From Almighty Scholar to Chief Scientist

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 kahler 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.

Chapter 297 Hodge's Conjecture is one month harder than Lin's Conjecture

The applause of the audience lasted for a long time, even if it was Goldbach's conjecture last time, the sound was only louder because there were more than 1 people in the audience, but now here, in the National Theater of St. Petersburg, although there is no applause It was so big at first, but it lasted a long, long time.

Until the end, the applause finally subsided, and Lin Xiao finally had time to speak: "Thank you for listening to all my process patiently. Next, it's time for questions."

He looked at the time, and then smiled: "The organizing committee gave us nearly an hour to ask questions, so come on, I'm ready to face a protracted battle."

There was laughter in the audience, and then, a group of people raised their hands.

Seeing so many hands, Lin Xiao smiled slightly, and then chose one of them.

Soon, the selected person stood up, first smiled and nodded at Lin Xiao, and then said: "Professor Lin, please tell me, in 4.3.6, Γ`0∈H^3et(W`0, k , why the restriction on the geometrically special fiber W`2k in Z/2(0) does not disappear under the mapping to Galvaroic cohomology?"

Lin Xiao smiled slightly and said, "This step is very simple."

Then he pulled a blackboard from the side and started writing.

【H^3et（W`0，k，Z/2（2））→H^3（F，Z/2（2））……其中F=k（W`0，k）】

"Well, that's about it."

Lin Xiao smiled and said: "Please note that the form of W`0 is U×S'0, through Lemma 4.2, we can get U≌Gm, and S`0 is S`→norm (o` ) special fiber."

The questioner suddenly realized, "Thank you for your explanation, I understand."

Lin Xiao nodded with a smile, and then said: "You're welcome, it's my responsibility, so please go next."

Soon, he chose another person.

"Professor Lin, why in 3.4.1, in order to increase β, we need to find a non-divergent Gavarro expansion L/Kp?"

"This step is also very simple..."

Lin Xiao quickly answered.

In this way, after one question after another, the report was finally coming to an end, and fewer and fewer hands were raised on the field, until finally, it was finally cleared.

This also means that the Hodge conjecture proved by Lin Xiao has been recognized by everyone in this report. The next step is to wait for the current International Congress of Mathematicians to sort out his report, and then use the conference papers The form was published.

I believe that the conference papers in this issue will be sold out by people.

In fact, at the last International Conference of Mathematicians, quite a few copies of the conference proceedings were finally sorted out. After all, Lin's conjecture was proposed in it.

And this time, Hodge's conjecture has been proved. I believe everyone is willing to buy a copy as a souvenir.

Seeing that no one asked any more questions, Lin Xiao smiled and said, "It seems that this is the end of my report, thank you all."

Then he bowed again to the people.

Off the court, the applause sounded again.

After the questioning session, everyone present knew that Hodge's conjecture had been completely proved.

At least, it has been recognized by people for the time being. Afterwards, the International Congress of Mathematicians will organize many mathematicians to conduct a final analysis of the entire proof process. The test, of course, is actually enough after a few months of testing.

After all, the proof of this heavyweight conjecture will inevitably be observed by people under a magnifying glass in the future to verify every possible error. Therefore, I believe that so many mathematicians in the mathematics world, within a few months, have already enough.

Of course, people believed Lin Xiao's proof, and there would be no problems.

After all, Lin Xiao's credit is worth several top guesses.

And at this moment, Jean-Pierre Serre stood up, picked up a bottle of champagne in the eyes of everyone, and walked to the stage.

Seeing this scene, how could people not know the purpose of this old man?

So the applause grew louder, and smiles appeared on people's faces, waiting for that moment to come.

When seeing Professor Searle come on stage, Lin Xiao was taken aback for a moment, but after seeing the bottle of champagne, he also smiled.

"Professor Searle."

"Lin, seeing you again, you surprised me a lot."

Searle laughed, and then he handed the champagne in his hand to Lin Xiao, and said, "Open it, this is the winner's moment."

After receiving the champagne, Lin Xiao smiled and said, "Thank you."

Then, saying "cleaner, I'm offended" in his heart, he shook the champagne vigorously, and then pushed the champagne cap off with his thumb.

"Boom~"

The wine rushed out of the bottle, and cheers of victory spilled out.

And the atmosphere of the audience reached another climax again.

At the same time, the media photographers in the back row also took pictures of this scene.

In the photo, Lin Xiao standing on the stage opened the champagne belonging to victory, and in the auditorium, the audience stood up and applauded, making this photo forever engraved in the history of mathematics, and a line of small words below it : "On July 2022, 7, Lin Xiao celebrated at the International Congress of Mathematicians for successfully proving Hodge's conjecture"

……

This report is over.

In fact, before the report was over, the news had already spread.

Needless to say, the mathematics world, or the entire academic world, has long been boiling because of this matter.

For the general public, Hodge's conjecture, as one of the most difficult mathematical problems in the world, is also a gimmick, so this matter alone has attracted a lot of attention. One of the big puzzles, the Hodge conjecture, which represents a prize of 100 million US dollars, has also become a point of great concern.

So under the propaganda of the media, ordinary people expressed their envy to Lin Xiao.