God's Crown

The full name of the BSD conjecture is the Birch and Swinnerton-Dyer conjecture (BirchandSwinnerton-Dyer conjecture), which is one of the top problems of the Abelian cluster. The theorem of the unraveled Modal conjecture is not wrong.

When An Yan was chatting with Gu Weize just now, substituting Modal's theorem and using Abelian clusters seemed to have solved the problem.But now he can't believe it at all, he really solved the BSD conjecture.

Open... What a joke, this is a BSD conjecture, not a cat or a dog's conjecture.This is one of the Millennium Prize puzzles, one of the seven conjectures of mathematics.How could it be untied by him so quickly?If he really solves it, countless mathematics awards will definitely be soft.

And after unraveling the BSD conjecture of Abelian clusters, the Hodge conjecture can also be solved by extension.That is - the Hodge conjecture, which is also one of the Millennium Prize puzzles.

Hodge's conjecture is a problem about algebraic varieties, that is, on nonsingular complex projective algebraic varieties, any Hodge class is a rational linear combination of algebraically closed classes.The Hodge conjecture itself constitutes one of the geometric topological carriers and tools of the M-theory that integrates general relativity and quantum mechanics.Proving Hodge's conjecture is equivalent to giving M theory a new lease of life.

Abelian variety is a complete algebraic variety, and Hodge's conjecture is a problem about algebraic varieties.Although An Yan is not very interested in Professor Witten's M-theory, he has to admit that Professor Witten's idea is indeed very good.

Going back and looking at it again, An Yan began to recalculate. The BSD conjecture is really important, and he didn't know that he really solved the BSD conjecture, maybe he just misunderstood it just now?

Thinking of this, An Yan continued to count again.

For the first time, it seemed that there was really no error and accurately described the arithmetic and analytical properties of Abelian varieties. The second time, there was no error, and he thought he seemed to have really solved the BSD conjecture.For the third time, there was still nothing wrong... until he calculated it more than ten times in the past ten days, he was completely stupid.

There are really no mistakes, which means that he has really made this thing.

No, it's impossible, right?He made the BSD conjecture so easily?While on the phone, I was writing a draft... Then I made a BSD conjecture, if this matter is known by others.I'm afraid people in the field of mathematics and physics will not let him go, can this work?It is estimated that everyone's jaws will drop.

Not to mention others, he himself... also finds it incredible.

Can this work?

Also, did you really make it?No, no way.After thinking about it, Professor Hudson's ability in mathematics, especially in Abelian clusters, is indeed limited, and he may not be able to help him.

He now has two options. One is to publish his paper on arXiv and let others check whether his BSD conjecture is correct.The second is to go to Germany to visit Faltings and show this paper to Faltings.Faltings is now the director of the Institute of Mathematics at the Max Planck Institute in Germany.

Faltings has not given him any news, indicating that Faltings is still very busy now.And if he is not sure whether the BSD conjecture he made is correct, he can only ask this great god who has top-notch knowledge on Abelian clusters.

Publishing an uncertain result on arXiv will not do his academic reputation any good if it turns out to be wrong.An Yan thought about it, and decided to write his thesis in a document first, save it, and finally visit Faltings, then publish the paper on arXiv and submit it to the Annals of Mathematics.

When he thought of this, he turned on the computer and began to type the thesis on the computer.

It wasn't until after he finished his thesis that he saw the letter Faltings replied to him.

[I have received your letter. You said that there is a special discovery on Abelian clusters. What is it about Abelian clusters?I hope you can give me an answer on this point. 】

This great god was very cold from the beginning to the end, and his reply seemed to be extremely cold as well.

After thinking about it, An Yan decided to reply to Faltings——

[Dear Mr. Faltings, it is about the arithmetic and analytical properties of Abelian series. I originally planned to visit you in Germany. I wonder when you will be free? 】

This time, Faltings responded quickly.

He happened to have a spare time to rest, and after seeing An Yan's email, he responded casually.Wanted to see what strange discoveries Anyan made on the Abelian clusters.For Faltings, perhaps An Yan's major discovery is something he has already discovered and checked, which is still unknown.

He himself is a cold person, what's more, An Yan really doesn't rank high in his heart.Many of the students taught by this great god are well-known figures in the field of mathematics, especially in the field of mathematics back then.

An Yan has some talents, but these talents are not worth mentioning in the eyes of Faltins.

Leaving An Yan's email address also felt that he was just a malleable talent, nothing more.

After taking a sip of coffee, Faltings found that An Yan had already replied to him an email.I didn't know what the email was, so I clicked on it and took a look.

After putting down his coffee, he confirmed the contents of the email again.

On the connection between the arithmetic and analytic properties of Abelian varieties?Isn't this... a BSD conjecture?Faltins was silent for a while, staring at the computer all the time, as if he wanted to see something from the computer.Regarding the BSD conjecture, did he make a BSD conjecture?After thinking for a while, Faltings rejected the idea again.If it's a BSD guess, that's pretty amazing.

At least, he doesn't think he can make the BSD conjecture right now.

After thinking about it, Faltings still wrote back to An Yan. An Yan said that he wanted to visit him, and it must have something to do with the arithmetic and analytical properties of the Abelian cluster.

But now it sounds like the Arabian Nights.However, he would not know the specific situation until An Yan came. Since he wanted to visit—let him visit.

[Ann, if you want to come, then you can come here.Are you sure it is a problem with the arithmetic properties of Abelian varieties and the Jessie properties? 】

[Dear Mr. Faltings, of course, I may——solve the BSD conjecture.But I'm not sure yet, further verification is needed. 】

After getting Faltings' reply, An Yan breathed a sigh of relief.

The Max Planck Institute, referred to as the Max Planck Institute, is a non-profit research institution supported by the German federal and state governments. Its research achievements are world-renowned.The Max Planck Institute consists of nearly 80 scientific research institutes, covering basic research in natural sciences, life sciences, social sciences, arts and humanities. ①

The Max Planck Institute for Mathematics is located in Bonn on the Rhine in the south of North Rhine-Westphalia, Germany.

Now, it will take a certain amount of time for him to go from California to Bonn, but this matter is not as important as the answer to the BSD conjecture for An Yan.If the BSD conjecture is really made, the prize money of the Clay Promotion Association is a trivial matter.The main reason is that it can have a strong stroke in the history of mathematics, and Abelian clusters may play some roles in quantum physics and grand unified theory.

After receiving an affirmative reply from Faltings, An Yan began to clean up.He needed to rush to Bonn to find Faltings as soon as possible, and when An Yan was packing up, Kai and Shinya knocked on An Yan's door.

Opening the door, An Yan looked at Kai and Shinya standing outside the door and said, "Shinya-kun, what's the matter?"

"Yan Jun——" Kai and Shinya looked at An Yan, blinked their eyes, and then said anxiously, "That's right, I'm going back to the Neon Kingdom soon. But, you seem to be busy?"

"Well, there are indeed some things." An Yan returned to the room and continued to pack her luggage.

Kai and Shinya looked at An Yan's movements, and said curiously, "Yan-jun, are you going back to China?"

"Huaguo? No, I'm going to Germany." An Yan said while tidying up, "I've got in touch with Mr. Faltings. I'm going to the Max-Planck Institute of Mathematics in Bonn to find Mr. Faltings and ask him for advice. Some questions." When he said this, An Yan glanced at Kai and Shinya.

This guy came to him now because there was nothing wrong, right?That being the case—then let Kai and Shinya do one thing for him.

Seen by An Yan like this, Kai and Shinya took several steps back, and then said cautiously, "Yan-jun, please don't look at me with that look."

"Shinya-kun, you have nothing to do right now, right?"

"Uh, there's really nothing wrong."

"I have a USB flash drive here, please print out the content on it."

An Yan took out the USB flash drive and put it in Kai and Shinya's hands, and told him, "This matter is very important, I hope you can get it back as soon as possible before I pack it up."

"What is the paper on the USB drive?"

"You'll know later." An Yan smiled mysteriously, watching Kai and Shinya startled.Although he didn't know what the contents of the U disk were.But An Yan has already told him to do something, as a friend, he will definitely do this kind of small favor.

Leaving An Yan's room, came to the office, and inserted the USB flash drive into the computer.

He wondered what paper An Yan had written?This is still a little curious. I just made a paper on Hilbert space before, and I made a new paper so soon. Is it about Hilbert space?Kai and Shinya opened the file while thinking.

What appeared in front of him was——

[About the correctness verification of the BSD conjecture]

Gan!Is this guy going crazy?Kai and Shinya felt a little magical, and found an article about the verification process of the BSD conjecture in the USB flash drive of a direct PhD student in the physics department of Stanford University.And judging by his appearance, it seems that it has been verified.Kai and Shinya are not sure whether it has been verified, but the publication of this paper must be shocking and cause an uproar.

Wait for the Max-Planck Institute and Faltings... Isn't that the Fields Medal god Faltings?This guy actually has a connection with Mr. Faltings.

What kind of monster did he know, Kai and Shinya complained while printing An Yan's thesis.After the first page was printed out, he took the paper and began to read it.He could still understand the previous summary and introduction, but the calculations became more and more complicated from the third page, and he felt that his brain was not enough.

What is this, what is this again?Who can answer him, what exactly is he looking at?Why can't I understand anything?

Is this the world of the Great God?It's really incomprehensible.

Kai and Shinya took a deep breath, printed out all the papers, handed them to An Yan, and said to An Yan, "An, did you really calculate the BSD conjecture?"

"I don't know." An Yan shook his head, his luggage was almost packed.

"Aren't I going to visit Mr. Faltings at the Max Planck Institute of Mathematics? Maybe I can get some answers from Mr. Faltings." An Yan spread his hands and said, "But this matter is not certain .”

"Okay..." Kai and Shinya wanted to say something more, but he couldn't come out.He could only look at An Yan, "Boss, boss!"

"Okay, stop flattering." An Yan raised his brows.

Kai and Shinya asked curiously, "If you really made the BSD conjecture, you can graduate directly, right?"

"I don't know."

"It's no problem to be a mathematics professor." Speaking of this, Kai and Shinya said with a bit of a cheap smile, "I said Yanjun, how do you think I will be your student?"

"It's not good." An Yan complained, "If there was a middle school student like you, I think I might collapse."

"Hey, our friendship for so many years, can't you accept me as a student?"

An Yan stared at Kai and Shinya and said, "Furthermore, even if you solve the BSD conjecture, you may not be able to graduate. Don't forget, I am a student of the Department of Physics, not the Department of Mathematics." An Yan pulled himself Luggage, waved to Kai and Shinya and said, "When you leave the room, don't forget to close the door."

"..." At this time, you still have the mood to say such things, you are also a genius.

An Yan left Stanford University and reported to his professor Hudson by the way, saying that he was going to visit Faltings in Bonn, Germany.

When Professor Hudson received the news from An Yan, he looked at Richard who was still doing calculations and sighed.

No need to think about it, An Yan was able to meet Faltins at the mathematics conference at Princeton University.And the guy Richard in front of him... took him to many physics academic conferences, but he still didn't get to know a few better physics professors.The gap between people is indeed quite large.

Although Professor Hudson knew it from the beginning, when this gap really appeared, his mood was a bit complicated.

"Professor." Richard felt that the professor's gaze had been staring at him, and she raised her head to look at the professor, "What's the matter?"

"An Yan left Stanford University." Hudson described the matter in a calm tone as much as possible, "He told me he was going to Bonn, Germany."

"Uh..." Richard didn't understand what was wrong with Professor Hudson's account, that is, why did An Yan leave Stanford University and why did he go to Bonn, Germany?Is it possible to drop out of school?Impossible, no matter how you say it, it is impossible to drop out of school.

"Professor, is he—is he going to Bonn for something?"

"Of course." The professor snorted and said, "He is visiting Faltings at the Max Planck Institute of Mathematics in Bonn."

"F... Faltings?" Richard gasped, or should he visit Mapu?Has this junior of his been so awesome?Not to mention knowing a great god like Faltings, you can still visit.

It is not so easy to know that it is not so easy to visit a well-known scholar, especially a cold and cold master like Faltins.

An Yan was able to visit, and he must have told Faltins about it in advance.

That means - An Yan has the contact information of Faltings.

God, this is insane.Ann, was able to visit Faltings, and got the approval of Faltings.There must be something wrong, right? Professor Hudson didn't care what Richard was thinking, but just stared at Richard and said, "Look at Ann, and then look at you, if you don't work hard. Maybe Ann You have already graduated with a Ph.D., so maybe you are just a Ph.D. student.”

He understands the truth, but he really can't be as outstanding as An. ,…………

When he arrived in Bonn, An Yan took his suitcase, found a hotel that was closer to the mathematics laboratory, and checked in.Then I made a call to Faltings. Perhaps what Mr. Faltings left was the number of the Max Planck Institute of Mathematics.

But anyway, An Yan has arrived in Bonn, and now the weather is fine, it is best for him to take this opportunity to contact Mr. Faltings.

Enjoying the afternoon sun, the phone in the office rang not long after Faltings finished his work.At this time, who will call him?Faltings frowned and picked up the phone.

"Mr. Faltings?"

A pure German accent, but an unfamiliar voice.

"you are?"

"Hello, Mr. Faltings, I'm An Yan. I'm from Stanford University. I sent you an email a few days ago to say that I want to visit you. There are some things about the arithmetic and analytical properties of Abelian clusters."

"It's you." Mr. Faltins was as cold as ever, "Have you arrived in Bonn now?"

"That's right, I'm already standing outside the Max-Planck Institute of Mathematics..."

"Well, you wait." Faltings hung up the phone, and he always kept this matter in mind.The main reason is that the BSD conjecture is so important, whether it is mathematics or physics.He also had some doubts about whether An Yan had really solved the BSD conjecture. He hadn't seen the paper yet, so he didn't dare to make a conclusion easily.

Accepting An Yan's visit is also because An Yan said confidently that he discovered the problem of the BSD conjecture. Maybe he failed to solve the BSD conjecture, but he must have made some achievements in conjecture.

Faltings still has this confidence in An Yan, although he is not the most talented mathematician in his opinion.However, it is undeniable that An Yan is an outstanding young mathematician.In the future, my achievements in mathematics will not be too low. I left the office and came to the Max-Planck Institute of Mathematics.

He saw An Yan standing outside the door, seemingly waiting for him.

Going forward, he said without any expression as before, "Ann, come with me."

"Mr. Faltings, hello." An Yan saluted politely, Faltings nodded slightly, and led An Yan to the Max-Planck Institute of Mathematics.

As he walked, he was thinking, how did this Ann—how did he prove or make achievements on the BSD conjecture?

Faltings was very curious.

When he came to the office, Faltings sat in his seat, pointed to the seat next to him and said, "Ann, sit down first."

After An Yan sat on the chair, Faltings asked, "What do you need to drink?"

"No, no need." An Yan said in a deep voice, "Mr. Faltins, you know that I came to you because of Abel's cluster."

"That's right." Faltings nodded and said, "What fun things did you find on the Abel cluster?"

"You can take a look at this paper." An Yan put the paper on the table and looked at Faltings, "Everything I found is in the paper."

"Oh?" Faltings raised his eyebrows, picked up the paper, and put it in front of his eyes.

First——what caught his eyes——

[About the correctness of the BSD conjecture]

"Hiss!" Taking a breath, Faltings stared at the title of the thesis in disbelief.Regardless of the right or wrong of this paper, just this topic has already made Faltings feel extremely shocked.

Next, what will happen to this paper?In addition to being shocked, Faltings seemed to have a little more expectation and doubts about An Yan's thesis.

The author has something to say: ①: Excerpted from the third update of the Maple Institute of 360 Encyclopedia! ! !