From Almighty Scholar to Chief Scientist

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.

Chapter 291 Scene [-], Fragmented Report

[...According to Formula 1, Formula 3, Formula 8, and Formula 12, we can get Hdg^k(X)=H^(2k)(X, Q)∩H^(k,k)(X)...]

[To sum up, we can know that when X is a projective complex manifold, each cohomology class H^(2k)(X, Z)∩H(k, k)(X) is an integral coefficient on X The sum of the torsional and cohomology classes of algebraic periods. 】

[So, after dividing by H^(2k)(X,Z)∩H(k,k)(X) by reversing the classes, each class is an image of the cohomology class of the integral algebraic period. 】

[Therefore, on non-singular complex projective algebraic varieties, any Hodge class is a rational linear combination of algebraic closed-chain classes]

[The certificate is completed. 】

After writing the last two words stroke by stroke, a slight smile appeared on Lin Xiao's face.

It's over, Hodge guesses.

The proponent of Hodge's conjecture, William Vallance Douglas Hodge, discovered this possible conjecture in his work from 1930 to 1940, but before 1950, this conjecture did not attract people's attention. attention.

It was not until Hodge mentioned this conjecture in his speech at the International Congress of Mathematicians in 1950 that people were surprised to find that this is a conjecture of great significance to mathematics, especially to algebraic geometry. and algebraic topology.

And with Grothendieck's great development of algebraic geometry, and the cohomology group that was expanded into an important mathematical tool under his single-handedly, and the Langlands program proposed later, Hodge conjectured that this could be achieved to a certain extent The conjecture that unifies the two different disciplines of algebraic geometry and topology is of great significance, and it has naturally become a major mathematical problem that people are vying to solve.

It is precisely because of this that when the Clay Institute organized many mathematicians to select the Millennium Problem, the Hodge Conjecture was also selected, and then became a problem that countless mathematicians remembered.

And until today, it finally finished in the hands of a 22-year-old math genius.

From 1930 to the present, it has spanned more than 90 years of history, experienced the worst world war, and also spanned more than 70 years of relatively peaceful periods, witnessing an increasingly prosperous mathematical community.

Its end is the end of a period of history.

Lin Xiao put down the pen, picked up the draft paper, and blew on the ink on it.

Well, although the ink has dried up long ago, it is still a piece of history. Let me blow it up, give the original Hodge conjecture a little dignity, and then clean up the dust for the Hodge-Lin theorem that will come in the future.

Suddenly realizing that something was missing, Lin Xiao frowned and said softly, "Come here!"

System: "Congratulations to the host, the proof of Hodge's conjecture has been completed, the intersection of algebra and topology, so that all qualified topologies can be expressed as polynomial solution sets, and the great unification of mathematics has moved forward again One step, your understanding of mathematics has made an important leap forward, I hope the host can make persistent efforts and grasp the ultimate truth as soon as possible! This time, you will be rewarded with 8000 mathematics experience, 150 truth points, and the halo of a mathematics master."

"Congratulations to the host, the mathematics level has been raised to level 6, and you have officially become a true mathematics master!"

"Mathematics Master Halo: When the host solves math problems, he will get a certain inspiration bonus."

The sound of the system brought surprise and surprise to Lin Xiao's face.

Actually rewarded 8000 math experience directly!

The last time he proved Lin's conjecture, he only got 4500 points of mathematical experience. He didn't expect that this time it was almost doubled.

To a certain extent, this also has the addition of the reputation of Hodge's conjecture. Of course, the most important thing is that Hodge's conjecture is more important to the great unification of mathematics. After all, it directly communicates the relationship between topology and algebraic geometry.

Because, the proof of Hodge's conjecture will enable mathematicians to know what conditions a shape needs after topological transformation before it can be described by polynomials.

Then, we can easily find out how to describe a shape and its topologically transformed homeomorphs algebraically.

This not only has important significance for mathematics research, but also has many significance for many other fields.

In any case, as one of the millennium problems, its significance to the world is self-evident.

Of course, a lot of experience is one thing. Lin Xiao quickly paid attention to another thing: "So, after I have been promoted to level 6 in mathematics, shouldn't it be time for me to develop my brain?"

The next moment, the familiar heaviness flooded his mind again.

However, due to his increasingly powerful brain development, this feeling disappeared after a while, replaced by the same familiar feeling of "I have become stronger".

Of course, his hair was still black and shiny, and since another ten days had passed and he still hadn't had it cut, it was thicker now.

"Well, compared to many mathematicians, it's obvious that my hair volume is pretty good."

Lin Xiao nodded with satisfaction.

He even had the luxury of cutting his head.

"It's time to take care of it. In five days, I have to make a report."

Letting down his hair, he asked how much the system had increased his brain development. This time it had increased by 0.7%, and his brain development had also reached 8.85%.

There is only 10% gap left from 1.15%.

With a sigh of emotion, Lin Xiao stopped thinking about it and went out to get a haircut.

……

The proof of Hodge's conjecture, Lin Xiao will naturally have to wait until the International Conference of Mathematicians to officially reveal the answer. Let's hope he gets the Fields Medal.

Otherwise, if you want to witness the proof of Hodge's conjecture, you can only go to Beijing University to listen to his report.

I don't know if the dean of their School of Mathematical Sciences hopes for a non-named permanent professor who won the Fields Medal, or is the academic report proving Hodge's conjecture conducted here?

In this way, the time came to June 6.

On this day, Lin Xiao will give a report on the proof of Lin's conjecture in the auditorium.

Because the time of this report is very close to that of the International Congress of Mathematicians, and it is more convenient to fly from Beijing to St. Petersburg, so many mathematicians came to listen to this report.