"Let i, j, a, b, q, n and N represent positive integers. The letters x, y, z and c represent real numbers, p always represents a prime number, and pn is the nth prime number. Here, p represents the first
The members are the twin prime pairs of p, and pn represents the nth twin prime pair."
"When (a,q)=1 and 0
As Lin Xiao's narration began, everyone present was thinking attentively and followed Lin Xiao's train of thought.
Regardless of whether they found errors in Lin Xiao's previous papers, the proof of an important theory absolutely requires a world-wide academic report. This is a necessary process.
Of course, before Lin Xiao got to the real point, many mathematicians present did not put all their attention on Lin Xiao's discussion, but on Lin Xiao.
They looked at the young man on the stage. Among them were many mathematicians who were Lin Xiao's "iron fans" because they had participated in all three reports Lin Xiao had given.
The first time was at the International Congress of Mathematicians in Rio de Janeiro, the second time was at the Goldbach Conjecture Lecture in the Great Hall of the People in Beijing, and the third time was right here.
Every time, Lin Xiao was able to bring them results that shocked the mathematics world.
The time span of these three reports has been two years. Looking at the young man on the stage and listening to his words, they even felt a sense of familiarity like an old friend.
In the seats below, in the second row, professors from Princeton University sat together, including Peter Sarnak, Enrique Pompieri, Pierre Deligne, and several other people from Princeton University.
Famous mathematicians are also here.
Pompieri sighed softly: "It feels like this young man has grown up a lot."
"yes."
Sanak also smiled and nodded.
Among them, the one who had the first interaction with Lin Xiao was Sarnak, because Lin Xiao’s first paper was submitted to the "Annals of Mathematics", and Sarnak, as the editor-in-chief of the "Annals of Mathematics", was responsible for
Review work.
As for the first person who met Lin Xiao, it was Pompieri. At that time, Lin Xiao was still participating in IMO, and his face still had the youthful air of eighteen years old that had not faded.
Now, Lin Xiao has been the prover who has successively completed the four major problems in mathematics, the founder of many theories and theorems that are widely used in the academic world, and is still being studied hard by the algebraic geometry community, but it has always been difficult to make effective progress.
The proposer of the conjecture.
At this time, he was speaking neither slow nor fast, and his breathing was steady. Even the steps under his feet were no longer small steps like before, but were taking big strides, confident and grand, facing the whole audience.
There were more than a thousand mathematicians in the field, and they showed no signs of cowardice.
And his face has become more mature.
"So, we have watched him grow up."
Deligne also smiled and said.
There was emotion and relief in the eyes of the three old people, as well as a sense of regret that they were already old. The youngest among them was Sanak, but he was already 67 years old this year, and the eldest Pengpi
Elie is 80 years old.
"You old guys, are you feeling emotional now?"
Another familiar voice sounded from behind.
They were stunned, turned their heads to look, and couldn't help but laugh and curse: "Oh, Andrew, why do you always sit behind us? And then you show up while we are chatting?"
Andrew Wiles spread his hands: "According to the theory of relativity, I can also turn this sentence around and ask you, why do you always sit in front of me?"
The first few people rolled their eyes, and it was based on the theory of relativity.
"Stop talking, it's impolite to chat in other people's lectures."
Pompieri waved his hand and stopped talking.
The other people said no more and continued to listen to Lin Xiao's story.
…
At the back of the conference hall, the few media outlets that were allowed to come here were setting up their cameras to record the report.
In addition to French local media, these approved media also include other international media, among which China Central Television is also prominently included.
Several reporters from CCTV were able to come over, naturally because of Lin Xiao.
They were sitting a few rows back, and they couldn't understand it anyway.
"The last time I saw him, he proved Goldbach's conjecture. Now that I see him, he has proved the twin prime conjecture. Do you think it is harder to find Goldbach's conjecture or this conjecture?"
Female reporter Zhang Ning looked at the mathematical formulas on the PPT, feeling a little numb in her head, and finally turned around and asked.
Another male reporter, Sun Xiang, said: "Who knows? Maybe it's this difficult? After all, he proved Goldbach's conjecture first."
"You two don't know how to check the information."
Chen Ming, who was standing next to him, said angrily: "Goldbach's conjecture is more difficult. You, as reporters, must be prepared."
Zhang Ning chuckled: "Anyway, it's Boss Chen, you go interview Lin Xiao, let's be lazy."
Chen Ming shook his head, too lazy to argue with them.
"By the way, there is a prize in mathematics called the Fields Medal, which is called the Nobel Prize in mathematics. Do you think he can win this prize in the future?"
"No need to ask, it's definitely possible." Chen Ming said, "But I just don't know whether it will be 2022 or 2026."
"If he gets it in 2022, he will only be 22 years old then, right?"
"Yes, that is the youngest Fields Medal winner..."
Chen Ming nodded with emotion, and then looked at the young man in front of him again, with envy in his eyes.
He was not envious of Lin Xiao's current achievements, but envied Lin Xiao's ability to realize his unfulfilled dream.
That is to become a mathematician.
In other words, there are countless people in the world who dreamed of becoming a mathematician when they were young.
Play with the numbers and symbols, and study things that no one else can understand.
Especially students from China.
After all, in the Chinese education system, the cultivation of mathematics begins in the first grade of primary school.
If girls’ dream when they grow up is to become a writer or musician, then boys’ dream when they grow up is not only to be an astronaut, but also to be a mathematician.
Unfortunately, as they grew up, the increasingly difficult math problems eventually dampened their passion.
Even Chen Ming claimed to be a mathematical genius back then. He was always the first in mathematics in his class. Even when he first went to college, he studied mathematics. As a result, after one and a half years of study, he was able to master topology and mathematics.
Differential geometry made him give up treatment directly. Even if he studied hard, he could not make up for his ability in this area. So in desperation, he had no choice but to drop out of school and read high school again for a year. When he applied for a volunteer for the second time, he read
I majored in foreign languages, and finally, after some twists and turns, I came to Paris to work as a reporter for CCTV.
So he envied Lin Xiao for being able to realize such a dream.
What a perfect life.
"Boss Chen?"
Seeing Chen Ming's absent-minded look, Zhang Ning couldn't help but push him, "What good thing are you thinking about?"
Chen Ming came to his senses, and then said with a smile: "I just hope that our country can have a few more geniuses like this."
Hearing what he said, Zhang Ning couldn't help but nodded, "Yes! It would be great if there were a thousand."
The chief designer of the last century once commented on Chen Jingrun: It would be great if there were a thousand Chen Jingruns in China.
And if they have so many Lin Xiaos, will they become a super mathematical power surpassing the United States and France?
The three of them shook their heads in unison. If this happened, it would really be a knife slashing God's ass.
…
"In order to find N(S1,Sk1...SkL), we write N(S1Sk1...Skl)=∑d|pln(AdPl)..."
"After calculation, we finally get φ2(N)=n∑d|nμ2(D)d."
"And here we're really bringing in ideas from geometric topology."
As Lin Xiao's talk came to the point, the mathematicians present also paid attention.
Having said this, Lin Xiao paused and continued: "Although I have completed all the arguments in detail using calculations on pages 45 to 47 of the paper, in order to allow everyone to better understand my theory, I will continue
Next, I will perform the calculation again on the blackboard to facilitate everyone’s understanding.”
Hearing what Lin Xiao said, the eyes of some people present who were not very good at calculations lit up. Many of them had problems with these calculations. Now Lin Xiao plans to do the calculations again, which is obviously a good thing for them.
.
In addition, there were many students from French universities in the audience. When Lin Xiao said this, his eyes lit up.
Through Lin Xiao's calculation process, they can also understand better.
However, the reality seems to be somewhat different from what they thought.
When a blackboard was pushed out by the staff, Lin Xiao began to write on it.
"Let F be the basis of the relevant I-cluster Tf, and let Pf be the set of rings embedded in S that are isotopes of the components of VTf, the REL boundary."
"Now, we call these rings the polished trajectories of Tf. Next, our calculations will begin. It may be a little complicated, so please be patient."
[SW^x(t,sp/n)=p*SWx(kx)+n·∑SW……]
…
Lines of style were carved out by Lin Xiao, and they were so beautiful that the patient audience below once again fell into confusion about beauty.
I originally thought that through Lin Xiao's on-site calculations, they would at least be able to understand it, but the reality was still cruel.
Except for a few relatively enlightened people, those who could not understand it still cannot understand it.
Just like when I was an undergraduate student, I made all kinds of preparations in order to take algebraic geometry well, and then came to the first algebraic geometry class with confidence, but in the end I was still rubbed on the ground by this subject.
.
Lin Xiao's narration obviously did not leave time for those who did not understand to understand. When they just lowered their heads and thought about how a certain line of formula was obtained, when they looked up again, the blackboard was already full of words.
And Lin Xiao is ready to flip it over - the reverse side of the blackboard can also be used.
Suddenly, those who couldn't understand finally gave up on understanding and chose to mess up. They should wait until they go back and ask their teachers or something.
Of course, Lin Xiao didn't care whether these people understood it or not. As long as the top people in the mathematics world understood it and didn't point out his problems, that would be fine.
However, he has already explained it perfectly in his paper, so there will naturally be no mistakes in his report.
In this way, while the mathematicians present were listening, or rather the first-class mathematicians sitting ten rows in front were listening, he finally ended this part of his narration.
"So, we successfully transformed the entire part into a problem in the topological domain."
"Next, we introduce the Green-Tao theorem and describe this theorem using topological geometry. We can get..."
Up to this point, most of the mathematicians sitting ten rows in front raised their heads and leaned back on their chairs.
They no longer have any problems, and they can deduce the following things by themselves.
Lin Xiao's report still amazed them, just like the original report on Goldbach's conjecture.
And then, there was no more suspense, and just like that, the report slowly came to an end.
"...In this defined topological space of infinite length, we can undoubtedly infer that there will be two points with a distance of 2 that will always appear suddenly and never become extinct."
"And these two points represent our twin prime numbers, so we can deduce without any suspense that in the endless natural sequence, twin prime numbers will always exist."
"This is the end of my proof."
"This is the Mona Lisa of mathematics that I drew. I hope everyone is satisfied."
Lin Xiao bowed slightly, with a smile on his face that was calm and magnanimous.
The people present had already extended their hands and applauded in celebration.
