The Science Fiction World of Xueba

At ten o'clock in the morning, the BSD conjecture report will officially begin.

The auditorium of Jiangcheng University, which can seat a thousand people, was crowded with more than 500 top scholars from all over the world and hundreds of students of Jiangcheng University who came to experience this top academic conference.

In the front row, apart from a few relevant leaders of Jiangcheng University and the Chinese Mathematical Society who came to observe, Deligne, Faltings, Andrew Wiles, Qiu Chengtong, Gross, Tao Zhexuan and other bigwigs sat side by side.

At the back of the auditorium, there are also a small number of foreign media reporters who are allowed to enter the auditorium.

"Dear guests, good morning, everyone. Thank you for coming to the beautiful Jiangcheng to participate in the academic report on the BSD conjecture proof of Professor Pang Xuelin. This report will be divided into two parts. The first part is the explanation part, which will be taught by Professor Pang Xuelin I will explain the main proof ideas and key steps in the thesis for everyone. The time is one and a half hours. The second part is the questioning part. Professor Pang Xuelin will answer the relevant questions for you. Next, we will invite Professor Pang to come on stage. "

As the host's voice sounded, the noisy venue gradually became quiet, and everyone focused their attention on Pang Xuelin.

Pang Xuelin walked onto the podium calmly. He had already experienced this kind of scene in the Three-Body World, so naturally he would not feel any pressure.

With the help of the staff, Pang Xuelin turned on the projection, entered the home page of the PPT, and pointed the red laser pointer at the projection screen.

"Hi everyone, it's a great honor for everyone to come to Jiangcheng to participate in the BSD conjecture proof report meeting. Next, I will explain to you the relevant ideas of BSD proof and the mathematical methods used in the paper. I believe everyone has read the paper. In the PPT , I will further elaborate on the skipped or doubtful parts of the paper. First, I will introduce my overall proof ideas to you.”

"Mr. Sweeneton Dell, who proposed the BSD conjecture, has a famous saying that any problem related to the number field can be solved by the Riemann ζ function. In recent years, with the confluence of number theory and algebraic geometry and the solution of the Weil conjecture , the current research focus has gradually shifted to the Weil-Hasse L-functions (arithmetic L-functions) of algebraic varieties (arithmetic probabilities) on the overall field, and they are supposed to know everything about arithmetic geometry."

"Therefore, on the issue of the BSD conjecture, I adopted a completely different way of proof from the traditional one. First, we assume that the BSD conjecture is true, and then we can deduce that the BSD conjecture is also true for the elliptic curve E(D): D is a certain 8k+5 type primes and some 8k+1 type primes, as long as the 4-fold mapping of the class of \\Bbb Q(\\sqrt{-D}) is simple. Given the basic role of the Gross-Zagier formula on low-order curves, we can Know……"

On the screen, the relevant content of the PPT appeared.

[For a given prime number p, (1)p \\equiv 3(\\mod 8): p is not a congruent number but 2 p is a congruent number; (2)p \\equiv 5(\\mod 8): p is a congruent number;( 3)p \\equiv 7(\\mod 8): Both p and 2 p are congruent numbers. 】

The original whispering discussions in the audience gradually disappeared, and only Pang Xuelin's voice echoed in the venue with hundreds of people.

Pang Xuelin's report did not go so smoothly when he gave a report in Three-Body World.

The tricky questions from various angles raised by the top mathematicians in the three-body world almost made him unable to step down.

After colliding with the top mathematicians of the Three-Body World and returning to the real world, Pang Xuelin further improved his method of exposition and made careful preparations for this report.

In the PPT, he not only fully explained the proof idea, but also filled in some omitted parts and ambiguous content in the paper, making the whole proof process more complete.

The logical system is also more rigorous.

Accompanied by his unhurried voice, Pang Xuelin explained the whole proof process in a more popular and ingenious language.

Most of the participating scholars also gradually immersed themselves in the huge mathematical world constructed by Pang Xuelin.

Its meticulous logic and ingenious ideas make everyone hooked.

Even some scholars who were about to come here to make trouble, after Pang Xuelin answered some doubts in the paper, their faces showed suddenly enlightened expressions.

Among them was Miguel Walsh.

Miguel Walsh is an Argentine mathematician, winner of the 2012 Ramanujan Prize, and a researcher at the Clay Institute of Mathematics in the United States.

Since Pang Xuelin released the BSD conjecture proof on arXiv, Miguel Walsh, as a member of the verification expert group of the Cray Mathematics Institute, verified Pang Xuelin's proof process.

After nearly a week of non-stop work, the six-member demonstration team had serious differences. Four of them believed that Pang Xuelin's proof was fine, while Walsh and his other colleague believed that the proof process was flawed, and the two sides argued. At the same time, Jiang University issued an announcement that Pang Xuelin would hold an academic report on BSD conjecture.

Walsh and his colleagues signed up for the meeting immediately.

Originally, he was thinking of attacking Pang Xuelin in the questioning session later.

Who would have thought that just now, Pang Xuelin would directly talk about what he thought was flawed.

After Pang Xuelin analyzed this content step by step, he not only answered the doubts in Walsh's mind, but also made Walsh involuntarily applaud him for his ingenious solution!

The same scene happened to many participating scholars.

Denelli, who was sitting in the front row, whispered to Faltins beside him: "It's really a formidable young man, this young man, I reviewed his thesis half a year ago, and although his level was not bad at that time, it was far away Not as amazing as today’s performance. I have studied his paper several times. Its logic is rigorous and the proof of thinking is ingenious. It can be called a textbook level. Today’s wonderful report perfectly complements the omissions in the paper. In this way, the entire proof process is almost impeccable, and what is even more frightening is that this little guy is only 23 years old this year..."

The German old man Faltins, who has always been a rare praise, said: "This little guy is really good. I originally planned to ask a few questions in the next question session, but I didn't expect him to include all the questions I wanted to ask in the report." Once completed, I think his paper can be published in the next issue of "Annual Journal of Mathematics."

Denelli said: "We have the same idea. After the report is over, I will ask Gross, Wiles and Sarnak for their opinions. If there is no problem, then publish it as soon as possible!"

...

On the podium, Pang Xuelin's explanation continued.

[When q=1, Dirichlet's theorem degenerates into Euclid's theorem.

Euler's proof gives a more refined result: taking the main branch of the logarithmic function on {Re}(s)\u003e1, logζ(s)=Σlog1/1-p^{-s}=Σ{n,p }1/np^{ns}, n≥2 partial absolute convergence. Let s to 1, get Σ1/p=loglog X+O(1), X to ∞】

...

[To sum up, we can conclude that the rank of the elliptic curve E(K) is exactly equal to the order of the zero point of L(E, s) at s=1, and the first non-zero coefficient of the Taylor expansion of the latter can be given by The algebraic properties of the curves are expressed precisely. Thus, the BSD conjecture proposition is established]

...

Pang Xuelin's voice fell, and there was silence in the auditorium.

After about a few seconds, Terence Tao got up first, smiling and applauding.

Immediately afterwards, everyone in the auditorium stood up one after another, and applause spread like thunder, resounding over the entire auditorium.

People who understood Pang Xuelin's argument showed excitement on their faces, and they were witnessing the truth with applause.

Those students who were at a loss heard from the applause that the international mathematics community recognized Pang Xuelin's proof process.

So they also applauded enthusiastically, paying tribute to the great soul on the podium.

The leaders of Jiang University and the Chinese Mathematical Society also showed excitement on their faces.

They also understand what this applause means!

They seem to have seen the Fields Medal, which the Chinese have never had before, and is waving to them.

Pang Xuelin stepped forward and bowed deeply to the audience.

As a result, the applause in the auditorium became more enthusiastic.

At the back of the auditorium, journalists from all over the world picked up their cameras to record this great moment.

"Okay, thank you everyone, thank you for your support!"

The applause lasted for four or five minutes before Pang Xuelin had to interrupt it.

"Next, we will enter the questioning session of this report meeting. If you have any questions, you can raise your hands now!"

The voice fell, and the auditorium suddenly fell into silence.

Pang Xuelin looked around and couldn't help being taken aback, because none of the more than 1,000 people in the hall raised their hands.

What's the situation?

He had to speak out again: "If you have any questions, you can raise your hands and ask!"

Pang Xuelin looked around, but still no one raised his hand.

For a moment, the entire auditorium fell into a strange atmosphere, and people whispered and talked a lot.

But in any academic report meeting, entering the questioning session is a moment for scholars to exchange ideas and collide with each other. Especially for an academic report meeting of this level, no one raised their hands after entering the questioning session, even those well-informed Big cows, this is also the first time I have seen it.

After about half a minute, Faltings, who was sitting in the first row, raised his right hand high.

Staff soon delivered microphones.

Faltins got up and smiled and said: "I have no problem. But I think everyone who sat down just now witnessed a miraculous moment. No one asked a question, which shows that Pang's proof is logical and impeccable, and has convinced us all. People. Pang, congratulations, as one of the five independent reviewers of BSD conjecture proof papers invited by "Annual Mathematics", I think you have done a great job, congratulations on passing my review!"

Then, Faltins handed the microphone to Deligne beside him.

Deligne stood up and smiled, "Pang, it's my honor to review such a great masterpiece. Congratulations on passing my review!"

Deligne then handed the mic to Andrew Wiles, who handed the mic to Benedict Gross, who handed the mic to John Coates.

John Coates finally concluded: "Since the BSD conjecture was put forward in the 1960s, this conjecture has inspired generations of mathematicians to continue, but they have never achieved a decisive victory. I even doubted whether I can live in my lifetime." I saw the day when the BSD conjecture was proved. Pang, thank you for allowing me to witness this great moment! Congratulations on passing my review, "Annual of Mathematics" will officially publish your paper in the latest issue released on October 1 paper!"

The unanimous approval of the five top mathematicians pushed this report to a climax.

Those Jiang university students who originally only wanted to come to see the world, looked at Pang Xuelin one by one, full of admiration and reverence.

There is even a sense of pride in being Chinese surging in my chest.

A man should be like this!

After finally squeezing into the auditorium, Ai Ai, who was watching the idol report meeting, looked at the figure of Pang Xuelin Wei'an on the podium, and her little heart was beating with excitement: "You really deserve to be my male god! He is so handsome! What should I do? Do it, Pang Shen, I found that I am falling in love with you hopelessly!"

Qi Xin, who was standing aside to maintain order, looked at Pang Xuelin with the same sparkle in his eyes. I am afraid that my cheap junior is going to make history today.

And the reporters at the scene tapped the keyboard quickly one by one, sending out the scenes that happened on the scene in text as soon as possible.