At 10 a.m., the BSD conjecture presentation officially began.

The auditorium of Gangseong University, which can seat 1,000 people, was packed with more than 500 top scholars from all over the world and hundreds of Gangseong University students who came to experience this top-level academic conference.

In the front row, in addition to a few leaders of Jiangcheng University and the Chinese Mathematical Society who came to observe, Deligne, Faltins, Andrew Wiles, Yau Chengtong, Gross, Tao Zhexuan and other bigwigs sat side by side.

At the back of the auditorium, there were also a small number of journalists from various countries who were allowed to enter the auditorium.

"Distinguished guests, good morning, thank you for coming to the beautiful Jiangcheng to participate in Professor Pang Xuelin's BSD conjecture proof academic report. The report will be divided into two parts, the first link is the explanation link, which will be explained by Professor Pang Xuelin for you to explain the main proof ideas and key steps in the paper, the time is one and a half hours, and the second link is the question session, Professor Pang Xuelin will answer relevant questions for you, and we will invite Professor Pang to the stage. “

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

Pang Xuelin calmly walked onto the podium, this kind of scene, he had already experienced in the three-body world, naturally there would be no pressure.

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

"Hello everyone, it is a great honor for you to come all the way to Jiangcheng to participate in the BSD conjecture proof report, and I will explain to you the relevant ideas of BSD proof and the mathematical methods used in the paper. I believe everyone has already read the paper, and in the PPT, I will further elaborate on the places that have been skipped or doubted in the paper. First of all, I would like to introduce to you my overall proof thinking. ”

"Mr. Swinaton Dyer, who came up with the BSD conjecture, famously said that any problem related to the field of numbers can be solved by the Riemann ζ function. In recent years, with the convergence of number theory and algebraic geometry and the resolution of the Weil conjecture, the focus of current research has gradually shifted to the Weil-Hasse L-function of algebraic clusters (arithmetic generalizations) on the global domain, which should know everything about arithmetic geometry. “

"So, for the BSD conjecture, I took a very different approach to the proof than the traditional one. First, if we assume that the BSD conjecture is true, we can deduce that the BSD conjecture also holds true for the elliptic curve E(D): D is the product of an 8k+5 prime and a number of 8k+1 primes, as long as the 4-fold mapping of \Bbb Q(\sqrt{-D}) is single. Given the fundamental role of the Gross-Zagier formula on low-order curves, we can know that ......"

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

[For a given prime p, (1)p \equiv 3(\mod 8):p is not the same remainder, but 2 p is the same remainder; (2) p \equiv 5(\mod 8):p is the same remainder; (3) p \equiv 7 (\mod 8) :p and 2 p are both congruent remainders. 】

The original head-to-head discussion in the audience gradually subsided, and only Pang Xuelin's voice echoed over the venue of hundreds of people.

When he gave a report in the Three-Body World before, Pang Xuelin's report did not go so smoothly.

The tricky questions from various angles raised by those top mathematicians in the three-body world almost made him unable to get off the stage.

After colliding with the ideas of the top mathematicians in the three-body world, after returning to the real world, Pang Xuelin further improved his way of discourse and made careful preparations for this presentation.

In the PPT, he not only completely expounded the proof idea, but also made up for some omitted parts of the paper and the content that is easy to cause ambiguity, so that the whole proof process is more complete and the logical system is more rigorous.

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

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

Its meticulous logic and ingenious thinking have made everyone addicted.

Even some scholars who were ready to come over to find trouble, after Pang Xuelin's answers to some doubts in the paper, their faces showed expressions of sudden realization.

Among them was Miguel Walsh.

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

Since Pang Xuelin released the BSD conjecture proof on arXiv, Miguel Walsh has been a member of the verification expert group of the Clay Institute of Mathematics to verify Pang Xuelin's proof process.

After nearly a week of sleepless work, the six-member argumentation team had serious disagreements, four of them thought that there was nothing wrong with Pang Xuelin's proof, while Walsh and another colleague thought that the proof process was flawed.

Walsh and his colleagues signed up for the conference as soon as possible.

Originally, he still thought that he would challenge Pang Xuelin in the question session later.

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

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

The same scene happened to many scholars attending the conference.

Denieri, who was sitting in the front row, whispered to Faltins beside him: "It's really terrifying, this young man, I reviewed his paper half a year ago, and although the level was not bad at that time, it was far from being as amazing as it is today." I have studied this paper several times, and its logic is rigorous and the proof of the ingenuity of the idea is almost textbook-level. Today's wonderful presentation perfectly fills in the omitted part of the paper, so that the whole proof process is almost flawless, and what is even more terrifying is that this little guy is only 23 years old this year......"

Faltins, an old German man who has always been rarely praised, said: "This little guy is really good, I was going to ask a few questions in the next question session, but I didn't expect him to fill in the questions I wanted to ask in the report, I think his paper can be published in the next issue of the Annals of Mathematics." ”

Denieli said: "We have the same idea, after the report is over, I will ask Gross, Wiles and Sanaik for their opinions, if it is all right, then publish it as soon as possible!" ”

……

On the podium, Pang Xuelin's explanation continued.

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

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

……

[In summary, we can conclude that the rank of the elliptic curve E(K) is exactly equal to the order of L(E,s) at the zero point at s=1, and that the first non-zero coefficient of the Taylor expansion of the latter can be accurately expressed by the algebraic properties of the curve. Thus, the BSD conjecture proposition holds]

……

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

After about a few seconds, Tao Zhexuan took the lead in getting up and clapping with a smile.

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

The people who understood the process of Pang Xuelin's argumentation had excitement on their faces, and they were witnessing the truth with applause.

Those students who were confused heard from the applause that the international mathematical community recognized Pang Xuelin's proof process.

They also applauded enthusiastically and paid tribute to the great soul on the podium.

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

They also understand what the applause means!

They seemed to see the Fields Medal, which the Chinese had never touched, and was waving to them from afar.

Pang Xuelin took a step forward and bowed deeply to the audience.

As a result, the applause in the auditorium became even 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, thank you for your support!"

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

"Next, we will enter the question session of this report meeting, and you can raise your hand now if you have any questions!"

As the words fell, the auditorium fell silent.

Pang Xuelin looked around and couldn't help but be stunned, because among the more than 1,000 people in the entire hall, not a single one raised his hand.

What's going on?

He had to speak up again: "If you have any questions, you can raise your hand and ask!" ”

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

For a while, the entire auditorium fell into a strange atmosphere, and people exchanged heads and talked about it.

But when an academic report is held, it is a time for scholars to communicate with each other and collide with each other, especially at an academic report of this level, no one raises their hand after entering the question session, even if they are well-informed, it is the first time to see it.

It was about half a minute before Faltins, who was sitting in the first row, raised his right hand in the air.

Soon a staff member brought the microphone.

Faltins got up and smiled, "I don't have a problem. But I think all of us here just now witnessed a miraculous moment. No one asked, indicating that Pang's proof was logically rigorous and impeccable, and had convinced us all. Congratulations, Pang, as one of the five independent reviewers of BSD conjecture proofs invited by Annals of Mathematics, I think you have done a great job, and congratulations on passing my review! ”

Then, Faltins handed the microphone to Deligne, who was beside him.

Deligne stood up and smiled: "Pang, it is my honor to have the honor to review such a great masterpiece, congratulations on passing my review!" ”

Deligne then gave the microphone to Andrew Wiles, who in turn gave the microphone to Benedict Gross, who finally gave the microphone to John Coates.

John Coates concludes: "Since the BSD conjecture was proposed in the sixties, it has inspired generations of mathematicians to succeed them, but they have never been able to achieve a decisive victory. I even doubted that I would ever see the day when the BSD conjecture was proven. Pong, thank you for allowing me to witness this great moment! Congratulations on passing my review, and your paper will be published in the latest issue of the Annals of Mathematics on October 1st! ”

The unanimous approval of the five top experts in the field of mathematics pushed the report to a climax.

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

There is also a sense of pride in being Chinese stirring in his chest.

That's how it should be!

Ai Ai, who finally squeezed into the auditorium and watched the idol report, looked at the figure of Pang Xuelin Wei'an on the podium, and her little heart pounded excitedly: "I really deserve to be my male god!" It's just so handsome! What to do, Pang Shen, I find that I am hopelessly in love with you! ”

Qi Xin, who was standing aside to maintain order, looked at Pang Xuelin's eyes and sparkled the same, I'm afraid that I'm going to make history today, I'm afraid I'm going to make history today.

And those reporters at the scene tapped the keyboard one by one, and sent the scene of the scene in text as soon as possible.