From Almighty Scholar to Chief Scientist

Chapter 298 Congratulations to the Mathematics World

2022年7月10日上午08:30。

St. Petersburg National Theater, the main venue.

Countless mathematicians poured into the venue from the door, and then began to take their seats. The top mathematicians sat in the front seats, and then they were basically arranged in the back row according to the level of strength in the mathematics world.

Here, regardless of age and seniority, whoever is most likely to understand the report will sit at the front.

In the front row seat, Pierre Deligne chose his seat, and suddenly found that an old man next to him was very familiar, and couldn't help being surprised: "Professor Searle, you are here too? It seems that you are in good health." .”

This old man is none other than Professor Jean-Pierre Serre, Lin Xiao's doctoral supervisor.

Searle said with a smile: "It's just a few hours of flying, and I can still bear the distance."

Then, he put his eyes on the stage and said with emotion: "What's more, Lin was also my student. He has made such important achievements. Of course, my teacher, I have to come and see."

Hearing this, Deligne's old face twitched.

He still couldn't forget this matter, if only Lin Xiao went to study for his Ph.D.

And look, Lin Xiao's recent achievements in mathematics are all in algebraic geometry and topology, which he is good at.

But no matter what, Lin Xiao is already someone else's Ph.D., he can only sigh, expressing helplessness, and then said: "You are so lucky."

"Hahaha, I think so too." Searle laughed, and then said: "Look, I won the Fields Medal at the age of 28, and I have always been the youngest winner. Now my students succeed I completed this breakthrough for me, and it will be difficult for others to make a breakthrough in the future. Think about it. In the future, the mathematics community will know that the two youngest winners of the Fields Medal are a pair of teachers and students. How interesting is that?"

"It's really interesting."

Deligne was even more envious.

"However, it's a pity that I wasn't there on the day he presented the award. Otherwise, I would have had a few drinks with him."

"Tonight, too."

"Hehe, there's no need tonight." Searle smiled, and then took out a bottle of champagne from a bag on the ground.

Deligne was taken aback for a moment, and then couldn't help laughing: "You are always so well prepared."

"Of course."

Searle smiled slightly, and when Lin Xiao completed the proof, he would go up with his own hands and deliver the bottle of champagne up.

Meanwhile, on the other side.

The team from Huaguo is also sitting together and talking.

"There are so many people."

A professor of mathematics from Peking University couldn't help but look at the number of people in the venue.

Not even the previous plenary sessions had so many people, not even the opening ceremony.

Now, the entire main venue is full of people, including many people in the aisle. It can be said that it is not as good as the situation where more than 1 people listened to the report in the Great Hall of the People.

Next to him, Xu Ji, who just arrived yesterday, said with a smile: "After all, what Lin Xiao wants to prove is Hodge's conjecture. There are so many people, it's normal. When he proved Goldbach's conjecture, there were more people than this." Woolen cloth."

"Oh, sometimes I really envy Lin Xiao's talent. I used to think that I could treat him calmly, but now, I still can't bear it."

On the other side, another professor couldn't help but said.

Everyone looked at it and said with a smile: "Professor E, let's not compare with Lin Xiao. You have received invitations for one-hour reports this year, and you have already made history for our country."

This Enan professor is an academician of the Chinese Academy of Sciences and is well-known in the domestic mathematics circles. At the same time, he also received an invitation from the International Conference of Mathematicians, and it was only an hour. History has been made.

After all, there are not many mathematicians who hold Hua nationality and have received a one-hour report.

Professor E'nan smiled. It was indeed a happy thing for him to receive an invitation for a one-hour report. After all, this is a relatively high honor in the international mathematics community.

Of course, compared to Lin Xiao's Fields Medal and the Hodge Conjecture that is about to be proved in his hands, the one-hour report suddenly became nothing worth mentioning.

However, when they were chatting, there was a sudden commotion behind them, and many people turned their eyes to the door.

When they saw this scene, they couldn't help wondering, what happened?

So they all turned their heads and looked towards the gate at the back, and then they all showed surprised expressions.

Because, a bearded man suddenly appeared at the door, looking rather scruffy.

However, it was precisely because of this man's big beard that the people present quickly recognized him.

"Perelman?!"

The mathematicians present all showed surprised expressions.

The prover of the Poincaré conjecture, who hadn't been seen for more than ten years, actually came to the scene?

Of course, this is most likely because Perelman lived in St. Petersburg, so it is very convenient, but no matter what, Perelman's appearance here still surprised everyone present.

It seems that the proof of Hodge's conjecture, even he, who has hardly any communication with the mathematics world, couldn't help but listen to it.

Of course, thinking of Perelman's character, the people present quickly looked away, so as not to get bored and run away again. After all, he said at the beginning that he didn't want to be displayed like an animal in a zoo.

Soon, Perelman found a corner seat and sat down, and people stopped paying attention.

At this time, it was already 8:55, and there were only 5 minutes left before the official start of the report.

Backstage, Lin Xiao sat in his seat, closed his eyes and meditated.

And in his mind, he recalled all his proof process.

There are quite a few staff members standing next to him, and they all cast their eyes on this person who is known as the smartest person in the world today, not even one of them.

Proved Goldbach's conjecture, proposed multi-dimensional field theory, and now will prove Hodge's conjecture, which of course can be regarded as the smartest person in the world, and can even be called the smartest human being in history. Want to see what's different about me.

But obviously, everyone has one nose and two eyes, there is no difference.

These staff had no choice but to give up the thoughts in their hearts, and then their eyes turned to admiration. Russia has always paid attention to basic mathematics education. Now facing Lin Xiao, they can only feel admiration.

Soon, it's nine o'clock.

First, the host went up to control the scene, and then a staff member said to Lin Xiao: "Professor Lin, it's nine o'clock, and you can go on stage."

Lin Xiao nodded, "Okay."

Then he stood up, smoothed the well-tailored clothes on his body, and then took a step and walked out of the stage.

The applause sounded like a wave, welcoming the appearance of this mathematical genius.

And until the applause died down, Lin Xiao smiled and said, "Hi, friends."

"Thank you for coming here from a long distance to listen to my report. Now, I have felt the enthusiasm of everyone. Next, please let me deliver a satisfactory report for you."

Then, on the big screen behind them, the page was turned, and a PPT appeared in front of them.

On the first page of the PPT, everyone who participated in Lin Xiao's last report was familiar with it. It was the colorful spring toy called Slinky.

And then, Lin Xiao took out the toy from his bosom again.

This time it was probably because he had practiced a few times in the past few days, so he played with this toy much better than before.

But the people off the field couldn't help but smile when they saw Lin Xiao playing with toys in such a serious academic report.

But soon, Lin Xiao played with this spring a few times, and then he said: "Okay everyone, I also showed you this toy in the last report. As I said last time, this toy It is a very typical one-dimensional manifold topological body."

"According to Lefschetz, the Hodge conjecture is true for the (1, 1) class, then we can obviously get a result, that is, in a certain low-dimensional space, our Hodge conjecture is true."

"Now, we let X be a compact Khler manifold. The first Chern class c1 gives the mapping from the holomorphic bundle to H^2(X, Z), according to the Hodge decomposition, the Durham cohomology group H^2(X, C) you can decompose into..."

Lin Xiao's narration started to get on the right track, and the mathematicians present also followed Lin Xiao's narration, fascinated.

As for those who came to join in the fun, they just took it as themselves to join in the fun. After all, such a historic scene, it’s not good to miss it. In addition, there are students from all over the world who basically use the expressions of looking at gods/God Looking at Lin Xiao above.

Everyone is in their 20s, why is it different for you?

At the end of the hall, there are still a bunch of media, even more than the media at the opening ceremony.

After all, this is a conjecture of world-class difficulty. There are at least two Fields Medals every year, but in the history of mathematics, there is only one Hodge conjecture. Of course, these media want to come and join in the fun.

Among them, the reporters from CCTV were the same few days ago, they looked at Lin Xiao on the stage, chatted with the Russian reporter next to him with a smile, and said proudly: "Lin Xiao is a genius in our country of China! "

The Russian reporter was not sour. He pouted at Perelman and said, "We also have Perelman."

The reporters from the United States, Britain, France and other countries all curled their lips. Why don't they have a mathematician who proved the Millennium Problem?

……

"...in the special case that X is a projective variety, the linearly equivalent bijection of the holomorphic line bundle with the divisor class, and given a divisor D on X with an associated line bundle O(D), the class c1(O( D)) is the Poincaré dual of the homology class given by D. This thus establishes the usual formulation of Hodge's conjecture for divisors of projective varieties."

"At this point, we also fully understand the Hodge conjectures in the low-dimensional case. Obviously, they are true, that is, when K=1."

"However, how do we extend Hodge's conjecture to other dimensions? That is when K=n."

Speaking of this, Lin Xiao showed a smile.

The mathematicians below immediately sat up straight.

Next, is the point.

How does Lin Xiao expand from low dimension to high dimension?
Whether Hodge's conjecture can complete the proof depends on this key point.

For algebraic topology, it is very common to study multiple dimensions. They do not have the three-dimensional human beings, but conduct research together from one dimension to n dimensions.

So if you want to prove the Hodge conjecture, you also need to extend it to the n-dimensional case.

In fact, in the past few days, the mathematicians who participated in the last report have also studied how to solve it along the line of thinking Lin Xiao gave that day, but most of them have studied what Lin Xiao said now. This part, but I still have no idea what to do next.

Seeing so many eager eyes, Lin Xiao raised his mouth and said, "Everyone, do you still know multidimensional field theory?"

The mathematicians present were all taken aback, multi-dimensional field theory?

Isn't that the theory of quantum physics?
What does it have to do with Hodge's conjecture, a purely mathematical theory?
But suddenly, many mathematicians who had studied multidimensional field theory were shocked.

Did Lin Xiao do the same work in multidimensional field theory?

From low-dimensional to high-dimensional!
Although it is a physical theory and a mathematical problem, isn't the mathematical method used in the physical theory universal to mathematical problems?
All mathematicians couldn't help showing awe.

Lin Xiao was able to think of using methods in physics theory to solve this problem!
What a brilliant flash of inspiration!
"This is the aura that truly belongs to a genius!"

Below, Deligne couldn't help murmuring, and Searle next to him nodded in the same way.

As for the other mathematicians, many of them were surprised.

That included Perelman, who was sitting in the corner, with the same "I see" look on his face.

Although the multidimensional field theory is a physical theory, the mathematical methods used in it are very good. There are quite a few mathematicians who have studied those mathematical methods. At this moment, they are all aware of it. Then go back and study by yourself.

Seeing the reactions of those mathematicians, Lin Xiao smiled lightly, and continued: "Of course, the methods in multidimensional field theory are not completely applicable to our solution to Hodge's conjecture, so I need to analyze the methods in multidimensional field theory. method, making some changes.”

Then he turned to the PPT on the next page again, and introduced his changed method to the people present.

And from then on, the steps to solve Hodge's conjecture have gradually become clearer.

The eyes of the mathematicians on the field became brighter and brighter, and Lin Xiao's PPT gradually bottomed out.

finally--

"So, we can now show that, on nonsingular complex projective algebraic varieties, any Hodge class is a rational linear combination of algebraically closed classes."

"In 1950, Mr. Hodge announced his conjecture to the mathematics community. Today, I can confidently say that this conjecture will become a theorem from today."

"So, please let me also congratulate the mathematics community here, because we have added another foundation to the completion of the Langlands Program Building!"

After Lin Xiao finished speaking, he bowed slightly to the audience.

The next moment, thunderous applause resounded throughout the venue.

The mathematicians in the front row stood up one by one, sending their congratulations on the birth of truth.

The audience in the back row also stood up one after another. Even if they couldn't understand, it didn't prevent them from shouting awesome 666.

At this point, in the human problem book, in the column of mathematics, another line can be added.

(End of this chapter)