost after transformation.

The form of incomplete information will naturally affect the process of solving mathematical problems, so how to solve this problem requires the development of new tools.

For Lin's theorem, it is a tool to achieve lossless transformation between functions and layers.

In the process of transforming Hodge's conjecture into integral Hodge's conjecture, it is necessary to use the function that cohomology can be converted into differential form. However, due to the limitation of tools, this conversion process will lead to the loss of some information, so it is also As a result, the errors of the past two integral Hodge conjectures appeared.

But now, Lin Xiao's brand-new motivational co-homology once again solves such a fatal problem, allowing the original "information" to be transformed without loss in two forms.

Therefore, for this, Oleyevich was very amazed by Lin Xiao's report. Undoubtedly, this is a very remarkable achievement.

The importance of this report cannot be overstated.

"It makes me look forward to Professor Lin's report."

Shaking his head, Oleyevich looked at the end of the report again, and suddenly he was taken aback.

At the end, there are several lines of mathematical formulas.

"Huh? Why is there still at the end...Professor Lin hasn't finished yet?"

With some doubts, he took a few more glances.

After a while, a serious color appeared in his eyes.

"This is...Professor Lin is actually going to start proving this conjecture?"

The few steps at the end are the proof that the integral Hodge conjecture begins to unfold.

But although it is only a few simple steps, it is enough to arouse the imagination of mathematicians like Olejevic.

According to the steps given by Lin Xiao, if we continue to work on it, maybe we can produce some important phased results?

At least for now, Lin Xiao's last few lines already have such potential.

Not to mention the real proof, but the staged results are also very important in mathematics, just like Perelman was able to prove the Poincaré conjecture because there is a mathematical tool called Ricci flow, which plays a very important role in it. Importantly, this also made Perelman publicly stated that the mathematician named Richard Hamilton who came up with the Ricci flow had made a greater contribution than him.

But even so, but——

"Why are there only so few steps!"

For the first time, Oleyevich felt the abhorrence of broken dogs, and even felt like sending Lin Xiao a blade.

This can obviously be written in the future, at least with Lin Xiao's ability, it is definitely possible to write in the future.

But he got stuck at such a critical step and stopped writing.

Oleyevich scratched his hair, feeling itchy.

I believe that no mathematician can resist the temptation to prove Hodge's conjecture, or any of the seven millennium problems. The $100 million award from the Clay Institute alone is enough to make many mathematicians Hungry.

Mathematicians are often not that rich, so they were surprised to learn that Perelman didn't even accept the $100 million.

And that’s not to mention the fame that comes with it, and the need for self-actualization, which is the Millennium Dilemma after all.

So Olejevic really wanted to know how to write after this crucial step.

"Professor Lin, what the hell is he going to do!"

But no matter how confused he was at this moment, even if he thought about it, he probably never thought that Lin Xiao wanted to reproduce the process of Andrew Wiles proving Fermat's last theorem.

If you can't figure it out, then don't think about it.

So Olejevic stopped meddling and put the report into the archives. After it was reviewed and it was completely confirmed that there was no problem with the content of the report, it could be uploaded to their 2022ICM official website.

Oleyevich could even imagine that when other mathematicians downloaded Lin Xiao's report and read it, they would, like him, hate Lin Xiao's step stuck in a critical point.

Maybe, after Lin Xiao finished his report in his speech, the audience would still make a fuss.

Oleyevich was already looking forward to that time.

Shaking his head and putting this matter behind him, he was about to start other work, but at this moment, someone suddenly called him.

He saw that it was his friend Zorelovsky, who was a professor of mathematics at St. Petersburg State University.

St. Petersburg State University is second only to Moscow State University in Russia, and its status is equivalent to Qingbei in China.

Although in the so-called international university rankings, the ranking of St. Petersburg State University can only compete with the 985 schools outside Huaguo and Qingbei, but in fact its own strength cannot be objectively expressed by those international rankings, because these international rankings are all Paying attention to an internationalization, in layman's terms, is the requirement for English, so in the QS university rankings, for example, universities in the English-speaking area are basically ranked in the forefront.

It is precisely because of this that the strength of St. Petersburg State University is actually very strong.

At the same time, Russia's basic mathematics education is also very strong, and St. Petersburg State University has naturally inherited this strength. Even Perelman graduated from St. Petersburg State University.

It is precisely because of this that Zorelovsky is quite famous in the world of mathematics.

After answering the phone, he smiled and said, "Dude, why are you in the mood to call me?"

Zorelovsky on the opposite side did not greet him, and said directly: "Did you know? Lin Xiao from Huaguo has decided to hold a report on the proof of Lin's conjecture at their Shangjing University. Are you planning to go?"

Oleyevich was taken aback, "Proof of Lin's conjecture?"

Of course, he is also very interested in this matter. As a researcher of algebraic geometry, he is certainly not unfamiliar with Lin's theorem. For example, in some of his recent research, he has used the research on Lin's theorem.

But then he said helplessly: "I'm in charge of the International Congress of Mathematicians now, so I probably don't have time to go."

"That's right, that's true." Zorelovsky said: "The report will be held until June [-]th. I guess you really don't have time."

"Hmm... wait, you said June [-]th?"

Suddenly, Oleyevich sat up directly, and when Zorelovsky said that Lin Xiao planned to give a report on June [-], he suddenly felt something was wrong.

One week after June [-]th, it will be the International Congress of Mathematicians, and there will be a one-hour report by Lin Xiao at that time.

So what is Lin Xiao planning to do?
Two reports in ten days?

No, there are Fields Lectures.

Although he, the chairman of the organizing committee, cannot comment on the Fields Medal, which is determined by the International Mathematical Union, but he can still get some news. The probability of this Lin Xiao winning the Fields Medal is [-]%. big.

This made him fantasize even more.

Lin's guess?Integral Hodge Conjecture?
There are also several steps that Lin Xiao will try to prove Hodge's conjecture at the end of the report.

Oleyevich always felt that Lin Xiao wanted to make a big deal.

"It's June [-]th, what's the matter?"

On the other end of the phone, a friend's inquiry came.

Oleyevich came back to his senses, then smiled and said, "It's nothing, I just think that this year's mathematics world may not be ordinary."

Zorelovsky said with a smile: "Professor Lin proved his own Lin's conjecture in January. This alone is enough to make this year's mathematics world extraordinary."

Olijevic shrugged: "Well, what I want to say is that this year's conference should not be too ordinary."

"Really? Then I can look forward to it."

"Well, look forward to it." Olejevic said: "I am looking forward to it too."

……

Time is fleeting.

April and May were spent in a dull manner, and June also arrived on time.

In Lin Xiao's room.

After nearly three months of retreat, at this time, Lin Xiao's hair reaches the eyebrows in front, the collar in the back, the ears in the side, and even a beard has grown out.

The originally 22-year-old young man now seems to have directly turned into a sloppy uncle.

Of course, it was also because his school classes were over before the ninth week of the semester, so he was able to stay indoors.

However, despite retreating for so long, he still hasn't completed the final proof of Hodge's conjecture.

"It's just the last bit..."

He rested his chin on the table with one hand, and many thoughts flashed through his mind.

[A flash of inspiration] has not been used yet, because he has not grasped the last and most critical idea.

"Transform a shape into small blocks in integral form, and then make them undergo topological transformation, and then how to describe its homeomorphism in a polynomial way?"

Lin Xiao scratched his head, and the thick feel told him that his hair was still there, and it was still thick, but it was a bit long.

He let out a long breath, then stood up, twisted his body, and relaxed his stiff body a little.

Then look at the time.

"It's already June 6th."

There is still half a month before the report on June 6. Similarly, it is less than a month away from the speech at the International Congress of Mathematicians.

Shaking my head, it won't work like this.

Now it seems that the car called Hodge's conjecture cannot be built behind closed doors.

"Let's go to school for a while, I haven't been there for a long time."

Thinking of this in his heart, he no longer hesitated, staying in the room for so long, people are going to be moldy, and it's time to go out for a walk.

After that, he left the house and called Shi Hao who was at the opposite door, and then Shi Hao drove the car and took him to Beijing University.

"Just find a parking lot and walk around the school."

Entering the campus of Peking University, Lin Xiao said.

"Okay, Professor Lin." Shi Hao replied.

Soon they found a parking lot, Shi Hao parked the car, the two got out of the car, and turned around in the school.

Because it happened to rain in the afternoon, and it was already in the evening, the temperature was no longer so hot, so it was a good time to go out for a stroll.

Walking around the campus, Lin Xiao, who looked like a slovenly uncle, was lucky enough not to go to the first floor, but was called all the way by the students, allowing him to relax a bit.

In this way, they walked all the way to the bank of Weiming Lake, looking at the slightly wavy lake water, Lin Xiao didn't think about any math problems at this time, but just felt the beauty of the natural scenery.

Then, he asked Shi Hao curiously: "If you will be my bodyguard, how long will you be there?"

Shi Hao replied: "Until I can't protect you."

"What happens when you can't protect me?"

"When my physical fitness declines, or when I am disabled and lose the ability to move normally." Shi Hao's tone seemed to be always so calm

Lin Xiao had no choice but to say, "Is there no deadline? Three or four years?"

"Look at the organizational decision."

Lin Xiao shook his head, and when he was about to speak, there was a burst of exclamation from behind.

"Damn it! Awesome!"

"6666!"

Lin Xiao was stunned for a moment, then turned his head to look, but saw a group of students watching a boy playing with a toy that everyone was familiar with. It looked like a colorful spring made of plastic, and its official name was Slinky.

And this boy played this thing very well, like an acrobat, which made many students around him look surprised.

But compared to the surprised eyes of these students, a bunch of mathematical formulas appeared in Lin Xiao's eyes.

Isn't this thing just a classic one-dimensional manifold topology?

Seeing the colorful spring beating like a clever ghost in the hands of the student, Lin Xiao's eyes gradually lit up, because he grasped the solution to Hodge's conjecture from this one-dimensional manifold. The essential.

Hodge conjectures to study the algebraic representation of topological bodies in three dimensions, but now he has found a similar answer in this one-dimensional manifold.

This is probably the magic of mathematics.

Looking at that boy, Lin Xiao wanted to thank him for the inspiration he had brought him, but at this moment, he found that this boy was still a student he had taught before.

He couldn't help walking up and shouting, "Wen Min, have you finished your thesis?"

The boy was taken aback, thinking he had met his mentor, but when he turned around, he saw a slovenly man walking towards him, which made him heave a sigh of relief, luckily it wasn't his mentor.

However, he stared at Lin Xiao for a while, and finally recognized the former teacher, and was extremely surprised: "Damn, Professor Lin, what's wrong with you?"

At this time, the people around also stared at Lin Xiao for a long time before they recognized him as Lin Xiao, so they were also surprised.

How did Professor Lin become like this?
Lin Xiao waved his hand and said, "Don't worry about it, where did you buy your toy? Is there any one near the school?"

Seeing Lin Xiao talking about the toy in his hand, Wen Min said, "Oh, this one, I bought it online, I don't know about it near the school."

Then he quickly handed the things to Lin Xiao, and said with a smile: "If you want this old man, I will give this to you. If you are drawn during the defense, you have to let me go."

Lin Xiao couldn't help laughing, took the Slinky, played with it a few times, and then said: "You are bribing the teacher in public, this is not acceptable, I will keep the stolen goods first, and you can write the paper for me, no If you know, you can ask me, as for letting you go, don't even think about it."

The students around all laughed, but Wen Min elongated his voice: "Ah~"

Lin Xiao smiled and patted him on the shoulder: "Stop it, you can ask me if you don't understand what you said, do you know what is the gold content of Professor Lin's personal guidance?"

Wen Min was taken aback for a moment, and immediately smiled: "That's right! You said that! I remember it."

The surrounding students immediately showed envious expressions.

Give a toy, you can get Professor Lin's personal guidance, such a good thing, they also want it!
Lin Xiao smiled, and then said: "Okay, that's it, thank you for the toy, you can play slowly."

Then, he left the group of students and said to Shi Hao: "Let's go, go back!"

"Yes!"

Although Lin Xiao didn't understand that Lin Xiao had only been out for less than an hour, and then he slipped a toy from a young student's hand and planned to go back, but Shi Hao always obeyed orders.

Afterwards, the two returned to the parking lot, and then returned to Yanbei Garden.

Going straight back to his room, Lin Xiao put Slinky on the table to play with for a while, and Mimi next to him was also curious about this moving thing, and finally pushed it over, and started playing with it by himself.

Lin Xiao couldn't help smiling, and then let Mimi play by herself, while he picked up the pen again and wrote down an equation describing Slinky on the scratch paper.

Thinking back to the Slinky's movement and its regular model, he smiled slightly.

"Hodge guesses it's officially over."

Then, "Use [A flash of inspiration]."

System: "[A flash of inspiration] has been used."

In the next moment, Lin Xiao grasped his train of thought and found the inspiration he needed.

Then, his pen wrote smart mathematical formulas on the paper.

One of the seven major mathematical problems of the millennium, Hodge conjectured that one of the most enchanting girls in mathematics began to take off her veil and clothes, waiting for the arrival of genius.

(End of this chapter)